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class="brand-code">IMM1033</span><span class="brand-title">Méthodes du coût en évaluation immobilière</span></span></a>80    <nav class="topnav" aria-label="Navigation principale"><div class="dd"><button type="button" aria-expanded="false" aria-haspopup="true">Séances <span class="caret" aria-hidden="true">▾</span></button><div class="dd-menu wide"><div class="dd-part"><i style="background:#2976bb"></i>Partie I — Fondements de la méthode du coût</div><a href="/seance/01/" data-ch="01"><span class="pastille" style="background:#2976bb">1</span><span>Introduction à la méthode du coût</span></a><a href="/seance/02/" data-ch="02"><span class="pastille" style="background:#2976bb">2</span><span>Cadre conceptuel et terminologie</span></a><div class="dd-part"><i style="background:#0f8b8d"></i>Partie II — Évaluation du terrain</div><a href="/seance/03/" data-ch="03"><span class="pastille" style="background:#0f8b8d">3</span><span>Méthodes d'évaluation du terrain</span></a><a href="/seance/04/" data-ch="04"><span class="pastille" style="background:#0f8b8d">4</span><span>Analyse du terrain et ajustements</span></a><div class="dd-part"><i style="background:#cca424"></i>Partie III — Coût de construction</div><a href="/seance/05/" data-ch="05"><span class="pastille" style="background:#cca424">5</span><span>Coût de reproduction et coût de remplacement</span></a><a href="/seance/06/" data-ch="06"><span class="pastille" style="background:#cca424">6</span><span>Méthodes d'estimation des coûts</span></a><a href="/seance/07/" data-ch="07"><span class="pastille" style="background:#cca424">7</span><span>Coûts directs de construction</span></a><a href="/seance/08/" data-ch="08"><span class="pastille" style="background:#cca424">8</span><span>Coûts indirects et profit entrepreneurial</span></a><div class="dd-part"><i style="background:#6b4fbb"></i>Partie IV — La dépréciation</div><a href="/seance/09/" data-ch="09"><span class="pastille" style="background:#6b4fbb">9</span><span>Concepts de dépréciation</span></a><a href="/seance/10/" data-ch="10"><span class="pastille" style="background:#6b4fbb">10</span><span>Dépréciation physique</span></a><a href="/seance/11/" data-ch="11"><span class="pastille" style="background:#6b4fbb">11</span><span>Dépréciation fonctionnelle</span></a><a href="/seance/12/" data-ch="12"><span class="pastille" style="background:#6b4fbb">12</span><span>Dépréciation économique (externe)</span></a><div class="dd-part"><i style="background:#107c4e"></i>Partie V — Applications et intégration</div><a href="/seance/13/" data-ch="13"><span class="pastille" style="background:#107c4e">13</span><span>Applications spécialisées</span></a><a href="/seance/14/" data-ch="14"><span class="pastille" style="background:#107c4e">14</span><span>Synthèse et révision</span></a><div class="dd-part">Annexes</div><a href="/aide-memoire/"><span class="pastille">A</span><span>Aide-mémoire des formules</span></a><a href="/glossaire/"><span class="pastille">B</span><span>Glossaire</span></a><a href="/rapport/"><span class="pastille" style="background:var(--teal)">R</span><span>Rapport — Le marché de l’habitation au Québec</span></a></div></div><div class="dd current"><button type="button" aria-expanded="false" aria-haspopup="true">Réviser <span class="caret" aria-hidden="true">▾</span></button><div class="dd-menu "><a href="/aide-memoire/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span>Aide-mémoire<span class="dd-desc">Toutes les formules commentées</span></span></a><a href="/glossaire/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span>Glossaire<span class="dd-desc">Termes du métier, équivalents anglais</span></span></a><a href="/definitions/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-list"/></svg></span><span>Toutes les définitions<span class="dd-desc">Les formulations attendues aux examens</span></span></a><a href="/fiches/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-cards"/></svg></span><span>Fiches de révision<span class="dd-desc">Recto-verso, suivi d’acquisition</span></span></a><a href="/carte/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-network"/></svg></span><span>Carte du cours<span class="dd-desc">Les 14 séances et leurs objectifs en un coup d’œil</span></span></a><a href="/exercices/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span>Banque d’exercices<span class="dd-desc">Tous les exercices corrigés</span></span></a></div></div><div class="dd"><button type="button" aria-expanded="false" aria-haspopup="true">S’exercer <span class="caret" aria-hidden="true">▾</span></button><div class="dd-menu "><a href="/quiz/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-quiz"/></svg></span><span>Quiz et examens blancs<span class="dd-desc">QCM avec rétroaction, chronomètre</span></span></a><a href="/entrainement/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-dumbbell"/></svg></span><span>Entraînement<span class="dd-desc">Problèmes à données aléatoires, corrigés pas à pas</span></span></a><a href="/jeux/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-game"/></svg></span><span>Jeux de révision<span class="dd-desc">Association, vrai ou faux, remise en ordre</span></span></a><a href="/outils/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-calc"/></svg></span><span>Calculateurs<span class="dd-desc">Les formules en interactif</span></span></a><a href="/progression/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-progress"/></svg></span><span>Ma progression<span class="dd-desc">Lecture, quiz, objectifs, notes</span></span></a></div></div><div class="dd"><button type="button" aria-expanded="false" aria-haspopup="true">Ressources <span class="caret" aria-hidden="true">▾</span></button><div class="dd-menu "><a href="/diapositives/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-slides"/></svg></span><span>Diapositives<span class="dd-desc">Les 14 présentations en ligne</span></span></a><a href="/ressources/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-download"/></svg></span><span>Téléchargements<span class="dd-desc">Manuel, plan, TP, gabarits Excel</span></span></a><a href="/rapport/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-report"/></svg></span><span>Rapport marché QC<span class="dd-desc">Indices de prix, macro, abordabilité — 26 sections, 67 figures</span></span></a><a href="/bibliographie/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-bib"/></svg></span><span>Bibliographie<span class="dd-desc">Références citées</span></span></a><a href="/recherche/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-search"/></svg></span><span>Recherche<span class="dd-desc">Tout le manuel indexé</span></span></a></div></div></nav>81    <div class="topbar-actions">82      <button class="icon-btn search-btn" type="button" data-action="search" aria-label="Rechercher"><svg class="" aria-hidden="true"><use href="#i-search"/></svg><span>Rechercher</span><kbd>⌘K</kbd></button>83      <button class="icon-btn" type="button" data-action="theme" aria-label="Thème clair ou sombre" title="Thème"><svg class="" aria-hidden="true"><use href="#i-sun"/></svg></button>84      <button class="icon-btn menu-btn" type="button" aria-label="Menu" aria-expanded="false"><svg class="" aria-hidden="true"><use href="#i-menu"/></svg></button>85    </div>86  </div>87  88</header>89<main id="main" class="page"><div class="page-head"><div class="eyebrow">S’exercer</div><h1>Banque d’exercices</h1><p class="lead">Les 89 exercices corrigés du manuel, regroupés. Cherchez d’abord la réponse, puis révélez la solution.</p></div><div class="two-col"><article class="prose" style="max-width:none"><h2 class="h-section" id="s-1"><span class="h-num">1</span><span class="h-text">Introduction à la méthode du coût</span></h2>90<p id="p1-98">Les exercices qui suivent couvrent l'ensemble de la séance, du calcul direct à la question de réflexion. Ils sont calibrés sur le format des questions d'examen : traitez-les par écrit, calculatrice en main, en rédigeant vos justifications comme si un réviseur devait les lire.</p>91<div class="box box-exo" id="exo-1-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 1.1</span><span class="box-title">— application directe de la formule</span><a class="box-anchor" href="#exo-1-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p1-99">Une propriété présente les caractéristiques suivantes : terrain <span class="num">150 000 $</span>; coût de remplacement neuf <span class="num">425 000 $</span>; dépréciation physique <span class="num">60 000 $</span>; dépréciation fonctionnelle <span class="num">25 000 $</span>; dépréciation externe <span class="num">15 000 $</span>. Quelle est la valeur estimée?</p></div></div>92<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p1-100">On calcule d'abord la dépréciation totale, puis on applique la formule fondamentale :</p>93<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>D</mi><mtext>totale</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>60</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>25</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>15</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>100</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mi>V</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>150</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mo stretchy="false">(</mo><mn>425</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>100</mn><mtext> </mtext><mn>000</mn><mo stretchy="false">)</mo><mo>=</mo><mn>150</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>325</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">475</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}D_{\text{totale}} &amp;= 60\,000 + 25\,000 + 15\,000 = 100\,000\ \$\\94V &amp;= 150\,000 + (425\,000 - 100\,000) = 150\,000 + 325\,00095   = \uqogreen{475\,000\ \$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:2.7em;vertical-align:-1.1em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6em;"><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.1em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6em;"><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">60</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">25</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">100</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace"> </span><span class="mord">$</span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">150</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord">425</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">100</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">150</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">325</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">475</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.1em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>96<p id="p1-101">La valeur dépréciée des améliorations est de <span class="num">325 000 $</span>; le terrain, lui, ne se déprécie pas.</p></div></details>97<div class="box box-exo" id="exo-1-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 1.2</span><span class="box-title">— retrouver la dépréciation implicite</span><a class="box-anchor" href="#exo-1-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p1-102">Un duplex de Hull est évalué à <span class="num">520 000 $</span> par la méthode du coût. Le terrain vaut <span class="num">110 000 $</span> et le coût de remplacement neuf des améliorations est de <span class="num">485 000 $</span>. Quelle dépréciation totale l'évaluateur a-t-il retenue, en dollars et en pourcentage du coût neuf?</p></div></div>98<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p1-103">On isole <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>totale</mtext></msub></mrow><annotation encoding="application/x-tex">D_{\text{totale}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> dans la formule fondamentale :</p>99<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mi>V</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><msub><mi>V</mi><mtext>terrain</mtext></msub><mo>+</mo><msub><mi>C</mi><mtext>neuf</mtext></msub><mo>−</mo><msub><mi>D</mi><mtext>totale</mtext></msub><mtext>  </mtext><mo>⟹</mo><mtext>  </mtext><msub><mi>D</mi><mtext>totale</mtext></msub><mo>=</mo><msub><mi>V</mi><mtext>terrain</mtext></msub><mo>+</mo><msub><mi>C</mi><mtext>neuf</mtext></msub><mo>−</mo><mi>V</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>D</mi><mtext>totale</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>110</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>485</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>520</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">75</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}V &amp;= V_{\text{terrain}} + C_{\text{neuf}} - D_{\text{totale}}100\;\Longrightarrow\;101D_{\text{totale}} = V_{\text{terrain}} + C_{\text{neuf}} - V\\102D_{\text{totale}} &amp;= 110\,000 + 485\,000 - 520\,000 = \uqogreen{75\,000\ \$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:2.7em;vertical-align:-1.1em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6em;"><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.1em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6em;"><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">terrain</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">neuf</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⟹</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">terrain</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">neuf</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">110</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">485</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">520</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">75</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.1em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>103<p id="p1-104">En pourcentage du coût neuf : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>75</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>485</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>15,5</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">75\,000 / 485\,000 = 15{,}5\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">75</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000/485</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">15</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>. Ce niveau est plausible pour un bâtiment d'une quinzaine d'années en bon état.</p></div></details>104<div class="box box-exo" id="exo-1-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 1.3</span><span class="box-title">— coût, contribution et surqualité</span><a class="box-anchor" href="#exo-1-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p1-105">Un propriétaire a investi <span class="num">90 000 $</span> dans un garage triple chauffé avec pont élévateur, dans un quartier de bungalows modestes de Gatineau. L'analyse des ventes montre que le marché local ne reconnaît qu'environ <span class="num">35 000 $</span> pour un garage, quel qu'en soit le luxe. (a) Quelle est la contribution du garage? (b) Quel principe économique est en jeu? (c) Comment la méthode du coût traitera-t-elle l'écart?</p></div></div>105<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p1-106">(a) La contribution est de <span class="num">35 000 $</span> : c'est ce que le marché paie, peu importe la facture. (b) Le <strong class="c-bleu">principe de contribution</strong> : la valeur d'une composante se mesure par son apport à la valeur totale, non par son coût. (c) L'écart de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>90</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>35</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>55</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">90\,000 - 35\,000 = 55\,000\ \$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">90</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">35</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">55</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace"> </span><span class="mord">$</span></span></span></span> constitue une <strong class="c-bleu">surqualité</strong> : dans un calcul par la méthode du coût, le coût neuf du garage serait inclus dans <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mtext>neuf</mtext></msub></mrow><annotation encoding="application/x-tex">C_{\text{neuf}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">neuf</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>, puis l'écart serait retranché à titre de dépréciation <strong class="c-bleu">fonctionnelle</strong>. Le résultat net reflète la contribution réelle.</p></div></details>106<div class="box box-exo" id="exo-1-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 1.4</span><span class="box-title">— choisir l'approche appropriée</span><a class="box-anchor" href="#exo-1-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p1-107">Pour chacune des propriétés suivantes, indiquez l'approche d'évaluation principale et justifiez en une phrase : (a) un bungalow de 1985 dans un quartier actif de Gatineau où 40 ventes comparables sont survenues cette année; (b) une bibliothèque municipale; (c) un immeuble de 24 logements à Trois-Rivières; (d) une usine de transformation alimentaire construite sur mesure; (e) une maison unifamiliale livrée le mois dernier.</p></div></div>107<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p1-108">(a) <strong class="c-bleu">Comparaison directe</strong> : abondance de comparables récents, marché actif — la lecture directe du marché prime. (b) <strong class="c-bleu">Méthode du coût</strong> : usage spécial, aucune vente comparable, aucun revenu — seule approche viable. (c) <strong class="c-bleu">Approche par le revenu</strong> : immeuble à revenus standard; les acheteurs raisonnent en multiplicateurs et taux de capitalisation. (d) <strong class="c-bleu">Méthode du coût</strong> : bâtiment industriel spécialisé, quasi absence de comparables; attention à la dépréciation fonctionnelle. (e) <strong class="c-bleu">Méthode du coût</strong> (avec vérification par comparaison si possible) : dépréciation nulle, coût réel documenté — indication de valeur de première qualité.</p></div></details>108<div class="box box-exo" id="exo-1-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 1.5</span><span class="box-title">— bâtiment commercial avec dépréciation en pourcentage</span><a class="box-anchor" href="#exo-1-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p1-109">Un bâtiment commercial de <span class="num">1200</span> m<sup>2</sup> à Sherbrooke : coût de remplacement neuf de <span class="num">2100</span> $/m<sup>2</sup>, dépréciation totale estimée à 32 % du coût neuf, terrain évalué à <span class="num">390 000 $</span>. Calculez la valeur de la propriété, puis le ratio terrain/valeur totale. Commentez brièvement ce ratio sachant que la fourchette typique du commercial urbain est de 30 à 50 %.</p></div></div>109<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>C</mi><mtext>neuf</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>1</mn><mtext> </mtext><mn>200</mn><mo>×</mo><mn>2</mn><mtext> </mtext><mn>100</mn><mo>=</mo><mn>2</mn><mtext> </mtext><mn>520</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>D</mi><mtext>totale</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>0,32</mn><mo>×</mo><mn>2</mn><mtext> </mtext><mn>520</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>806</mn><mtext> </mtext><mn>400</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mi>V</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>390</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mo stretchy="false">(</mo><mn>2</mn><mtext> </mtext><mn>520</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>806</mn><mtext> </mtext><mn>400</mn><mo stretchy="false">)</mo><mo>=</mo><mn>390</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>1</mn><mtext> </mtext><mn>713</mn><mtext> </mtext><mn>600</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">2</mn><mtext> </mtext><mn mathvariant="bold">103</mn><mtext> </mtext><mn mathvariant="bold">600</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}C_{\text{neuf}} &amp;= 1\,200 \times 2\,100 = 2\,520\,000\ \$\\110D_{\text{totale}} &amp;= 0{,}32 \times 2\,520\,000 = 806\,400\ \$\\111V &amp;= 390\,000 + (2\,520\,000 - 806\,400) = 390\,000 + 1\,713\,600112   = \uqogreen{2\,103\,600\ \$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:4.2em;vertical-align:-1.85em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35em;"><span style="top:-4.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">neuf</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-1.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.85em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35em;"><span style="top:-4.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">100</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">520</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace"> </span><span class="mord">$</span></span></span><span style="top:-3.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">32</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">520</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">806</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace"> </span><span class="mord">$</span></span></span><span style="top:-1.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">390</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">520</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">806</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">390</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">713</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">2</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">103</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">600</span><span class="mspace" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.85em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>113<p id="p1-110">Ratio terrain/total : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>390</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>2</mn><mtext> </mtext><mn>103</mn><mtext> </mtext><mn>600</mn><mo>=</mo><mn>18,5</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">390\,000 / 2\,103\,600 = 18{,}5\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">390</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000/2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">103</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">18</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>. Ce ratio est <strong class="c-rouge">sous</strong> la fourchette typique de 30–50 % du commercial urbain : soit le terrain est sous-évalué, soit le secteur présente des valeurs foncières faibles (périphérie), soit le bâtiment est inhabituellement imposant pour son site. Le ratio ne prouve rien à lui seul, mais il <strong class="c-bleu">déclenche une vérification</strong> — c'est exactement son rôle.</p></div></details>114<div class="box box-exo" id="exo-1-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 1.6</span><span class="box-title">— question de réflexion — les limites de la méthode</span><a class="box-anchor" href="#exo-1-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p1-111">Un promoteur soutient : « J'ai payé le terrain <span class="num">300 000 $</span> et la construction m'a coûté <span class="num">900 000 $</span>; ma propriété vaut donc <span class="num">1 200 000 $</span>. » Donnez trois raisons distinctes, appuyées sur les principes de cette séance, pour lesquelles cette affirmation peut être fausse — dans un sens comme dans l'autre.</p></div></div>115<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p1-112">Trois arguments parmi les suivants : (1) <strong class="c-bleu">Coût <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo mathvariant="normal">≠</mo></mrow><annotation encoding="application/x-tex">\neq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mrel"><span class="mrel"><span class="mord katex-vbox"><span class="katex-thinbox"><span class="rlap"><span class="katex-strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="katex-inner"><span class="mord"><span class="mrel"></span></span></span><span class="katex-fix"></span></span></span></span></span><span class="mspace nobreak"></span><span class="mrel">=</span></span></span></span></span> valeur</strong> : le coût mesure des dépenses de production; la valeur dépend de l'offre et de la demande — si le marché local plafonne à <span class="num">1 000 000 $</span>, l'écart est une dépréciation externe. (2) <strong class="c-bleu">Principe de contribution</strong> : certaines dépenses (finitions surdimensionnées, équipements de luxe) peuvent contribuer moins que leur coût — surqualité. (3) <strong class="c-bleu">Utilisation optimale</strong> : si le bâtiment ne représente pas l'usage optimal du terrain, le total coût-terrain surestime la valeur. (4) À l'inverse, dans un marché en forte demande ou après une flambée des coûts de construction, la valeur peut <em>excéder</em> le coût historique : le coût pertinent est le coût <strong class="c-bleu">actuel</strong> d'un substitut, pas la facture d'origine. L'affirmation du promoteur confond systématiquement fait comptable et opinion de valeur.</p></div></details>116<h2 class="h-section" id="s-2"><span class="h-num">2</span><span class="h-text">Cadre conceptuel et terminologie</span></h2>117<p id="p2-78">Les six exercices qui suivent balaient la séance entière, de la qualification conceptuelle au bordereau chiffré. Les exercices 3, 4 et 6 préfigurent directement le TP2 et les questions calculatoires de l'examen : rédigez vos bordereaux en colonnes, avec les bases de calcul explicites.</p>118<div class="box box-exo" id="exo-2-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 2.1</span><span class="box-title">— coût, prix ou valeur?</span><a class="box-anchor" href="#exo-2-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p2-79">Qualifiez chaque montant (coût, prix, valeur — ou autre chose) : (a) un entrepreneur facture <span class="num">425 000 $</span> pour la construction d'un bungalow; (b) l'acte notarié indique <span class="num">389 000 $</span> pour la vente; (c) l'évaluateur agréé estime la propriété à <span class="num">410 000 $</span>; (d) le rôle d'évaluation municipale affiche <span class="num">375 000 $</span>; (e) le vendeur demande <span class="num">429 000 $</span>.</p></div></div>119<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p2-80">(a) <strong class="c-bleu">Coût</strong> — dépenses de production facturées par le constructeur. (b) <strong class="c-bleu">Prix</strong> — fait transactionnel objectif constaté dans l'acte. (c) <strong class="c-bleu">Valeur</strong> — opinion professionnelle motivée de valeur marchande. (d) <strong class="c-bleu">Valeur</strong> — estimation à des fins fiscales (valeur inscrite au rôle, à la date de référence du rôle). (e) <strong class="c-bleu">Prix demandé</strong> — aspiration du vendeur : ni transaction conclue, ni opinion professionnelle. Aucun de ces cinq montants n'a à coïncider avec les autres.</p></div></details>120<div class="box box-exo" id="exo-2-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 2.2</span><span class="box-title">— reproduction ou remplacement?</span><a class="box-anchor" href="#exo-2-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p2-81">Pour chaque bâtiment, indiquez la base de coût appropriée et justifiez : (a) maison contemporaine construite en 2022; (b) église en pierre de 1895; (c) immeuble de bureaux de 1975; (d) usine de 1960 avec composantes en amiante-ciment; (e) maison de ferme ancestrale à assurer.</p></div></div>121<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p2-82">(a) <strong class="c-bleu">Reproduction</strong> : bâtiment récent, matériaux et techniques encore courants — les deux bases coïncident presque, la reproduction est directe. (b) <strong class="c-bleu">Reproduction</strong> : valeur patrimoniale; matériaux et savoir-faire ont une valeur intrinsèque. (c) <strong class="c-bleu">Remplacement</strong> : matériaux et méthodes de 1975 obsolètes; on chiffre un équivalent moderne conforme au code actuel. (d) <strong class="c-bleu">Remplacement</strong> : la reproduction est impossible et illégale (amiante interdit). (e) <strong class="c-bleu">Reproduction</strong> : en assurance patrimoniale, on cherche le coût de reconstruction à l'identique.</p></div></details>122<div class="box box-exo" id="exo-2-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 2.3</span><span class="box-title">— bordereau complet d'un immeuble commercial</span><a class="box-anchor" href="#exo-2-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p2-83">Un immeuble commercial de <span class="num">5000</span> pi<sup>2</sup> à Gatineau : coût direct de 200 $/pi<sup>2</sup>; honoraires professionnels 8 %, permis 1,5 %, financement 4 %, assurances et frais légaux 1 % (tous en % des coûts directs); profit entrepreneurial 12 % de (directs <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> indirects). Les baux étant taxables, les TPS/TVQ sont récupérables. Calculez le coût total de construction.</p></div></div>123<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Coûts directs : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>200</mn></mrow><annotation encoding="application/x-tex">5\,000 \times 200</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">200</span></span></span></span></th><th class="al-r"><span class="num">1 000 000 $</span></th></tr></thead><tbody><tr><td>Honoraires professionnels (8 %)</td><td class="al-r"><span class="num">80 000 $</span></td></tr><tr><td>Permis et inspections (1,5 %)</td><td class="al-r"><span class="num">15 000 $</span></td></tr><tr><td>Financement (4 %)</td><td class="al-r"><span class="num">40 000 $</span></td></tr><tr><td>Assurances et frais légaux (1 %)</td><td class="al-r"><span class="num">10 000 $</span></td></tr><tr><td><strong>Coûts indirects (14,5 % des directs)</strong></td><td class="al-r"><strong><span class="num">145 000 $</span></strong></td></tr><tr class="rule-above"><td>Directs <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> indirects</td><td class="al-r"><span class="num">1 145 000 $</span></td></tr><tr><td>Profit entrepreneurial (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>12</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>×</mo><mn>1</mn><mtext> </mtext><mn>145</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">12\,\% \times 1\,145\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">145</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>)</td><td class="al-r"><span class="num">137 400 $</span></td></tr><tr class="rule-above"><td><strong>Coût total (hors terrain)</strong></td><td class="al-r"><strong><span class="num">1 282 400 $</span></strong></td></tr></tbody></table></div></div>124<p id="p2-84">Les taxes sont exclues (récupérables — immeuble commercial à baux taxables). Le terrain s'ajouterait séparément.</p></div></details>125<div class="box box-exo" id="exo-2-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 2.4</span><span class="box-title">— l'erreur de base de calcul</span><a class="box-anchor" href="#exo-2-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p2-85">Un étudiant calcule le profit entrepreneurial d'un projet ainsi : directs <span class="num">800 000 $</span>, indirects <span class="num">160 000 $</span>, profit <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>12</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>×</mo><mn>800</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>96</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 12\,\% \times126800\,000 = 96\,000\ \$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">96</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace"> </span><span class="mord">$</span></span></span></span>. (a) Quelle erreur commet-il? (b) Recalculez le profit et le coût total corrects. (c) Quel est l'impact en dollars de l'erreur?</p></div></div>127<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p2-86">(a) Le profit se calcule sur la somme <strong class="c-bleu">(directs <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> indirects)</strong>, pas sur les seuls directs. (b) Profit correct <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>0,12</mn><mo>×</mo><mo stretchy="false">(</mo><mn>800</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>160</mn><mtext> </mtext><mn>000</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0,12</mn><mo>×</mo><mn>960</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">115</mn><mtext> </mtext><mn mathvariant="bold">200</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= 0{,}12 \times (800\,000 +128160\,000) = 0{,}12 \times 960\,000 = \uqogreen{115\,200\ \$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">12</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">160</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">12</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">960</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">115</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">200</span><span class="mspace" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>; coût total <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>960</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>115</mn><mtext> </mtext><mn>200</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">1</mn><mtext> </mtext><mn mathvariant="bold">075</mn><mtext> </mtext><mn mathvariant="bold">200</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">=129960\,000 + 115\,200 = \uqogreen{1\,075\,200\ \$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">960</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">115</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">1</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">075</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">200</span><span class="mspace" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>. (c) L'erreur sous-estime le profit de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>115</mn><mtext> </mtext><mn>200</mn><mo>−</mo><mn>96</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>19</mn><mtext> </mtext><mn>200</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">115\,200 - 96\,000 = 19\,200\ \$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">115</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">96</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">19</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace"> </span><span class="mord">$</span></span></span></span>, soit près de 1,8 % du coût total — une erreur matérielle dans un rapport professionnel.</p></div></details>130<div class="box box-exo" id="exo-2-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 2.5</span><span class="box-title">— divergences coût–valeur</span><a class="box-anchor" href="#exo-2-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p2-87">Expliquez, en mobilisant les concepts de la séance, pourquoi chacune de ces situations est économiquement cohérente : (a) une maison neuve de <span class="num">800 000 $</span> (coût complet documenté) ne trouve preneur qu'à <span class="num">650 000 $</span> dans son quartier; (b) un duplex ancien dont le coût de remplacement déprécié des améliorations est de <span class="num">190 000 $</span> se vend <span class="num">520 000 $</span>.</p></div></div>131<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p2-88">(a) <strong class="c-bleu">Coût <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>&gt;</mo></mrow><annotation encoding="application/x-tex">&gt;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">&gt;</span></span></span></span> valeur</strong> : surqualité par rapport au quartier (principe de contribution — le marché local ne paie pas les finitions excédentaires) et/ou dépréciation externe (l'environnement plafonne les valeurs). Le coût est un fait; la valeur dépend de la demande. (b) <strong class="c-bleu">Valeur <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>&gt;</mo></mrow><annotation encoding="application/x-tex">&gt;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">&gt;</span></span></span></span> coût déprécié des améliorations</strong> : l'écart loge dans le <strong class="c-bleu">terrain</strong>. Si le duplex est bien situé, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mtext>terrain</mtext></msub></mrow><annotation encoding="application/x-tex">V_{\text{terrain}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">terrain</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> peut valoir <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>520</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>190</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>330</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">520\,000 - 190\,000 = 330\,000\ \$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">520</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">190</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">330</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace"> </span><span class="mord">$</span></span></span></span> — parfaitement cohérent avec la formule fondamentale : la valeur totale n'est jamais bornée par le seul coût déprécié du bâtiment.</p></div></details>132<div class="box box-exo" id="exo-2-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 2.6</span><span class="box-title">— classes de qualité et sensibilité</span><a class="box-anchor" href="#exo-2-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p2-89">Le coût de base (classe C) d'un bungalow est de 210 $/pi<sup>2</sup> pour <span class="num">1400</span> pi<sup>2</sup>. (a) Chiffrez le coût direct si le bâtiment est de classe B (retenez 125 %) puis de classe D (retenez 80 %). (b) Quel écart total en dollars sépare les deux classements? (c) Qu'en concluez-vous sur l'importance du jugement de classement?</p></div></div>133<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p2-90">Coût de base : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>210</mn><mo>×</mo><mn>1</mn><mtext> </mtext><mn>400</mn><mo>=</mo><mn>294</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">210 \times 1\,400 = 294\,000\ \$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">210</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">294</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace"> </span><span class="mord">$</span></span></span></span>. (a) Classe B : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>294</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>1,25</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">367</mn><mtext> </mtext><mn mathvariant="bold">500</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">294\,000 \times 1{,}25 = \uqogreen{367\,500\ \$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">294</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">25</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">367</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">500</span><span class="mspace" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>; classe D : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>294</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,80</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">235</mn><mtext> </mtext><mn mathvariant="bold">200</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">294\,000 \times 0{,}80 = \uqogreen{235\,200\ \$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">294</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">80</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">235</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">200</span><span class="mspace" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>. (b) Écart : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>367</mn><mtext> </mtext><mn>500</mn><mo>−</mo><mn>235</mn><mtext> </mtext><mn>200</mn><mo>=</mo><mn>132</mn><mtext> </mtext><mn>300</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">367\,500 - 235\,200 = 132\,300\ \$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">367</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">235</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">132</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">300</span><span class="mspace"> </span><span class="mord">$</span></span></span></span>, soit 45 % du coût de base. (c) Le classement de qualité est un <strong class="c-bleu">jugement à fort levier</strong> : une erreur d'une classe déplace le coût neuf de plusieurs dizaines de milliers de dollars, avant toute considération de dépréciation. D'où l'importance de l'inspection et des critères objectifs (matériaux, finitions, équipements) documentés au dossier.</p></div></details>134<h2 class="h-section" id="s-3"><span class="h-num">3</span><span class="h-text">Méthodes d'évaluation du terrain</span></h2>135<p id="p3-76">Les six exercices couvrent les cinq méthodes et le PHMU. L'exercice 2 reproduit la mécanique exacte de la grille du TP1 (cascade transactionnelle, puis ajustements additifs, puis seuils) : maîtrisez-le avant d'ouvrir le gabarit Excel.</p>136<div class="box box-exo" id="exo-3-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 3.1</span><span class="box-title">— PHMU et zonage</span><a class="box-anchor" href="#exo-3-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p3-77">Un terrain de <span class="num">12 000</span> pi<sup>2</sup> porte un bungalow de 1962 en bon état. Le zonage permet désormais du multifamilial de 6 logements. Des terrains comparables se vendent 14 $/pi<sup>2</sup> pour l'usage unifamilial et <span class="num">32 000 $</span> par unité constructible pour le multifamilial; la démolition du bungalow coûterait <span class="num">25 000 $</span>. (a) Évaluez le terrain selon chaque usage. (b) Lequel retient l'évaluateur, et en vertu de quel principe? (c) Quelle condition supplémentaire faudrait-il vérifier avant de conclure?</p></div></div>137<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p3-78">(a) Usage unifamilial : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>12</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>14</mn><mo>=</mo><mn>168</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">12\,000 \times 14 = 168\,000\ \$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">14</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">168</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace"> </span><span class="mord">$</span></span></span></span>. Usage multifamilial : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>6</mn><mo>×</mo><mn>32</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>192</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">6 \times 32\,000 = 192\,000\ \$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">6</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">32</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">192</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace"> </span><span class="mord">$</span></span></span></span>, moins la démolition nécessaire pour libérer le site : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>192</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>25</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">167</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">192\,000 - 25\,000 =138\uqogreen{167\,000\ \$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">192</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">25</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">167</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span> net... contre <span class="num">168 000 $</span> pour l'usage unifamilial, qui conserve le bâtiment. (b) Les deux usages franchissent les trois premiers tests (légal, possible, faisable); le quatrième — <strong class="c-bleu">maximalement productif</strong> — départage : ici l'usage unifamilial domine de justesse une fois la démolition comptée. Le principe en jeu est l'<strong class="c-bleu">utilisation optimale</strong> : la valeur retenue est la valeur résiduelle nette la plus élevée, pas le revenu brut le plus élevé. (c) Vérifier que le marché absorbe réellement du multifamilial dans ce secteur (faisabilité), que les exigences réglementaires (stationnement, marges, implantation) permettent bien 6 logements sur ce terrain précis — et refaire le calcul si l'un des paramètres change : à <span class="num">33 000 $</span>/unité, la conclusion s'inverse.</p></div></details>139<div class="box box-exo" id="exo-3-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 3.2</span><span class="box-title">— grille d'ajustements — sens et cascade</span><a class="box-anchor" href="#exo-3-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p3-79">Un comparable s'est vendu 18,40 $/pi<sup>2</sup> il y a 10 mois. Le marché progresse de 3 %/an. Le comparable est mieux localisé que le sujet (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>0,90 $/pi<sup>2</sup>) et n'a pas l'égout (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>1,10 $/pi<sup>2</sup>); le sujet et le comparable sont autrement équivalents. (a) Calculez le prix ajusté transactionnel puis l'indication finale. (b) Calculez les ajustements net et brut en pourcentage et vérifiez les seuils usuels.</p></div></div>140<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p3-80">(a) Conditions de marché : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo><mn>3</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>×</mo><mstyle scriptlevel="0" displaystyle="false"><mfrac><mn>10</mn><mn>12</mn></mfrac></mstyle><mo>=</mo><mo>+</mo><mn>2,5</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">+3\,\% \times \tfrac{10}{12} = +2{,}5\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">+</span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">12</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">+</span><span class="mord">2</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>, soit <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>18,40</mn><mo>×</mo><mn>1,025</mn><mo>=</mo><mn>18,86</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">18{,}40 \times 1{,}025 = 18{,}86~\$/\text{pi}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">18</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">40</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">025</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1219em;vertical-align:-0.25em;"></span><span class="mord">18</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">86</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span> (prix ajusté transactionnel). Ajustements de propriété (additifs) : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>18,86</mn><mo>−</mo><mn>0,90</mn><mo>+</mo><mn>1,10</mn><mo>=</mo><mn>19,06</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">18{,}86 - 0{,}90 +1411{,}10 = 19{,}06~\$/\text{pi}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">18</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">86</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">90</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">10</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1219em;vertical-align:-0.25em;"></span><span class="mord">19</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">06</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>, soit <strong class="c-vert">19,06 $/pi<sup>2</sup></strong>. (b) Ajustement net (hors temps, sur le prix ajusté) : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mo>−</mo><mn>0,90</mn><mo>+</mo><mn>1,10</mn><mo stretchy="false">)</mo><mi mathvariant="normal">/</mi><mn>18,86</mn><mo>=</mo><mo>+</mo><mn>1,1</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">(-0{,}90 + 1{,}10)/18{,}86 = +1{,}1\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">−</span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">90</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">10</span><span class="mclose">)</span><span class="mord">/18</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">86</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">+</span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>; en incluant le temps sur le prix initial : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>19,06</mn><mo>−</mo><mn>18,40</mn><mo stretchy="false">)</mo><mi mathvariant="normal">/</mi><mn>18,40</mn><mo>=</mo><mo>+</mo><mn>3,6</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">(19{,}06 - 18{,}40)/18{,}40 = +3{,}6\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">19</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">06</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">18</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">40</span><span class="mclose">)</span><span class="mord">/18</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">40</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">+</span><span class="mord">3</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">6</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>. Ajustement brut : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>0,46</mn><mo>+</mo><mn>0,90</mn><mo>+</mo><mn>1,10</mn><mo stretchy="false">)</mo><mi mathvariant="normal">/</mi><mn>18,40</mn><mo>=</mo><mn>13,4</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">(0{,}46 + 0{,}90 + 1{,}10)/18{,}40 = 13{,}4\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">46</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">90</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">10</span><span class="mclose">)</span><span class="mord">/18</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">40</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">13</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">4</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>. Les deux mesures respectent largement les seuils usuels (net <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≤</mo><mn>25</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">\leq 25\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">25</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>, brut <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≤</mo><mn>50</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">\leq 50\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>) : le comparable est de bonne qualité.</p></div></details>142<div class="box box-exo" id="exo-3-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 3.3</span><span class="box-title">— extraction avec validation par ratio</span><a class="box-anchor" href="#exo-3-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p3-81">Un jumelé de 12 ans s'est vendu <span class="num">485 000 $</span> à Gatineau. Coût de remplacement neuf des améliorations : <span class="num">340 000 $</span>; durée de vie économique : 55 ans; dépréciation linéaire. (a) Extrayez la valeur du terrain. (b) Calculez le ratio terrain/total et confrontez-le à la fourchette de banlieue (25–40 %). (c) Refaites le calcul avec une durée de vie de 45 ans et commentez.</p></div></div>143<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p3-82">(a) Dépréciation : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>340</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mstyle scriptlevel="0" displaystyle="false"><mfrac><mn>12</mn><mn>55</mn></mfrac></mstyle><mo>=</mo><mn>74</mn><mtext> </mtext><mn>182</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">340\,000 \times \tfrac{12}{55} = 74\,182\ \$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">340</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">55</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">12</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">74</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">182</span><span class="mspace"> </span><span class="mord">$</span></span></span></span>; bâtiment déprécié : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>340</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>74</mn><mtext> </mtext><mn>182</mn><mo>=</mo><mn>265</mn><mtext> </mtext><mn>818</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">340\,000 - 74\,182 = 265\,818\ \$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">340</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">74</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">182</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">265</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">818</span><span class="mspace"> </span><span class="mord">$</span></span></span></span>; terrain : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>485</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>265</mn><mtext> </mtext><mn>818</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">219</mn><mtext> </mtext><mn mathvariant="bold">182</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">485\,000 -144265\,818 = \uqogreen{219\,182\ \$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">485</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">265</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">818</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">219</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">182</span><span class="mspace" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>, arrondi à <span class="num">219 000 $</span>. (b) Ratio : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>219</mn><mtext> </mtext><mn>182</mn><mi mathvariant="normal">/</mi><mn>485</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>45,2</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">219\,182/485\,000 = 45{,}2\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">219</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">182/485</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">45</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> — <strong class="c-rouge">au-dessus</strong> de la fourchette de banlieue : à corroborer (secteur central? bâtiment sous-estimé?). (c) Avec 45 ans : dépréciation <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>340</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mstyle scriptlevel="0" displaystyle="false"><mfrac><mn>12</mn><mn>45</mn></mfrac></mstyle><mo>=</mo><mn>90</mn><mtext> </mtext><mn>667</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 340\,000 \times145\tfrac{12}{45} = 90\,667\ \$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">340</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">45</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">12</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">90</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">667</span><span class="mspace"> </span><span class="mord">$</span></span></span></span>; bâtiment <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>249</mn><mtext> </mtext><mn>333</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 249\,333\ \$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">249</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">333</span><span class="mspace"> </span><span class="mord">$</span></span></span></span>; terrain <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">235</mn><mtext> </mtext><mn mathvariant="bold">667</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">=146\uqogreen{235\,667\ \$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">235</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">667</span><span class="mspace" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span> (ratio 48,6 %). Dix ans de durée de vie déplacent le terrain de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span></span></span></span> <span class="num">16 500 $</span> : illustration directe de la sensibilité de l'extraction aux hypothèses de dépréciation.</p></div></details>147<div class="box box-exo" id="exo-3-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 3.4</span><span class="box-title">— lotissement — effet du rythme d'absorption</span><a class="box-anchor" href="#exo-3-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p3-83">Reprenez l'exemple du lotissement de Sherbrooke (revenus <span class="num">3 400 000 $</span>, coûts <span class="num">1 780 000 $</span>, profit 15 % des revenus). Le service d'urbanisme signale que l'absorption prendra 5 ans plutôt que 3, portant le coût d'actualisation de <span class="num">210 000 $</span> à <span class="num">345 000 $</span> et les frais de financement de <span class="num">90 000 $</span> à <span class="num">150 000 $</span>. Recalculez la valeur résiduelle et l'écart en pourcentage.</p></div></div>148<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p3-84">Nouveaux coûts de développement : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mtext> </mtext><mn>780</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>90</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>150</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>840</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">1\,780\,000 - 90\,000 + 150\,000 =1491\,840\,000\ \$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">780</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">90</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">150</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">840</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace"> </span><span class="mord">$</span></span></span></span>. Cascade : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mtext> </mtext><mn>400</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>1</mn><mtext> </mtext><mn>840</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>510</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>345</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">705</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">3\,400\,000 - 1\,840\,000 - 510\,000 - 345\,000150= \uqogreen{705\,000\ \$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">840</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">510</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">345</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">705</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span> (contre <span class="num">900 000 $</span>), soit une baisse de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>195</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>900</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mstyle mathcolor="#B22A20"><mrow><mn mathvariant="bold">21,7</mn><mtext> </mtext><mi mathvariant="bold">%</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">195\,000/900\,000 = \uqoalert{21{,}7\,\%}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">195</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000/900</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord" style="color:#B22A20;"><span class="mord mathbf" style="color:#B22A20;">21</span><span class="mord" style="color:#B22A20;"><span class="mpunct" style="color:#B22A20;">,</span></span><span class="mord mathbf" style="color:#B22A20;">7</span><span class="mspace" style="color:#B22A20;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#B22A20;">%</span></span></span></span></span>. Deux années d'absorption de plus amputent la valeur du terrain de plus du cinquième : le <strong class="c-bleu">rythme d'absorption</strong> est l'une des variables les plus sensibles de la méthode — d'où l'importance d'une étude de marché sérieuse.</p></div></details>151<div class="box box-exo" id="exo-3-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 3.5</span><span class="box-title">— résidu foncier</span><a class="box-anchor" href="#exo-3-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p3-85">Un promoteur projette un petit immeuble commercial neuf : RNE stabilisé <span class="num">224 000 $</span>; coût neuf du bâtiment (indirects et profit compris) <span class="num">2 450 000 $</span>; <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mi>b</mi></msub><mo>=</mo><mn>8,0</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">R_b = 8{,}0\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0077em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">8</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>; <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mi>t</mi></msub><mo>=</mo><mn>5,5</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">R_t = 5{,}5\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0077em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">5</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>. (a) Évaluez le terrain. (b) Expliquez pourquoi <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mi>b</mi></msub><mo>&gt;</mo><msub><mi>R</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">R_b &gt; R_t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0077em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0077em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>. (c) Donnez deux conditions de validité de votre résultat.</p></div></div>152<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p3-86">(a) Rendement du bâtiment : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mn>450</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,08</mn><mo>=</mo><mn>196</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">2\,450\,000 \times 0{,}08 = 196\,000\ \$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">450</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">08</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">196</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace"> </span><span class="mord">$</span></span></span></span>; résidu du terrain : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>224</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>196</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>28</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">224\,000 - 196\,000 = 28\,000\ \$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">224</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">196</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">28</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace"> </span><span class="mord">$</span></span></span></span>; valeur : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>28</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>0,055</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">509</mn><mtext> </mtext><mn mathvariant="bold">091</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">28\,000/0{,}055 = \uqogreen{509\,091\ \$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">28</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000/0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">055</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">509</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">091</span><span class="mspace" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>, arrondie à <span class="num">510 000 $</span>. (b) Le bâtiment a une durée de vie finie : son taux doit couvrir le rendement <em>sur</em> le capital <em>et</em> la récupération <em>du</em> capital. Le terrain, perpétuel, n'exige que le rendement — d'où <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mi>b</mi></msub><mo>&gt;</mo><msub><mi>R</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">R_b &gt; R_t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0077em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0077em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>. (c) Conditions : bâtiment neuf représentant le PHMU du site; RNE stabilisé; taux <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mi>b</mi></msub></mrow><annotation encoding="application/x-tex">R_b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0077em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> et <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">R_t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0077em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> solidement étayés par le marché; et validation par une seconde méthode — le résultat bouge de dizaines de milliers de dollars par demi-point de taux.</p></div></details>153<div class="box box-exo" id="exo-3-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 3.6</span><span class="box-title">— choix de méthode</span><a class="box-anchor" href="#exo-3-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p3-87">Pour chaque situation, identifiez la méthode d'évaluation du terrain la plus appropriée : (a) terrain unifamilial dans un nouveau développement où huit terrains vacants se sont vendus cette année; (b) terrain sous un immeuble de bureaux au centre-ville de Gatineau, aucune vente de terrain vacant depuis dix ans, mais bonnes données de revenus et de coûts pour un projet neuf; (c) emplacement résidentiel dans un quartier établi, quelques ventes récentes de maisons dont les bâtiments sont récents; (d) terre de 8 hectares en bordure de l'urbanisation, zonée blanche, propice à une subdivision; (e) vérification rapide d'une estimation, avec pour seules données les rôles d'évaluation du secteur.</p></div></div>154<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p3-88">(a) <strong class="c-bleu">Comparaison directe</strong> : comparables vacants abondants — la méthode reine s'applique. (b) <strong class="c-bleu">Résidu foncier</strong> : pas de comparables, mais revenus, coûts et taux disponibles pour un projet au PHMU. (c) <strong class="c-bleu">Extraction</strong> : ventes améliorées récentes avec bâtiments récents, donc dépréciation estimable de façon fiable. (d) <strong class="c-bleu">Analyse de lotissement</strong> : grand terrain subdivisible — revenus des lots moins coûts de développement. (e) <strong class="c-bleu">Affectation</strong> : ratio terrain/total dérivé des rôles — acceptable comme vérification, jamais comme méthode principale.</p></div></details>155<h2 class="h-section" id="s-4"><span class="h-num">4</span><span class="h-text">Analyse du terrain et ajustements</span></h2>156<div class="box box-exo" id="exo-4-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 4.1</span><span class="box-title">— règle de Harper</span><a class="box-anchor" href="#exo-4-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p4-104">Un terrain de référence de 120 pi de profondeur, entièrement comparable au sujet, vaut <span class="num">96 000 $</span>. Le sujet, identique en tous points, n'a que 90 pi de profondeur. Estimez sa valeur par la règle de Harper, puis par la règle de Davis, et commentez l'écart.</p></div></div>157<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p4-105">Chaque quart de profondeur fait <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>120</mn><mi mathvariant="normal">/</mi><mn>4</mn><mo>=</mo><mn>30</mn></mrow><annotation encoding="application/x-tex">120/4 = 30</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">120/4</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">30</span></span></span></span> pi. Le sujet (90 pi) conserve les trois premiers quarts.  <strong>Harper (40-30-20-10)</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mo stretchy="false">(</mo><mn>0,40</mn><mo>+</mo><mn>0,30</mn><mo>+</mo><mn>0,20</mn><mo stretchy="false">)</mo><mo>×</mo><mn>96</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>0,90</mn><mo>×</mo><mn>96</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mrow><mtext>86</mtext><mtext> </mtext><mtext>400</mtext><mtext> </mtext><mtext>$</mtext></mrow></mrow><annotation encoding="application/x-tex">V = (0{,}40 + 0{,}30 + 0{,}20) \times 96\,000 = 0{,}90 \times 96\,000 =158\text{86\,400\,\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">40</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">30</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">20</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">96</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">90</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">96</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord text"><span class="mord">86</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span></span>.  <strong>Davis (50-25-15-10)</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mo stretchy="false">(</mo><mn>0,50</mn><mo>+</mo><mn>0,25</mn><mo>+</mo><mn>0,15</mn><mo stretchy="false">)</mo><mo>×</mo><mn>96</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>0,90</mn><mo>×</mo><mn>96</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mrow><mtext>86</mtext><mtext> </mtext><mtext>400</mtext><mtext> </mtext><mtext>$</mtext></mrow></mrow><annotation encoding="application/x-tex">V = (0{,}50 + 0{,}25 + 0{,}15) \times 96\,000 = 0{,}90 \times 96\,000 =159\text{86\,400\,\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">50</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">25</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">15</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">96</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">90</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">96</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord text"><span class="mord">86</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span></span>.  Ici les deux règles coïncident, car elles attribuent toutes deux 10 % au dernier quart. L'écart apparaîtrait pour une prise plus profonde : avec 60 pi (deux quarts), Harper donne <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0,70</mn><mo>×</mo><mn>96</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>67</mn><mtext> </mtext><mn>200</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">0{,}70 \times 96\,000 = 67\,200~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">70</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">96</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">67</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span> et Davis <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0,75</mn><mo>×</mo><mn>96</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>72</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">0{,}75 \times 96\,000 = 72\,000~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">75</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">96</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">72</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span> — Davis, plus « conservatrice », concentre davantage la valeur côté rue.</p></div></details>160<div class="box box-exo" id="exo-4-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 4.2</span><span class="box-title">— ajustement pour le temps</span><a class="box-anchor" href="#exo-4-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p4-106">Un comparable s'est vendu <span class="num">89 000 $</span> il y a 17 mois dans un marché qui s'apprécie de 5 % par année. Calculez le prix ajusté pour le temps. Expliquez pourquoi cet ajustement se fait avant celui de la localisation.</p></div></div>161<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p4-107"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mtext>temps</mtext></msub><mo>=</mo><mn>89</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,05</mn><mo>×</mo><mfrac><mn>17</mn><mn>12</mn></mfrac><mo>=</mo><mn>89</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,07083</mn><mo>≈</mo><mo>+</mo><mtext> </mtext><mn>6</mn><mtext> </mtext><mn>304</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">A_{\text{temps}} = 89\,000 \times 0{,}05 \times \frac{17}{12} =16289\,000 \times 0{,}07083 \approx +\,6\,304~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">temps</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">89</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">05</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">12</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">17</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">89</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">07083</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">+</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">6</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">304</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>, d'où un prix ajusté d'environ <span class="num">95 304 $</span>, que l'on arrondirait à <span class="num">95 300 $</span>.  L'ajustement de temps précède les autres parce qu'il corrige la <em>base</em> du prix : les écarts de localisation ou de caractéristiques physiques doivent être mesurés entre le sujet et un comparable exprimé <em>en dollars d'aujourd'hui</em>. Ajuster la localisation sur un prix vieux de 17 mois reviendrait à appliquer un pourcentage juste à une assiette fausse.</p></div></details>163<div class="box box-exo" id="exo-4-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 4.3</span><span class="box-title">— analyse par paires</span><a class="box-anchor" href="#exo-4-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p4-108">Vente A : terrain plat, <span class="num">9000</span> pi<sup>2</sup>, tous services, <span class="num">90 000 $</span>. Vente B : terrain identique de la même rue, mais en pente modérée, <span class="num">81 500 $</span>. Vente C : autre paire du secteur, plat contre pente modérée, écart observé de 8,7 %. Extrayez l'ajustement de topographie et formulez la conclusion qu'en tirerait un évaluateur.</p></div></div>164<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p4-109">Paire A–B : écart <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mo stretchy="false">(</mo><mn>90</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>81</mn><mtext> </mtext><mn>500</mn><mo stretchy="false">)</mo><mi mathvariant="normal">/</mi><mn>90</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>9,4</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">= (90\,000 - 81\,500)/90\,000 = 9{,}4\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">90</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">81</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mclose">)</span><span class="mord">/90</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">9</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">4</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>. La seconde paire indique 8,7 %. Les deux mesures convergent vers une décote d'environ <strong>9 %</strong> pour une pente modérée dans ce secteur — cohérente avec la fourchette indicative de 5 à 15 %. L'évaluateur retiendrait un ajustement d'environ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>9 % (ou son équivalent en dollars) en le documentant par les deux paires; une seule paire n'aurait constitué qu'un indice, la convergence de deux paires en fait une donnée défendable.</p></div></details>165<div class="box box-exo" id="exo-4-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 4.4</span><span class="box-title">— sens et ampleur des ajustements</span><a class="box-anchor" href="#exo-4-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p4-110">Le sujet est un terrain rectangulaire, plat, tous services, localisation moyenne. Pour chacun des comparables suivants, indiquez le <em>sens</em> (+/-) de chaque ajustement requis : (a) comparable trapézoïdal, par ailleurs identique; (b) comparable dans un secteur supérieur, en pente légère; (c) comparable sans égout sanitaire, dans un secteur inférieur.</p></div></div>166<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p4-111">(a) Le comparable est <em>inférieur</em> (forme) : ajustement <strong>positif</strong> sur la forme.  (b) Localisation supérieure : ajustement <strong>négatif</strong>; pente légère (le sujet est plat, donc le comparable est inférieur sur ce point) : ajustement <strong>positif</strong>. Les deux corrections jouent en sens contraires — c'est normal et fréquent.  (c) Sans égout sanitaire : <strong>positif</strong> (comparable inférieur); localisation inférieure : <strong>positif</strong> également. Attention à ne pas « compenser » mentalement : chaque ligne se juge séparément, la grille fait la somme.</p></div></details>167<div class="box box-exo" id="exo-4-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 4.5</span><span class="box-title">— qualité de la grille</span><a class="box-anchor" href="#exo-4-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p4-112">Une grille de quatre comparables produit les valeurs ajustées suivantes : <span class="num">71 200 $</span>, <span class="num">74 800 $</span>, <span class="num">93 500 $</span> et <span class="num">73 900 $</span>, avec des ajustements bruts respectifs de 9 %, 12 %, 38 % et 11 %. Analysez la qualité de cette grille et proposez une conclusion de valeur.</p></div></div>168<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p4-113">Trois comparables convergent étroitement (71 200 à 74 800 $, écart <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span></span></span></span> 5 %) avec des ajustements bruts sains (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>&lt;</mo></mrow><annotation encoding="application/x-tex">&lt;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">&lt;</span></span></span></span> 15 %). Le troisième comparable est un cas aberrant : ajustement brut de 38 % (au-delà du seuil préoccupant de 25–40 %) et valeur ajustée décalée de plus de 25 % des autres. Deux traitements défendables : l'écarter (en le documentant) ou lui donner un poids marginal (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≤</mo></mrow><annotation encoding="application/x-tex">\leq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mrel">≤</span></span></span></span> 5–10 %). Avec une pondération de 35/30/0/35 sur les trois fiables, la valeur ressort autour de <span class="num">73 300 $</span>; conclusion arrondie : environ <strong><span class="num">73 000 $</span></strong> à <strong><span class="num">73 500 $</span></strong>. Le réflexe attendu : la convergence des comparables peu ajustés prime toujours sur un comparable spectaculairement corrigé.</p></div></details>169<div class="box box-exo" id="exo-4-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 4.6</span><span class="box-title">— contraintes superposées</span><a class="box-anchor" href="#exo-4-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p4-114">Un terrain de <span class="num">20 000</span> pi<sup>2</sup> vaudrait 10 $/pi<sup>2</sup> libre de toute contrainte. Une servitude d'Hydro-Québec grève <span class="num">3000</span> pi<sup>2</sup> en fond de lot (décote de 40 % sur la zone grevée) et <span class="num">2500</span> pi<sup>2</sup> en façade sont désormais cartographiés en zone inondable de risque modéré (décote de 25 % sur la zone touchée). Estimez la valeur nette du terrain.</p></div></div>170<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p4-115">Valeur brute : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>20</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>10</mn><mo>=</mo><mn>200</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">20\,000 \times 10 = 200\,000~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>.  Servitude : perte <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>3</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>10</mn><mo>×</mo><mn>0,40</mn><mo>=</mo><mn>12</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 3\,000 \times 10 \times 0{,}40 = 12\,000~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">40</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>.  Zone inondable : perte <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>2</mn><mtext> </mtext><mn>500</mn><mo>×</mo><mn>10</mn><mo>×</mo><mn>0,25</mn><mo>=</mo><mn>6</mn><mtext> </mtext><mn>250</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 2\,500 \times 10 \times 0{,}25 = 6\,250~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">25</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">6</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">250</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>.  Valeur nette <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>200</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>12</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>6</mn><mtext> </mtext><mn>250</mn><mo>=</mo><mn>181</mn><mtext> </mtext><mn>750</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\approx 200\,000 - 12\,000 - 6\,250 = 181\,750~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">6</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">250</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">181</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">750</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>, arrondie à <strong><span class="num">182 000 $</span></strong>. Nuances attendues d'un bon raisonnement : la zone grevée en fond de lot valait peut-être déjà moins que la moyenne (règle de Harper), ce qui réduirait la perte réelle; et l'inondabilité en <em>façade</em> pourrait au contraire peser sur la constructibilité de tout le lot — l'évaluateur vérifierait l'implantation possible avant de conclure.</p></div></details>171<h2 class="h-section" id="s-5"><span class="h-num">5</span><span class="h-text">Coût de reproduction et coût de remplacement</span></h2>172<div class="box box-exo" id="exo-5-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 5.1</span><span class="box-title">— reproduction ou remplacement?</span><a class="box-anchor" href="#exo-5-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p5-98">Pour chacun des mandats suivants, indiquez le coût à privilégier et justifiez en une phrase : (a) évaluation d'assurance d'une chapelle classée de 1870; (b) valeur marchande d'un duplex de 1985; (c) valeur marchande d'un entrepôt livré il y a 3 ans; (d) indemnité d'expropriation d'une résidence cossue de 1910 aux boiseries d'origine.</p></div></div>173<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p5-99">(a) <strong>Reproduction</strong> : la police valeur à neuf intégrale couvre la reconstruction à l'identique d'un bien patrimonial. (b) <strong>Remplacement</strong> : bâtiment de plus de 10 ans, mandat courant — l'acheteur paie l'utilité. (c) <strong>Indifférent</strong> : à moins de 5 ans, les deux coûts coïncident pratiquement; le remplacement est le plus simple. (d) <strong>Reproduction</strong> le plus souvent : en expropriation d'un bien à caractère unique, la reproduction sert fréquemment de base d'indemnisation — en veillant à déduire les obsolescences reproduites.</p></div></details>174<div class="box box-exo" id="exo-5-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 5.2</span><span class="box-title">— relation fondamentale</span><a class="box-anchor" href="#exo-5-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p5-100">Le coût de reproduction d'un immeuble est estimé à <span class="num">412 000 $</span> et son obsolescence fonctionnelle curable à <span class="num">34 000 $</span>. (a) Quel est le coût de remplacement? (b) Si la dépréciation physique est de <span class="num">88 000 $</span>, l'incurable fonctionnelle de <span class="num">21 000 $</span> et l'externe de <span class="num">15 000 $</span>, calculez la valeur dépréciée par les deux chemins et vérifiez l'équivalence.</p></div></div>175<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p5-101">(a) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mtext>rempl.</mtext></msub><mo>=</mo><mn>412</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>34</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mrow><mtext>378</mtext><mtext> </mtext><mtext>000</mtext><mtext> </mtext><mtext>$</mtext></mrow></mrow><annotation encoding="application/x-tex">C_{\text{rempl.}} = 412\,000 - 34\,000 = \text{378\,000\,\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">rempl.</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">412</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">34</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord text"><span class="mord">378</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span></span> (éq. <a class="xref" href="/seance/05/#form-5-1">5.1</a>).  (b) <em>Via reproduction</em> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>412</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>88</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>34</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>21</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>15</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mrow><mtext>254</mtext><mtext> </mtext><mtext>000</mtext><mtext> </mtext><mtext>$</mtext></mrow></mrow><annotation encoding="application/x-tex">412\,000 - 88\,000 - 34\,000 - 21\,000 -17615\,000 = \text{254\,000\,\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">412</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">88</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">34</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">21</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord text"><span class="mord">254</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span></span>. <em>Via remplacement</em> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>378</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>88</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>21</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>15</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mrow><mtext>254</mtext><mtext> </mtext><mtext>000</mtext><mtext> </mtext><mtext>$</mtext></mrow></mrow><annotation encoding="application/x-tex">378\,000 - 88\,000 - 21\,000 - 15\,000 =177\text{254\,000\,\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">378</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">88</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">21</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord text"><span class="mord">254</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span></span>. Les deux chemins convergent — la curable n'est déduite que du côté reproduction, où elle est incluse dans le coût neuf.</p></div></details>178<div class="box box-exo" id="exo-5-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 5.3</span><span class="box-title">— indexation</span><a class="box-anchor" href="#exo-5-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p5-102">Un bâtiment a coûté 180 $/pi<sup>2</sup> en 2021 (indice illustratif 85,2). (a) Quel est le coût en 2025 (indice 105,5)? (b) Même question pour un immeuble dont le coût 2015 était de <span class="num">225 000 $</span> (indice 2015 : 62,6). (c) Quel est le taux annuel moyen composé sur la période 2015–2025?</p></div></div>179<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p5-103">(a) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>180</mn><mo>×</mo><mfrac><mn>105,5</mn><mn>85,2</mn></mfrac><mo>=</mo><mn>180</mn><mo>×</mo><mn>1,2383</mn><mo>=</mo><mn>222,89</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">180 \times \frac{105{,}5}{85{,}2} = 180 \times 1{,}2383 =180222{,}89~\$/\text{pi}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">180</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.3783em;vertical-align:-0.4811em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8972em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">85</span><span class="mord mtight"><span class="mpunct mtight">,</span></span><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.4461em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">105</span><span class="mord mtight"><span class="mpunct mtight">,</span></span><span class="mord mtight">5</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4811em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">180</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">2383</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1219em;vertical-align:-0.25em;"></span><span class="mord">222</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">89</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>.  (b) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>225</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mfrac><mn>105,5</mn><mn>62,6</mn></mfrac><mo>=</mo><mn>225</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>1,6853</mn><mo>≈</mo><mrow><mtext>379</mtext><mtext> </mtext><mtext>193</mtext><mtext> </mtext><mtext>$</mtext></mrow></mrow><annotation encoding="application/x-tex">225\,000 \times \frac{105{,}5}{62{,}6} = 225\,000 \times 1{,}6853181\approx \text{379\,193\,\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">225</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.3783em;vertical-align:-0.4811em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8972em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">62</span><span class="mord mtight"><span class="mpunct mtight">,</span></span><span class="mord mtight">6</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.4461em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">105</span><span class="mord mtight"><span class="mpunct mtight">,</span></span><span class="mord mtight">5</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4811em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">225</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">6853</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord text"><span class="mord">379</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">193</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span></span>, soit <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>68,5 % en dix ans.  (c) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow><mo fence="true">(</mo><mn>1,6853</mn><mo fence="true">)</mo></mrow><mrow><mn>1</mn><mi mathvariant="normal">/</mi><mn>10</mn></mrow></msup><mo>−</mo><mn>1</mn><mo>≈</mo><mn>0,0536</mn></mrow><annotation encoding="application/x-tex">\left(1{,}6853\right)^{1/10} - 1 \approx 0{,}0536</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.2779em;vertical-align:-0.25em;"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">6853</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.0279em;"><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1/10</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0536</span></span></span></span>, soit environ <strong>5,4 % par an</strong> — mais ce lissage masque la concentration de la hausse en 2021–2022; sur une aussi longue période, l'indexation doit être validée par une seconde méthode.</p></div></details>182<div class="box box-exo" id="exo-5-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 5.4</span><span class="box-title">— facteurs régionaux</span><a class="box-anchor" href="#exo-5-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p5-104">Un bâtiment commercial coûte 295 $/pi<sup>2</sup> sur base Toronto (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> 1,00) selon Altus. (a) Quel serait le coût à Trois-Rivières (facteur 0,89)? (b) Un coût de 260 $/pi<sup>2</sup> établi pour Montréal (0,98) doit être transposé à Gatineau (0,95) : calculez-le. (c) Pourquoi utilise-t-on le ratio des facteurs plutôt que le facteur de la ville cible seul?</p></div></div>183<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p5-105">(a) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>295</mn><mo>×</mo><mn>0,89</mn><mo>=</mo><mn>262,55</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">295 \times 0{,}89 = 262{,}55~\$/\text{pi}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">295</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">89</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1219em;vertical-align:-0.25em;"></span><span class="mord">262</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">55</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>.  (b) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>260</mn><mo>×</mo><mfrac><mn>0,95</mn><mn>0,98</mn></mfrac><mo>=</mo><mn>260</mn><mo>×</mo><mn>0,9694</mn><mo>≈</mo><mn>252,04</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">260 \times \frac{0{,}95}{0{,}98} = 260 \times 0{,}9694 \approx184252{,}04~\$/\text{pi}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">260</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.3783em;vertical-align:-0.4811em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8972em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span><span class="mord mtight"><span class="mpunct mtight">,</span></span><span class="mord mtight">98</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.4461em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span><span class="mord mtight"><span class="mpunct mtight">,</span></span><span class="mord mtight">95</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4811em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">260</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">9694</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1219em;vertical-align:-0.25em;"></span><span class="mord">252</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">04</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>.  (c) Parce que le coût de départ est déjà exprimé <em>dans le niveau de prix d'une ville donnée</em> (Montréal), pas dans la base du guide (Toronto). Multiplier directement par 0,95 reviendrait à appliquer deux fois l'écart Toronto–Montréal. Le ratio <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0,95</mn><mi mathvariant="normal">/</mi><mn>0,98</mn></mrow><annotation encoding="application/x-tex">0{,}95/0{,}98</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">95/0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">98</span></span></span></span> neutralise la base commune.</p></div></details>185<div class="box box-exo" id="exo-5-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 5.5</span><span class="box-title">— unités de comparaison</span><a class="box-anchor" href="#exo-5-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p5-106">(a) Convertissez 240 $/pi<sup>2</sup> en $/m<sup>2</sup>. (b) Un immeuble de bureaux affiche un coût de 310 $/pi<sup>2</sup> en NRA; expliquez pourquoi ce chiffre n'est pas directement comparable à un coût GBA et dans quel sens irait la correction. (c) Un entrepôt de <span class="num">38 000</span> pi<sup>2</sup> et 30 pi de hauteur libre coûte <span class="num">3 078 000 $</span> : calculez le coût au pied cube et comparez-le à celui de l'exemple du chapitre (3,00 $/pi<sup>3</sup>, 24 pi).</p></div></div>186<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p5-107">(a) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>240</mn><mo>×</mo><mn>10,764</mn><mo>=</mo><mn>2</mn><mtext> </mtext><mn>583</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>m</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">240 \times 10{,}764 = 2\,583~\$/\text{m}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">240</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">10</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">764</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">583</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">m</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span> (arrondi).  (b) La NRA exclut murs et circulations : elle est plus petite que la GBA, donc le coût <em>unitaire</em> NRA est mécaniquement plus élevé pour un même coût total. Pour comparer à une référence GBA, il faut soit convertir la superficie (NRA <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>→</mo></mrow><annotation encoding="application/x-tex">\rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">→</span></span></span></span> GBA via le facteur d'efficacité de l'immeuble), soit recalculer le coût sur la GBA — le coût unitaire baisserait.  (c) Volume <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>38</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>30</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>140</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">= 38\,000 \times 30 = 1\,140\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">38</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">140</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span> pi<sup>3</sup>; <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>c</mi><mo>=</mo><mn>3</mn><mtext> </mtext><mn>078</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>1</mn><mtext> </mtext><mn>140</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>2,70</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>3</mn></msup></mrow><annotation encoding="application/x-tex">c = 3\,078\,000 / 1\,140\,000 = 2{,}70~\$/\text{pi}^3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4306em;"></span><span class="mord mathnormal">c</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">078</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000/1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">140</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1219em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">70</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span></span></span></span>. Malgré une hauteur supérieure, le coût volumique est plus faible que les 3,00 $/pi<sup>3</sup> de l'exemple : l'unité volumique neutralise l'effet de hauteur et révèle ici une construction plus économique par unité de volume.</p></div></details>187<div class="box box-exo" id="exo-5-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 5.6</span><span class="box-title">— mini-cas de synthèse</span><a class="box-anchor" href="#exo-5-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p5-108">Un cottage de <span class="num">1600</span> pi<sup>2</sup> (classe D, qualité moyenne) à Gatineau : coût direct de base 220 $/pi<sup>2</sup> (référence Montréal, indice 2024 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> 102,4); date d'évaluation 2025 (indice 105,5); garage de 400 pi<sup>2</sup> à 60 $/pi<sup>2</sup>; coûts indirects 12 %; profit 14 % (sur directs <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> indirects). Facteurs : Montréal 0,98, Gatineau 0,95. Calculez le coût de remplacement neuf.</p></div></div>188<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p5-109">Coût de base : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>220</mn><mo>×</mo><mn>1</mn><mtext> </mtext><mn>600</mn><mo>=</mo><mn>352</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">220 \times 1\,600 = 352\,000~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">220</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">352</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>; garage : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>400</mn><mo>×</mo><mn>60</mn><mo>=</mo><mn>24</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">400 \times 60 = 24\,000~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">60</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>; directs (Montréal, 2024) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>376</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 376\,000~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">376</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>.  Indexation 2024 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>→</mo></mrow><annotation encoding="application/x-tex">\rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">→</span></span></span></span> 2025 : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo><mtext> </mtext><mn>105,5</mn><mi mathvariant="normal">/</mi><mn>102,4</mn><mo>=</mo><mn>1,0303</mn></mrow><annotation encoding="application/x-tex">\times\,105{,}5/102{,}4 = 1{,}0303</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">×</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">105</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5/102</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">4</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0303</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>387</mn><mtext> </mtext><mn>393</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">387\,393~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">387</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">393</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>.  Conversion régionale : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo><mtext> </mtext><mn>0,95</mn><mi mathvariant="normal">/</mi><mn>0,98</mn><mo>=</mo><mn>0,9694</mn></mrow><annotation encoding="application/x-tex">\times\,0{,}95/0{,}98 = 0{,}9694</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">×</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">95/0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">98</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">9694</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>375</mn><mtext> </mtext><mn>532</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">375\,532~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">375</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">532</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>.  Indirects : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>375</mn><mtext> </mtext><mn>532</mn><mo>×</mo><mn>0,12</mn><mo>=</mo><mn>45</mn><mtext> </mtext><mn>064</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">375\,532 \times 0{,}12 = 45\,064~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">375</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">532</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">12</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">45</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">064</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>; sous-total <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>420</mn><mtext> </mtext><mn>596</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">420\,596~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">596</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>; profit : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo><mtext> </mtext><mn>0,14</mn><mo>=</mo><mn>58</mn><mtext> </mtext><mn>883</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\times\,0{,}14 = 58\,883~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">×</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">14</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">58</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">883</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>.  <strong>Coût de remplacement neuf</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>479</mn><mtext> </mtext><mn>479</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\approx 479\,479~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">479</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">479</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>, arrondi à <strong><span class="num">480 000 $</span></strong> (environ 300 $/pi<sup>2</sup> sur la superficie habitable).</p></div></details>189<h2 class="h-section" id="s-6"><span class="h-num">6</span><span class="h-text">Méthodes d'estimation des coûts</span></h2>190<div class="box box-exo" id="exo-6-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 6.1</span><span class="box-title">— méthode comparative</span><a class="box-anchor" href="#exo-6-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-90">Un sujet de <span class="num">1700</span> pi<sup>2</sup> (standard, Gatineau, 2025) doit être estimé à partir de deux comparables à coût complet connu : comp. A, <span class="num">1500</span> pi<sup>2</sup>, 198 $/pi<sup>2</sup>, construit en 2024 (ajustements : taille <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>2 %, date <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>3 %); comp. B, <span class="num">1900</span> pi<sup>2</sup>, 182 $/pi<sup>2</sup>, construit en 2025, qualité légèrement inférieure (taille <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>2 %, qualité <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>4 %). Calculez le coût neuf du sujet.</p></div></div>191<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p6-91">Comp. A : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>198</mn><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mn>0,02</mn><mo>+</mo><mn>0,03</mn><mo stretchy="false">)</mo><mo>=</mo><mn>198</mn><mo>×</mo><mn>1,01</mn><mo>=</mo><mn>199,98</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">198 \times (1 - 0{,}02 + 0{,}03) = 198 \times 1{,}01 =192199{,}98~\$/\text{pi}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">198</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">02</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">03</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">198</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">01</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1219em;vertical-align:-0.25em;"></span><span class="mord">199</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">98</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>. Comp. B : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>182</mn><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mn>0,02</mn><mo>+</mo><mn>0,04</mn><mo stretchy="false">)</mo><mo>=</mo><mn>182</mn><mo>×</mo><mn>1,06</mn><mo>=</mo><mn>192,92</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">182 \times (1 + 0{,}02 + 0{,}04) = 182 \times 1{,}06 =193192{,}92~\$/\text{pi}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">182</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">02</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">04</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">182</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">06</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1219em;vertical-align:-0.25em;"></span><span class="mord">192</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">92</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>. Moyenne <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>196,45</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">\approx 196{,}45~\$/\text{pi}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1219em;vertical-align:-0.25em;"></span><span class="mord">196</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">45</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mtext> </mtext><mn>700</mn><mo>×</mo><mn>196,45</mn><mo>≈</mo><mn>333</mn><mtext> </mtext><mn>965</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">1\,700 \times 196{,}45 \approx 333\,965~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">700</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">196</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">45</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">333</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">965</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>, arrondi à <strong><span class="num">334 000 $</span></strong>. (Application des ajustements en somme algébrique des pourcentages, comme dans l'exemple du chapitre; en toute rigueur on peut aussi les composer multiplicativement — l'écart est négligeable à ces ordres de grandeur.)</p></div></details>194<div class="box box-exo" id="exo-6-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 6.2</span><span class="box-title">— coût chargé de la main-d'œuvre</span><a class="box-anchor" href="#exo-6-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-92">Un estimateur prévoit 260 heures d'électricien (taux de base 50,67 $/h) et 340 heures de charpentier-menuisier (47,77 $/h), secteur IC. En utilisant une charge de 52 %, calculez le coût total de main-d'œuvre, et l'erreur qu'aurait commise un estimé fondé sur les seuls taux de base.</p></div></div>195<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p6-93">Coûts chargés : électricien <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50,67</mn><mo>×</mo><mn>1,52</mn><mo>=</mo><mn>77,02</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><mi>h</mi></mrow><annotation encoding="application/x-tex">50{,}67 \times 1{,}52 = 77{,}02~\$/h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">50</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">67</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">52</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">77</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">02</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord mathnormal">h</span></span></span></span>; charpentier <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>47,77</mn><mo>×</mo><mn>1,52</mn><mo>=</mo><mn>72,61</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><mi>h</mi></mrow><annotation encoding="application/x-tex">47{,}77 \times 1{,}52 = 72{,}61~\$/h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">47</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">77</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">52</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">72</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">61</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord mathnormal">h</span></span></span></span>.  Total chargé : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>260</mn><mo>×</mo><mn>77,02</mn><mo>+</mo><mn>340</mn><mo>×</mo><mn>72,61</mn><mo>=</mo><mn>20</mn><mtext> </mtext><mn>025</mn><mo>+</mo><mn>24</mn><mtext> </mtext><mn>687</mn><mo>=</mo><mn>44</mn><mtext> </mtext><mn>712</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">260 \times 77{,}02 + 340 \times 72{,}61 =19620\,025 + 24\,687 = 44\,712~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">260</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">77</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">02</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">340</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">72</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">61</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">025</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">687</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">44</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">712</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>.  Aux taux de base : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>260</mn><mo>×</mo><mn>50,67</mn><mo>+</mo><mn>340</mn><mo>×</mo><mn>47,77</mn><mo>=</mo><mn>13</mn><mtext> </mtext><mn>174</mn><mo>+</mo><mn>16</mn><mtext> </mtext><mn>242</mn><mo>=</mo><mn>29</mn><mtext> </mtext><mn>416</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">260 \times 50{,}67 + 340 \times 47{,}77 =19713\,174 + 16\,242 = 29\,416~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">260</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">50</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">67</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">340</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">47</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">77</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">13</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">174</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">242</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">29</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">416</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>.  L'estimé « taux de base » manquerait <span class="num">15 296 $</span>, soit une sous-estimation de 34 % de la main-d'œuvre — exactement le genre d'erreur que la règle du coût chargé prévient.</p></div></details>198<div class="box box-exo" id="exo-6-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 6.3</span><span class="box-title">— portée des coûts</span><a class="box-anchor" href="#exo-6-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-94">Trois sources donnent, pour le même modèle de maison : (i) un bordereau d'estimateur à 138 $/pi<sup>2</sup>; (ii) un contrat d'entrepreneur général à 172 $/pi<sup>2</sup>; (iii) des projets récents complets à 196 $/pi<sup>2</sup>. Expliquez la cohérence de ces trois chiffres et dites lequel utiliser pour la méthode du coût.</p></div></div>199<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p6-95">(i) est un coût <em>direct</em> (matériaux <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> main-d'œuvre); (ii) est le coût de <em>construction</em> — directs <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> frais généraux de chantier <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> profit de l'entrepreneur (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>138</mn><mo>×</mo><mo>≈</mo><mn>1,25</mn><mo>≈</mo><mn>172</mn></mrow><annotation encoding="application/x-tex">138 \times \approx 1{,}25 \approx 172</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">138</span><span class="mord">×</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">25</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">172</span></span></span></span>); (iii) est le coût <em>complet du projet</em>, ajoutant les indirects du promoteur (honoraires, permis, financement, marge : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>172</mn><mo>×</mo><mo>≈</mo><mn>1,14</mn></mrow><annotation encoding="application/x-tex">172 \times \approx 1{,}14</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">172</span><span class="mord">×</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">14</span></span></span></span>, ou <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>138</mn><mo>×</mo><mo>≈</mo><mn>1,42</mn></mrow><annotation encoding="application/x-tex">138 \times \approx 1{,}42</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">138</span><span class="mord">×</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">42</span></span></span></span>). Les trois sont cohérents entre eux. Pour la méthode du coût en évaluation, on recherche le <strong>coût complet</strong> (iii) : c'est lui qui correspond à ce qu'un acheteur devrait débourser pour se procurer un bâtiment neuf équivalent, terrain exclu.</p></div></details>200<div class="box box-exo" id="exo-6-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 6.4</span><span class="box-title">— méthode par composantes</span><a class="box-anchor" href="#exo-6-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-96">Estimez le coût de remplacement d'un bungalow de <span class="num">1300</span> pi<sup>2</sup> avec les coûts installés suivants : fondations 30 $/pi<sup>2</sup> de dalle (<span class="num">1300</span> pi<sup>2</sup>); murs extérieurs 26 $/pi<sup>2</sup> de mur (<span class="num">1500</span> pi<sup>2</sup>); toiture 18 $/pi<sup>2</sup> projeté (<span class="num">1400</span>); plomberie 7 appareils à 3 300 $; électricité 14 $/pi<sup>2</sup>; chauffage 9 $/pi<sup>2</sup>; finitions 36 $/pi<sup>2</sup>; structure de plancher 10 $/pi<sup>2</sup>. Indirects 14 %, profit 11 %.</p></div></div>201<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p6-97">Directs : fondations <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>39</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">39\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">39</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>; murs <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>39</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">39\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">39</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>; toiture <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>25</mn><mtext> </mtext><mn>200</mn></mrow><annotation encoding="application/x-tex">25\,200</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">25</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span></span></span></span>; plomberie <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>23</mn><mtext> </mtext><mn>100</mn></mrow><annotation encoding="application/x-tex">23\,100</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">23</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">100</span></span></span></span>; électricité <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>18</mn><mtext> </mtext><mn>200</mn></mrow><annotation encoding="application/x-tex">18\,200</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">18</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span></span></span></span>; chauffage <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>11</mn><mtext> </mtext><mn>700</mn></mrow><annotation encoding="application/x-tex">11\,700</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">11</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">700</span></span></span></span>; finitions <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>46</mn><mtext> </mtext><mn>800</mn></mrow><annotation encoding="application/x-tex">46\,800</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">46</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span></span></span></span>; planchers <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>13</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">13\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">13</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>; total <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>216</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 216\,000~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">216</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>.  Indirects : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>216</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,14</mn><mo>=</mo><mn>30</mn><mtext> </mtext><mn>240</mn></mrow><annotation encoding="application/x-tex">216\,000 \times 0{,}14 = 30\,240</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">216</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">14</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">240</span></span></span></span>; sous-total <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>246</mn><mtext> </mtext><mn>240</mn></mrow><annotation encoding="application/x-tex">246\,240</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">246</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">240</span></span></span></span>; profit : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo><mn>0,11</mn><mo>=</mo><mn>27</mn><mtext> </mtext><mn>086</mn></mrow><annotation encoding="application/x-tex">\times 0{,}11 = 27\,086</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">×</span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">11</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">27</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">086</span></span></span></span>.  <strong>Coût de remplacement</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>273</mn><mtext> </mtext><mn>326</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\approx 273\,326~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">273</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">326</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>, arrondi à <strong><span class="num">273 000 $</span></strong> (210 $/pi<sup>2</sup>) — une valeur plausible pour un bungalow standard, à valider par la comparative.</p></div></details>202<div class="box box-exo" id="exo-6-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 6.5</span><span class="box-title">— coût indexé avec rénovations</span><a class="box-anchor" href="#exo-6-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-98">Un triplex construit en 2012 (<span class="num">420 000 $</span>, indice 57,8) a reçu une toiture neuve en 2022 (<span class="num">38 000 $</span>, indice 97,1) et des balcons en 2024 (<span class="num">22 000 $</span>, indice 102,4). Indice 2025 : 105,5. Calculez le coût indexé 2025 et identifiez la principale fragilité de cette estimation.</p></div></div>203<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p6-99">Construction : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>420</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>105,5</mn><mi mathvariant="normal">/</mi><mn>57,8</mn><mo>=</mo><mn>420</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>1,8253</mn><mo>=</mo><mn>766</mn><mtext> </mtext><mn>609</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">420\,000 \times 105{,}5/57{,}8 = 420\,000 \times 1{,}8253 =204766\,609~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">105</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5/57</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">8</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">8253</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">766</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">609</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>. Toiture : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>38</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>105,5</mn><mi mathvariant="normal">/</mi><mn>97,1</mn><mo>=</mo><mn>38</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>1,0865</mn><mo>=</mo><mn>41</mn><mtext> </mtext><mn>287</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">38\,000 \times 105{,}5/97{,}1 = 38\,000 \times 1{,}0865 =20541\,287~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">38</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">105</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5/97</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">38</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0865</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">41</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">287</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>. Balcons : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>22</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>105,5</mn><mi mathvariant="normal">/</mi><mn>102,4</mn><mo>=</mo><mn>22</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>1,0303</mn><mo>=</mo><mn>22</mn><mtext> </mtext><mn>666</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">22\,000 \times 105{,}5/102{,}4 = 22\,000 \times 1{,}0303 =20622\,666~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">105</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5/102</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">4</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0303</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">666</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>.  <strong>Total indexé</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>830</mn><mtext> </mtext><mn>562</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\approx 830\,562~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">830</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">562</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>, arrondi à <strong><span class="num">830 000 $</span></strong>.  Fragilité principale : 13 ans séparent le coût de construction de la date d'évaluation, et l'essentiel du total repose sur cette strate — l'indice est une moyenne régionale qui peut mal représenter ce bâtiment précis (qualité atypique, autoconstruction, marché local). Il y a aussi un risque de <em>double comptage</em> : la toiture de 2022 remplace une composante déjà incluse dans le coût de 2012. La bonne pratique : valider par la comparative ou les composantes.</p></div></details>207<div class="box box-exo" id="exo-6-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 6.6</span><span class="box-title">— facteurs de forme et de hauteur</span><a class="box-anchor" href="#exo-6-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-100">(a) Un bâtiment de <span class="num">2000</span> pi<sup>2</sup> a un périmètre de 200 pi : calculez le ratio de périmètre et l'ajustement suggéré. (b) Un coût de base de 210 $/pi<sup>2</sup> (1 étage) doit servir pour un immeuble de 3 étages (facteur 1,10) de qualité « bon » (facteur 1,20) : calculez le coût unitaire ajusté.</p></div></div>208<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p6-101">(a) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mtext>carr</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover></mrow></msub><mo>=</mo><mn>4</mn><msqrt><mrow><mn>2</mn><mtext> </mtext><mn>000</mn></mrow></msqrt><mo>=</mo><mn>4</mn><mo>×</mo><mn>44,72</mn><mo>=</mo><mn>178,89</mn></mrow><annotation encoding="application/x-tex">P_{\text{carré}} = 4\sqrt{2\,000} = 4 \times 44{,}72 = 178{,}89</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.1389em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">carr</span><span class="mord katex-accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight">e</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˊ</span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.04em;vertical-align:-0.1328em;"></span><span class="mord">4</span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9072em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span><span style="top:-2.8672em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702209c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14210c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54211c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10212s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429213c69,-144,104.5,-217.7,106.5,-221214l0 -0215c5.3,-9.3,12,-14,20,-14216H400000v40H845.2724217s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7218c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z219M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1328em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">4</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">44</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">72</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">178</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">89</span></span></span></span> pi; <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mi>p</mi></msub><mo>=</mo><mn>200</mn><mi mathvariant="normal">/</mi><mn>178,89</mn><mo>=</mo><mn>1,118</mn></mrow><annotation encoding="application/x-tex">R_p = 200/178{,}89 = 1{,}118</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0077em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">200/178</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">89</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">118</span></span></span></span> — environ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>12 % de périmètre excédentaire, d'où un ajustement d'environ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>3 à <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>4 % du coût unitaire (l'enveloppe ne représente qu'une partie du coût total).  (b) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>210</mn><mo>×</mo><mn>1,10</mn><mo>×</mo><mn>1,20</mn><mo>=</mo><mn>277,20</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">210 \times 1{,}10 \times 1{,}20 = 277{,}20~\$/\text{pi}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">210</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">10</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">20</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1219em;vertical-align:-0.25em;"></span><span class="mord">277</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">20</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>. Les facteurs se composent multiplicativement — comme dans la formule calculator de Marshall &amp; Swift.</p></div></details>220<h2 class="h-section" id="s-7"><span class="h-num">7</span><span class="h-text">Coûts directs de construction</span></h2>221<div class="box box-exo" id="exo-7-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 7.1</span><span class="box-title">— classement direct / indirect</span><a class="box-anchor" href="#exo-7-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p7-102">Classez chacune des dépenses suivantes en coût <strong>direct</strong>, coût <strong>indirect</strong> ou <strong>profit entrepreneurial</strong> : (a) salaires des charpentiers-menuisiers; (b) honoraires de l'ingénieur en structure; (c) marge de 12 % du sous-traitant en plomberie incluse dans sa soumission; (d) intérêts sur le prêt de construction; (e) rémunération attendue du promoteur qui pilote le projet; (f) location d'une grue de chantier; (g) permis de construction; (h) supervision de chantier par le contremaître.</p></div></div>222<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p7-103">(a) direct (main-d'œuvre); (b) indirect (honoraires professionnels); (c) <strong>direct</strong> — la marge du sous-traitant fait partie du prix soumis, donc des coûts directs, à ne pas confondre avec le profit entrepreneurial; (d) indirect (financement); (e) profit entrepreneurial; (f) direct (équipement de chantier); (g) indirect (taxes et permis); (h) direct (supervision directe des travaux).</p></div></details>223<div class="box box-exo" id="exo-7-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 7.2</span><span class="box-title">— ventilation d'un bungalow à Gatineau</span><a class="box-anchor" href="#exo-7-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p7-104">Estimez les coûts directs d'un bungalow neuf à Gatineau et ventilez-les par composante. Caractéristiques : 1 400 pi<sup>2</sup>, sous-sol complet non fini, garage simple intégré, qualité moyenne; revêtement brique et vinyle; toiture en bardeaux architecturaux; plinthes électriques et thermopompe murale; 16 fenêtres de PVC double vitrage; planchers de bois franc et céramique; comptoirs de quartz et armoires thermoplastiques; entrée d'asphalte. Présentez un bordereau à huit postes avec les pourcentages, puis vérifiez la cohérence du total avec les fourchettes de coût complet de la séance 5.</p></div></div>224<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p7-105">Bordereau plausible (les montants peuvent varier de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>±</mo></mrow><annotation encoding="application/x-tex">\pm</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">±</span></span></span></span>10 % selon les hypothèses, l'important étant la cohérence des proportions) :</p>225<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Composante</th><th class="al-r">Estimation</th><th class="al-r">%</th></tr></thead><tbody><tr><td>Structure et fondations (sous-sol + garage)</td><td class="al-r"><span class="num">50 000 $</span></td><td class="al-r">23 %</td></tr><tr><td>Enveloppe (brique/vinyle, bardeaux, 16 fenêtres)</td><td class="al-r"><span class="num">60 000 $</span></td><td class="al-r">27 %</td></tr><tr><td>CVAC (plinthes + thermopompe + VRC)</td><td class="al-r"><span class="num">16 000 $</span></td><td class="al-r">7 %</td></tr><tr><td>Plomberie (2 salles de bain, cuisine, chauffe-eau)</td><td class="al-r"><span class="num">18 000 $</span></td><td class="al-r">8 %</td></tr><tr><td>Électricité (200 A, éclairage standard)</td><td class="al-r"><span class="num">16 000 $</span></td><td class="al-r">7 %</td></tr><tr><td>Finitions intérieures (bois franc, céramique, quartz)</td><td class="al-r"><span class="num">38 000 $</span></td><td class="al-r">17 %</td></tr><tr><td>Finitions extérieures (asphalte, terrasse, gazon)</td><td class="al-r"><span class="num">15 000 $</span></td><td class="al-r">7 %</td></tr><tr><td>Équipements spécialisés (aspirateur central, alarme)</td><td class="al-r"><span class="num">5000 $</span></td><td class="al-r">2 %</td></tr><tr class="rule-above"><td><strong>Total coûts directs</strong></td><td class="al-r"><strong><span class="num">218 000 $</span></strong></td><td class="al-r"><strong>100 %</strong></td></tr></tbody></table></div></div>226<p id="p7-106">Soit <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>218</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>1</mn><mtext> </mtext><mn>400</mn><mo>=</mo><mn>156</mn></mrow><annotation encoding="application/x-tex">218\,000 / 1\,400 = 156</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">218</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000/1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">156</span></span></span></span> $/pi<sup>2</sup> de coûts directs. Vérification : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>156</mn><mo>×</mo><mn>1,35</mn><mo>≈</mo><mn>210</mn></mrow><annotation encoding="application/x-tex">156 \times 1{,}35 \approx 210</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">156</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">35</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">210</span></span></span></span> $/pi<sup>2</sup> de coût total, dans la fourchette de 200–260 $/pi<sup>2</sup> de la séance 5. Le bordereau est vraisemblable.</p></div></details>227<div class="box box-exo" id="exo-7-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 7.3</span><span class="box-title">— lecture d'un guide de coûts</span><a class="box-anchor" href="#exo-7-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p7-107">À l'aide de la méthode <em>Calculator</em> de Marshall &amp; Swift, estimez le coût unitaire en dollars canadiens d'un cottage de qualité moyenne de 1 800 pi<sup>2</sup> à Gatineau. Données : coût de base 142 $ US/pi<sup>2</sup>; ajustement de superficie 0,99; multiplicateur régional 1,15; taux de change 1,36; index de date 1,03. Calculez ensuite le coût total indiqué pour le bâtiment et nommez deux vérifications à faire avant d'utiliser ce chiffre dans un rapport.</p></div></div>228<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p7-108">Coût unitaire :</p>229<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>142</mn><mo>×</mo><mn>0,99</mn><mo>×</mo><mn>1,15</mn><mo>×</mo><mn>1,36</mn><mo>×</mo><mn>1,03</mn><mo>=</mo><mn>142</mn><mo>×</mo><mn>0,99</mn><mo>=</mo><mn>140,58</mn><mo separator="true">;</mo><mspace width="1em"/><mn>140,58</mn><mo>×</mo><mn>1,15</mn><mo>=</mo><mn>161,67</mn><mo separator="true">;</mo></mrow><annotation encoding="application/x-tex">142 \times 0{,}99 \times 1{,}15 \times 1{,}36 \times 1{,}03230= 142 \times 0{,}99 = 140{,}58;\quad231140{,}58 \times 1{,}15 = 161{,}67;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">142</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">99</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">15</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">36</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">03</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">142</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">99</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">140</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">58</span><span class="mpunct">;</span><span class="mspace" style="margin-right:1em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">140</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">58</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">15</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">161</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">67</span><span class="mpunct">;</span></span></span></span></span></div>232<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>161,67</mn><mo>×</mo><mn>1,36</mn><mo>=</mo><mn>219,87</mn><mo separator="true">;</mo><mspace width="1em"/><mn>219,87</mn><mo>×</mo><mn>1,03</mn><mo>≈</mo><mn>226,47</mn><mtext> $/pi²</mtext><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">161{,}67 \times 1{,}36 = 219{,}87;\quad233219{,}87 \times 1{,}03 \approx 226{,}47~\text{\$/pi²}.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">161</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">67</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">36</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">219</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">87</span><span class="mpunct">;</span><span class="mspace" style="margin-right:1em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">219</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">87</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">03</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">226</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">47</span><span class="mspace nobreak"> </span><span class="mord text"><span class="mord">$/pi²</span></span><span class="mord">.</span></span></span></span></span></div>234<p id="p7-109">Coût indiqué : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>226,47</mn><mo>×</mo><mn>1</mn><mtext> </mtext><mn>800</mn><mo>≈</mo><mn>407</mn><mtext> </mtext><mn>600</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">226{,}47 \times 1\,800 \approx 407\,600\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">226</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">47</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">407</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> (arrondi). Vérifications : (1) déterminer ce que le coût de base <strong>inclut</strong> (portion d'indirects? profit?) pour éviter tout double comptage avec le reste du bordereau; (2) <strong>croiser avec une deuxième source</strong> (Altus ou RSMeans) et investiguer si l'écart dépasse <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>±</mo></mrow><annotation encoding="application/x-tex">\pm</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">±</span></span></span></span>10–15 %. On pourrait ajouter : vérifier la date de l'index et l'adéquation de la classe de qualité.</p></div></details>235<div class="box box-exo" id="exo-7-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 7.4</span><span class="box-title">— sensibilité aux erreurs d'estimation</span><a class="box-anchor" href="#exo-7-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p7-110">Un bordereau affiche 240 000 $ de coûts directs, des indirects de 20 % des directs et un profit de 10 % de (directs + indirects). (a) Calculez le coût total. (b) L'évaluateur découvre qu'il a sous-estimé l'enveloppe de 12 000 $ : recalculez le coût total et exprimez l'erreur initiale en pourcentage. (c) Expliquez pourquoi une erreur sur les coûts directs se <em>propage</em> aux autres postes.</p></div></div>236<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p7-111">(a) Indirects : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>240</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,20</mn><mo>=</mo><mn>48</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">240\,000 \times 0{,}20 = 48\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">240</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">20</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">48</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; sous-total : <span class="num">288 000 $</span>; profit : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>288</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,10</mn><mo>=</mo><mn>28</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">288\,000 \times 0{,}10 = 28\,800\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">288</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">10</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">28</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; coût total : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn mathvariant="bold">316</mn><mtext> </mtext><mn mathvariant="bold">800</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow><annotation encoding="application/x-tex">\mathbf{316\,800\,\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord"><span class="mord mathbf">316</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathbf">800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathbf">$</span></span></span></span></span>.  (b) Directs corrigés : <span class="num">252 000 $</span>; indirects : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>252</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,20</mn><mo>=</mo><mn>50</mn><mtext> </mtext><mn>400</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">252\,000 \times 0{,}20237= 50\,400\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">252</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">20</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; sous-total : <span class="num">302 400 $</span>; profit : <span class="num">30 240 $</span>; coût total corrigé : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn mathvariant="bold">332</mn><mtext> </mtext><mn mathvariant="bold">640</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow><annotation encoding="application/x-tex">\mathbf{332\,640\,\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord"><span class="mord mathbf">332</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathbf">640</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathbf">$</span></span></span></span></span>. Écart : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>332</mn><mtext> </mtext><mn>640</mn><mo>−</mo><mn>316</mn><mtext> </mtext><mn>800</mn><mo>=</mo><mn>15</mn><mtext> </mtext><mn>840</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">332\,640 - 316\,800 = 15\,840\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">332</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">640</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">316</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">840</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>, soit une sous-estimation initiale de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>15</mn><mtext> </mtext><mn>840</mn><mi mathvariant="normal">/</mi><mn>332</mn><mtext> </mtext><mn>640</mn><mo>≈</mo><mn>4,8</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">15\,840 / 332\,640 \approx 4{,}8\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">840/332</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">640</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">4</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">8</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> du coût total.  (c) Les indirects et le profit étant calculés <em>en pourcentage des directs</em>, toute erreur sur les directs est amplifiée mécaniquement : ici, 12 000 $ d'erreur directe deviennent 15 840 $ d'erreur totale (facteur <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1,20</mn><mo>×</mo><mn>1,10</mn><mo>=</mo><mn>1,32</mn></mrow><annotation encoding="application/x-tex">1{,}20 \times 1{,}10 = 1{,}32</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">20</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">10</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">32</span></span></span></span>).</p></div></details>238<div class="box box-exo" id="exo-7-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 7.5</span><span class="box-title">— coût et valeur : équipements particuliers</span><a class="box-anchor" href="#exo-7-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p7-112">Une résidence de qualité moyenne à Gatineau comprend une installation géothermique neuve (38 000 $) et une piscine creusée récente (55 000 $). (a) À quel montant ces deux éléments figurent-ils dans le bordereau de coût de remplacement à neuf? (b) Le marché local ne reconnaît que 60 % du coût de la géothermie et 40 % de celui de la piscine : quelle perte de valeur totale cela annonce-t-il, et sous quelle rubrique sera-t-elle traitée dans la méthode du coût? (c) Que révèle cet exemple sur la relation entre coût et valeur?</p></div></div>239<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p7-113">(a) Au <strong>plein coût</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>38</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>55</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>93</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">38\,000 + 55\,000 = 93\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">38</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">55</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">93</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> — le bordereau de coût neuf recense ce qu'il en coûterait de reproduire les améliorations, sans jugement de marché.  (b) Perte : géothermie <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>38</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,40</mn><mo>=</mo><mn>15</mn><mtext> </mtext><mn>200</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">38\,000 \times 0{,}40 = 15\,200\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">38</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">40</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; piscine <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>55</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,60</mn><mo>=</mo><mn>33</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">55\,000 \times 0{,}60 = 33\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">55</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">60</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">33</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; total <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn mathvariant="bold">48</mn><mtext> </mtext><mn mathvariant="bold">200</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow><annotation encoding="application/x-tex">\mathbf{48\,200\,\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord"><span class="mord mathbf">48</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathbf">200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathbf">$</span></span></span></span></span>. Cette perte sera comptabilisée en <strong>dépréciation fonctionnelle pour suradéquation</strong> (séance 11), en déduction du coût neuf.  (c) Le coût est un <em>fait de production</em>; la valeur est un <em>fait de marché</em>. Ils ne coïncident que lorsque le marché reconnaît pleinement la dépense — ce qui n'est jamais garanti pour les équipements dont l'acheteur type ne veut pas payer le plein prix.</p></div></details>240<div class="box box-exo" id="exo-7-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 7.6</span><span class="box-title">— question de réflexion — uniformité des coûts québécois</span><a class="box-anchor" href="#exo-7-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p7-114">Expliquez en quelques phrases pourquoi les coûts de main-d'œuvre de construction sont relativement uniformes d'un chantier à l'autre au Québec, et nommez les trois principales sources résiduelles d'écart de coûts entre deux projets comparables.</p></div></div>241<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p7-115">Les chantiers assujettis à la Loi R-20 emploient des métiers réglementés dont les taux horaires et avantages sociaux sont fixés par les conventions collectives CCQ 2025–2029, uniformes par métier et par secteur; la licence RBQ et la garantie GCR ajoutent un cadre commun. Les salaires étant standardisés, les écarts résiduels proviennent surtout : (1) des <strong>matériaux</strong> (choix, gammes, prix régionaux); (2) de la <strong>complexité</strong> du projet (architecture, site, sol); (3) de la <strong>région</strong> (transport, éloignement, disponibilité de la main-d'œuvre, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>±</mo></mrow><annotation encoding="application/x-tex">\pm</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">±</span></span></span></span>15–25 %).</p></div></details>242<h2 class="h-section" id="s-8"><span class="h-num">8</span><span class="h-text">Coûts indirects et profit entrepreneurial</span></h2>243<div class="box box-exo" id="exo-8-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 8.1</span><span class="box-title">— intérêts intercalaires</span><a class="box-anchor" href="#exo-8-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p8-83">Un projet présente des coûts directs de <span class="num">950 000 $</span>, un prêt de construction au taux annuel de 6,8 % et une durée de chantier de 14 mois. (a) Calculez les intérêts intercalaires. (b) Recalculez-les si le taux passe à 8,3 % et commentez la sensibilité. (c) Pourquoi applique-t-on le facteur <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle scriptlevel="0" displaystyle="false"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\tfrac{1}{2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>?</p></div></div>244<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p8-84">(a) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi><mo>=</mo><mn>950</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,068</mn><mo>×</mo><mfrac><mn>14</mn><mn>12</mn></mfrac><mo>×</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mn>950</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,068</mn><mo>×</mo><mn>1,1667</mn><mo>×</mo><mn>0,5</mn><mo>≈</mo><mn>37</mn><mtext> </mtext><mn>683</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">I = 950\,000 \times 0{,}068 \times \frac{14}{12} \times \frac{1}{2}245= 950\,000 \times 0{,}068 \times 1{,}1667 \times 0{,}5 \approx24637\,683\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.0785em;">I</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">950</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">068</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">12</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">14</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">950</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">068</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">1667</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">37</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">683</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>.  (b) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi><mo>=</mo><mn>950</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,083</mn><mo>×</mo><mn>1,1667</mn><mo>×</mo><mn>0,5</mn><mo>≈</mo><mn>45</mn><mtext> </mtext><mn>996</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">I = 950\,000 \times 0{,}083 \times 1{,}1667 \times 0{,}5 \approx24745\,996\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.0785em;">I</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">950</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">083</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">1667</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">45</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">996</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>, soit environ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo><mn>8</mn><mtext> </mtext><mn>300</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">+8\,300~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">+</span><span class="mord">8</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">300</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span> (+22 %). Les intérêts varient proportionnellement au taux : une hausse de 150 points de base sur un chantier de 14 mois déplace le poste de plus de 8 000 $.  (c) Le prêt de construction est déboursé <strong>progressivement</strong> selon l'avancement des travaux; en moyenne, la moitié seulement du montant est empruntée pendant la durée du chantier. Le facteur <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle scriptlevel="0" displaystyle="false"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\tfrac{1}{2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span> modélise ce profil de décaissement.</p></div></details>248<div class="box box-exo" id="exo-8-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 8.2</span><span class="box-title">— bordereau d'indirects — immeuble de 6 logements</span><a class="box-anchor" href="#exo-8-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p8-85">Complétez le bordereau des coûts indirects du sixplex du secteur Hull (coûts directs fournis : <span class="num">692 200 $</span>; durée 10 mois; taux 7,5 %) avec les hypothèses suivantes : architecte 6 %; ingénieurs (structure + méca./élec.) 4 %; arpenteur-géomètre 3 000 $; frais de dossier bancaire 0,75 %; permis municipal 10 $/1 000 $; assurance chantier 1 %; GCR 2 500 $/unité <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\times</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">×</span></span></span></span> 6; frais notariaux 3 500 $; marketing et administration 3 %. Calculez le total des indirects et le ratio indirects/directs, puis commentez sa vraisemblance.</p></div></div>249<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Catégorie</th><th class="al-c">Taux / base</th><th class="al-r">Montant</th></tr></thead><tbody><tr><td>Architecte</td><td class="al-c">6 %</td><td class="al-r"><span class="num">41 532 $</span></td></tr><tr><td>Ingénieurs</td><td class="al-c">4 %</td><td class="al-r"><span class="num">27 688 $</span></td></tr><tr><td>Arpenteur-géomètre</td><td class="al-c">forfait</td><td class="al-r"><span class="num">3000 $</span></td></tr><tr><td>Intérêts intercalaires</td><td class="al-c"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>7,5</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>×</mo><mn>10</mn><mi mathvariant="normal">/</mi><mn>12</mn><mo>×</mo><mn>0,5</mn></mrow><annotation encoding="application/x-tex">7{,}5\,\% \times 10/12 \times 0{,}5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">7</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">10/12</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span></span></span></span></td><td class="al-r"><span class="num">21 631 $</span></td></tr><tr><td>Frais de dossier</td><td class="al-c">0,75 %</td><td class="al-r"><span class="num">5192 $</span></td></tr><tr><td>Permis municipal</td><td class="al-c">10 $/1 000 $</td><td class="al-r"><span class="num">6922 $</span></td></tr><tr><td>Assurance chantier</td><td class="al-c">1 %</td><td class="al-r"><span class="num">6922 $</span></td></tr><tr><td>GCR</td><td class="al-c"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>6</mn><mo>×</mo><mn>2</mn><mtext> </mtext><mn>500</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">6 \times 2\,500~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">6</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span></td><td class="al-r"><span class="num">15 000 $</span></td></tr><tr><td>Frais notariaux</td><td class="al-c">forfait</td><td class="al-r"><span class="num">3500 $</span></td></tr><tr><td>Marketing et administration</td><td class="al-c">3 %</td><td class="al-r"><span class="num">20 766 $</span></td></tr><tr class="rule-above"><td><strong>Total indirects</strong></td><td class="al-c"></td><td class="al-r"><strong><span class="num">152 153 $</span></strong></td></tr></tbody></table></div></div>250<p id="p8-86">Détail des intérêts : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>692</mn><mtext> </mtext><mn>200</mn><mo>×</mo><mn>0,075</mn><mo>×</mo><mn>0,8333</mn><mo>×</mo><mn>0,5</mn><mo>=</mo><mn>21</mn><mtext> </mtext><mn>631</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">692\,200 \times 0{,}075 \times 0{,}8333 \times 0{,}5251= 21\,631~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">692</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">075</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">8333</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">21</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">631</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>. Ratio : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>152</mn><mtext> </mtext><mn>153</mn><mi mathvariant="normal">/</mi><mn>692</mn><mtext> </mtext><mn>200</mn><mo>=</mo><mn>22,0</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">152\,153 / 692\,200 = 22{,}0\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">152</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">153/692</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">22</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> — dans la fourchette de 15–25 % typique du résidentiel locatif : vraisemblable.</p></div></details>252<div class="box box-exo" id="exo-8-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 8.3</span><span class="box-title">— coût total et profit — suite du sixplex</span><a class="box-anchor" href="#exo-8-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p8-87">En reprenant l'exercice précédent : (a) calculez le coût total de remplacement avec un profit entrepreneurial de 11 %; (b) exprimez le résultat en $/pi<sup>2</sup> (superficie de 5 400 pi<sup>2</sup>) et par logement; (c) justifiez en trois arguments le choix de 11 % plutôt que 8 % ou 15 %.</p></div></div>253<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p8-88">(a) Sous-total : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>692</mn><mtext> </mtext><mn>200</mn><mo>+</mo><mn>152</mn><mtext> </mtext><mn>153</mn><mo>=</mo><mn>844</mn><mtext> </mtext><mn>353</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">692\,200 + 152\,153 = 844\,353\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">692</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">152</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">153</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">844</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">353</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; profit : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>844</mn><mtext> </mtext><mn>353</mn><mo>×</mo><mn>0,11</mn><mo>=</mo><mn>92</mn><mtext> </mtext><mn>879</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">844\,353 \times 0{,}11 = 92\,879\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">844</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">353</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">11</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">92</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">879</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; <strong>coût total : <span class="num">937 232 $</span></strong>.  (b) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>937</mn><mtext> </mtext><mn>232</mn><mi mathvariant="normal">/</mi><mn>5</mn><mtext> </mtext><mn>400</mn><mo>≈</mo><mn>174</mn></mrow><annotation encoding="application/x-tex">937\,232 / 5\,400 \approx 174</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">937</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">232/5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">174</span></span></span></span> $/pi<sup>2</sup>; <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>937</mn><mtext> </mtext><mn>232</mn><mi mathvariant="normal">/</mi><mn>6</mn><mo>≈</mo><mn>156</mn><mtext> </mtext><mn>205</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">937\,232 / 6 \approx 156\,205\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">937</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">232/6</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">156</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">205</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> par logement.  (c) Un taux médian de 11 % se justifie par : (1) un marché locatif Gatineau–Ottawa à demande soutenue (risque de vacance faible <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span> pas besoin de 15 %); (2) un projet de taille modeste et de conception standard (complexité faible); (3) mais un projet <em>spéculatif</em> sans pré-location signée et un chantier de 10 mois exposé aux dépassements (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span> davantage que le plancher de 8 % réservé aux projets quasi sans risque).</p></div></details>254<div class="box box-exo" id="exo-8-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 8.4</span><span class="box-title">— question théorique — l'inclusion du profit</span><a class="box-anchor" href="#exo-8-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p8-89">Un propriétaire-occupant a fait construire sa résidence en gérant lui-même le projet, sans promoteur. Son comptable soutient qu'aucun profit entrepreneurial ne doit figurer dans le coût de remplacement puisque « personne n'a encaissé de profit ». Réfutez cet argument en mobilisant le principe de substitution, puis indiquez une situation où l'évaluateur pourrait légitimement moduler le taux de profit à la baisse.</p></div></div>255<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p8-90">L'argument confond <em>décaissement</em> et <em>coût économique</em>. Le coût de remplacement mesure ce qu'un <strong>acheteur type</strong> devrait payer pour obtenir une propriété équivalente (principe de substitution); or l'offre de substitution sur le marché émane de promoteurs qui exigent une rémunération pour leur risque, leur temps, leur capital et leur expertise. Le propriétaire-gestionnaire n'a pas « économisé » le profit : il l'a <em>gagné</em> en assumant lui-même ces fonctions — son temps et son risque ont une valeur économique, qu'il l'ait facturée ou non. L'omettre sous-évaluerait le coût de création de 8 à 15 %. Modulation possible : un marché en fort déséquilibre (suroffre, projets invendus) où le profit <em>observable</em> des promoteurs est comprimé — l'extraction du marché peut alors justifier un taux vers le bas de la fourchette, à documenter.</p></div></details>256<div class="box box-exo" id="exo-8-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 8.5</span><span class="box-title">— question de calcul type mi-session</span><a class="box-anchor" href="#exo-8-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p8-91">Un bâtiment résidentiel de 2 000 pi<sup>2</sup> a des coûts directs de 175 $/pi<sup>2</sup>. Calculez le coût total avec : honoraires professionnels 14 %, financement 3,5 %, taxes et permis 1,2 %, assurances et légal 2,5 %, administration 1,5 % (le tout en % des coûts directs), et profit entrepreneurial de 10 % de (directs + indirects).</p></div></div>257<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p8-92">Directs : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>175</mn><mo>=</mo><mn>350</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">2\,000 \times 175 = 350\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">175</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">350</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Indirects : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>14</mn><mo>+</mo><mn>3,5</mn><mo>+</mo><mn>1,2</mn><mo>+</mo><mn>2,5</mn><mo>+</mo><mn>1,5</mn><mo>=</mo><mn>22,7</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">14 + 3{,}5 + 1{,}2 + 2{,}5 + 1{,}5 = 22{,}7\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">14</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">3</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">2</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">2</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">22</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">7</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> des directs, soit <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>350</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,227</mn><mo>=</mo><mn>79</mn><mtext> </mtext><mn>450</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">350\,000 \times 0{,}227 = 79\,450\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">350</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">227</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">79</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">450</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Sous-total : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>429</mn><mtext> </mtext><mn>450</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">429\,450\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">429</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">450</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Profit : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>429</mn><mtext> </mtext><mn>450</mn><mo>×</mo><mn>0,10</mn><mo>=</mo><mn>42</mn><mtext> </mtext><mn>945</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">429\,450 \times 0{,}10 = 42\,945\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">429</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">450</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">10</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">42</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">945</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. <strong>Coût total : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>472</mn><mtext> </mtext><mn>395</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">472\,395\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">472</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">395</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span></strong>, soit environ 236 $/pi<sup>2</sup> (+35 % sur les directs).</p></div></details>258<div class="box box-exo" id="exo-8-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 8.6</span><span class="box-title">— chasse au double comptage</span><a class="box-anchor" href="#exo-8-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p8-93">Un bordereau soumis à votre révision contient les postes suivants, en sus des coûts directs : (a) cotisations CCQ des ouvriers, 4,2 % des salaires; (b) marge bénéficiaire de l'entrepreneur général, 8 %; (c) honoraires d'architecte, 7 %; (d) profit du promoteur, 10 %; (e) prime CNESST, 2,1 % des salaires; (f) assurance chantier, 1 %. Identifiez les postes erronés et corrigez le bordereau en expliquant chaque décision.</p></div></div>259<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p8-94">Postes erronés : <strong>(a)</strong>, <strong>(b)</strong> et <strong>(e)</strong>. Les cotisations CCQ (a) et CNESST (e) sont déjà incluses dans les taux horaires conventionnés de la main-d'œuvre, donc dans les coûts directs : les inscrire en indirects les compte deux fois. La marge de l'entrepreneur général (b) est incluse dans les prix soumis (coût direct) — à ne pas confondre avec le profit du promoteur (d), qui est légitime et distinct. Restent en indirects : honoraires d'architecte (c) et assurance chantier (f); le profit (d) demeure, appliqué sur (directs + indirects).</p></div></details>260<h2 class="h-section" id="s-9"><span class="h-num">9</span><span class="h-text">Concepts de dépréciation</span></h2>261<div class="box box-exo" id="exo-9-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 9.5</span><span class="box-title">— durées de vie</span><a class="box-anchor" href="#exo-9-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p9-84">Un immeuble commercial (acier et béton) construit en 1996 est visité en 2026. Bien entretenu, il a subi une rénovation majeure en 2016. Vie économique totale estimée : 50 ans; vie physique totale : 65 ans; âge effectif estimé : 22 ans. Calculez : (a) l'âge chronologique; (b) la vie économique restante; (c) le ratio de dépréciation âge-vie.</p></div></div>262<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p9-85">(a) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2026</mn><mo>−</mo><mn>1996</mn><mo>=</mo><mrow><mtext mathvariant="bold">30</mtext><mtext> </mtext><mtext mathvariant="bold">ans</mtext></mrow></mrow><annotation encoding="application/x-tex">2026 - 1996 = \textbf{30 ans}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">2026</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">1996</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord text"><span class="mord textbf">30 ans</span></span></span></span></span>. (b) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50</mn><mo>−</mo><mn>22</mn><mo>=</mo><mrow><mtext mathvariant="bold">28</mtext><mtext> </mtext><mtext mathvariant="bold">ans</mtext></mrow></mrow><annotation encoding="application/x-tex">50 - 22 = \textbf{28 ans}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord text"><span class="mord textbf">28 ans</span></span></span></span></span>. (c) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>22</mn><mi mathvariant="normal">/</mi><mn>50</mn><mo>=</mo><mn>0,44</mn><mo>=</mo><mrow><mtext mathvariant="bold">44</mtext><mtext> </mtext><mtext mathvariant="bold">%</mtext></mrow></mrow><annotation encoding="application/x-tex">22/50 = 0{,}44 = \textbf{44\,\%}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">22/50</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">44</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord text"><span class="mord textbf">44</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">%</span></span></span></span></span>. L'âge effectif (22 ans) est inférieur à l'âge chronologique (30 ans) grâce à l'entretien et à la rénovation de 2016 — sans elle, il aurait pu atteindre 30 ans ou plus, et la dépréciation 60 %.</p></div></details>263<div class="box box-exo" id="exo-9-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 9.6</span><span class="box-title">— méthode âge-vie</span><a class="box-anchor" href="#exo-9-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p9-86">Maison unifamiliale à Gatineau : coût de remplacement à neuf <span class="num">420 000 $</span>; construite en 2002, évaluée en 2026; entretien moyen, sans rénovation majeure; âge effectif estimé 26 ans; hypothèse de vie économique totale de 55 ans. Calculez : (a) la dépréciation totale; (b) la valeur contributrice du bâtiment; (c) la valeur de la propriété si le terrain vaut <span class="num">150 000 $</span>.</p></div></div>264<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p9-87">(a) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo>=</mo><mfrac><mn>26</mn><mn>55</mn></mfrac><mo>×</mo><mn>420</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>0,4727</mn><mo>×</mo><mn>420</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>198</mn><mtext> </mtext><mn>545</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">D = \frac{26}{55} \times 420\,000 = 0{,}4727 \times 420\,000 =265198\,545\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">55</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">26</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">4727</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">198</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">545</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span></span></span></span> 47,3 %). (b) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>420</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>198</mn><mtext> </mtext><mn>545</mn><mo>=</mo><mn>221</mn><mtext> </mtext><mn>455</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">420\,000 - 198\,545 =266221\,455\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">198</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">545</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">221</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">455</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. (c) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>150</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>221</mn><mtext> </mtext><mn>455</mn><mo>=</mo><mrow><mn mathvariant="bold">371</mn><mtext> </mtext><mn mathvariant="bold">455</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mrow><annotation encoding="application/x-tex">150\,000 + 221\,455 = \mathbf{371\,455\,\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">150</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">221</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">455</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord"><span class="mord mathbf">371</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathbf">455</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathbf">$</span></span></span></span></span>. Remarquez que l'âge effectif (26) dépasse ici l'âge chronologique (24) : l'entretien seulement moyen a vieilli le bâtiment plus vite que le calendrier.</p></div></details>267<div class="box box-exo" id="exo-9-7"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 9.7</span><span class="box-title">— méthode âge-vie modifiée</span><a class="box-anchor" href="#exo-9-7" aria-label="Lien">#</a></div><div class="box-body"><p id="p9-88">Même propriété, mais l'évaluateur relève un entretien différé : toiture à remplacer <span class="num">18 000 $</span>, peinture extérieure <span class="num">6000 $</span>, réparation des fenêtres <span class="num">8000 $</span> (total <span class="num">32 000 $</span>). Calculez la dépréciation totale par la méthode âge-vie modifiée et comparez avec l'exercice précédent.</p></div></div>268<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mi>D</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>32</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mfrac><mn>26</mn><mn>55</mn></mfrac><mo>×</mo><mo stretchy="false">(</mo><mn>420</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>32</mn><mtext> </mtext><mn>000</mn><mo stretchy="false">)</mo><mo>=</mo><mn>32</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>0,4727</mn><mo>×</mo><mn>388</mn><mtext> </mtext><mn>000</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>32</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>183</mn><mtext> </mtext><mn>418</mn><mo>=</mo><mn>215</mn><mtext> </mtext><mn>418</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo separator="true">,</mo></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}D &amp;= 32\,000 + \frac{26}{55} \times (420\,000 - 32\,000)269   = 32\,000 + 0{,}4727 \times 388\,000\\270  &amp;= 32\,000 + 183\,418 = 215\,418\,\$,\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:3.5074em;vertical-align:-1.5037em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0037em;"><span style="top:-4.0037em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span></span></span><span style="top:-2.1777em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5037em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0037em;"><span style="top:-4.0037em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">32</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">55</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">26</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">32</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">32</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">4727</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">388</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span><span style="top:-2.1777em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">32</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">183</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">418</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">215</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">418</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span><span class="mpunct">,</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5037em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>271<p id="p9-89">soit environ 51,3 %. Comparaison : l'âge-vie simple donnait <span class="num">198 545 $</span>; la méthode modifiée capte <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>215</mn><mtext> </mtext><mn>418</mn><mo>−</mo><mn>198</mn><mtext> </mtext><mn>545</mn><mo>=</mo><mn>16</mn><mtext> </mtext><mn>873</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">215\,418 - 198\,545 =27216\,873~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">215</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">418</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">198</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">545</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">873</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span> de plus, car l'entretien différé est mesuré directement et s'ajoute au ratio appliqué au solde (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>388</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">388\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">388</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span> au lieu de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>420</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">420\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>). Valeur du bâtiment : <span class="num">204 582 $</span>; valeur de la propriété (terrain 150 k$) : <span class="num">354 582 $</span>. Conservez les fractions exactes (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>26</mn><mi mathvariant="normal">/</mi><mn>55</mn></mrow><annotation encoding="application/x-tex">26/55</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">26/55</span></span></span></span>) jusqu'au bout pour éviter les écarts d'arrondi.</p></div></details>273<div class="box box-exo" id="exo-9-8"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 9.8</span><span class="box-title">— extraction du marché</span><a class="box-anchor" href="#exo-9-8" aria-label="Lien">#</a></div><div class="box-body"><p id="p9-90">Trois ventes récentes dans un secteur de Gatineau :</p>274<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th></th><th class="al-r">Vente A</th><th class="al-r">Vente B</th><th class="al-r">Vente C</th></tr></thead><tbody><tr><td>Prix de vente</td><td class="al-r"><span class="num">485 000 $</span></td><td class="al-r"><span class="num">510 000 $</span></td><td class="al-r"><span class="num">465 000 $</span></td></tr><tr><td>Valeur du terrain</td><td class="al-r"><span class="num">155 000 $</span></td><td class="al-r"><span class="num">170 000 $</span></td><td class="al-r"><span class="num">145 000 $</span></td></tr><tr><td>Coût de remplacement à neuf</td><td class="al-r"><span class="num">450 000 $</span></td><td class="al-r"><span class="num">470 000 $</span></td><td class="al-r"><span class="num">440 000 $</span></td></tr><tr><td>Âge effectif</td><td class="al-r">20 ans</td><td class="al-r">25 ans</td><td class="al-r">18 ans</td></tr></tbody></table></div></div>275<p id="p9-91">Calculez la dépréciation extraite et le taux annuel de chaque vente, le taux moyen, puis appliquez-le au sujet de l'exercice précédent (âge effectif 26 ans, coût neuf <span class="num">420 000 $</span>).</p></div></div>276<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p9-92"><strong>Vente A</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>450</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mo stretchy="false">(</mo><mn>485</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>155</mn><mtext> </mtext><mn>000</mn><mo stretchy="false">)</mo><mo>=</mo><mn>120</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">450\,000 - (485\,000 - 155\,000) = 120\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">450</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">485</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">155</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">120</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> (26,7 %) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo><mn>26,7</mn><mi mathvariant="normal">/</mi><mn>20</mn><mo>=</mo><mn>1,33</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">\Rightarrow 26{,}7/20 = 1{,}33\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">26</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">7/20</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">33</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>/an. <strong>Vente B</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>470</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mo stretchy="false">(</mo><mn>510</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>170</mn><mtext> </mtext><mn>000</mn><mo stretchy="false">)</mo><mo>=</mo><mn>130</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">470\,000 - (510\,000 - 170\,000) = 130\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">470</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">510</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">170</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">130</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> (27,7 %) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo><mn>27,7</mn><mi mathvariant="normal">/</mi><mn>25</mn><mo>=</mo><mn>1,11</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">\Rightarrow 27{,}7/25 = 1{,}11\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">27</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">7/25</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">11</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>/an. <strong>Vente C</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>440</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mo stretchy="false">(</mo><mn>465</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>145</mn><mtext> </mtext><mn>000</mn><mo stretchy="false">)</mo><mo>=</mo><mn>120</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">440\,000 - (465\,000 - 145\,000) = 120\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">440</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">465</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">145</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">120</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> (27,3 %) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo><mn>27,3</mn><mi mathvariant="normal">/</mi><mn>18</mn><mo>=</mo><mn>1,52</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">\Rightarrow 27{,}3/18 = 1{,}52\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">27</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">3/18</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">52</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>/an. Taux moyen : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>1,33</mn><mo>+</mo><mn>1,11</mn><mo>+</mo><mn>1,52</mn><mo stretchy="false">)</mo><mi mathvariant="normal">/</mi><mn>3</mn><mo>=</mo><mrow><mtext mathvariant="bold">1,32</mtext><mtext> </mtext><mtext mathvariant="bold">%/an</mtext></mrow></mrow><annotation encoding="application/x-tex">(1{,}33 + 1{,}11 + 1{,}52)/3 = \textbf{1,32\,\%/an}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">33</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">11</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">52</span><span class="mclose">)</span><span class="mord">/3</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord text"><span class="mord textbf">1,32</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">%/an</span></span></span></span></span>. Application au sujet : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo>=</mo><mn>26</mn><mo>×</mo><mn>1,32</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>×</mo><mn>420</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>34,32</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>×</mo><mn>420</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>144</mn><mtext> </mtext><mn>144</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">D = 26 \times 1{,}32\,\% \times 420\,000 =27734{,}32\,\% \times 420\,000 = 144\,144\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">26</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">32</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">34</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">32</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">144</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">144</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. L'écart avec l'âge-vie (198 k$) illustre que les méthodes doivent être <em>réconciliées</em>, pas moyennées aveuglément : ici le marché se déprécie moins vite que l'hypothèse de vie économique de 55 ans ne le suppose.</p></div></details>278<div class="box box-exo" id="exo-9-9"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 9.9</span><span class="box-title">— classement des dépréciations</span><a class="box-anchor" href="#exo-9-9" aria-label="Lien">#</a></div><div class="box-body"><p id="p9-93">Classez chaque situation (type de dépréciation + curable ou incurable) : (a) bardeaux d'asphalte en fin de vie; (b) maison sans garage dans un quartier où 90 % en ont un; (c) autoroute bruyante construite à 50 m; (d) cuisine fermée démodée; (e) comptoirs de marbre dans un quartier modeste; (f) fissures capillaires dans les murs de fondation; (g) zonage modifié interdisant l'usage le plus rentable; (h) une seule salle de bain pour quatre chambres.</p></div></div>279<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p9-94">(a) physique curable (remplacement rentable); (b) fonctionnelle <strong>incurable</strong> (déficience structurelle du plan); (c) externe — toujours incurable; (d) fonctionnelle curable par substitution; (e) fonctionnelle incurable — superadéquation; (f) physique incurable (structure, longue durée de vie); (g) externe (réglementaire), incurable; (h) fonctionnelle curable par ajout (si le coût de l'ajout est inférieur au gain de valeur — appliquer le test économique).</p></div></details>280<h2 class="h-section" id="s-10"><span class="h-num">10</span><span class="h-text">Dépréciation physique</span></h2>281<div class="box box-exo" id="exo-10-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 10.1</span><span class="box-title">— classification curable / incurable</span><a class="box-anchor" href="#exo-10-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-99">Pour chacune des situations suivantes (bâtiment résidentiel, marché de Gatineau), classez l'item : <strong>curable</strong>, <strong>incurable court terme</strong> ou <strong>incurable long terme</strong>. Justifiez en une phrase.</p>282<ol class="enum"><li>Toiture de bardeaux de 28 ans, durée de vie utile de 25 ans; coût de         remplacement <span class="num">14 000 $</span>, valeur ajoutée estimée <span class="num">16 000 $</span>.</li><li>Chauffe-eau de 6 ans (vie utile de 12 ans), fonctionnel.</li><li>Fissure structurale majeure de la fondation; coût de correction         <span class="num">85 000 $</span>, valeur ajoutée estimée <span class="num">40 000 $</span>.</li><li>Peinture intérieure défraîchie; coût <span class="num">5000 $</span>, valeur ajoutée         <span class="num">7000 $</span>.</li><li>Charpente saine d'un bâtiment de 35 ans (vie économique de 60 ans).</li></ol></div></div>283<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li><strong>Curable</strong> : la composante est en fin de vie (ratio plafonné à         100 %) et le test économique est satisfait         (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>14</mn><mtext> </mtext><mn>000</mn><mo>≤</mo><mn>16</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">14\,000 \leq 16\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7804em;vertical-align:-0.136em;"></span><span class="mord">14</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>); on la mesure au coût de remplacement.</li><li><strong>Incurable court terme</strong> : composante à courte vie en cours de         vie, ratio <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>6</mn><mi mathvariant="normal">/</mi><mn>12</mn><mo>=</mo><mn>50</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">6/12 = 50\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">6/12</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> appliqué à son coût neuf.</li><li><strong>Incurable</strong> : le coût de correction (<span class="num">85 000 $</span>) excède         la valeur ajoutée (<span class="num">40 000 $</span>); la déficience structurale se         reflète dans le long terme (âge effectif alourdi), non comme item         curable.</li><li><strong>Curable</strong> : entretien différé classique,         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn><mtext> </mtext><mn>000</mn><mo>≤</mo><mn>7</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">5\,000 \leq 7\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7804em;vertical-align:-0.136em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">7</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>.</li><li><strong>Incurable long terme</strong> : composante structurale saine,         dépréciée par le ratio âge/vie économique du bâtiment         (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>35</mn><mi mathvariant="normal">/</mi><mn>60</mn><mo>≈</mo><mn>58</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">35/60 \approx 58\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">35/60</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">58</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> sur le résidu).</li></ol></div></details>284<div class="box box-exo" id="exo-10-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 10.2</span><span class="box-title">— composante à courte vie</span><a class="box-anchor" href="#exo-10-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-110">Un système CVAC a un coût neuf de <span class="num">24 000 $</span> et une durée de vie utile de 20 ans. Le bâtiment a 15 ans, mais le CVAC a été remplacé il y a 6 ans; son entretien annuel est impeccable.</p>285<ol class="enum"><li>Quel âge effectif retenez-vous pour le CVAC?</li><li>Calculez sa dépréciation incurable court terme et sa valeur         résiduelle.</li><li>Qu'adviendrait-il du calcul si le CVAC, jamais entretenu, présentait         un âge effectif de 9 ans?</li></ol></div></div>286<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>L'âge effectif suit la composante, pas le bâtiment : <strong>6 ans</strong>         (remplacement documenté, entretien impeccable).</li><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo>=</mo><mn>24</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>6</mn><mi mathvariant="normal">/</mi><mn>20</mn><mo>=</mo><mn>24</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>30</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">7</mn><mtext> </mtext><mn mathvariant="bold">200</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">D = 24\,000 \times 6/20 = 24\,000 \times 30\,\% =287        \uqogreen{7\,200~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">6/20</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">7</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">200</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>; valeur résiduelle         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>24</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>7</mn><mtext> </mtext><mn>200</mn><mo>=</mo><mn>16</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 24\,000 - 7\,200 = 16\,800\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">7</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> (il reste 14 ans de vie         utile).</li><li>Avec un âge effectif de 9 ans : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo>=</mo><mn>24</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>9</mn><mi mathvariant="normal">/</mi><mn>20</mn><mo>=</mo><mn>10</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">D = 24\,000 \times 9/20 =288        10\,800\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">9/20</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>, valeur résiduelle <span class="num">13 200 $</span>. Le même         équipement, selon son entretien, porte une dépréciation qui varie de         <span class="num">3600 $</span> — d'où l'importance des observations d'inspection.</li></ol></div></details>289<div class="box box-exo" id="exo-10-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 10.3</span><span class="box-title">— cottage à Aylmer — ventilation complète</span><a class="box-anchor" href="#exo-10-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-117">Cottage de 2 étages, <span class="num">1500</span> pi<sup>2</sup>, construit en 1995 à Aylmer (Gatineau). Coût de remplacement à neuf : <span class="num">420 000 $</span>; âge effectif du bâtiment : 22 ans; hypothèse du cas : vie économique de 65 ans. Items curables constatés : peinture intérieure (<span class="num">7000 $</span>), gouttières (<span class="num">1800 $</span>), robinetterie (<span class="num">1200 $</span>). Composantes à courte vie :</p>290<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Composante</th><th class="al-r">Coût neuf</th><th class="al-c">Durée de vie</th><th class="al-c">Âge effectif</th></tr></thead><tbody><tr><td>Toiture</td><td class="al-r">18 000 $</td><td class="al-c">25 ans</td><td class="al-c">18 ans</td></tr><tr><td>CVAC</td><td class="al-r">22 000 $</td><td class="al-c">20 ans</td><td class="al-c">15 ans</td></tr><tr><td>Fenêtres</td><td class="al-r">25 000 $</td><td class="al-c">35 ans</td><td class="al-c">20 ans</td></tr><tr><td>Couvre-planchers</td><td class="al-r">15 000 $</td><td class="al-c">20 ans</td><td class="al-c">12 ans</td></tr><tr><td>Cuisine / salle de bain</td><td class="al-r">30 000 $</td><td class="al-c">25 ans</td><td class="al-c">18 ans</td></tr><tr><td>Système électrique</td><td class="al-r">12 000 $</td><td class="al-c">35 ans</td><td class="al-c">22 ans</td></tr><tr><td>Revêtement extérieur</td><td class="al-r">20 000 $</td><td class="al-c">30 ans</td><td class="al-c">20 ans</td></tr><tr><td>Plomberie</td><td class="al-r">8 000 $</td><td class="al-c">25 ans</td><td class="al-c">15 ans</td></tr></tbody></table></div></div>291<p id="p10-118">Calculez la dépréciation curable, l'incurable court terme (composante par composante), l'incurable long terme et la dépréciation physique totale, en pourcentage du coût neuf.</p></div></div>292<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p10-119"><strong>Étape 1 — curable :</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>7</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>1</mn><mtext> </mtext><mn>800</mn><mo>+</mo><mn>1</mn><mtext> </mtext><mn>200</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">10</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">7\,000 + 1\,800 + 1\,200 =293\uqogreen{10\,000~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">7</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">10</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</p>294<p id="p10-120"><strong>Étape 2 — incurable court terme :</strong></p>295<div class="center"><div class="table-wrap"><table class="tbl table-wide"><thead><tr><th>Composante</th><th class="al-r">Coût neuf</th><th class="al-c">Âge / Vie</th><th class="al-r">%</th><th class="al-r">Dépréc.</th></tr></thead><tbody><tr><td>Toiture</td><td class="al-r">18 000 $</td><td class="al-c">18 / 25</td><td class="al-r">72,0</td><td class="al-r">12 960 $</td></tr><tr><td>CVAC</td><td class="al-r">22 000 $</td><td class="al-c">15 / 20</td><td class="al-r">75,0</td><td class="al-r">16 500 $</td></tr><tr><td>Fenêtres</td><td class="al-r">25 000 $</td><td class="al-c">20 / 35</td><td class="al-r">57,1</td><td class="al-r">14 286 $</td></tr><tr><td>Couvre-planchers</td><td class="al-r">15 000 $</td><td class="al-c">12 / 20</td><td class="al-r">60,0</td><td class="al-r">9 000 $</td></tr><tr><td>Cuisine / salle de bain</td><td class="al-r">30 000 $</td><td class="al-c">18 / 25</td><td class="al-r">72,0</td><td class="al-r">21 600 $</td></tr><tr><td>Système électrique</td><td class="al-r">12 000 $</td><td class="al-c">22 / 35</td><td class="al-r">62,9</td><td class="al-r">7 543 $</td></tr><tr><td>Revêtement extérieur</td><td class="al-r">20 000 $</td><td class="al-c">20 / 30</td><td class="al-r">66,7</td><td class="al-r">13 333 $</td></tr><tr><td>Plomberie</td><td class="al-r">8 000 $</td><td class="al-c">15 / 25</td><td class="al-r">60,0</td><td class="al-r">4 800 $</td></tr><tr class="rule-above"><td><strong>Total CT</strong></td><td class="al-r"><strong>150 000 $</strong></td><td class="al-c"></td><td class="al-r"></td><td class="al-r"><strong>100 022 $</strong></td></tr></tbody></table></div></div>296<p id="p10-121"><strong>Étape 3 — incurable long terme :</strong></p>297<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>R</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>sidu</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>420</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>10</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>150</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>260</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>D</mi><mtext>LT</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>260</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mfrac><mn>22</mn><mn>65</mn></mfrac><mo>=</mo><mrow><mtext mathvariant="bold">88</mtext><mtext> </mtext><mtext mathvariant="bold">000</mtext><mtext> </mtext><mtext mathvariant="bold">$</mtext></mrow></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Résidu} &amp;= 420\,000 - 10\,000 - 150\,000 = 260\,000\,\$ \\298D_{\text{LT}} &amp;= 260\,000 \times \frac{22}{65} = \textbf{88\,000\,\$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:3.5074em;vertical-align:-1.5037em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0037em;"><span style="top:-4.4852em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord text"><span class="mord">R</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">sidu</span></span></span></span><span style="top:-2.5037em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">LT</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5037em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0037em;"><span style="top:-4.4852em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">150</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">260</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-2.5037em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">260</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">65</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">22</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord textbf">88</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">$</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5037em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>299<p id="p10-122"><strong>Total :</strong></p>300<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><menclose notation="box"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mrow><msub><mi>D</mi><mtext>totale</mtext></msub><mo>=</mo><mn>10</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>100</mn><mtext> </mtext><mn>022</mn><mo>+</mo><mn>88</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mrow><mtext mathvariant="bold">198</mtext><mtext> </mtext><mtext mathvariant="bold">022</mtext><mtext> </mtext><mtext mathvariant="bold">$</mtext></mrow><mspace width="1em"/><mo stretchy="false">(</mo><mn>47,1</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mrow><mtext> du co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t neuf</mtext></mrow><mo stretchy="false">)</mo></mrow></mstyle></mstyle></mstyle></menclose></mrow><annotation encoding="application/x-tex">\boxed{D_{\text{totale}} = 10\,000 + 100\,022 + 88\,000 = \textbf{198\,022\,\$}301\quad (47{,}1\,\% \text{ du coût neuf})}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.68em;vertical-align:-0.59em;"></span><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.09em;"><span style="top:-3.68em;"><span class="pstrut" style="height:3.68em;"></span><span class="boxpad"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">100</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">022</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">88</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord textbf">198</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">022</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">$</span></span><span class="mspace" style="margin-right:1em;"></span><span class="mopen">(</span><span class="mord">47</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mord text"><span class="mord"> du co</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">u</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˆ</span></span></span></span></span></span></span><span class="mord">t neuf</span></span><span class="mclose">)</span></span></span></span></span><span style="top:-3.09em;"><span class="pstrut" style="height:3.68em;"></span><span class="katex-stretchy fbox" style="height:1.68em;border-style:solid;border-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.59em;"><span></span></span></span></span></span></span></span></span></span></div>302<p id="p10-123">Le bâtiment a consommé près de la moitié de son coût neuf en dépréciation physique — lecture plausible pour 22 ans d'âge effectif avec des composantes mécaniques et de finition bien avancées dans leur vie utile.</p></div></details>303<div class="box box-exo" id="exo-10-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 10.4</span><span class="box-title">— comparaison des méthodes</span><a class="box-anchor" href="#exo-10-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-124">Reprenez les données du cottage d'Aylmer (exercice précédent). Calculez la dépréciation physique par la méthode âge-vie <strong>simple</strong>, puis par l'âge-vie <strong>modifiée</strong>, et comparez avec le résultat de la ventilation (<span class="num">198 022 $</span>). Expliquez la source des écarts et indiquez la méthode à privilégier dans un rapport détaillé.</p></div></div>304<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p10-125"><strong>Âge-vie simple :</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo>=</mo><mn>420</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>22</mn><mi mathvariant="normal">/</mi><mn>65</mn><mo>=</mo><mn>142</mn><mtext> </mtext><mn>154</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">D = 420\,000 \times 22/65 = 142\,154\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">22/65</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">142</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">154</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> (33,8 %).  <strong>Âge-vie modifiée :</strong> curable <span class="num">10 000 $</span>; solde <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>420</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>10</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>410</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">420\,000 - 10\,000 = 410\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">410</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>; incurable <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>410</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>22</mn><mi mathvariant="normal">/</mi><mn>65</mn><mo>=</mo><mn>138</mn><mtext> </mtext><mn>769</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">410\,000 \times 22/65 = 138\,769\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">410</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">22/65</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">138</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">769</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; total <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>148</mn><mtext> </mtext><mn>769</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\approx 148\,769\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">148</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">769</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> (35,4 %).  <strong>Ventilation :</strong> <span class="num">198 022 $</span> (47,1 %).  L'écart (11 à 13 points, soit 50 000 à 56 000 $) vient du fait que les ratios âge-vie appliquent le rythme moyen du bâtiment (22/65 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span></span></span></span> 34 %) à des composantes courtes déjà consommées à 57–75 % (toiture, CVAC, cuisine). Dans un rapport détaillé, la <strong>ventilation</strong> s'impose; l'âge-vie sert d'estimation préliminaire ou de contre-vérification d'ordre de grandeur.</p></div></details>305<div class="box box-exo" id="exo-10-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 10.5</span><span class="box-title">— erreur de double comptage</span><a class="box-anchor" href="#exo-10-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-126">Un étudiant remet la ventilation suivante pour un duplex (coût neuf <span class="num">380 000 $</span>, âge effectif 18 ans, vie économique 60 ans) : entretien différé <span class="num">22 000 $</span>, dont remplacement de la toiture en fin de vie <span class="num">15 000 $</span>; composantes à courte vie : toiture (coût neuf <span class="num">15 000 $</span>, ratio 100 %, dépréciation <span class="num">15 000 $</span>), autres composantes CT (coûts neufs <span class="num">105 000 $</span>, dépréciation <span class="num">52 000 $</span>); long terme : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>380</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>22</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>120</mn><mtext> </mtext><mn>000</mn><mo stretchy="false">)</mo><mo>×</mo><mn>18</mn><mi mathvariant="normal">/</mi><mn>60</mn><mo>=</mo><mn>71</mn><mtext> </mtext><mn>400</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">(380\,000 - 22\,000 - 120\,000) \times 18/60 =30671\,400\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">380</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">120</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">18/60</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">71</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Total déclaré : <span class="num">160 400 $</span>. Identifiez l'erreur, corrigez la ventilation et recalculez le total.</p></div></div>307<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p10-127"><strong>L'erreur :</strong> la toiture en fin de vie est comptée <strong class="c-rouge">deux fois</strong> — une fois comme curable (<span class="num">15 000 $</span> dans l'entretien différé) et une fois comme incurable CT à 100 % (<span class="num">15 000 $</span>). Une composante complètement usée est <strong>curable seulement</strong>.  <strong>Correction :</strong> retirer la toiture de l'étape 2. Curable : <span class="num">22 000 $</span> (inchangé, la toiture y est à sa place). Incurable CT : <span class="num">52 000 $</span> sur coûts neufs CT de <span class="num">105 000 $</span>. Long terme : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>380</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>22</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>105</mn><mtext> </mtext><mn>000</mn><mo stretchy="false">)</mo><mo>×</mo><mn>18</mn><mi mathvariant="normal">/</mi><mn>60</mn><mo>=</mo><mn>253</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>30</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mn>75</mn><mtext> </mtext><mn>900</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">(380\,000 - 22\,000 - 105\,000) \times 18/60 = 253\,000 \times 30\,\% =30875\,900\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">380</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">105</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">18/60</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">253</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">75</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">900</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>.  <strong>Total corrigé :</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>22</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>52</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>75</mn><mtext> </mtext><mn>900</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">149</mn><mtext> </mtext><mn mathvariant="bold">900</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">22\,000 + 52\,000 + 75\,900 =309\uqogreen{149\,900~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">52</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">75</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">900</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">149</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">900</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span> (au lieu de <span class="num">160 400 $</span> — l'erreur gonflait la dépréciation de <span class="num">10 500 $</span> : <span class="num">15 000 $</span> comptés en trop à l'étape 2, moins <span class="num">4500 $</span> de long terme calculé sur une assiette indûment réduite de <span class="num">15 000 $</span>).</p></div></details>310<div class="box box-exo" id="exo-10-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 10.6</span><span class="box-title">— mini-cas : sixplex avec historique de rénovations</span><a class="box-anchor" href="#exo-10-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-128">Un sixplex de 1988 à Hull présente : coût de remplacement <span class="num">820 000 $</span>; âge effectif global 24 ans; vie économique 55 ans; entretien différé <span class="num">31 000 $</span>. Composantes à courte vie (coûts neufs) : toitures et membranes <span class="num">48 000 $</span> (refaites il y a 10 ans, vie 25 ans); balcons et escaliers <span class="num">36 000 $</span> (âge effectif 20 ans, vie 30 ans); systèmes mécaniques <span class="num">94 000 $</span> (âge effectif 15 ans, vie 22 ans); finitions locatives <span class="num">72 000 $</span> (âge effectif 12 ans, vie 18 ans).</p>311<ol class="enum"><li>Calculez la dépréciation incurable court terme totale.</li><li>Calculez l'incurable long terme et la dépréciation physique totale.</li><li>Le propriétaire fournit ensuite des reçus montrant que les systèmes         mécaniques ont été remplacés il y a 8 ans (et non 15). Recalculez le         total et commentez l'impact d'un seul document sur la valeur.</li></ol></div></div>312<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>Incurable CT :         toitures <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>48</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>10</mn><mi mathvariant="normal">/</mi><mn>25</mn><mo>=</mo><mn>19</mn><mtext> </mtext><mn>200</mn></mrow><annotation encoding="application/x-tex">48\,000 \times 10/25 = 19\,200</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">48</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">10/25</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">19</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span></span></span></span>;         balcons <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>36</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>20</mn><mi mathvariant="normal">/</mi><mn>30</mn><mo>=</mo><mn>24</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">36\,000 \times 20/30 = 24\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">36</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">20/30</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>;         mécanique <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>94</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>15</mn><mi mathvariant="normal">/</mi><mn>22</mn><mo>=</mo><mn>64</mn><mtext> </mtext><mn>091</mn></mrow><annotation encoding="application/x-tex">94\,000 \times 15/22 = 64\,091</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">94</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">15/22</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">64</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">091</span></span></span></span>;         finitions <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>72</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>12</mn><mi mathvariant="normal">/</mi><mn>18</mn><mo>=</mo><mn>48</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">72\,000 \times 12/18 = 48\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">72</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">12/18</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">48</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>.         Total CT <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">155</mn><mtext> </mtext><mn mathvariant="bold">291</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= \uqogreen{155\,291~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">155</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">291</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span> sur coûts neufs CT de         <span class="num">250 000 $</span>.</li><li>Résidu <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>820</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>31</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>250</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>539</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">= 820\,000 - 31\,000 - 250\,000 = 539\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">820</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">31</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">250</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">539</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>;         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>LT</mtext></msub><mo>=</mo><mn>539</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>24</mn><mi mathvariant="normal">/</mi><mn>55</mn><mo>=</mo><mn>235</mn><mtext> </mtext><mn>200</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">D_{\text{LT}} = 539\,000 \times 24/55 = 235\,200\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">LT</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">539</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">24/55</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">235</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> (arrondi).         Total <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>31</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>155</mn><mtext> </mtext><mn>291</mn><mo>+</mo><mn>235</mn><mtext> </mtext><mn>200</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">421</mn><mtext> </mtext><mn mathvariant="bold">491</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= 31\,000 + 155\,291 + 235\,200 = \uqogreen{421\,491~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">31</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">155</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">291</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">235</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">421</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">491</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>         (51,4 % du coût neuf).</li><li>Mécanique corrigée : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>94</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>8</mn><mi mathvariant="normal">/</mi><mn>22</mn><mo>=</mo><mn>34</mn><mtext> </mtext><mn>182</mn></mrow><annotation encoding="application/x-tex">94\,000 \times 8/22 = 34\,182</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">94</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">8/22</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">34</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">182</span></span></span></span>, soit         <span class="num">29 909 $</span> de moins. Nouveau total CT <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>125</mn><mtext> </mtext><mn>382</mn></mrow><annotation encoding="application/x-tex">= 125\,382</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">125</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">382</span></span></span></span>; le long         terme est inchangé (mêmes coûts neufs CT). Total corrigé         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>31</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>125</mn><mtext> </mtext><mn>382</mn><mo>+</mo><mn>235</mn><mtext> </mtext><mn>200</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">391</mn><mtext> </mtext><mn mathvariant="bold">582</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= 31\,000 + 125\,382 + 235\,200 = \uqogreen{391\,582~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">31</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">125</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">382</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">235</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">391</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">582</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>. Un seul         jeu de reçus déplace la dépréciation de près de <span class="num">30 000 $</span>,         soit environ 3,6 % du coût neuf : la collecte documentaire n'est         pas une formalité, c'est de la valeur.</li></ol></div></details>313<h2 class="h-section" id="s-11"><span class="h-num">11</span><span class="h-text">Dépréciation fonctionnelle</span></h2>314<div class="box box-exo" id="exo-11-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 11.1</span><span class="box-title">— classification des déficiences</span><a class="box-anchor" href="#exo-11-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-98">Classez chaque situation dans l'une des quatre catégories (curable–ajout, curable–substitution, incurable–superadéquation, incurable–conception) et indiquez la méthode de calcul applicable.</p>315<ol class="enum"><li>Maison de 1970 sans hotte de cuisine; installation dans l'existant         <span class="num">1800 $</span>, valeur ajoutée <span class="num">2500 $</span>.</li><li>Spa intérieur avec solarium (<span class="num">95 000 $</span> à neuf) dans un         quartier de maisons à <span class="num">300 000 $</span>; contribution au marché         estimée à <span class="num">25 000 $</span>.</li><li>Plomberie en fonte d'origine; remplacement dans l'existant         <span class="num">18 000 $</span>, coût au neuf <span class="num">9000 $</span>, valeur ajoutée         <span class="num">22 000 $</span>.</li><li>Immeuble de bureaux dont les étages de <span class="num">2500</span> pi<sup>2</sup> sont trop         petits pour la demande locative (standard local :         <span class="num">5000</span> pi<sup>2</sup> et plus); loyers inférieurs de         1,50 $/pi<sup>2</sup>/an au marché.</li><li>Bungalow sans salle d'eau au rez-de-chaussée; ajout <span class="num">16 000 $</span>,         valeur ajoutée <span class="num">14 000 $</span>.</li></ol></div></div>316<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li><strong>Curable–ajout</strong> : élément absent, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mtext> </mtext><mn>800</mn><mo>≤</mo><mn>2</mn><mtext> </mtext><mn>500</mn></mrow><annotation encoding="application/x-tex">1\,800 \leq 2\,500</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7804em;vertical-align:-0.136em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span></span></span></span>;         dépréciation <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> <span class="num">1800 $</span> (coût dans l'existant).</li><li><strong>Incurable–superadéquation</strong> : excès de qualité pour le         secteur; coût neuf déprécié physiquement moins contribution         (<span class="num">25 000 $</span>).</li><li><strong>Curable–substitution</strong> : élément présent mais désuet,         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>18</mn><mtext> </mtext><mn>000</mn><mo>≤</mo><mn>22</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">18\,000 \leq 22\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7804em;vertical-align:-0.136em;"></span><span class="mord">18</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>; dépréciation <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>18</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>9</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">= 18\,000 - 9\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">18</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span> (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>         récupération, ici nulle) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> <span class="num">9000 $</span>.</li><li><strong>Incurable–conception</strong> : défaut structurel d'agencement;         capitalisation de la perte de loyer au TGA, moins la portion         terrain.</li><li><strong class="c-rouge">Piège</strong> : le test de curabilité échoue         (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>16</mn><mtext> </mtext><mn>000</mn><mo>&gt;</mo><mn>14</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">16\,000 &gt; 14\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6835em;vertical-align:-0.0391em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">14</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>). La déficience est <strong>incurable</strong> malgré         sa nature d'« ajout » : on ne retient pas le coût de correction; la         perte se mesure par la contribution manquante au marché (par ventes         appariées ou capitalisation), plafonnée ici à environ         <span class="num">14 000 $</span>.</li></ol></div></details>317<div class="box box-exo" id="exo-11-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 11.2</span><span class="box-title">— substitution complète</span><a class="box-anchor" href="#exo-11-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-109">Une maison de 1972 à Hull est chauffée par plinthes désuètes avec un panneau de 100 A. Le marché exige une thermopompe centrale et un panneau de 200 A. Données : thermopompe installée dans l'existant <span class="num">16 500 $</span> (dont modification des conduits <span class="num">3800 $</span>); retrait des plinthes et remise en état des murs <span class="num">2100 $</span>; valeur de récupération des plinthes <span class="num">150 $</span>; coût de la thermopompe dans une construction neuve <span class="num">9500 $</span>. Panneau : coût dans l'existant <span class="num">11 000 $</span>, au neuf <span class="num">5200 $</span>, récupération nulle. Valeurs ajoutées estimées : chauffage <span class="num">24 000 $</span>; panneau <span class="num">9000 $</span>.</p>318<ol class="enum"><li>Vérifiez la curabilité de chaque poste.</li><li>Calculez la dépréciation fonctionnelle curable totale.</li></ol></div></div>319<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>Chauffage : coût de correction complet         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>16</mn><mtext> </mtext><mn>500</mn><mo>+</mo><mn>2</mn><mtext> </mtext><mn>100</mn><mo>−</mo><mn>150</mn><mo>=</mo><mn>18</mn><mtext> </mtext><mn>450</mn><mo>≤</mo><mn>24</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">= 16\,500 + 2\,100 - 150 = 18\,450 \leq 24\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">100</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">150</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7804em;vertical-align:-0.136em;"></span><span class="mord">18</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">450</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span> <strong class="c-vert">curable</strong>. Panneau :         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>11</mn><mtext> </mtext><mn>000</mn><mo>≤</mo><mn>9</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">11\,000 \leq 9\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7804em;vertical-align:-0.136em;"></span><span class="mord">11</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>? Non — <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>11</mn><mtext> </mtext><mn>000</mn><mo>&gt;</mo><mn>9</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">11\,000 &gt; 9\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6835em;vertical-align:-0.0391em;"></span><span class="mord">11</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span> <strong class="c-rouge">incurable</strong> au sens strict du test. (Si         l'énoncé d'un examen retient une valeur ajoutée de <span class="num">12 000 $</span>,         il redevient curable : toujours dérouler le test explicitement.)</li><li>Seul le chauffage est curable :         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>subst</mtext></msub><mo>=</mo><mn>16</mn><mtext> </mtext><mn>500</mn><mo>−</mo><mn>9</mn><mtext> </mtext><mn>500</mn><mo>+</mo><mn>2</mn><mtext> </mtext><mn>100</mn><mo>−</mo><mn>150</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">8</mn><mtext> </mtext><mn mathvariant="bold">950</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">D_{\text{subst}} = 16\,500 - 9\,500 + 2\,100 - 150320        = \uqogreen{8\,950~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">subst</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">100</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">150</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">8</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">950</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>. Le panneau, incurable, se mesure par sa         contribution manquante (au plus <span class="num">9000 $</span>), non par son coût de         correction; il s'ajoute au volet incurable du dossier.</li></ol></div></details>321<div class="box box-exo" id="exo-11-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 11.3</span><span class="box-title">— superadéquation avec charges excédentaires</span><a class="box-anchor" href="#exo-11-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-114">Une résidence de Chelsea comprend une piscine intérieure : coût à neuf <span class="num">110 000 $</span>; âge effectif 12 ans, vie économique 40 ans; contribution au marché <span class="num">35 000 $</span>. Le chauffage et l'entretien de la piscine coûtent <span class="num">4200 $</span>/an de plus que ce que le marché accepte d'absorber; TGA de 6,0 %; portion terrain 25 %.</p>322<ol class="enum"><li>Calculez la dépréciation par superadéquation (volet coût).</li><li>Capitalisez la pénalité d'exploitation excédentaire.</li><li>Concluez la dépréciation fonctionnelle totale de l'élément.</li></ol></div></div>323<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>Dépréciation physique de l'élément : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>110</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>12</mn><mi mathvariant="normal">/</mi><mn>40</mn><mo>=</mo><mn>33</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">110\,000 \times 12/40 =324        33\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">110</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">12/40</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">33</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>. Coût déprécié : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>110</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>33</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>77</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">110\,000 - 33\,000 = 77\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">110</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">33</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">77</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>.         Superadéquation : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>77</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>35</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">42</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">77\,000 - 35\,000 = \uqogreen{42\,000~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">77</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">35</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">42</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</li><li>Perte capitalisée : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4</mn><mtext> </mtext><mn>200</mn><mo>÷</mo><mn>0,06</mn><mo>=</mo><mn>70</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">4\,200 \div 0{,}06 = 70\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">4</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">06</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">70</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>; portion         améliorations : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>70</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mn>0,25</mn><mo stretchy="false">)</mo><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">52</mn><mtext> </mtext><mn mathvariant="bold">500</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">70\,000 \times (1 - 0{,}25) =325        \uqogreen{52\,500~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">70</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">25</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">52</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">500</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</li><li>Total de l'élément : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>42</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>52</mn><mtext> </mtext><mn>500</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">94</mn><mtext> </mtext><mn mathvariant="bold">500</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">42\,000 + 52\,500 = \uqogreen{94\,500~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">42</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">52</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">94</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">500</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.         Vérification d'ordre de grandeur : la perte approche le coût neuf de         l'élément (<span class="num">110 000 $</span>) — cohérent pour un équipement que le         marché local ne valorise presque pas et qui coûte cher à exploiter.         Ne pas oublier : les <span class="num">33 000 $</span> de dépréciation physique de la         piscine sont comptés <em>ici</em> et doivent être exclus de la         ventilation physique générale.</li></ol></div></details>326<div class="box box-exo" id="exo-11-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 11.4</span><span class="box-title">— obsolescence de conception — commercial</span><a class="box-anchor" href="#exo-11-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-121">Un immeuble de bureaux de <span class="num">12 000</span> pi<sup>2</sup> à Gatineau souffre de deux défauts structurels : absence d'ascenseur (deux étages) et fenestration insuffisante au deuxième étage. Loyer obtenu : 14,50 $/pi<sup>2</sup>/an; loyer des immeubles comparables sans ces défauts : 16,25 $/pi<sup>2</sup>/an. Hypothèses : TGA de 7,5 %; valeur du terrain <span class="num">380 000 $</span>; valeur totale de la propriété (avant dépréciation fonctionnelle) <span class="num">2 100 000 $</span>.</p>327<ol class="enum"><li>Calculez la perte de loyer annuelle.</li><li>Calculez la dépréciation fonctionnelle incurable de conception.</li><li>Pourquoi ne pas plutôt chiffrer l'installation d'un ascenseur?</li></ol></div></div>328<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>16,25</mn><mo>−</mo><mn>14,50</mn><mo stretchy="false">)</mo><mo>×</mo><mn>12</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>1,75</mn><mo>×</mo><mn>12</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">21</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi><mi mathvariant="bold">/</mi><mi mathvariant="bold">a</mi><mi mathvariant="bold">n</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">(16{,}25 - 14{,}50) \times 12\,000 = 1{,}75 \times 12\,000 =329        \uqogreen{21\,000~\$/an}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">16</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">25</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">14</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">50</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">75</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">21</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$/an</span></span></span></span></span>.</li><li>Perte capitalisée : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>21</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>0,075</mn><mo>=</mo><mn>280</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">21\,000 \div 0{,}075 = 280\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">21</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">075</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">280</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>. Ratio         terrain : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>380</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>2</mn><mtext> </mtext><mn>100</mn><mtext> </mtext><mn>000</mn><mo>≈</mo><mn>18,1</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">380\,000 \div 2\,100\,000 \approx 18{,}1\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">380</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">100</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">18</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>; portion         terrain <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>280</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>18,1</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>≈</mo><mn>50</mn><mtext> </mtext><mn>667</mn></mrow><annotation encoding="application/x-tex">= 280\,000 \times 18{,}1\,\% \approx 50\,667</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">280</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">18</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">667</span></span></span></span>.         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>conception</mtext></msub><mo>=</mo><mn>280</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>50</mn><mtext> </mtext><mn>667</mn><mo>≈</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">229</mn><mtext> </mtext><mn mathvariant="bold">333</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">D_{\text{conception}} = 280\,000 - 50\,667 \approx330        \uqogreen{229\,333~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">conception</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">280</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">667</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">229</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">333</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</li><li>Parce que la déficience est présumée <strong>incurable</strong> : le coût         d'insérer un ascenseur et de refaire la fenestration dans la         structure existante excéderait la valeur ajoutée. On mesure donc la         perte subie (capitalisation), pas un coût de correction que nul         n'engagerait. Si une vérification montrait que la correction coûte         <em>moins</em> que la valeur ajoutée, la déficience basculerait en         curable–substitution et se mesurerait alors par le coût de         correction.</li></ol></div></details>331<div class="box box-exo" id="exo-11-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 11.5</span><span class="box-title">— cas intégrateur — maison d'Aylmer</span><a class="box-anchor" href="#exo-11-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-128">Maison à deux étages (1978), Aylmer (Gatineau) : trois chambres, une salle de bain, garage simple, secteur haut de gamme. Coût de remplacement : <span class="num">350 000 $</span>; terrain : <span class="num">110 000 $</span>. Hypothèses du cas : portion terrain 24 %; TGA de 5,5 % (2026).</p>332<ol class="enum"><li><strong>Ajout</strong> — salle d'eau au rez-de-chaussée : coût dans         l'existant <span class="num">15 000 $</span>; valeur ajoutée <span class="num">20 000 $</span>.</li><li><strong>Substitution</strong> — mazout <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>→</mo></mrow><annotation encoding="application/x-tex">\rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">→</span></span></span></span> thermopompe :         existant <span class="num">22 000 $</span>; neuf <span class="num">9000 $</span>; récupération         <span class="num">300 $</span>.</li><li><strong>Superadéquation</strong> — piscine creusée : coût neuf         <span class="num">65 000 $</span>; dépréciation physique 20 %; contribution         <span class="num">20 000 $</span>.</li><li><strong>Conception</strong> — cuisine fermée : perte de loyer de         175 $/mois.</li></ol>333<p id="p11-133">Calculez la dépréciation fonctionnelle totale et commentez l'ordre de grandeur.</p></div></div>334<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p11-134"><strong>Volet curable.</strong> Salle d'eau : test <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>20</mn><mtext> </mtext><mn>000</mn><mo>&gt;</mo><mn>15</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">20\,000 &gt; 15\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6835em;vertical-align:-0.0391em;"></span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span> curable; dépréciation <span class="num">15 000 $</span> (coût dans l'existant). Chauffage : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>22</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>9</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>300</mn><mo>=</mo><mn>12</mn><mtext> </mtext><mn>700</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">22\,000 - 9\,000 - 300 = 12\,700\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">300</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">700</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Sous-total curable : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">27</mn><mtext> </mtext><mn mathvariant="bold">700</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">\uqogreen{27\,700~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">27</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">700</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</p>335<p id="p11-135"><strong>Volet incurable.</strong> Piscine : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>65</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>13</mn><mtext> </mtext><mn>000</mn><mtext>  </mtext><mo stretchy="false">(</mo><mn>20</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo stretchy="false">)</mo><mo>−</mo><mn>20</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>32</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">65\,000 - 13\,000\;(20\,\%) - 20\,000 = 32\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">65</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">13</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mopen">(</span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">32</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Cuisine fermée : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>175</mn><mo>×</mo><mn>12</mn><mo stretchy="false">)</mo><mo>÷</mo><mn>0,055</mn><mo>=</mo><mn>38</mn><mtext> </mtext><mn>182</mn></mrow><annotation encoding="application/x-tex">(175 \times 12) \div 0{,}055 = 38\,182</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">175</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">12</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">055</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">38</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">182</span></span></span></span>; moins portion terrain 24 % (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>9</mn><mtext> </mtext><mn>164</mn></mrow><annotation encoding="application/x-tex">9\,164</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">164</span></span></span></span>) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>29</mn><mtext> </mtext><mn>018</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 29\,018\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">29</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">018</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Sous-total incurable : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">61</mn><mtext> </mtext><mn mathvariant="bold">018</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">\uqogreen{61\,018~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">61</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">018</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</p>336<p id="p11-136"><strong>Total :</strong></p>337<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><menclose notation="box"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mrow><msub><mi>D</mi><mtext>fonctionnelle</mtext></msub><mo>=</mo><mn>27</mn><mtext> </mtext><mn>700</mn><mo>+</mo><mn>61</mn><mtext> </mtext><mn>018</mn><mo>=</mo><mrow><mtext mathvariant="bold">88</mtext><mtext> </mtext><mtext mathvariant="bold">718</mtext><mtext> </mtext><mtext mathvariant="bold">$</mtext></mrow></mrow></mstyle></mstyle></mstyle></menclose></mrow><annotation encoding="application/x-tex">\boxed{D_{\text{fonctionnelle}} = 27\,700 + 61\,018 = \textbf{88\,718~\$}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.58em;vertical-align:-0.49em;"></span><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.09em;"><span style="top:-3.58em;"><span class="pstrut" style="height:3.58em;"></span><span class="boxpad"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">fonctionnelle</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">27</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">700</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">61</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">018</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord textbf">88</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">718</span><span class="mord textbf nobreak"> </span><span class="mord textbf">$</span></span></span></span></span></span><span style="top:-3.09em;"><span class="pstrut" style="height:3.58em;"></span><span class="katex-stretchy fbox" style="height:1.58em;border-style:solid;border-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.49em;"><span></span></span></span></span></span></span></span></span></span></div>338<p id="p11-137">Ordre de grandeur : environ 25 % du coût de remplacement (<span class="num">350 000 $</span>) — plausible pour une construction de 1978 au plan et aux équipements d'origine dans un secteur haut de gamme exigeant.</p></div></details>339<div class="box box-exo" id="exo-11-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 11.6</span><span class="box-title">— chasse au double comptage</span><a class="box-anchor" href="#exo-11-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-138">Un rapport d'évaluation contient les postes suivants pour une même maison (coût de <em>remplacement</em> retenu comme coût neuf) : (a) ventilation physique : incurable CT sur le système de chauffage au mazout (coût neuf <span class="num">12 000 $</span>, ratio 80 %, soit <span class="num">9600 $</span>); (b) fonctionnelle curable–substitution : remplacement du même chauffage au mazout, <span class="num">14 300 $</span>; (c) fonctionnelle : <span class="num">7500 $</span> pour « matériaux désuets » (revêtements intérieurs d'origine), alors que le coût de remplacement retenu est déjà fondé sur des matériaux modernes; (d) superadéquation d'un foyer de pierre : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>28</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>5</mn><mtext> </mtext><mn>600</mn></mrow><annotation encoding="application/x-tex">28\,000 - 5\,600</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">28</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span></span></span></span> (physique) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>12</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">- 12\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">12</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span> (contribution) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>10</mn><mtext> </mtext><mn>400</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 10\,400\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>, et la même dépréciation physique de <span class="num">5600 $</span> figure aussi dans la ventilation physique générale. Identifiez chaque double comptage et corrigez le total fonctionnel<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>physique en conséquence.</p></div></div>340<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li class="labeled"><span class="li-label">(a)<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>(b)</span><div class="li-body"><strong class="c-rouge">Physique et fonctionnelle</strong> : le chauffage traité         en substitution fonctionnelle ne doit pas aussi porter         <span class="num">9600 $</span> d'incurable CT. On retire <span class="num">9600 $</span> de la         ventilation physique (et l'assiette du long terme doit être         recalculée en conséquence).</div></li><li class="labeled"><span class="li-label">(c)</span><div class="li-body"><strong class="c-rouge">Remplacement et fonctionnelle</strong> : les matériaux         désuets sont déjà éliminés du coût de remplacement; les         <span class="num">7500 $</span> sont retirés.</div></li><li class="labeled"><span class="li-label">(d)</span><div class="li-body"><strong class="c-rouge">Superadéquation et physique</strong> : les <span class="num">5600 $</span> de         dépréciation physique du foyer se comptent une seule fois, dans le         poste superadéquation; on les retire de la ventilation physique         générale.</div></li></ol>341<p id="p11-142">Correction nette : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>9</mn><mtext> </mtext><mn>600</mn><mo>−</mo><mn>7</mn><mtext> </mtext><mn>500</mn><mo>−</mo><mn>5</mn><mtext> </mtext><mn>600</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mo>−</mo><mn mathvariant="bold">22</mn><mtext> </mtext><mn mathvariant="bold">700</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">-9\,600 - 7\,500 - 5\,600 = \uqogreen{-22\,700~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">9</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">7</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.0833em;"></span><span class="mord" style="color:#107C4E;"><span class="mord" style="color:#107C4E;">−</span><span class="mord mathbf" style="color:#107C4E;">22</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">700</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span> sur le total combiné (avant recalcul du long terme). Le rapport initial sous-évaluait la propriété d'au moins <span class="num">22 700 $</span> — l'ampleur typique que peuvent atteindre des doubles comptages non détectés.</p></div></details>342<h2 class="h-section" id="s-12"><span class="h-num">12</span><span class="h-text">Dépréciation économique (externe)</span></h2>343<div class="box box-exo" id="exo-12-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 12.1</span><span class="box-title">— qualifier la dépréciation</span><a class="box-anchor" href="#exo-12-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-89">Pour chaque situation, dites s'il s'agit d'une dépréciation <strong>économique (externe)</strong>, <strong>fonctionnelle</strong>, <strong>physique</strong> — ou d'aucune dépréciation au sens de la méthode du coût. Justifiez brièvement.</p>344<ol class="enum"><li>Le terrain du sujet est contaminé aux hydrocarbures.</li><li>Le terrain voisin du sujet est contaminé et inscrit au répertoire du         MELCCFP.</li><li>La Ville rezone le secteur : le potentiel passe de 15 logements à         3 unifamiliales.</li><li>Le marché locatif local traverse un creux cyclique de 18 mois lié à         une suroffre temporaire de condos.</li><li>L'immeuble n'a qu'une salle de bain pour quatre chambres.</li><li>Une papetière, principal employeur de la ville, ferme         définitivement.</li></ol></div></div>345<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li><strong>Physique</strong> (de la propriété) : la contamination du propre         terrain du sujet est un état de la propriété, pas un facteur         externe.</li><li><strong>Économique</strong> : facteur extérieur, hors du contrôle du         propriétaire (stigmatisation de voisinage).</li><li><strong>Économique</strong> (réglementaire) : perte de potentiel imposée de         l'extérieur, toujours incurable.</li><li><strong class="c-rouge">Aucune</strong> : condition <strong>cyclique</strong> temporaire; seuls         les changements structurels fondent une dépréciation économique —         et l'effet du creux est probablement déjà dans les comparables.</li><li><strong>Fonctionnelle</strong> : défaut interne de conception (chapitre 11).</li><li><strong>Économique</strong> (facteur de marché structurel) : perte         d'employeur majeur, mesurable par capitalisation ou ventes         appariées.</li></ol></div></details>346<div class="box box-exo" id="exo-12-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 12.2</span><span class="box-title">— capitalisation de la perte de revenus</span><a class="box-anchor" href="#exo-12-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-102">Un immeuble de dix logements à Buckingham borde une nouvelle voie de camionnage lourd. Loyer normal des comparables non affectés : 1 250 $/mois par logement; loyer réel obtenu : 1 120 $/mois; ratio de dépenses : 38 % du revenu brut. Hypothèses du cas : TGA de 5,75 %; ratio terrain/propriété de 22 % (valeur du terrain issue de comparables non affectés).</p>347<ol class="enum"><li>Calculez la perte de revenu net annuelle.</li><li>Calculez la dépréciation économique totale.</li><li>Allouez entre terrain et améliorations, et indiquez le montant à         déduire du coût neuf.</li></ol></div></div>348<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>Perte brute <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mtext> </mtext><mn>250</mn><mo>−</mo><mn>1</mn><mtext> </mtext><mn>120</mn><mo stretchy="false">)</mo><mo>×</mo><mn>12</mn><mo>×</mo><mn>10</mn><mo>=</mo><mn>15</mn><mtext> </mtext><mn>600</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><mtext>an</mtext></mrow><annotation encoding="application/x-tex">= (1\,250 - 1\,120) \times 12 \times 10 =349        15\,600\,\$/\text{an}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">250</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">120</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$/</span><span class="mord text"><span class="mord">an</span></span></span></span></span>; perte nette         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>15</mn><mtext> </mtext><mn>600</mn><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mn>0,38</mn><mo stretchy="false">)</mo><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">9</mn><mtext> </mtext><mn mathvariant="bold">672</mn><mtext> </mtext><mi mathvariant="bold">$</mi><mi mathvariant="bold">/</mi><mi mathvariant="bold">a</mi><mi mathvariant="bold">n</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= 15\,600 \times (1 - 0{,}38) = \uqogreen{9\,672~\$/an}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">38</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">9</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">672</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$/an</span></span></span></span></span>.</li><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>totale</mtext></msub><mo>=</mo><mn>9</mn><mtext> </mtext><mn>672</mn><mo>÷</mo><mn>0,0575</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">168</mn><mtext> </mtext><mn mathvariant="bold">209</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">D_{\text{totale}} = 9\,672 \div 0{,}0575 =350        \uqogreen{168\,209~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">672</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0575</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">168</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">209</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</li><li>Portion terrain <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>168</mn><mtext> </mtext><mn>209</mn><mo>×</mo><mn>22</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mn>37</mn><mtext> </mtext><mn>006</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 168\,209 \times 22\,\% = 37\,006\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">168</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">209</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">37</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">006</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> (reflétée         dans la valeur du terrain, puisque les comparables de terrain sont         non affectés); portion améliorations         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>168</mn><mtext> </mtext><mn>209</mn><mo>×</mo><mn>78</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">131</mn><mtext> </mtext><mn mathvariant="bold">203</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= 168\,209 \times 78\,\% = \uqogreen{131\,203~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">168</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">209</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">131</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">203</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span> — seul ce         montant se déduit du coût neuf.</li></ol></div></details>351<div class="box box-exo" id="exo-12-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 12.3</span><span class="box-title">— ventes appariées et fiabilité</span><a class="box-anchor" href="#exo-12-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-109">Pour mesurer l'impact d'un poste de transformation électrique, un évaluateur réunit cinq paires de ventes : différences de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>28 000, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>31 000, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>26 000, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>34 000 et <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>29 000 $ sur des propriétés non affectées se vendant en moyenne <span class="num">310 000 $</span>.</p>352<ol class="enum"><li>Calculez la dépréciation moyenne en dollars et en pourcentage.</li><li>La médiane et la dispersion appuient-elles la conclusion?</li><li>Un collègue propose plutôt une seule « super-paire » très propre         montrant <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>52 000 $. Que lui répondez-vous?</li></ol></div></div>353<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>Moyenne <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mo stretchy="false">(</mo><mn>28</mn><mo>+</mo><mn>31</mn><mo>+</mo><mn>26</mn><mo>+</mo><mn>34</mn><mo>+</mo><mn>29</mn><mo stretchy="false">)</mo><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>5</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">29</mn><mtext> </mtext><mn mathvariant="bold">600</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= (28 + 31 + 26 + 34 + 29)\,000 \div 5 =354        \uqogreen{29\,600~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">28</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">31</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">26</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">34</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">29</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">29</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">600</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>, soit <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>29</mn><mtext> </mtext><mn>600</mn><mo>÷</mo><mn>310</mn><mtext> </mtext><mn>000</mn><mo>≈</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">9,5</mn><mtext> </mtext><mi mathvariant="bold">%</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">29\,600 \div 310\,000 \approx355        \uqogreen{9{,}5\,\%}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">29</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">310</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">9</span><span class="mord" style="color:#107C4E;"><span class="mpunct" style="color:#107C4E;">,</span></span><span class="mord mathbf" style="color:#107C4E;">5</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">%</span></span></span></span></span>.</li><li>Médiane <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>29</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 29\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">29</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>, proche de la moyenne; étendue de 26 000 à         34 000 (dispersion modérée, signe constant) : la conclusion         d'environ 9 à 10 % est <strong>robuste</strong> — cinq paires         cohérentes valent mieux qu'une moyenne isolée.</li><li>Une paire unique, si « propre » soit-elle, ne permet ni de mesurer         la dispersion ni d'exclure un facteur idiosyncratique (vente         pressée, rénovation cachée). L'écart de la super-paire         (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>52 000 $, soit près de 17 %) s'éloigne nettement du faisceau         des cinq autres : elle mérite d'être examinée, pas de gouverner la         conclusion. Privilégier la <strong>cohérence</strong> de l'échantillon.</li></ol></div></details>356<div class="box box-exo" id="exo-12-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 12.4</span><span class="box-title">— allocation et double comptage</span><a class="box-anchor" href="#exo-12-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-116">Une maison borde une emprise ferroviaire. Dépréciation économique totale mesurée par ventes appariées : <span class="num">45 000 $</span>. Coût de remplacement déprécié (physique et fonctionnelle déjà déduites) : <span class="num">265 000 $</span>.</p>357<ol class="enum"><li><strong>Scénario A</strong> : la valeur du terrain (<span class="num">90 000 $</span>)         provient de comparables <strong>non affectés</strong> par la voie ferrée.         Calculez l'allocation et la valeur finale.</li><li><strong>Scénario B</strong> : la valeur du terrain (<span class="num">78 500 $</span>)         provient de comparables <strong>eux-mêmes bordant la voie ferrée</strong>.         Que change ce fait? Calculez la valeur finale.</li></ol></div></div>358<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>Valeur totale avant dépréciation externe         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>90</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>265</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>355</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 90\,000 + 265\,000 = 355\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">90</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">265</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">355</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; ratio terrain         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>90</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>355</mn><mtext> </mtext><mn>000</mn><mo>≈</mo><mn>25,4</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">= 90\,000 \div 355\,000 \approx 25{,}4\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">90</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">355</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">25</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">4</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>. Portion terrain         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>45</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>25,4</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>≈</mo><mn>11</mn><mtext> </mtext><mn>430</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 45\,000 \times 25{,}4\,\% \approx 11\,430\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">45</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">25</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">4</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">11</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">430</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; portion         améliorations <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>33</mn><mtext> </mtext><mn>570</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\approx 33\,570\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">33</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">570</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Valeur finale : terrain         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>90</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>11</mn><mtext> </mtext><mn>430</mn><mo>=</mo><mn>78</mn><mtext> </mtext><mn>570</mn></mrow><annotation encoding="application/x-tex">90\,000 - 11\,430 = 78\,570</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">90</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">11</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">430</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">570</span></span></span></span>; améliorations         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>265</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>33</mn><mtext> </mtext><mn>570</mn><mo>=</mo><mn>231</mn><mtext> </mtext><mn>430</mn></mrow><annotation encoding="application/x-tex">265\,000 - 33\,570 = 231\,430</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">265</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">33</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">570</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">231</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">430</span></span></span></span>;         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>≈</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">310</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">V \approx \uqogreen{310\,000~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">310</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</li><li>Les comparables affectés reflètent <strong>déjà</strong> la portion terrain         de la dépréciation (d'ailleurs <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>78</mn><mtext> </mtext><mn>500</mn><mo>≈</mo><mn>78</mn><mtext> </mtext><mn>570</mn></mrow><annotation encoding="application/x-tex">78\,500 \approx 78\,570</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">570</span></span></span></span> du         scénario A). Déduire de nouveau la portion terrain serait un         <strong class="c-rouge">double comptage</strong>. On ne déduit que la portion         améliorations (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>33</mn><mtext> </mtext><mn>570</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\approx 33\,570\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">33</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">570</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>) :         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mn>78</mn><mtext> </mtext><mn>500</mn><mo>+</mo><mo stretchy="false">(</mo><mn>265</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>33</mn><mtext> </mtext><mn>570</mn><mo stretchy="false">)</mo><mo>=</mo><mn>78</mn><mtext> </mtext><mn>500</mn><mo>+</mo><mn>231</mn><mtext> </mtext><mn>430</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">309</mn><mtext> </mtext><mn mathvariant="bold">930</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">V = 78\,500 + (265\,000 - 33\,570) = 78\,500 + 231\,430 =359        \uqogreen{309\,930~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">265</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">33</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">570</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">231</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">430</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">309</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">930</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span> — même conclusion, deux chemins. L'erreur         (déduire deux fois) aurait amputé la valeur d'environ         <span class="num">11 400 $</span>.</li></ol></div></details>360<div class="box box-exo" id="exo-12-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 12.5</span><span class="box-title">— cas intégrateur — entreposage de matières résiduelles</span><a class="box-anchor" href="#exo-12-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-121">Un immeuble commercial de trois étages à Gatineau se trouve à 100 m d'un nouveau site d'entreposage de matières résiduelles (données fictives). Revenu net : <span class="num">95 000 $</span>/an avant la nuisance, <span class="num">78 000 $</span>/an après. Hypothèse du cas : TGA de 6,5 % (2026). Coût de remplacement (après dépréciations physique et fonctionnelle) : <span class="num">650 000 $</span>; valeur du terrain (comparables non affectés) : <span class="num">200 000 $</span>.</p>361<ol class="enum"><li>Calculez la dépréciation économique totale.</li><li>Déterminez la portion améliorations.</li><li>Calculez la valeur finale de la propriété.</li></ol></div></div>362<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>Perte de revenu net <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>95</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>78</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>17</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><mtext>an</mtext></mrow><annotation encoding="application/x-tex">= 95\,000 - 78\,000 = 17\,000\,\$/\text{an}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">95</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">17</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$/</span><span class="mord text"><span class="mord">an</span></span></span></span></span>;         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>totale</mtext></msub><mo>=</mo><mn>17</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>0,065</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">261</mn><mtext> </mtext><mn mathvariant="bold">538</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">D_{\text{totale}} = 17\,000 \div 0{,}065 =363        \uqogreen{261\,538~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">17</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">065</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">261</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">538</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</li><li>Ratio améliorations <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>650</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>850</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>76,5</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">= 650\,000 \div 850\,000 = 76{,}5\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">650</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">850</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">76</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> :         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mrow><mtext>am</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>l.</mtext></mrow></msub><mo>=</mo><mn>261</mn><mtext> </mtext><mn>538</mn><mo>×</mo><mn>650</mn><mi mathvariant="normal">/</mi><mn>850</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">200</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">D_{\text{amél.}} = 261\,538 \times 650/850 =364        \uqogreen{200\,000~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">am</span><span class="mord katex-accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight">e</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˊ</span></span></span></span></span></span></span><span class="mord mtight">l.</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">261</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">538</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">650/850</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">200</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>; portion terrain         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>261</mn><mtext> </mtext><mn>538</mn><mo>×</mo><mn>200</mn><mi mathvariant="normal">/</mi><mn>850</mn><mo>=</mo><mn>61</mn><mtext> </mtext><mn>538</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 261\,538 \times 200/850 = 61\,538\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">261</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">538</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">200/850</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">61</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">538</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>.</li><li>Améliorations : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>650</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>200</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>450</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">650\,000 - 200\,000 = 450\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">650</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">450</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; terrain :         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>200</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>61</mn><mtext> </mtext><mn>538</mn><mo>=</mo><mn>138</mn><mtext> </mtext><mn>462</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">200\,000 - 61\,538 = 138\,462\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">61</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">538</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">138</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">462</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>;         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">588</mn><mtext> </mtext><mn mathvariant="bold">462</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle><mo>≈</mo><mn>588</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">V = \uqogreen{588\,462~\$} \approx 588\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">588</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">462</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">588</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>.</li></ol></div></details>365<div class="box box-exo" id="exo-12-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 12.6</span><span class="box-title">— synthèse du bloc dépréciation</span><a class="box-anchor" href="#exo-12-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-128">Un cottage de 1982 à Hull présente : coût de remplacement neuf <span class="num">390 000 $</span>; valeur du terrain <span class="num">95 000 $</span> (comparables non affectés). Dépréciations mesurées : physique curable <span class="num">14 000 $</span>; physique incurable <span class="num">88 000 $</span>; fonctionnelle curable <span class="num">11 000 $</span>; fonctionnelle incurable <span class="num">21 000 $</span>; dépréciation économique totale <span class="num">29 000 $</span> (nuisance de circulation, ventes appariées). Hypothèse : ratio terrain/propriété de 19,6 % (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>95</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>485</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">95\,000 \div 485\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">95</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">485</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>).</p>366<ol class="enum"><li>Allouez la dépréciation économique.</li><li>Dressez le tableau séquentiel complet des déductions et concluez la         valeur par la méthode du coût.</li><li>Quel pourcentage du coût neuf la dépréciation totale des         améliorations représente-t-elle?</li></ol></div></div>367<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>Portion terrain <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>29</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>19,6</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>≈</mo><mn>5</mn><mtext> </mtext><mn>684</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 29\,000 \times 19{,}6\,\% \approx 5\,684\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">29</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">19</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">6</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">684</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>;         portion améliorations <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>29</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>5</mn><mtext> </mtext><mn>684</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">23</mn><mtext> </mtext><mn mathvariant="bold">316</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= 29\,000 - 5\,684 =368        \uqogreen{23\,316~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">29</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">684</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">23</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">316</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</li><li>Déductions sur les améliorations :         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>14</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>88</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>11</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>21</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>23</mn><mtext> </mtext><mn>316</mn><mo>=</mo><mn>157</mn><mtext> </mtext><mn>316</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">14\,000 + 88\,000 + 11\,000 + 21\,000 + 23\,316 = 157\,316\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">14</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">88</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">11</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">21</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">23</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">316</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">157</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">316</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>.         Améliorations : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>390</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>157</mn><mtext> </mtext><mn>316</mn><mo>=</mo><mn>232</mn><mtext> </mtext><mn>684</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">390\,000 - 157\,316 = 232\,684\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">390</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">157</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">316</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">232</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">684</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Terrain         ajusté : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>95</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>5</mn><mtext> </mtext><mn>684</mn><mo>=</mo><mn>89</mn><mtext> </mtext><mn>316</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">95\,000 - 5\,684 = 89\,316\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">95</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">684</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">89</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">316</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>.</p>369<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>V</mi><mo>=</mo><mn>89</mn><mtext> </mtext><mn>316</mn><mo>+</mo><mn>232</mn><mtext> </mtext><mn>684</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">322</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">V = 89\,316 + 232\,684 = \uqogreen{322\,000~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">89</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">316</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">232</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">684</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">322</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span></span></div>370<p id="p12-134">•  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>157</mn><mtext> </mtext><mn>316</mn><mo>÷</mo><mn>390</mn><mtext> </mtext><mn>000</mn><mo>≈</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">40,3</mn><mtext> </mtext><mi mathvariant="bold">%</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">157\,316 \div 390\,000 \approx \uqogreen{40{,}3\,\%}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">157</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">316</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">390</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">40</span><span class="mord" style="color:#107C4E;"><span class="mpunct" style="color:#107C4E;">,</span></span><span class="mord mathbf" style="color:#107C4E;">3</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">%</span></span></span></span></span> —         plausible pour un cottage de 44 ans portant les trois formes de         dépréciation. Réflexe final de l'évaluateur : confronter ces         <span class="num">322 000 $</span> aux indications des méthodes de comparaison et du         revenu avant de conclure le rapport.</li></ol></div></details>371<h2 class="h-section" id="s-13"><span class="h-num">13</span><span class="h-text">Applications spécialisées</span></h2>372<div class="box box-exo" id="exo-13-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 13.1</span><span class="box-title">— base de coût d'une église classée</span><a class="box-anchor" href="#exo-13-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p13-124">Une église <strong>classée</strong> en vertu de la Loi sur le patrimoine culturel doit être assurée « à sa juste valeur de reconstruction ». Par ailleurs, la fabrique souhaite connaître la valeur marchande de l'immeuble en vue d'une vente éventuelle à un promoteur (conversion en salle de spectacle). Indiquez la base de coût appropriée pour chacun des deux mandats et justifiez.</p></div></div>373<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p13-125"><strong>Assurance</strong> : coût de <strong>reproduction</strong>. Le statut de classement impose une remise en état à l'identique (matériaux d'origine, techniques artisanales); l'indemnité doit permettre de reconstruire ce qui existait. <strong>Valeur marchande</strong> : coût de <strong>remplacement</strong> — et, en réalité, l'analyse dominante sera celle de l'utilisation optimale après conversion : la valeur dépendra du projet de salle de spectacle (revenus potentiels, coût de conversion), le coût de remplacement servant de balise. Dans les deux rapports, la base retenue doit être explicitement énoncée : entre reproduction et remplacement, la valeur peut varier du simple au double (voir l'exemple de l'église de 1925).</p></div></details>374<div class="box box-exo" id="exo-13-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 13.2</span><span class="box-title">— pont roulant — entretien déficient</span><a class="box-anchor" href="#exo-13-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p13-126">Reprenez le pont roulant de la section <a class="xref" href="/seance/13/#s-13-7">13.7</a> (coût installé <span class="num">425 000 $</span>, vie économique 30 ans), mais supposez cette fois un entretien déficient : âge réel 18 ans, âge effectif <strong>24 ans</strong>. De plus, la capacité de 20 tonnes est devenue insuffisante pour les besoins de l'usine, qui loue une grue mobile d'appoint <span class="num">9000 $</span> par année (taux de capitalisation applicable : 7,5 %). Calculez la valeur dépréciée du pont roulant.</p></div></div>375<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p13-127"><strong>Physique (âge/vie)</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>phys</mtext></msub><mo>=</mo><mn>425</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>24</mn><mi mathvariant="normal">/</mi><mn>30</mn><mo>=</mo><mn>425</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>80</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mn>340</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">D_{\text{phys}} = 425~000 \times 24/30 = 425~000 \times 80\,\% =376340~000~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">phys</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">425</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">24/30</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">425</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">80</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">340</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>. <strong>Fonctionnelle incurable</strong> (capacité insuffisante, mesurée par la capitalisation du coût d'appoint) : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>fonc</mtext></msub><mo>=</mo><mn>9</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>0,075</mn><mo>=</mo><mn>120</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">D_{\text{fonc}} = 9~000 / 0{,}075 = 120~000~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">fonc</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">9</span><span class="mspace nobreak"> </span><span class="mord">000/0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">075</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">120</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>, plafonnée à la valeur restante : après la physique, il ne reste que <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>425</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>340</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>85</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">425~000 - 340~000 = 85~000~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">425</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">340</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">85</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>. La dépréciation totale ne peut excéder le coût neuf : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>fonc</mtext></msub></mrow><annotation encoding="application/x-tex">D_{\text{fonc}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">fonc</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> retenue <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>85</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 85~000~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">85</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>. <strong>Valeur dépréciée</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>425</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>340</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>85</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">0</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= 425~000 - 340~000 - 85~000 =377\uqogreen{0~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">425</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">340</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">85</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">0</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>. Interprétation : l'équipement ne contribue plus à la valeur de l'immeuble; sa vie économique est terminée même si sa vie physique ne l'est pas. C'est l'illustration du plafond « dépréciation totale <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≤</mo></mrow><annotation encoding="application/x-tex">\le</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mrel">≤</span></span></span></span> coût neuf » et de la distinction durée physique / durée économique.</p></div></details>378<div class="box box-exo" id="exo-13-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 13.3</span><span class="box-title">— améliorations locatives d'un restaurant</span><a class="box-anchor" href="#exo-13-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p13-128">Un restaurateur a investi <span class="num">480 000 $</span> en améliorations locatives (cuisine, ventilation, salle) dans un local loué. Durée de vie physique des aménagements : 12 ans. Bail : 10 ans, signé il y a 6 ans, avec une option de renouvellement de 5 ans que le locataire exercera très probablement (emplacement stratégique, achalandage établi). Calculez la dépréciation et la valeur des améliorations : a) sans tenir compte de l'option; b) en tenant compte de l'option. Commentez.</p></div></div>379<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p13-129"><strong>a) Sans l'option.</strong> Bail restant : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>10</mn><mo>−</mo><mn>6</mn><mo>=</mo><mn>4</mn></mrow><annotation encoding="application/x-tex">10 - 6 = 4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">6</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">4</span></span></span></span> ans. Dénominateur <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mi>min</mi><mo>⁡</mo><mo stretchy="false">(</mo><mn>12</mn><mo separator="true">,</mo><mtext> </mtext><mn>4</mn><mo stretchy="false">)</mo><mo>=</mo><mn>4</mn></mrow><annotation encoding="application/x-tex">= \min(12,\ 4) = 4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">min</span><span class="mopen">(</span><span class="mord">12</span><span class="mpunct">,</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">4</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">4</span></span></span></span>... mais attention : la formule utilise l'âge effectif sur la durée limitante <em>totale</em> pertinente. Approche usuelle : durée utile <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mi>min</mi><mo>⁡</mo><mo stretchy="false">(</mo><mtext>vie physique</mtext><mo separator="true">,</mo><mtext> terme initial</mtext><mo stretchy="false">)</mo><mo>=</mo><mi>min</mi><mo>⁡</mo><mo stretchy="false">(</mo><mn>12</mn><mo separator="true">,</mo><mn>10</mn><mo stretchy="false">)</mo><mo>=</mo><mn>10</mn></mrow><annotation encoding="application/x-tex">= \min(\text{vie physique},\ \text{terme initial}) = \min(12, 10)380= 10</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">min</span><span class="mopen">(</span><span class="mord text"><span class="mord">vie physique</span></span><span class="mpunct">,</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">terme initial</span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">min</span><span class="mopen">(</span><span class="mord">12</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">10</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">10</span></span></span></span> ans; âge 6 ans <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo><mi>D</mi><mo>=</mo><mn>6</mn><mi mathvariant="normal">/</mi><mn>10</mn><mo>=</mo><mn>60</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">\Rightarrow D = 6/10 = 60\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">6/10</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">60</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>; valeur <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>480</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,40</mn><mo>=</mo><mn>192</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 480~000 \times 0{,}40 = 192~000~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">480</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">40</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">192</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span> — à amortir toutefois sur les 4 ans restants seulement. <strong>b) Avec l'option probable.</strong> Durée utile <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mi>min</mi><mo>⁡</mo><mo stretchy="false">(</mo><mn>12</mn><mo separator="true">,</mo><mtext> </mtext><mn>10</mn><mo>+</mo><mn>5</mn><mo stretchy="false">)</mo><mo>=</mo><mn>12</mn></mrow><annotation encoding="application/x-tex">= \min(12,\ 10 + 5) = 12</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">min</span><span class="mopen">(</span><span class="mord">12</span><span class="mpunct">,</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">5</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">12</span></span></span></span> ans (la vie physique devient limitante); <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo>=</mo><mn>6</mn><mi mathvariant="normal">/</mi><mn>12</mn><mo>=</mo><mn>50</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">D = 6/12 = 50\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">6/12</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>; valeur <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>480</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,50</mn><mo>=</mo><mn>240</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 480~000 \times 0{,}50 = 240~000~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">480</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">50</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">240</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>. <strong>Commentaire.</strong> La probabilité d'exercice de l'option ajoute ici 48 000 $ de valeur : l'évaluateur doit juger cette probabilité et la documenter (achalandage, clauses, loyer d'option vs marché). Sans option, les aménagements très spécifiques (cuisine) perdraient l'essentiel de leur valeur à l'échéance — pour le propriétaire, leur valeur résiduelle serait faible.</p></div></details>381<div class="box box-exo" id="exo-13-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 13.4</span><span class="box-title">— entrepôt — hauteur libre insuffisante</span><a class="box-anchor" href="#exo-13-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p13-130">Un entrepôt de <span class="num">4000</span> m<sup>2</sup> (structure acier, 2005) offre une hauteur libre de 5,5 m dans un marché où le standard moderne est de 8 m. Le loyer des entrepôts modernes du secteur est de 95 $/m<sup>2</sup>/an; l'immeuble sujet ne peut obtenir que 82 $/m<sup>2</sup>/an. Taux de capitalisation : 6,5 %. Rehausser la toiture coûterait environ 2,4 M$. a) La déficience est-elle curable? b) Calculez la dépréciation fonctionnelle. c) De quel type de dépréciation s'agirait-il si la perte de loyer venait plutôt d'un taux d'inoccupation généralisé dans le secteur?</p></div></div>382<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p13-131"><strong>a)</strong> Perte de loyer : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>95</mn><mo>−</mo><mn>82</mn><mo stretchy="false">)</mo><mo>×</mo><mn>4</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>52</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><mtext>an</mtext></mrow><annotation encoding="application/x-tex">(95 - 82) \times 4~000 = 52~000~\$/\text{an}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">95</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">82</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">4</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">52</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord text"><span class="mord">an</span></span></span></span></span>; valeur de la correction <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>52</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>0,065</mn><mo>=</mo><mn>800</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 52~000 / 0{,}065 = 800~000~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">52</span><span class="mspace nobreak"> </span><span class="mord">000/0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">065</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">800</span><span class="mspace nobreak"> </span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>. Coût de correction (2,4 M$) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>&gt;</mo></mrow><annotation encoding="application/x-tex">&gt;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">&gt;</span></span></span></span> valeur ajoutée (0,8 M$) : déficience <strong class="c-rouge">incurable</strong>. <strong>b)</strong> Dépréciation fonctionnelle incurable <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> perte capitalisée <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">800</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= \uqogreen{800~000~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">800</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span> (sous réserve d'en retrancher la portion attribuable au terrain, le cas échéant). <strong>c)</strong> Une perte de loyer causée par l'inoccupation généralisée du secteur serait <strong>externe</strong> (économique) et non fonctionnelle : la cause serait extérieure à la propriété. Le classement de la cause — interne (conception) ou externe (marché) — détermine la catégorie; c'est un critère d'examen classique.</p></div></details>383<div class="box box-exo" id="exo-13-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 13.5</span><span class="box-title">— maison patrimoniale citée — impact net</span><a class="box-anchor" href="#exo-13-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p13-132">Une maison en rangée du Vieux-Hull, <strong>citée</strong> par la Ville de Gatineau, nécessite un rejointoiement de maçonnerie (180 m<sup>2</sup>) et le remplacement de 14 fenêtres. Aux coûts standards : 80 $/m<sup>2</sup> et 600 $/fenêtre. Aux coûts patrimoniaux : 275 $/m<sup>2</sup> et 3 200 $/fenêtre. Une subvention municipale couvre 40 % des surcoûts patrimoniaux. Calculez : a) le coût standard des travaux; b) le coût patrimonial; c) le surcoût net après subvention, que l'évaluateur pourrait traiter comme dépréciation additionnelle liée au statut.</p></div></div>384<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p13-133"><strong>a) Standard</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>180</mn><mo>×</mo><mn>80</mn><mo>=</mo><mn>14</mn><mtext> </mtext><mn>400</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">180 \times 80 = 14~400~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">180</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">80</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">14</span><span class="mspace nobreak"> </span><span class="mord">400</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span> (maçonnerie) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>14</mn><mo>×</mo><mn>600</mn><mo>=</mo><mn>8</mn><mtext> </mtext><mn>400</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">14 \times 600 = 8~400~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">14</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">8</span><span class="mspace nobreak"> </span><span class="mord">400</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span> (fenêtres) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>22</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 22~800~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">22</span><span class="mspace nobreak"> </span><span class="mord">800</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>. <strong>b) Patrimonial</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>180</mn><mo>×</mo><mn>275</mn><mo>=</mo><mn>49</mn><mtext> </mtext><mn>500</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">180 \times 275 = 49~500~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">180</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">275</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">49</span><span class="mspace nobreak"> </span><span class="mord">500</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>14</mn><mo>×</mo><mn>3</mn><mtext> </mtext><mn>200</mn><mo>=</mo><mn>44</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">14 \times 3~200 = 44~800~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">14</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">3</span><span class="mspace nobreak"> </span><span class="mord">200</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">44</span><span class="mspace nobreak"> </span><span class="mord">800</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>94</mn><mtext> </mtext><mn>300</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 94~300~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">94</span><span class="mspace nobreak"> </span><span class="mord">300</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>. <strong>c) Surcoût brut</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>94</mn><mtext> </mtext><mn>300</mn><mo>−</mo><mn>22</mn><mtext> </mtext><mn>800</mn><mo>=</mo><mn>71</mn><mtext> </mtext><mn>500</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 94~300 - 22~800 = 71~500~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">94</span><span class="mspace nobreak"> </span><span class="mord">300</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">22</span><span class="mspace nobreak"> </span><span class="mord">800</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">71</span><span class="mspace nobreak"> </span><span class="mord">500</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>; subvention <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>71</mn><mtext> </mtext><mn>500</mn><mo>×</mo><mn>40</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mn>28</mn><mtext> </mtext><mn>600</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 71~500 \times 40\,\% = 28~600~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">71</span><span class="mspace nobreak"> </span><span class="mord">500</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">40</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">28</span><span class="mspace nobreak"> </span><span class="mord">600</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>; <strong>surcoût net</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>71</mn><mtext> </mtext><mn>500</mn><mo>−</mo><mn>28</mn><mtext> </mtext><mn>600</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">42</mn><mtext> </mtext><mn mathvariant="bold">900</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= 71~500 - 28~600 = \uqogreen{42~900~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">71</span><span class="mspace nobreak"> </span><span class="mord">500</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">28</span><span class="mspace nobreak"> </span><span class="mord">600</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">42</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">900</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>. C'est l'illustration chiffrée du principe « impact net » : les contraintes patrimoniales déprécient (surcoût), les programmes d'aide compensent partiellement; l'évaluateur mesure le solde — et vérifie ensuite si le marché local paie ou non un prestige compensatoire.</p></div></details>385</article><aside class="side"><h4>Séances</h4><ol><li class="lvl2"><a href="#s-1">1 Introduction à la méthode du coût</a></li><li class="lvl2"><a href="#s-2">2 Cadre conceptuel et terminologie</a></li><li class="lvl2"><a href="#s-3">3 Méthodes d'évaluation du terrain</a></li><li class="lvl2"><a href="#s-4">4 Analyse du terrain et ajustements</a></li><li class="lvl2"><a href="#s-5">5 Coût de reproduction et coût de remplacement</a></li><li class="lvl2"><a href="#s-6">6 Méthodes d'estimation des coûts</a></li><li class="lvl2"><a href="#s-7">7 Coûts directs de construction</a></li><li class="lvl2"><a href="#s-8">8 Coûts indirects et profit entrepreneurial</a></li><li class="lvl2"><a href="#s-9">9 Concepts de dépréciation</a></li><li class="lvl2"><a href="#s-10">10 Dépréciation physique</a></li><li class="lvl2"><a href="#s-11">11 Dépréciation fonctionnelle</a></li><li class="lvl2"><a href="#s-12">12 Dépréciation économique (externe)</a></li><li class="lvl2"><a href="#s-13">13 Applications spécialisées</a></li><li class="lvl2"><a href="#s-14">14 Synthèse et révision</a></li></ol></aside></div></main>386<footer class="site-footer">387  <div class="footer-inner">388    <div class="footer-brand">389      <img src="/assets/brand/uqo-logo-white.png" alt="UQO" width="140" height="59" style="width:140px;height:auto;margin-bottom:10px">390      <div class="brand-code">IMM1033</div>391      <div>Méthodes du coût en évaluation immobilière</div>392      <div style="opacity:.7;margin-top:6px;font-size:.85rem">Hiver 2026 · 3 crédits · premier cycle · 14 séances</div>393      <div style="margin-top:14px;font-size:.85rem">Simon-Pierre Boucher, professeur<br>Département des sciences administratives<br>Université du Québec en Outaouais<br><a href="mailto:simon-pierre.boucher@uqo.ca" style="display:inline;padding:0">simon-pierre.boucher@uqo.ca</a></div>394    </div>395    <div><h4>Étudier</h4><a href="/seance/01/">Séances</a><a href="/aide-memoire/">Aide-mémoire</a><a href="/glossaire/">Glossaire</a><a href="/definitions/">Toutes les définitions</a><a href="/carte/">Carte du cours</a><a href="/exercices/">Banque d’exercices</a></div>396    <div><h4>S’exercer</h4><a href="/quiz/">Quiz et examens blancs</a><a href="/entrainement/">Entraînement</a><a href="/jeux/">Jeux de révision</a><a href="/fiches/">Fiches de révision</a><a href="/outils/">Calculateurs</a><a href="/progression/">Ma progression</a></div>397    <div><h4>Ressources</h4><a href="/diapositives/">Diapositives</a><a href="/ressources/">Téléchargements</a><a href="/rapport/">Rapport — marché de l’habitation</a><a href="/bibliographie/">Bibliographie</a><a href="/recherche/">Recherche</a><a href="https://www.uqo-imm1003.app" rel="noopener">IMM1003 — Éléments d’évaluation immobilière</a></div>398  </div>399  <div class="footer-legal"><div><span>© 2026 Simon-Pierre Boucher — Université du Québec en Outaouais. Document destiné aux étudiantes et étudiants inscrits au cours IMM1033 ; toute reproduction ou diffusion sans autorisation écrite de l’auteur est interdite.</span><span>Généré depuis les sources LaTeX · KaTeX · TikZ</span></div></div>400</footer>401<div id="search-modal" class="search-modal" role="dialog" aria-modal="true" aria-label="Recherche dans les notes">402  <div class="search-box">403    <input type="search" placeholder="Rechercher une notion, une formule, un exemple…" autocomplete="off" spellcheck="false">404    <div class="search-results"></div>405    <div class="search-foot"><span><kbd>↑</kbd><kbd>↓</kbd> naviguer</span><span><kbd>↵</kbd> ouvrir</span><span><kbd>Échap</kbd> fermer</span><span style="margin-left:auto"><a href="/recherche/">Page de recherche complète</a></span></div>406  </div>407</div>408409<script src="/assets/js/app.js" defer></script>410</body>411</html>412
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