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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 l’évaluation immobilière</div><a href="/seance/01/" data-ch="01"><span class="pastille" style="background:#2976bb">1</span><span>Introduction à l'évaluation immobilière</span></a><a href="/seance/02/" data-ch="02"><span class="pastille" style="background:#2976bb">2</span><span>Le cadre professionnel au Québec</span></a><a href="/seance/03/" data-ch="03"><span class="pastille" style="background:#2976bb">3</span><span>Les principes fondamentaux de l'évaluation</span></a><div class="dd-part"><i style="background:#0f8b8d"></i>Partie II — Valeur, marché et données</div><a href="/seance/04/" data-ch="04"><span class="pastille" style="background:#0f8b8d">4</span><span>La valeur : concepts et types</span></a><a href="/seance/05/" data-ch="05"><span class="pastille" style="background:#0f8b8d">5</span><span>Le marché immobilier québécois</span></a><a href="/seance/06/" data-ch="06"><span class="pastille" style="background:#0f8b8d">6</span><span>Collecte et analyse des données</span></a><a href="/seance/07/" data-ch="07"><span class="pastille" style="background:#0f8b8d">7</span><span>Examen mi-session : révision des blocs 1 et 2</span></a><div class="dd-part"><i style="background:#cca424"></i>Partie III — Les trois méthodes d’évaluation</div><a href="/seance/08/" data-ch="08"><span class="pastille" style="background:#cca424">8</span><span>La méthode de comparaison — Partie 1 : principes et sélection des comparables</span></a><a href="/seance/09/" data-ch="09"><span class="pastille" style="background:#cca424">9</span><span>La méthode de comparaison — Partie 2 : ajustements et réconciliation</span></a><a href="/seance/10/" data-ch="10"><span class="pastille" style="background:#cca424">10</span><span>La méthode du coût</span></a><a href="/seance/11/" data-ch="11"><span class="pastille" style="background:#cca424">11</span><span>La méthode du revenu — Partie 1 : du revenu brut au RNE</span></a><a href="/seance/12/" data-ch="12"><span class="pastille" style="background:#cca424">12</span><span>La méthode du revenu — Partie 2 : le taux et le DCF</span></a><div class="dd-part"><i style="background:#6b4fbb"></i>Partie IV — Synthèse et pratique professionnelle</div><a href="/seance/13/" data-ch="13"><span class="pastille" style="background:#6b4fbb">13</span><span>Le rapport d'évaluation</span></a><a href="/seance/14/" data-ch="14"><span class="pastille" style="background:#6b4fbb">14</span><span>Révision générale et cas intégrateur</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 82 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 l'évaluation immobilière</span></h2>90<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">— valeur, prix ou coût?</span><a class="box-anchor" href="#exo-1-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p1-80">Pour chacune des situations suivantes, indiquez si le montant mentionné est un <em>prix</em>, un <em>coût</em> ou une <em>valeur</em>. <strong>a)</strong> Une maison d'Aylmer s'est vendue <span class="num">462 000 $</span> après une guerre d'offres impliquant sept acheteurs. <strong>b)</strong> Un entrepreneur estime à <span class="num">385 000 $</span> les dépenses totales (terrain, matériaux, main-d'œuvre, profit) pour construire un bungalow équivalent. <strong>c)</strong> Un évaluateur agréé conclut que le prix le plus probable de la même maison, dans des conditions normales de marché, est de <span class="num">440 000 $</span>. <strong>d)</strong> Le rôle d'évaluation municipal inscrit la propriété à <span class="num">398 000 $</span>.</p></div></div>91<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="p1-81"><strong>a)</strong> Un <strong>prix</strong> : c'est un fait historique, le montant effectivement payé — possiblement gonflé par la surenchère. <strong>b)</strong> Un <strong>coût</strong> : la somme des dépenses de production du bien, qui ne préjuge ni du prix ni de la valeur. <strong>c)</strong> Une <strong>valeur</strong> (marchande) : une opinion professionnelle sur le prix le plus probable. L'écart avec le prix payé (<span class="num">22 000 $</span>) illustre qu'un prix particulier peut s'écarter de la valeur. <strong>d)</strong> Une <strong>valeur</strong> également, mais de type <em>fiscal</em> : établie par évaluation de masse à une date de référence antérieure, elle ne constitue pas une preuve de la valeur marchande actuelle.</p></div></details>92<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">— ratio prêt/valeur et mise de fonds</span><a class="box-anchor" href="#exo-1-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p1-82">Une acheteuse fait accepter une offre de <span class="num">520 000 $</span> sur une propriété de Hull. L'évaluation mandatée par le prêteur conclut à <span class="num">495 000 $</span>. L'acheteuse souhaite un prêt conventionnel (sans assurance). <strong>a)</strong> Quelle valeur le prêteur retiendra-t-il? <strong>b)</strong> Quel est le prêt maximal conventionnel? <strong>c)</strong> Quelle mise de fonds l'acheteuse doit-elle verser? <strong>d)</strong> Quel pourcentage du <em>prix</em> cette mise de fonds représente-t-elle?</p></div></div>93<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="p1-83"><strong>a)</strong> La moindre du prix et de l'évaluation : <span class="num">495 000 $</span>. <strong>b)</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>495</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>80</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mn>396</mn><mtext> </mtext><mn>000</mn><mtext> $</mtext></mrow><annotation encoding="application/x-tex">495\,000 \times 80\,\% = 396\,000~\text{\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">495</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">80</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">396</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord text"><span class="mord">$</span></span></span></span></span>. <strong>c)</strong> Le prix payé moins le prêt : <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>396</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>124</mn><mtext> </mtext><mn>000</mn><mtext> $</mtext></mrow><annotation encoding="application/x-tex">520\,000 - 396\,000 =94124\,000~\text{\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">520</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">396</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">124</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord text"><span class="mord">$</span></span></span></span></span>. <strong>d)</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>124</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>520</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>23,8</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">124\,000 / 520\,000 = 23{,}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">124</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000/520</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><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">23</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>. Bien que le seuil conventionnel soit de 20 %, l'écart entre prix et évaluation force une mise de fonds effective de 23,8 % du prix. C'est la conséquence directe de la règle de la <em>moindre valeur retenue</em>.</p></div></details>95<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">— droits de mutation</span><a class="box-anchor" href="#exo-1-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p1-84">Calculez les droits de mutation exigibles (barème de base 2026 : 0,5 % jusqu'à <span class="num">62 900 $</span>; 1,0 % de <span class="num">62 900 $</span> à <span class="num">315 000 $</span>; 1,5 % au-delà) pour : <strong>a)</strong> un condo de Gatineau acquis <span class="num">299 000 $</span>; <strong>b)</strong> une résidence de luxe acquise <span class="num">815 000 $</span>.</p></div></div>96<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="p1-85"><strong>a)</strong> Tranche 1 : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>62</mn><mtext> </mtext><mn>900</mn><mo>×</mo><mn>0,5</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mn>314,50</mn><mtext> $</mtext></mrow><annotation encoding="application/x-tex">62\,900 \times 0{,}5\,\% = 314{,}50~\text{\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">62</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">900</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">314</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">50</span><span class="mspace nobreak"> </span><span class="mord text"><span class="mord">$</span></span></span></span></span>. Tranche 2 : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>299</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>62</mn><mtext> </mtext><mn>900</mn><mo stretchy="false">)</mo><mo>×</mo><mn>1,0</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mn>2</mn><mtext> </mtext><mn>361,00</mn><mtext> $</mtext></mrow><annotation encoding="application/x-tex">(299\,000 - 62\,900) \times 1{,}0\,\% = 2\,361{,}00~\text{\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">299</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">62</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">900</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">361</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">00</span><span class="mspace nobreak"> </span><span class="mord text"><span class="mord">$</span></span></span></span></span>. Il n'y a pas de tranche 3 puisque le prix est inférieur à <span class="num">315 000 $</span>. <strong>Total :</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>314,50</mn><mo>+</mo><mn>2</mn><mtext> </mtext><mn>361,00</mn><mo>=</mo><mn>2</mn><mtext> </mtext><mn>675,50</mn><mtext> $</mtext></mrow><annotation encoding="application/x-tex">314{,}50 + 2\,361{,}00 = 2\,675{,}50~\text{\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">314</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">50</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">361</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">00</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">675</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">50</span><span class="mspace nobreak"> </span><span class="mord text"><span class="mord">$</span></span></span></span></span>. <strong>b)</strong> Tranche 1 : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>314,50</mn><mtext> $</mtext></mrow><annotation encoding="application/x-tex">314{,}50~\text{\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">314</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">50</span><span class="mspace nobreak"> </span><span class="mord text"><span class="mord">$</span></span></span></span></span>. Tranche 2 : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>315</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>62</mn><mtext> </mtext><mn>900</mn><mo stretchy="false">)</mo><mo>×</mo><mn>1,0</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mn>2</mn><mtext> </mtext><mn>521,00</mn><mtext> $</mtext></mrow><annotation encoding="application/x-tex">(315\,000 - 62\,900) \times 1{,}0\,\% = 2\,521{,}00~\text{\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">315</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">62</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">900</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">521</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">00</span><span class="mspace nobreak"> </span><span class="mord text"><span class="mord">$</span></span></span></span></span>. Tranche 3 : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>815</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>315</mn><mtext> </mtext><mn>000</mn><mo stretchy="false">)</mo><mo>×</mo><mn>1,5</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mn>7</mn><mtext> </mtext><mn>500,00</mn><mtext> $</mtext></mrow><annotation encoding="application/x-tex">(815\,000 - 315\,000) \times 1{,}5\,\% = 7\,500{,}00~\text{\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">815</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">315</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">7</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">00</span><span class="mspace nobreak"> </span><span class="mord text"><span class="mord">$</span></span></span></span></span>. <strong>Total :</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>314,50</mn><mo>+</mo><mn>2</mn><mtext> </mtext><mn>521,00</mn><mo>+</mo><mn>7</mn><mtext> </mtext><mn>500,00</mn><mo>=</mo><mn>10</mn><mtext> </mtext><mn>335,50</mn><mtext> $</mtext></mrow><annotation encoding="application/x-tex">314{,}50 + 2\,521{,}00 + 7\,500{,}00 =9710\,335{,}50~\text{\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">314</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">50</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">521</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">00</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">7</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">00</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">335</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">50</span><span class="mspace nobreak"> </span><span class="mord text"><span class="mord">$</span></span></span></span></span>. Remarque : si la municipalité avait adopté un taux majoré de 3 % sur l'excédent de <span class="num">500 000 $</span>, il faudrait scinder la dernière tranche — vérifiez toujours le règlement municipal applicable.</p></div></details>98<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 le bon professionnel</span><a class="box-anchor" href="#exo-1-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p1-86">Pour chacun des besoins suivants, identifiez le professionnel approprié (évaluateur agréé, courtier immobilier, inspecteur en bâtiment, arpenteur-géomètre ou notaire) et justifiez en une phrase. <strong>a)</strong> Établir la juste indemnité pour un immeuble exproprié par la Ville. <strong>b)</strong> Vérifier si la toiture et les fondations présentent des défauts. <strong>c)</strong> Certifier l'emplacement exact des limites du terrain et des bâtiments. <strong>d)</strong> Recevoir l'acte de vente et publier le transfert au Registre foncier. <strong>e)</strong> Mettre la propriété en marché et négocier avec les acheteurs.</p></div></div>99<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="p1-87"><strong>a)</strong> <strong>Évaluateur agréé</strong> : l'indemnité d'expropriation repose sur une opinion de valeur indépendante, souvent débattue devant le tribunal. <strong>b)</strong> <strong>Inspecteur en bâtiment</strong> : il se prononce sur l'état physique, jamais sur la valeur. <strong>c)</strong> <strong>Arpenteur-géomètre</strong> : le certificat de localisation et le bornage relèvent de son monopole professionnel. <strong>d)</strong> <strong>Notaire</strong> : au Québec, la vente immobilière est reçue en minute devant notaire, qui en assure la publicité foncière. <strong>e)</strong> <strong>Courtier immobilier</strong> : intermédiaire de mise en marché, encadré par l'OACIQ, rémunéré à commission.</p></div></details>100<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">— type de valeur approprié</span><a class="box-anchor" href="#exo-1-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p1-88">Dans chaque scénario, quel type de valeur (marchande, d'assurance, fiscale, liquidative, d'investissement) l'évaluateur doit-il estimer? <strong>a)</strong> Une banque veut connaître ce qu'elle récupérerait en cas de reprise et de revente rapide de l'immeuble. <strong>b)</strong> Un assureur veut fixer le montant de la garantie « bâtiment » d'une police habitation. <strong>c)</strong> Un fonds immobilier évalue ce que vaut un immeuble <em>pour lui</em>, compte tenu de son coût de capital de 6 % et de synergies avec ses autres actifs. <strong>d)</strong> Un tribunal doit trancher la valeur d'une résidence dans un partage de patrimoine familial.</p></div></div>101<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="p1-89"><strong>a)</strong> <strong>Valeur liquidative</strong> : délai de vente réduit, conditions de vente forcée — typiquement inférieure à la valeur marchande. <strong>b)</strong> <strong>Valeur d'assurance</strong> : coût de remplacement du bâtiment, excluant le terrain (le terrain ne brûle pas). <strong>c)</strong> <strong>Valeur d'investissement</strong> : propre à cet investisseur et à ses critères; elle peut différer de la valeur marchande sans que personne n'ait tort. <strong>d)</strong> <strong>Valeur marchande</strong> : le standard des litiges civils — prix le plus probable entre parties non liées, informées et non contraintes.</p></div></details>102<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">— réflexion — l'indépendance de l'évaluateur</span><a class="box-anchor" href="#exo-1-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p1-90">Un promoteur offre à un évaluateur agréé le mandat d'évaluer les 40 condos de son nouveau projet, en précisant : « J'ai besoin que chaque unité s'évalue au moins au prix de vente, sinon mes acheteurs perdront leur financement. » Identifiez les enjeux professionnels et la réponse appropriée.</p></div></div>103<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="p1-91">Le promoteur tente de dicter la <strong>conclusion</strong> de l'évaluation, ce qui heurte de front l'exigence d'<strong>indépendance</strong> et d'objectivité : l'opinion de valeur ne se négocie pas. L'évaluateur peut accepter le mandat — évaluer 40 condos est légitime — mais il doit préciser par écrit que ses conclusions seront celles que les données de marché supportent, sans égard aux besoins de financement du client. Si le promoteur conditionne le mandat (ou les honoraires) à l'atteinte des prix de vente, l'évaluateur doit <strong class="c-rouge">refuser</strong>. Comme nous le verrons à la séance 2, lier la rémunération ou l'obtention du mandat à une conclusion prédéterminée contrevient au Code de déontologie et expose à des sanctions disciplinaires.</p></div></details>104<h2 class="h-section" id="s-2"><span class="h-num">2</span><span class="h-text">Le cadre professionnel au Québec</span></h2>105<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">— inspection ou discipline?</span><a class="box-anchor" href="#exo-2-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p2-57">Pour chaque situation, indiquez si elle relève de l'<em>inspection professionnelle</em> ou du processus <em>disciplinaire</em>, et justifiez. <strong>a)</strong> L'Ordre vérifie périodiquement la tenue de dossiers d'un membre choisi au programme annuel. <strong>b)</strong> Une cliente allègue que son évaluateur a divulgué son rapport à un tiers sans autorisation. <strong>c)</strong> À la suite d'une vague d'erreurs observées sur les évaluations de terrains contaminés, l'Ordre lance une vérification ciblée sur ce thème chez plusieurs membres. <strong>d)</strong> Le syndic reçoit une dénonciation selon laquelle un membre facture des honoraires calculés en pourcentage de la valeur conclue.</p></div></div>106<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="p2-58"><strong>a)</strong> <strong>Inspection</strong> (générale) : démarche préventive et périodique, sans allégation de faute. <strong>b)</strong> <strong>Discipline</strong> : allégation d'un manquement au secret professionnel — plainte au bureau du syndic, enquête, et éventuellement conseil de discipline. <strong>c)</strong> <strong>Inspection</strong> (thématique) : vérification préventive sur un sujet d'actualité, visant l'amélioration des pratiques. <strong>d)</strong> <strong>Discipline</strong> : les honoraires conditionnels à la conclusion sont un acte interdit; le syndic enquêtera en vue d'une plainte disciplinaire.</p></div></details>107<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">— la triade de la responsabilité civile</span><a class="box-anchor" href="#exo-2-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p2-59">Une évaluatrice omet de mentionner, dans son rapport sur un duplex de Hull, que le sous-sol a subi des infiltrations d'eau récurrentes — fait notoire dans le quartier et visible lors de l'inspection (cernes, odeur). Se fiant au rapport concluant à <span class="num">540 000 $</span>, l'acheteur paie ce prix. Deux ans plus tard, il découvre les dommages : la valeur réelle au moment de l'achat était de <span class="num">465 000 $</span>. Analysez la responsabilité civile de l'évaluatrice en identifiant la faute, le préjudice et le lien de causalité, puis indiquez le délai dont dispose l'acheteur pour poursuivre.</p></div></div>108<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="p2-60"><strong>Faute</strong> : un professionnel prudent et diligent devait constater les indices d'infiltration lors de l'inspection et en tenir compte (ou, à tout le moins, les signaler et recommander une expertise). L'omission constitue un manquement à l'obligation de moyens et aux normes de pratique. <strong>Préjudice</strong> : l'acheteur a payé <span class="num">540 000 $</span> un immeuble valant <span class="num">465 000 $</span>, soit <span class="num">75 000 $</span> de perte (plus, le cas échéant, les frais de réparation non reflétés dans la valeur). <strong>Causalité</strong> : le rapport a directement fondé la décision d'achat au prix payé; sans l'omission, l'acheteur aurait payé moins ou renoncé. <strong>Prescription</strong> : trois ans à compter de la <em>connaissance</em> du préjudice (art. 2925 C.c.Q.) — ici, à partir de la découverte des dommages, et non de la date du rapport. L'acheteur a donc jusqu'à trois ans après la découverte pour intenter son recours; le FARP de l'évaluatrice couvrira l'indemnité si la responsabilité est retenue (garantie de 2 M$ par sinistre).</p></div></details>109<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">— actes interdits — repérage</span><a class="box-anchor" href="#exo-2-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p2-61">Parmi les comportements suivants, identifiez ceux qui contreviennent au Code de déontologie et nommez l'obligation violée. <strong>a)</strong> Facturer un forfait de <span class="num">650 $</span> convenu avant le mandat. <strong>b)</strong> Évaluer l'immeuble de sa belle-sœur sans le mentionner au client prêteur. <strong>c)</strong> Refuser un mandat d'évaluation d'une usine de transformation alimentaire faute d'expérience dans ce type d'actif. <strong>d)</strong> Transmettre une copie du rapport au courtier du vendeur « pour information », sans autorisation du client. <strong>e)</strong> Publier une publicité affirmant « valeurs garanties acceptées par toutes les banques ».</p></div></div>110<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="p2-62"><strong>a)</strong> <strong class="c-vert">Conforme</strong> : honoraires forfaitaires convenus d'avance, indépendants de la conclusion. <strong>b)</strong> <strong class="c-rouge">Interdit</strong> : conflit d'intérêts non divulgué — lien personnel avec la propriétaire du bien évalué. <strong>c)</strong> <strong class="c-vert">Conforme</strong>, et même exemplaire : c'est l'application de l'obligation de compétence (refuser, s'associer ou se former). <strong>d)</strong> <strong class="c-rouge">Interdit</strong> : violation du secret professionnel et de la confidentialité — le rapport appartient au client et ne circule qu'avec son autorisation. <strong>e)</strong> <strong class="c-rouge">Interdit</strong> : publicité trompeuse (aucune valeur n'est « garantie »; l'évaluateur a une obligation de moyens) et atteinte à la dignité de la profession.</p></div></details>111<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">— référentiels croisés</span><a class="box-anchor" href="#exo-2-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p2-63">Une évaluatrice de Gatineau détient le titre d'É.A. (OEAQ) et la désignation AACI (AIC). Elle accepte un mandat d'évaluation d'un immeuble de bureaux à Ottawa pour une banque pancanadienne. <strong>a)</strong> Quels référentiels de normes s'appliquent à son travail? <strong>b)</strong> L'immeuble étant en Ontario, le Code de déontologie de l'OEAQ cesse-t-il de s'appliquer à elle? <strong>c)</strong> Quelle édition du CUSPAP doit-elle respecter en 2026?</p></div></div>112<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="p2-64"><strong>a)</strong> Les <strong>deux</strong> : les normes de l'OEAQ (elle est É.A.) et le CUSPAP (elle est membre de l'AIC). En cas de divergence, elle satisfait à l'exigence la plus stricte. <strong>b)</strong> <strong>Non</strong> : les obligations déontologiques suivent le professionnel, pas l'immeuble. Membre de l'OEAQ, elle demeure soumise à son code de déontologie où qu'elle exerce; s'y ajoutent les exigences applicables en Ontario et celles de l'AIC. <strong>c)</strong> Le <strong>CUSPAP 2026</strong>, en vigueur depuis le 1<sup>er</sup> avril 2026 (il remplace l'édition 2024).</p></div></details>113<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">— chiffres clés du cadre professionnel</span><a class="box-anchor" href="#exo-2-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p2-65">Sans consulter vos notes, complétez : durée du stage professionnel; note de passage de l'examen d'admission; heures de formation continue et période de référence; garantie du FARP; fourchette des amendes disciplinaires; délai de prescription civile; durée minimale de conservation des dossiers.</p></div></div>114<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="p2-66">Stage : <strong>48 semaines</strong> à temps complet. Examen : note de passage de <strong>65 %</strong>. Formation continue : <strong>30 heures par période de deux ans</strong>. FARP : <strong>2 000 000 $ par sinistre</strong> et par période de garantie. Amendes : <strong>2 500 $ à 62 500 $ par infraction</strong> (art. 156, Code des professions). Prescription civile : <strong>3 ans</strong> de la connaissance du préjudice (art. 2925 C.c.Q.). Conservation des dossiers : au moins <strong>5 ans</strong>. Ces sept chiffres constituent l'ossature factuelle de la séance — sachez-les parfaitement.</p></div></details>115<h2 class="h-section" id="s-3"><span class="h-num">3</span><span class="h-text">Les principes fondamentaux de l'évaluation</span></h2>116<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">— quel principe est à l'œuvre?</span><a class="box-anchor" href="#exo-3-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p3-64">Identifiez le principe illustré par chaque situation. <strong>a)</strong> Une maison de <span class="num">900 000 $</span> construite dans un quartier où tout se vend <span class="num">400 000 $</span> ne trouve preneur qu'à <span class="num">650 000 $</span>. <strong>b)</strong> Un investisseur refuse de payer plus de <span class="num">1 090 000 $</span> pour un immeuble dont le RNE est de <span class="num">60 000 $</span>, car les immeubles comparables rapportent 5,5 %. <strong>c)</strong> L'annonce d'une nouvelle station de transport structurant fait grimper les valeurs dans un rayon de 800 mètres. <strong>d)</strong> Après trois années de marges records dans les mini-entrepôts, douze projets concurrents sont annoncés dans la même ville. <strong>e)</strong> Un spa de <span class="num">30 000 $</span> installé dans un jumelé n'augmente sa valeur que de <span class="num">8000 $</span>.</p></div></div>117<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="p3-65"><strong>a)</strong> <strong>Conformité</strong> (effet de régression) : le bien supérieur est tiré vers le bas par son voisinage. <strong>b)</strong> <strong>Substitution</strong> (et anticipation) : l'investisseur compare aux rendements des placements substituts — <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>60</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>0,055</mn><mo>≈</mo><mn>1</mn><mtext> </mtext><mn>090</mn><mtext> </mtext><mn>909</mn><mtext> $</mtext></mrow><annotation encoding="application/x-tex">60\,000/0{,}055 \approx1181\,090\,909~\text{\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">60</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000/0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">055</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">090</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">909</span><span class="mspace nobreak"> </span><span class="mord text"><span class="mord">$</span></span></span></span></span>. <strong>c)</strong> <strong>Externalités</strong> (positives), amplifiées par l'<strong>anticipation</strong> : le marché capitalise dès l'annonce des bénéfices futurs. <strong>d)</strong> <strong>Concurrence</strong> : les profits excédentaires attirent l'offre nouvelle, qui les érodera. <strong>e)</strong> <strong>Contribution</strong> (et rendements décroissants) : la valeur ajoutée (<span class="num">8000 $</span>) est très inférieure au coût (<span class="num">30 000 $</span>) — suréquipement.</p></div></details>119<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">— utilisation optimale — le filtre complet</span><a class="box-anchor" href="#exo-3-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p3-66">Un terrain de <span class="num">1400</span> m² au centre de Hull fait l'objet de quatre hypothèses d'usage. Le zonage actuel permet le résidentiel jusqu'à huit logements (pas de commercial). Les études montrent :</p>120<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Usage envisagé</th><th class="al-r">Valeur totale du projet</th><th class="al-r">Coût de construction</th></tr></thead><tbody><tr><td>Unifamiliale de prestige</td><td class="al-r">780 000 $</td><td class="al-r">620 000 $</td></tr><tr><td>Triplex</td><td class="al-r">940 000 $</td><td class="al-r">720 000 $</td></tr><tr><td>8 logements</td><td class="al-r">1 650 000 $</td><td class="al-r">1 430 000 $</td></tr><tr><td>Petit immeuble commercial</td><td class="al-r">1 900 000 $</td><td class="al-r">1 500 000 $</td></tr></tbody></table></div></div>121<p id="p3-67">Le sol présente une capacité portante limitée rendant impossible toute structure de plus de trois étages; l'immeuble de 8 logements exigerait quatre étages, mais une variante de trois étages n'est pas réalisable sur ce terrain. Déterminez l'utilisation optimale en appliquant les quatre critères dans l'ordre.</p></div></div>122<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="p3-68"><strong>Critère 1 — légalement permis :</strong> le commercial est éliminé (zonage résidentiel seulement), malgré sa valeur résiduelle apparente de <span class="num">400 000 $</span>. Restent : unifamiliale, triplex, 8 logements. <strong>Critère 2 — physiquement possible :</strong> le 8 logements exige quatre étages, impossibles vu la capacité portante; éliminé. Restent : unifamiliale et triplex. <strong>Critère 3 — financièrement faisable :</strong> résiduel de l'unifamiliale <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>780</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>620</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>160</mn><mtext> </mtext><mn>000</mn><mtext> $</mtext></mrow><annotation encoding="application/x-tex">780\,000 - 620\,000 = 160\,000~\text{\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">780</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">620</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">160</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord text"><span class="mord">$</span></span></span></span></span>; du triplex : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>940</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>720</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>220</mn><mtext> </mtext><mn>000</mn><mtext> $</mtext></mrow><annotation encoding="application/x-tex">940\,000 - 720\,000 = 220\,000~\text{\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">940</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">720</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">220</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord text"><span class="mord">$</span></span></span></span></span>. Les deux sont positifs et faisables. <strong>Critère 4 — maximalement productif :</strong> le triplex laisse <span class="num">220 000 $</span> au terrain contre <span class="num">160 000 $</span> pour l'unifamiliale. <strong>Conclusion : l'utilisation optimale est le triplex</strong>, et la valeur du terrain à retenir est <span class="num">220 000 $</span>. Le piège de l'exercice : conclure au commercial (critère 1) ou au 8 logements (critère 2) en sautant des étapes du filtre séquentiel.</p></div></details>123<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">— capitalisation et substitution</span><a class="box-anchor" href="#exo-3-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p3-69">Un sixplex de Gatineau produit un RNE de <span class="num">78 000 $</span>. Les transactions récentes d'immeubles comparables révèlent des taux de capitalisation entre 5,8 % et 6,2 %. <strong>a)</strong> Dans quelle fourchette de valeurs le principe de substitution borne-t-il le prix? <strong>b)</strong> Le vendeur demande <span class="num">1 500 000 $</span>. Qu'en conclure?</p></div></div>124<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="p3-70"><strong>a)</strong> Borne haute : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>78</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>0,058</mn><mo>≈</mo><mn>1</mn><mtext> </mtext><mn>344</mn><mtext> </mtext><mn>828</mn><mtext> $</mtext></mrow><annotation encoding="application/x-tex">78\,000 / 0{,}058 \approx 1\,344\,828~\text{\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000/0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">058</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">344</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">828</span><span class="mspace nobreak"> </span><span class="mord text"><span class="mord">$</span></span></span></span></span>. Borne basse : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>78</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>0,062</mn><mo>≈</mo><mn>1</mn><mtext> </mtext><mn>258</mn><mtext> </mtext><mn>065</mn><mtext> $</mtext></mrow><annotation encoding="application/x-tex">78\,000 / 0{,}062 \approx 1\,258\,065~\text{\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000/0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">062</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">258</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">065</span><span class="mspace nobreak"> </span><span class="mord text"><span class="mord">$</span></span></span></span></span>. La fourchette est d'environ <span class="num">1 258 000 $</span> à <span class="num">1 345 000 $</span>. <strong>b)</strong> À <span class="num">1 500 000 $</span>, le taux implicite serait <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>78</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>1</mn><mtext> </mtext><mn>500</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>5,2</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">78\,000 / 1\,500\,000 = 5{,}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">78</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">500</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">5</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>, nettement sous le rendement des substituts (5,8–6,2 %). Un investisseur rationnel placerait plutôt son capital dans un immeuble comparable offrant un meilleur rendement : le prix demandé excède la valeur marchande indiquée par le marché, sauf attributs exceptionnels à documenter (potentiel de densification, loyers nettement sous-optimaux, etc.).</p></div></details>125<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">— contribution et décision de rénovation</span><a class="box-anchor" href="#exo-3-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p3-71">Une propriétaire de Buckingham envisage trois travaux avant la mise en vente : réfection de la cuisine (coût <span class="num">40 000 $</span>, contribution estimée <span class="num">48 000 $</span>), ajout d'une salle de bain au sous-sol (coût <span class="num">25 000 $</span>, contribution <span class="num">22 000 $</span>), aménagement paysager haut de gamme (coût <span class="num">18 000 $</span>, contribution <span class="num">7000 $</span>). <strong>a)</strong> Quels travaux sont justifiés du strict point de vue de la valeur? <strong>b)</strong> Quel principe gouverne l'analyse, et quel phénomène illustre le troisième projet?</p></div></div>126<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="p3-72"><strong>a)</strong> Seule la <strong>cuisine</strong> crée une valeur nette positive (<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>000</mn><mtext> $</mtext></mrow><annotation encoding="application/x-tex">+8\,000~\text{\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">+</span><span class="mord">8</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord text"><span class="mord">$</span></span></span></span></span>). La salle de bain détruit <span class="num">3000 $</span> et l'aménagement paysager <span class="num">11 000 $</span> : à éviter dans une optique de revente. <strong>b)</strong> Le principe de <strong>contribution</strong> : chaque composante vaut ce qu'elle ajoute à la valeur totale, non ce qu'elle coûte. Le paysager illustre les <strong>rendements décroissants</strong> et le <strong>suréquipement</strong> : un investissement dont la contribution est très inférieure au coût, typique des améliorations excédant les attentes du marché local (principe de conformité en toile de fond).</p></div></details>127<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">— offre, demande et lecture du marché</span><a class="box-anchor" href="#exo-3-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p3-73">Au premier trimestre, le marché des unifamiliales d'un secteur de Gatineau affiche : délai de vente moyen passé de 45 à 21 jours en un an, ratio inscriptions/ventes passé de 8 à 3 mois de stock, 40 % des ventes conclues au-dessus du prix demandé. <strong>a)</strong> Qualifiez l'état du marché et son déséquilibre. <strong>b)</strong> Quels facteurs pourraient avoir déplacé la courbe de demande vers la droite? <strong>c)</strong> Pourquoi les prix réagissent-ils si vite, alors que les quantités vendues augmentent peu?</p></div></div>128<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="p3-74"><strong>a)</strong> Marché de <strong>vendeurs</strong> en <strong>excès de demande</strong> : délais courts, stock faible, surenchères fréquentes — le prix courant est sous le prix d'équilibre et monte. <strong>b)</strong> Baisse des taux hypothécaires, migration interprovinciale et immigration, hausse des revenus, regain de confiance — tout facteur augmentant le nombre d'acheteurs qualifiés à chaque niveau de prix. <strong>c)</strong> Parce que l'offre est <strong>inélastique à court terme</strong> : le stock de maisons ne peut croître rapidement (construction longue, terrains rares). L'ajustement passe donc presque entièrement par les <strong>prix</strong>, peu par les quantités — c'est la signature des marchés immobiliers.</p></div></details>129<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">— anticipation et date effective</span><a class="box-anchor" href="#exo-3-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p3-75">En mars, un évaluateur conclut à <span class="num">455 000 $</span> pour une maison de Gatineau. En novembre de la même année, après deux baisses du taux directeur et l'annonce d'un important employeur s'installant à proximité, une consœur conclut à <span class="num">489 000 $</span> pour la même propriété, inchangée. Les deux rapports peuvent-ils être simultanément corrects? Expliquez à l'aide de deux principes.</p></div></div>130<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="p3-76">Oui. Le principe de <strong>changement</strong> rappelle que la valeur est <strong>datée</strong> : chaque rapport photographie le marché à sa date effective, et les conditions (taux, emploi local) ont changé entre mars et novembre. Le principe d'<strong>anticipation</strong> explique le mécanisme de la hausse : le marché capitalise immédiatement les bénéfices futurs attendus de la baisse des taux (capacité d'emprunt accrue) et de l'arrivée de l'employeur (demande future de logements). Aucune contradiction : deux photographies exactes d'un sujet qui a bougé.</p></div></details>131<h2 class="h-section" id="s-4"><span class="h-num">4</span><span class="h-text">La valeur : concepts et types</span></h2>132<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">— identifier le type de valeur</span><a class="box-anchor" href="#exo-4-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p4-113">Pour chacune des situations suivantes, identifiez le type de valeur requis et justifiez en une phrase : (a) un syndic de faillite doit réaliser rapidement un entrepôt; (b) une compagnie d'assurance établit la couverture d'un duplex; (c) un contribuable conteste son compte de taxes; (d) une caisse populaire évalue la garantie d'un prêt; (e) un promoteur calcule ce qu'il peut payer pour un terrain compte tenu de son propre coût de financement.</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="p4-114">(a) <strong>Valeur liquidative</strong> : vente forcée dans un délai restreint. (b) <strong>Valeur d'assurance</strong> : coût de reconstruction du bâtiment seulement, terrain exclu. (c) <strong>Valeur réelle</strong> au sens de l'art. 43 LFM, à la date de référence du rôle (18 mois avant son entrée en vigueur) — et non la valeur marchande actuelle. (d) <strong>Valeur hypothécaire</strong> : lecture prudente et durable de la garantie, base du ratio prêt-valeur. (e) <strong>Valeur d'investissement</strong> : critères propres à cet investisseur (financement, rendement exigé), qui peut différer de la valeur marchande.</p></div></details>134<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">— valeur, prix ou coût</span><a class="box-anchor" href="#exo-4-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p4-115">Classez chaque montant comme valeur, prix ou coût, et précisez la temporalité : (a) <span class="num">312 000 $</span> déboursés en 2021 pour construire un jumelé; (b) <span class="num">529 000 $</span> conclus chez le notaire le 12 mars 2026; (c) <span class="num">545 000 $</span>, opinion d'un évaluateur au 1<sup>er</sup> septembre 2026; (d) <span class="num">560 000 $</span>, montant affiché sur Centris depuis 45 jours; (e) <span class="num">498 000 $</span>, montant qu'exigerait aujourd'hui un entrepreneur pour reconstruire le même jumelé.</p></div></div>135<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="p4-116">(a) <strong>Coût</strong> historique (production, 2021). (b) <strong>Prix</strong> — fait transactionnel daté du 12 mars 2026. (c) <strong>Valeur</strong> — opinion motivée au 1<sup>er</sup> septembre 2026. (d) Ni l'un ni l'autre au sens strict : c'est un <strong>prix demandé</strong>, une intention du vendeur — ce n'est ni un fait transactionnel ni une opinion d'évaluation. (e) <strong>Coût</strong> de remplacement actuel (production, 2026). L'écart entre (c) et (e) s'explique notamment par la valeur du terrain et la dépréciation du bâtiment existant.</p></div></details>136<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">— décote de liquidation</span><a class="box-anchor" href="#exo-4-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p4-117">Un immeuble de bureaux a une valeur marchande de <span class="num">2 400 000 $</span>. Le créancier demande une valeur liquidative sous l'hypothèse d'une vente en 90 jours. Les données de marché suggèrent une décote de 20 à 30 % pour ce segment. (a) Calculez la fourchette de valeur liquidative. (b) Expliquez quelles conditions de la valeur marchande sont violées dans ce scénario. (c) Le créancier détient une hypothèque de <span class="num">1 900 000 $</span> : commentez sa position.</p></div></div>137<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p4-118">(a) Borne haute : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mn>400</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mn>0,20</mn><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mtext> </mtext><mn>920</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">2\,400\,000 \times (1-0{,}20) = 1\,920\,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">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: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">20</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">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">920</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">$</span></span></span></span>; borne basse : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mn>400</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mn>0,30</mn><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mtext> </mtext><mn>680</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">2\,400\,000 \times (1-0{,}30) = 1\,680\,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">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: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">30</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">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">680</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>. Fourchette : <span class="num">1 680 000 $</span> à <span class="num">1 920 000 $</span>. (b) Deux conditions tombent : le <strong>délai raisonnable</strong> de mise en marché (90 jours imposés) et l'<strong>absence de contrainte</strong> (vendeur forcé). (c) La créance de <span class="num">1 900 000 $</span> se situe <em>dans</em> la fourchette : en scénario défavorable, le produit de la vente forcée (<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">1 680 000 $</span>) ne couvrirait pas la créance — il manquerait environ <span class="num">220 000 $</span>. Le prêteur est exposé; il pourrait exiger des garanties additionnelles ou privilégier une vente ordonnée sur un délai plus long.</p></div></details>138<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">— valeur d'investissement et capitalisation</span><a class="box-anchor" href="#exo-4-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p4-119">Un immeuble locatif de Gatineau génère un RNE de <span class="num">78 000 $</span>. Le marché transige ce type d'actif à un taux global de capitalisation d'environ 5,5 %. L'investisseur X exige 5,0 %; l'investisseur Y exige 7,0 %. (a) Estimez la valeur marchande. (b) Calculez la valeur d'investissement de chacun. (c) Lequel est susceptible d'acheter, et pourquoi?</p></div></div>139<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p4-120">(a) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>M</mi></msub><mo>=</mo><mn>78</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>0,055</mn><mo>≈</mo><mn>1</mn><mtext> </mtext><mn>418</mn><mtext> </mtext><mn>182</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">V_M = 78\,000 / 0{,}055 \approx 1\,418\,182\,\$</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:0.3283em;"><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 mathnormal mtight" style="margin-right:0.109em;">M</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">78</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">1</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">182</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>, arrondie 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">\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">1 420 000 $</span>. (b) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>X</mi></msub><mo>=</mo><mn>78</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>0,050</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>560</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">V_X = 78\,000 / 0{,}050 =1401\,560\,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:0.2222em;">V</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:-0.2222em;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" style="margin-right:0.0785em;">X</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">78</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">050</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">560</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">$</span></span></span></span>; <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>Y</mi></msub><mo>=</mo><mn>78</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>0,070</mn><mo>≈</mo><mn>1</mn><mtext> </mtext><mn>114</mn><mtext> </mtext><mn>286</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">V_Y = 78\,000 / 0{,}070 \approx 1\,114\,286\,\$</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:0.3283em;"><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 mathnormal mtight" style="margin-right:0.2222em;">Y</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">78</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">070</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">114</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">286</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. (c) X est susceptible d'acheter : sa valeur d'investissement (<span class="num">1 560 000 $</span>) excède la valeur marchande (<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">1 420 000 $</span>); il peut payer le prix du marché tout en atteignant son rendement cible. Y ne peut offrir qu'environ <span class="num">1 114 000 $</span> sans sacrifier son exigence de 7 % : il sera systématiquement devancé par des acheteurs comme X.</p></div></details>141<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">— analyse PEGS d'un scénario</span><a class="box-anchor" href="#exo-4-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p4-121">La municipalité de votre secteur annonce simultanément : (i) un nouveau règlement permettant les triplex dans les zones auparavant réservées à l'unifamiliale; (ii) une hausse de 8 % des taxes foncières; (iii) l'arrivée confirmée d'un employeur de 1 200 emplois; et (iv) la Banque du Canada abaisse son taux directeur de 50 points de base. Classez chaque événement dans la grille PEGS et analysez l'effet net probable sur la valeur des terrains unifamiliaux du secteur.</p></div></div>142<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="p4-122">(i) Facteur <strong>G</strong> (zonage) : effet haussier marqué sur les <em>terrains</em>, dont le potentiel de densification augmente (l'utilisation optimale peut passer de l'unifamiliale au triplex). (ii) Facteur <strong>G</strong> (taxation) : effet légèrement baissier — coût de détention accru. (iii) Facteur <strong>S/É</strong> (emploi et démographie locale) : effet haussier sur la demande résidentielle. (iv) Facteur <strong>É</strong> (taux) : effet haussier via le pouvoir d'achat (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mo>+</mo><mn>5</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">\approx +5\,\%</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:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">+</span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> de capacité d'emprunt pour 50 pb, selon la règle de pouce). <strong>Effet net</strong> : nettement haussier pour les terrains unifamiliaux bien situés — trois forces haussières convergentes (dont une spécifique au foncier) contre une force baissière modeste. L'exercice illustre l'<em>interaction</em> des familles : c'est la combinaison, non chaque facteur isolé, qui détermine le mouvement.</p></div></details>143<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">— vrai ou faux, avec justification</span><a class="box-anchor" href="#exo-4-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p4-123">(a) La valeur au rôle est une bonne approximation de la valeur marchande actuelle. (b) La valeur d'assurance inclut toujours le terrain. (c) Un prix payé supérieur à la valeur marchande implique une erreur de l'évaluateur. (d) La valeur marchande existe même si le propriétaire n'a aucune intention de vendre. (e) Le Code civil du Québec définit la valeur marchande.</p></div></div>144<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="p4-124">(a) <strong>Faux</strong> : la valeur au rôle est établie en masse, à une date de référence antérieure de 18 mois à l'entrée en vigueur du rôle; en marché mouvant, l'écart peut être important. (b) <strong>Faux</strong> : la valeur d'assurance vise le bâtiment seulement — le terrain ne brûle pas. (c) <strong>Faux</strong> : le prix est le résultat d'une négociation particulière (émotion, surenchère, lien entre parties); un écart prix–valeur est normal et documenté. (d) <strong>Vrai</strong> : la valeur marchande modélise une transaction <em>hypothétique</em>; aucune mise en vente réelle n'est requise. (e) <strong>Faux</strong> : le C.c.Q. est muet sur la valeur marchande; la notion relève de la jurisprudence et de la doctrine, et l'art. 43 LFM définit la « valeur réelle » aux fins municipales.</p></div></details>145<h2 class="h-section" id="s-5"><span class="h-num">5</span><span class="h-text">Le marché immobilier québécois</span></h2>146<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">— diagnostic de phase</span><a class="box-anchor" href="#exo-5-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p5-84">Un secteur affiche les indicateurs suivants : 9,5 mois d'inventaire; délai moyen de vente de 104 jours; ratio prix vendu/demandé de 93 %; transactions en baisse de 12 % sur un an; mises en chantier au plus bas depuis 8 ans; inoccupation locative de 4,6 %. (a) Qualifiez le marché et la phase du cycle. (b) Quelles conséquences pour la sélection et l'ajustement des comparables? (c) Un client vous demande si c'est « le bon moment d'acheter » : que répondez-vous, dans les limites de votre rôle?</p></div></div>147<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="p5-85">(a) Tous les indicateurs convergent : inventaire <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>></mo><mn>8</mn></mrow><annotation encoding="application/x-tex">>8</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">></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">8</span></span></span></span> mois, délais <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>></mo><mn>90</mn></mrow><annotation encoding="application/x-tex">>90</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">></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">90</span></span></span></span> jours, ratio <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><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex"><95\,\%</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"><</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">95</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>, volume en baisse, inoccupation <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>></mo><mn>4</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">>4\,\%</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">></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">4</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> — c'est un <strong>marché d'acheteurs</strong>, en phase de <strong>contraction avancée</strong>, possiblement à l'approche du creux (les mises en chantier au plancher annoncent le tarissement de l'offre future). (b) Les comparables récents reflètent un marché baissier : ajustements temporels <em>négatifs</em> pour les ventes plus anciennes conclues en marché plus fort; privilégier les ventes les plus récentes; se méfier des prix demandés (systématiquement au-dessus des prix de vente). (c) L'évaluateur n'est pas conseiller en placement : il peut décrire objectivement l'état du marché (conditions favorables aux acheteurs, inventaire élevé, pouvoir de négociation) sans recommander une décision. La frontière déontologique entre <em>informer</em> et <em>conseiller l'investissement</em> doit être respectée.</p></div></details>148<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">— mois d'inventaire</span><a class="box-anchor" href="#exo-5-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p5-86">En juin, un secteur compte 640 inscriptions en vigueur et il s'y est vendu 80 propriétés dans le mois. (a) Calculez les mois d'inventaire. (b) Qualifiez le marché. (c) Trois mois plus tard, les inscriptions montent à 780 et les ventes mensuelles tombent à 65 : recalculez et interprétez la trajectoire.</p></div></div>149<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="p5-87">(a) Mois d'inventaire <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>640</mn><mi mathvariant="normal">/</mi><mn>80</mn><mo>=</mo><mn>8,0</mn></mrow><annotation encoding="application/x-tex">= 640 / 80 = 8{,}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:1em;vertical-align:-0.25em;"></span><span class="mord">640/80</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:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">8</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span></span></span></span> mois. (b) À la frontière du marché d'acheteurs (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>></mo><mn>8</mn></mrow><annotation encoding="application/x-tex">>8</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">></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">8</span></span></span></span> mois); le pouvoir de négociation bascule vers les acheteurs. (c) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>780</mn><mi mathvariant="normal">/</mi><mn>65</mn><mo>=</mo><mn>12,0</mn></mrow><annotation encoding="application/x-tex">780 / 65 = 12{,}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">780/65</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:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">12</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span></span></span></span> mois : le marché s'enfonce nettement en territoire d'acheteurs. La détérioration vient des deux côtés (offre <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><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">+22\,\%</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">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>, demande <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>19</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">-19\,\%</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">19</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>) — signature d'une phase de contraction. L'évaluateur devra intégrer une tendance de prix baissière dans ses ajustements temporels et documenter l'évolution rapide des conditions dans son rapport.</p></div></details>150<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">— effet des taux sur la capacité d'emprunt</span><a class="box-anchor" href="#exo-5-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p5-88">Un ménage peut consacrer <span class="num">2400 $</span> par mois au service de son prêt hypothécaire (amortissement 25 ans). En utilisant la règle de pouce du cours (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>±</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\pm 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">±</span><span class="mord">1</span></span></span></span> point de taux <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mo>∓</mo><mn>10</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">\approx \mp 10\,\%</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:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">∓</span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> de capacité), et sachant qu'à 4,5 % ce ménage peut emprunter environ <span class="num">432 000 $</span> : (a) estimez sa capacité à 5,5 % et à 3,5 %; (b) expliquez pourquoi le test de résistance du BSIF amplifie l'effet des mouvements de taux; (c) reliez ce mécanisme aux quatre éléments constitutifs de la valeur (chapitre 4).</p></div></div>151<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p5-89">(a) À 5,5 % : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>432</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,90</mn><mo>≈</mo><mn>388</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">432\,000 \times 0{,}90 \approx 388\,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">432</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">90</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">388</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> (<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">389 000 $</span>). À 3,5 % : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>432</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>1,10</mn><mo>≈</mo><mn>475</mn><mtext> </mtext><mn>200</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">432\,000 \times 1{,}10 \approx152475\,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">432</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">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">475</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> (<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">475 000 $</span>). (b) Le test de résistance qualifie l'emprunteur à un taux <em>supérieur</em> au taux contractuel : toute hausse du taux contractuel déplace aussi le taux de qualification, excluant des acheteurs marginaux du marché — l'effet sur la demande dépasse donc le simple effet mécanique sur le paiement. (c) Les taux agissent sur le <strong>pouvoir d'achat effectif</strong>, quatrième élément constitutif de la valeur : l'utilité, la rareté et le désir peuvent être intacts, mais si le pouvoir d'achat se contracte, la valeur marchande fléchit.</p></div></details>153<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">— lecture régionale</span><a class="box-anchor" href="#exo-5-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p5-90">Votre bureau reçoit trois mandats simultanés : (i) un immeuble locatif de 12 logements à Québec; (ii) un immeuble locatif neuf de 12 logements à Gatineau; (iii) une unifamiliale dans une municipalité gaspésienne de 2 000 habitants. Pour chaque mandat, identifiez le principal facteur de marché régional dont il faudra tenir compte et son effet sur l'analyse.</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="p5-91">(i) Québec : inoccupation de 0,9 % — marché locatif très tendu. Revenus stables et prévisibles, risque locatif faible : les taux de capitalisation exigés y sont comprimés, et les loyers courants sont probablement inférieurs aux loyers de marché (potentiel encadré par le TAL). (ii) Gatineau : inoccupation de 3,8 % et offre neuve abondante — prudence dans la projection des revenus du neuf : concessions (mois gratuits), délais d'absorption, écart loyer affiché / loyer encaissé. (iii) Gaspésie : marché <strong>peu liquide</strong> en contexte de déclin démographique — comparables rares (élargir le territoire et la période de recherche), délais de vente longs, incertitude accrue de l'opinion de valeur à divulguer dans le rapport.</p></div></details>155<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">— cycle et comparables</span><a class="box-anchor" href="#exo-5-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p5-92">Vous évaluez une unifamiliale de Gatineau à la date du 1<sup>er</sup> mars 2023, dans un contexte où le marché vient de corriger d'environ 6 % depuis son sommet de mars 2022. Vous disposez de trois ventes comparables par ailleurs identiques : A vendue <span class="num">465 000 $</span> en février 2022; B vendue <span class="num">452 000 $</span> en septembre 2022; C vendue <span class="num">438 000 $</span> en janvier 2023. (a) Pourquoi ne pas simplement faire la moyenne des trois prix? (b) Quel comparable est le plus fiable et pourquoi? (c) Esquissez l'ajustement temporel du comparable A.</p></div></div>156<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p5-93">(a) Les trois prix datent de phases différentes d'un marché en mouvement : une moyenne brute mélangerait des niveaux de marché différents et surestimerait la valeur au 1<sup>er</sup> mars 2023. (b) C, vendue en janvier 2023 : la plus proche de la date d'évaluation, donc le moindre ajustement temporel — et l'on sait qu'un comparable est d'autant plus fiable qu'il exige moins d'ajustements. (c) A a été vendue près du sommet (février 2022). Si le marché a reculé d'environ 6 % entre mars 2022 et mars 2023, l'ajustement temporel est d'environ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>6</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">-6\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">6</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>465</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,94</mn><mo>≈</mo><mn>437</mn><mtext> </mtext><mn>100</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">465\,000 \times 0{,}94 \approx 437\,100\,\$</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">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:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">94</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">437</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">$</span></span></span></span> — remarquablement cohérent avec le prix de C, ce qui conforte le diagnostic de tendance.</p></div></details>157<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">— vrai ou faux, avec justification</span><a class="box-anchor" href="#exo-5-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p5-94">(a) Le marché immobilier est efficient : les prix intègrent immédiatement toute l'information disponible. (b) Au Québec, environ 40 % des ménages sont locataires. (c) Un taux d'inoccupation élevé implique nécessairement des loyers bas. (d) Les phases d'expansion et de contraction des cycles immobiliers québécois ont des durées à peu près égales. (e) Le baromètre Centris qualifie de « marché de vendeurs » un ratio ventes/nouvelles inscriptions supérieur à 60 %.</p></div></div>158<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="p5-95">(a) <strong>Faux</strong> : hétérogénéité, transactions rares, information imparfaite — le marché immobilier est structurellement inefficient; c'est la raison d'être de l'évaluateur. (b) <strong>Vrai</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>40</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">\approx 40\,\%</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">40</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>, une proportion nettement supérieure à la moyenne canadienne. (c) <strong>Faux</strong> : Gatineau le démontre — inoccupation la plus élevée des grandes RMR québécoises (3,8 %) <em>et</em> loyer moyen 2 chambres le plus élevé au Québec (<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> 1 420 $) : le niveau des loyers dépend aussi du parc (neuf), des revenus locaux et du marché voisin (Ottawa). (d) <strong>Faux</strong> : les expansions durent historiquement 4 à 10 ans, les corrections 1 à 2 ans — le cycle est asymétrique. (e) <strong>Vrai</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>></mo><mn>60</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">>60\,\%</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">></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> = vendeurs; 40–60 % = équilibré; <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo><</mo><mn>40</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex"><40\,\%</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"><</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">40</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> = acheteurs.</p></div></details>159<h2 class="h-section" id="s-6"><span class="h-num">6</span><span class="h-text">Collecte et analyse des données</span></h2>160<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">— choisir la bonne source</span><a class="box-anchor" href="#exo-6-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-92">Pour chaque information recherchée, nommez la source québécoise la plus autorisée : (a) le prix officiel d'une vente conclue il y a 4 mois; (b) le délai d'exposition sur le marché de cette même vente; (c) l'existence d'une servitude de passage; (d) l'année de construction et les dimensions du bâtiment, sans frais; (e) la présence du bien en zone inondable; (f) le fait que le vendeur et l'acheteur sont des sociétés ayant le même actionnaire.</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="p6-93">(a) Le <strong>Registre foncier</strong> (acte de vente publié — la donnée officielle). (b) <strong>Centris</strong> (dates de mise en marché et de vente — information commerciale absente du Registre). (c) Le <strong>Registre foncier</strong> (servitudes publiées), complété par le <strong>certificat de localisation</strong> (servitudes apparentes). (d) Le <strong>rôle d'évaluation</strong> (gratuit : année, dimensions, valeurs). (e) Les <strong>géoportails</strong> (Géo-Index du MERN, cartographie fédérale, cartes municipales). (f) Le <strong>Registre des entreprises</strong> (REQ) — liens corporatifs entre les parties.</p></div></details>162<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">— tests de cohérence</span><a class="box-anchor" href="#exo-6-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-94">Dans un secteur où les unifamiliales se vendent en moyenne 295 $/pi<sup>2</sup> et où le ratio prix/valeur au rôle des ventes récentes tourne autour de 1,30, vous examinez trois ventes : A — <span class="num">455 000 $</span>, 1 540 pi<sup>2</sup>, valeur au rôle <span class="num">350 000 $</span>; B — <span class="num">368 000 $</span>, 1 490 pi<sup>2</sup>, valeur au rôle <span class="num">352 000 $</span>; C — <span class="num">610 000 $</span>, 1 610 pi<sup>2</sup>, valeur au rôle <span class="num">365 000 $</span>. Calculez pour chacune le prix au pied carré et le ratio prix/rôle, identifiez les ventes suspectes et formulez une hypothèse à investiguer pour chacune.</p></div></div>163<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">A : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>455</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>1</mn><mtext> </mtext><mn>540</mn><mo>≈</mo><mn>295</mn></mrow><annotation encoding="application/x-tex">455\,000/1\,540 \approx 295</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">455</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">540</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">295</span></span></span></span> $/pi<sup>2</sup>; ratio <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>455</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>350</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>1,30</mn></mrow><annotation encoding="application/x-tex">455\,000/350\,000 = 1{,}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">455</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000/350</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">30</span></span></span></span>. Parfaitement dans les normes du secteur : aucun signal d'alarme. B : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>368</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>1</mn><mtext> </mtext><mn>490</mn><mo>≈</mo><mn>247</mn></mrow><annotation encoding="application/x-tex">368\,000/1\,490 \approx164247</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">368</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">490</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">247</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><mo>−</mo><mn>16</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">-16\,\%</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">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> sous le marché); ratio <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1,05</mn></mrow><annotation encoding="application/x-tex">1{,}05</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">05</span></span></span></span>, nettement sous le 1,30 attendu. <strong class="c-rouge">Suspecte à la baisse</strong> : hypothèses — vente entre parties liées, vente sous pression (succession, saisie), état déficient non documenté. C : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>610</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>1</mn><mtext> </mtext><mn>610</mn><mo>≈</mo><mn>379</mn></mrow><annotation encoding="application/x-tex">610\,000/1\,610 \approx165379</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">610</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">610</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">379</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><mo>+</mo><mn>28</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">+28\,\%</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">28</span><span class="mspace" style="margin-right:0.1667em;"></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>1,67</mn></mrow><annotation encoding="application/x-tex">1{,}67</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">67</span></span></span></span>. <strong class="c-rouge">Suspecte à la hausse</strong> : hypothèses — rénovations majeures non reflétées au rôle, inclusions inhabituelles (meubles, spa), surenchère émotive, ou erreur de superficie. Dans les deux cas : confirmer au Registre foncier et auprès du courtier <em>avant</em> d'utiliser ou de rejeter.</p></div></details>166<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">— conditions particulières</span><a class="box-anchor" href="#exo-6-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-96">Pour chaque situation, indiquez le traitement approprié (utiliser tel quel, ajuster, ou exclure) et justifiez : (a) vente incluant un tracteur et les meubles du chalet, valeur estimée <span class="num">18 000 $</span>; (b) vente d'une maison par une succession, conclue en 3 semaines à un prix 12 % sous les ventes similaires; (c) vente où le vendeur consent une balance de prix de <span class="num">100 000 $</span> à 2 % alors que le marché est à 5 %; (d) vente d'un terrain au propriétaire du lot voisin, 25 % au-dessus du marché; (e) vente de plein gré, exposée 45 jours, sans condition, confirmée au Registre.</p></div></div>167<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p6-97">(a) <strong>Ajuster</strong> : déduire la valeur des inclusions (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>18</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">-18\,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">−</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:0.1667em;"></span><span class="mord">$</span></span></span></span>) pour isoler la composante immobilière. (b) <strong>Exclure</strong> (ou n'utiliser qu'à titre indicatif avec décote documentée) : vente sous pression — délai anormalement court et prix décoté cohérents avec une liquidation successorale. (c) <strong>Ajuster</strong> : le financement avantageux a une valeur que l'acheteur a payée dans le prix; il faut estimer l'équivalent comptant (<em>cash equivalency</em>) en actualisant l'avantage de taux. (d) <strong>Exclure</strong> ou ajuster fortement : motivation particulière (assemblage/voisinage) — la prime de convenance ne reflète pas le marché. (e) <strong>Utiliser tel quel</strong> : toutes les conditions de la valeur marchande sont réunies; c'est le comparable idéal.</p></div></details>168<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">— le certificat de localisation</span><a class="box-anchor" href="#exo-6-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-98">Le certificat de localisation d'un bien sujet révèle : (i) un cabanon du voisin empiétant de 0,8 m sur le lot; (ii) une servitude d'Hydro-Québec de 3 m le long de la ligne arrière; (iii) un agrandissement du bâtiment principal à 1,2 m de la ligne latérale alors que le règlement exige 1,5 m. Pour chaque constat, expliquez la nature du problème et son incidence possible sur la valeur ou sur le mandat.</p></div></div>169<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">(i) <strong>Empiétement subi</strong> : le voisin occupe une partie du lot; à régulariser (déplacement, servitude conventionnelle ou vente de parcelle). Incidence : nuisance juridique, incertitude — effet modérément négatif et obstacle possible au financement. (ii) <strong>Servitude d'utilité publique</strong> : bande arrière inconstructible; réduit la superficie utilisable et le potentiel (piscine, agrandissement). Effet négatif à quantifier selon l'usage du terrain. (iii) <strong>Non-conformité au zonage</strong> (marge latérale insuffisante) : selon le cas, droits acquis, dérogation mineure à demander, ou risque d'ordonnance. Incidence : incertitude juridique à divulguer au rapport; peut retarder ou compromettre une vente. Dans les trois cas, le certificat démontre son rôle : aucune de ces informations n'était visible dans Centris ni au rôle.</p></div></details>170<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">— monter un plan de collecte</span><a class="box-anchor" href="#exo-6-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-100">On vous confie l'évaluation d'un triplex de 1965 dans le Vieux-Hull, acheté par le client en 2019, avec locataires en place. Dressez, en six points, le plan de collecte complet : sources à consulter (dans l'ordre), données spécifiques au locatif à recueillir, et vérifications particulières qu'impose ce type de bien.</p></div></div>171<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">(1) <strong>Rôle d'évaluation</strong> : dimensions, année, valeurs, matricule. (2) <strong>Registre foncier</strong> : titres, acte d'achat 2019, hypothèques, servitudes, déclarations. (3) <strong>Zonage et géoportails</strong> : usages permis (le triplex est-il conforme?), zone inondable (Vieux-Hull : vigilance particulière — proximité des ruisseaux et de la rivière). (4) <strong>Données locatives</strong> : baux en vigueur, loyers réels, échéances, historique des augmentations (encadrement TAL), dépenses d'exploitation — taxes, assurances, énergie, entretien. (5) <strong>Inspection</strong> : état des trois logements, systèmes (électricité d'époque? plomberie galvanisée?), conformité incendie. (6) <strong>Comparables</strong> : ventes de plex du secteur (Centris + Registre foncier + entrevues, les ventes privées étant fréquentes pour les plex), avec confirmation systématique. Vérifications particulières du locatif : concordance loyers déclarés / baux; logements vacants ou loyers de complaisance (parenté); dossiers TAL en cours.</p></div></details>172<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">— vrai ou faux, avec justification</span><a class="box-anchor" href="#exo-6-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-102">(a) Centris capte la totalité des transactions résidentielles du Québec. (b) Le prix inscrit à l'acte de vente publié au Registre foncier prévaut sur le prix affiché dans Centris en cas de divergence. (c) Un ratio prix de vente / valeur au rôle très différent de celui des ventes voisines est un motif automatique de rejet du comparable. (d) Les NUPPEC exigent un niveau de vérification proportionnel à l'importance de la donnée. (e) Un certificat de localisation demeure valide indéfiniment.</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="p6-103">(a) <strong>Faux</strong> : les ventes privées (sans courtier), environ 15 à 20 % des transactions, y échappent. (b) <strong>Vrai</strong> : l'acte publié est la donnée officielle et opposable; Centris reflète la saisie du courtier. (c) <strong>Faux</strong> : c'est un motif d'<em>investigation</em>, pas de rejet automatique — l'écart peut s'expliquer (rénovations majeures, erreur au rôle) et la vente demeurer utilisable, éventuellement avec ajustement. (d) <strong>Vrai</strong> : diligence raisonnable et vérification proportionnelle — plus la donnée pèse dans la conclusion, plus la vérification doit être poussée. (e) <strong>Faux</strong> : il vaut tant que la situation de l'immeuble n'a pas changé; en pratique, on exige un certificat d'au plus une dizaine d'années, et à jour de toute modification.</p></div></details>174<h2 class="h-section" id="s-8"><span class="h-num">8</span><span class="h-text">La méthode de comparaison — Partie 1 : principes et sélection des comparables</span></h2>175<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">— vérification d'une vente</span><a class="box-anchor" href="#exo-8-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p8-93">Vous envisagez d'utiliser comme comparable une vente conclue à <span class="num">392 000 $</span> entre M. Tremblay et sa belle-sœur, incluant les électroménagers (valeur : <span class="num">6000 $</span>). Le prix demandé sur Centris était de <span class="num">429 000 $</span> et le délai de mise en marché de 9 jours seulement. Identifiez les indices qui commandent la prudence et indiquez le traitement approprié.</p></div></div>176<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">Trois signaux d'alarme. (1) <strong>Lien de dépendance</strong> : la transaction entre membres d'une même famille ne reflète généralement pas le marché libre — c'est le motif d'exclusion le plus fort. (2) <strong>Écart marqué</strong> entre prix demandé (<span class="num">429 000 $</span>) et prix payé (<span class="num">392 000 $</span>) combiné à un délai très court : cohérent avec un prix de faveur plutôt qu'avec une négociation de marché. (3) <strong>Inclusions</strong> : les électroménagers (<span class="num">6000 $</span>) devraient de toute façon être retranchés. <strong>Traitement :</strong> exclure ce comparable. On ne « répare » pas un lien de dépendance par un ajustement, car l'écart au marché est inconnu; on ne le conserverait, lourdement documenté, qu'en l'absence totale d'autres ventes — situation exceptionnelle.</p></div></details>177<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">— ajustement temporel</span><a class="box-anchor" href="#exo-8-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p8-95">Le marché d'un secteur de Gatineau progresse de 6 % par année. Un comparable s'est vendu <span class="num">380 000 $</span> il y a 10 mois. Calculez l'ajustement temporel et le prix ajusté. Que devient le résultat si le marché avait plutôt <em>reculé</em> de 4 % par année?</p></div></div>178<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p8-96">Marché haussier : ajustement <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>380</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,06</mn><mo>×</mo><mn>10</mn><mi mathvariant="normal">/</mi><mn>12</mn><mo>=</mo><mn>19</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 380\,000 \times 0{,}06 \times 10/12 =17919\,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">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:0.8389em;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:0.2222em;"></span><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:0.2778em;"></span><span 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">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; prix ajusté <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>380</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>19</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>399</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 380\,000 + 19\,000 = 399\,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">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">19</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">399</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">$</span></span></span></span>. Marché baissier : ajustement <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>380</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mo stretchy="false">(</mo><mo>−</mo><mn>0,04</mn><mo stretchy="false">)</mo><mo>×</mo><mn>10</mn><mi mathvariant="normal">/</mi><mn>12</mn><mo>=</mo><mo>−</mo><mtext> </mtext><mn>12</mn><mtext> </mtext><mn>667</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>≈</mo><mo>−</mo><mtext> </mtext><mn>12</mn><mtext> </mtext><mn>700</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 380\,000 \times (-0{,}04) \times 10/12 =180-\,12\,667\,\$ \approx -\,12\,700\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">380</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">−</span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">04</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">10/12</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">667</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</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:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mspace" style="margin-right:0.1667em;"></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">$</span></span></span></span>; prix ajusté <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>367</mn><mtext> </mtext><mn>300</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\approx181367\,300\,\$</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">367</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">300</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. L'ajustement temporel joue dans les deux sens : en marché baissier, un comparable ancien <em>surestime</em> la valeur actuelle et doit être ajusté à la baisse.</p></div></details>182<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">— sens des ajustements</span><a class="box-anchor" href="#exo-8-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p8-97">Pour chacune des situations suivantes, indiquez le signe de l'ajustement à appliquer <em>au comparable</em> : (a) le comparable possède une piscine creusée, pas le sujet; (b) le sujet a un garage double, le comparable un garage simple; (c) le comparable est situé sur une artère bruyante, le sujet dans une rue calme; (d) le comparable s'est vendu avec une balance de prix de vente à taux avantageux.</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="p8-98">(a) <strong>Négatif</strong> : le comparable est supérieur (piscine), on retranche sa contribution marchande. (b) <strong>Positif</strong> : le comparable est inférieur (garage simple contre double), on ajoute l'écart de valeur. (c) <strong>Positif</strong> : la localisation du comparable est inférieure (nuisance sonore), on le remonte au niveau du sujet. (d) <strong>Négatif</strong> : l'avantage de financement a gonflé le prix; on le retranche pour retrouver le prix comptant équivalent. Règle cardinale : on ajuste toujours <em>le comparable vers le sujet</em> — comparable supérieur <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> ajustement négatif; comparable inférieur <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> ajustement positif.</p></div></details>184<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">— mini grille complète</span><a class="box-anchor" href="#exo-8-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p8-99">Sujet : plain-pied de <span class="num">1100</span> pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><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>, terrain de <span class="num">5000</span> pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><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>, garage simple, bon état, secteur Aylmer. Comparable : vendu <span class="num">402 000 $</span> il y a 4 mois (marché : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo><mn>4,5</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">+4{,}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">+</span><span class="mord">4</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>/an), <span class="num">1180</span> pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><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>, terrain de <span class="num">5400</span> pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><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>, aucun garage, bon état, même secteur; vente libre, financement conventionnel; électroménagers inclus pour <span class="num">4000 $</span>. Valeurs unitaires : superficie 95 $/pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><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>; terrain 8 $/pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><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>; garage simple <span class="num">18 000 $</span>. Calculez l'indication de valeur, puis les pourcentages net et brut, et commentez la fiabilité.</p></div></div>185<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p8-100"><strong>Transactionnel.</strong> Composantes non immobilières : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mtext> </mtext><mn>4000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">-\,4000\,\$</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="mspace" style="margin-right:0.1667em;"></span><span class="mord">4000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> (électroménagers) — on peut le traiter d'emblée avec les vérifications transactionnelles : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>402</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>4</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>398</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">402\,000 - 4\,000 = 398\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">402</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">4</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">398</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>. Temps : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>398</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,045</mn><mo>×</mo><mn>4</mn><mi mathvariant="normal">/</mi><mn>12</mn><mo>=</mo><mn>5</mn><mtext> </mtext><mn>970</mn><mo>≈</mo><mo>+</mo><mtext> </mtext><mn>6000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">398\,000 \times 0{,}045 \times 4/12 = 5\,970 \approx186+\,6000\,\$</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">398</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">045</span><span class="mspace" style="margin-right:0.2222em;"></span><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">4/12</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:0.6444em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">970</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">6000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; base ajustée <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>404</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 404\,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">404</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">$</span></span></span></span>. <strong>Propriété.</strong> Superficie : le comparable a <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>80</mn></mrow><annotation encoding="application/x-tex">80</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">80</span></span></span></span> pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span> de plus : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>80</mn><mo>×</mo><mn>95</mn><mo>=</mo><mo>−</mo><mtext> </mtext><mn>7600</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">80 \times 95 = -\,7600\,\$</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">80</span><span class="mspace" style="margin-right:0.2222em;"></span><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">95</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">7600</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Terrain : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>400</mn></mrow><annotation encoding="application/x-tex">400</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">400</span></span></span></span> pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span> de plus : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>400</mn><mo>×</mo><mn>8</mn><mo>=</mo><mo>−</mo><mtext> </mtext><mn>3200</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">400 \times 8 = -\,3200\,\$</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">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:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">3200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Garage : le comparable n'en a pas : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo><mtext> </mtext><mn>18</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">+\,18\,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">+</span><span class="mspace" style="margin-right:0.1667em;"></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:0.1667em;"></span><span class="mord">$</span></span></span></span>. Ajustement net de propriété <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mo>−</mo><mn>7</mn><mtext> </mtext><mn>600</mn><mo>−</mo><mn>3</mn><mtext> </mtext><mn>200</mn><mo>+</mo><mn>18</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mo>+</mo><mtext> </mtext><mn>7200</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= -7\,600 - 3\,200 +18718\,000 = +\,7200\,\$</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">−</span><span class="mord">7</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">3</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">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:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">+</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">7200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. <strong>Indication de valeur</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>404</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>7</mn><mtext> </mtext><mn>200</mn><mo>=</mo><mn>411</mn><mtext> </mtext><mn>200</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>≈</mo><mn>411</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 404\,000 + 7\,200 = 411\,200\,\$188\approx 411\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">404</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">7</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">411</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">411</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>. <strong>Seuils</strong> (sur le prix de vente de <span class="num">402 000 $</span>) : net <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mo>−</mo><mn>4</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>6</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>7</mn><mtext> </mtext><mn>600</mn><mo>−</mo><mn>3</mn><mtext> </mtext><mn>200</mn><mo>+</mo><mn>18</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mo>+</mo><mtext> </mtext><mn>9200</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= -4\,000 + 6\,000 - 7\,600 - 3\,200 + 18\,000 = +\,9200\,\$</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">−</span><span class="mord">4</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">6</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">7</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">3</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">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:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">+</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">9200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>, soit <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2,3</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">2{,}3\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">2</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>; brut <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>4</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>6</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>7</mn><mtext> </mtext><mn>600</mn><mo>+</mo><mn>3</mn><mtext> </mtext><mn>200</mn><mo>+</mo><mn>18</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>38</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 4\,000 + 6\,000 + 7\,600 + 3\,200 + 18\,000 =18938\,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">4</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">6</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">7</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">3</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">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:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">38</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>, soit <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>9,7</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">9{,}7\,\%</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">9</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>. Les deux seuils sont largement respectés : comparable de <strong class="c-vert">haute fiabilité</strong>, qui mériterait un poids fort dans la réconciliation.</p></div></details>190<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">— réconciliation critique</span><a class="box-anchor" href="#exo-8-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p8-101">Quatre comparables ajustés donnent : <span class="num">424 600 $</span> (net <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2,4</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">2{,}4\,\%</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">2</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>), <span class="num">481 900 $</span> (net <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>16,1</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">16{,}1\,\%</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">16</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>), <span class="num">369 900 $</span> (net <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>19,6</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">19{,}6\,\%</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">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></span></span>) et <span class="num">448 600 $</span> (net <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5,6</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">5{,}6\,\%</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">5</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>). Un collègue propose de conclure à la moyenne, <span class="num">431 250 $</span>. Critiquez cette approche et proposez une conclusion mieux fondée.</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="p8-102">La moyenne arithmétique accorde <em>le même poids</em> à chaque indication, alors que leur fiabilité diffère radicalement : les comparables à <span class="num">481 900 $</span> et <span class="num">369 900 $</span> excèdent le repère de 15 % net — leurs indications sont les plus incertaines — tandis que ceux à <span class="num">424 600 $</span> et <span class="num">448 600 $</span> sont très fiables. La moyenne se trouve de surcroît tirée vers le bas par l'indication la plus faible (<span class="num">369 900 $</span>). Une réconciliation professionnelle pondère fortement les deux comparables fiables, dont les indications encadrent <span class="num">424 600 $</span>–<span class="num">448 600 $</span>, et conclut autour de <strong class="c-or"><span class="num">435 000 $</span></strong>, en mentionnant que les deux autres indications, quoique faibles individuellement, confirment que la valeur se situe bien dans l'étendue observée. La justification écrite du raisonnement fait partie intégrante de la conclusion.</p></div></details>192<h2 class="h-section" id="s-9"><span class="h-num">9</span><span class="h-text">La méthode de comparaison — Partie 2 : ajustements et réconciliation</span></h2>193<div class="box box-exo" id="exo-9-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 9.1</span><span class="box-title">— quiz éclair — seuils</span><a class="box-anchor" href="#exo-9-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p9-81">Un comparable vendu <span class="num">350 000 $</span> reçoit trois ajustements : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo><mtext> </mtext><mn>20</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">+\,20\,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">+</span><span class="mspace" style="margin-right:0.1667em;"></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:0.1667em;"></span><span class="mord">$</span></span></span></span>, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mtext> </mtext><mn>15</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">-\,15\,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">−</span><span class="mspace" style="margin-right:0.1667em;"></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:0.1667em;"></span><span class="mord">$</span></span></span></span> et <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo><mtext> </mtext><mn>8000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">+\,8000\,\$</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="mspace" style="margin-right:0.1667em;"></span><span class="mord">8000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Calculez ses ajustements net et brut, en dollars et en pourcentage, et vérifiez les seuils.</p></div></div>194<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p9-82">Net <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>20</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>15</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>8</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mo>+</mo><mtext> </mtext><mn>13</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 20\,000 - 15\,000 + 8\,000 = +\,13\,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">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:0.7278em;vertical-align:-0.0833em;"></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:0.2222em;"></span><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">8</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:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">+</span><span class="mspace" style="margin-right:0.1667em;"></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:0.1667em;"></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>13</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>350</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>3,7</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>≤</mo><mn>15</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">13\,000/350\,000 = 3{,}7\,\% \leq 15\,\%</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">13</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000/350</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">3</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 class="mspace" style="margin-right:0.2778em;"></span><span 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">%</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>20</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>15</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>8</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>43</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 20\,000 +19515\,000 + 8\,000 = 43\,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">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:0.7278em;vertical-align:-0.0833em;"></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:0.2222em;"></span><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">8</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">43</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>, soit <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>12,3</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>≤</mo><mn>25</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">12{,}3\,\% \leq19625\,\%</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">12</span><span class="mord"><span class="mpunct">,</span></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:0.2778em;"></span><span 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> ✓. Les deux seuils sont respectés : le comparable conserve une bonne fiabilité. Noter le contraste entre le net (les signes se compensent) et le brut (rien ne se compense) : c'est le brut qui révèle le volume réel de corrections.</p></div></details>197<div class="box box-exo" id="exo-9-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 9.2</span><span class="box-title">— analyse par paires imparfaites</span><a class="box-anchor" href="#exo-9-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p9-83">Vous disposez de deux ventes pour estimer la contribution d'un sous-sol fini. Vente A (sous-sol fini) : <span class="num">432 000 $</span>. Vente B (sous-sol non fini, mais terrain plus grand de <span class="num">600</span> pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><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> à 8 $/pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><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>) : <span class="num">412 000 $</span>. Estimez la contribution du sous-sol fini.</p></div></div>198<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p9-84">La paire est imparfaite : il faut d'abord neutraliser la différence de terrain. Avantage terrain de B : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>600</mn><mo>×</mo><mn>8</mn><mo>=</mo><mn>4800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">600 \times 8 = 4800\,\$</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">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">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:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">4800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Prix de B « à terrain égal » : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>412</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>4</mn><mtext> </mtext><mn>800</mn><mo>=</mo><mn>407</mn><mtext> </mtext><mn>200</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">412\,000 - 4\,800 = 407\,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">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">4</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">200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Contribution du sous-sol fini <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>432</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>407</mn><mtext> </mtext><mn>200</mn><mo>=</mo><mn>24</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>≈</mo><mn>25</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 432\,000 - 407\,200 = 24\,800\,\$ \approx19925\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">432</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">407</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. La démarche générale : purger la paire de ses différences secondaires <em>avant</em> d'isoler l'élément cible; chaque purge ajoutant de l'incertitude, on privilégie les paires exigeant le moins de corrections et l'on confirme par une seconde technique (coût déprécié : un aménagement de sous-sol d'environ <span class="num">35 000 $</span> contribuant à 70 % donnerait <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>24</mn><mtext> </mtext><mn>500</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\approx 24\,500\,\$</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">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> — convergence rassurante).</p></div></details>200<div class="box box-exo" id="exo-9-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 9.3</span><span class="box-title">— grille chaînée en pourcentages</span><a class="box-anchor" href="#exo-9-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p9-85">Un comparable s'est vendu <span class="num">500 000 $</span> il y a 6 mois. Analyse : vente avec légère pression du vendeur (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo><mn>2</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">+2\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">+</span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> pour ramener aux conditions libres), marché en hausse de 4 % par année, localisation supérieure au sujet (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>6</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">-6\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">6</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>), garage inférieur (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo><mtext> </mtext><mn>15</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">+\,15\,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">+</span><span class="mspace" style="margin-right:0.1667em;"></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:0.1667em;"></span><span class="mord">$</span></span></span></span>). Calculez l'indication de valeur en respectant l'ordre séquentiel.</p></div></div>201<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p9-86">Étape 3 (conditions de vente) : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>500</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>1,02</mn><mo>=</mo><mn>510</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">500\,000 \times 1{,}02 = 510\,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">500</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">02</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">510</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">$</span></span></span></span>. Étape 4 (marché, 6 mois à <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo><mn>4</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">+4\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">+</span><span class="mord">4</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>/an) : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>510</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mn>0,04</mn><mo>×</mo><mn>6</mn><mi mathvariant="normal">/</mi><mn>12</mn><mo stretchy="false">)</mo><mo>=</mo><mn>510</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>1,02</mn><mo>=</mo><mn>520</mn><mtext> </mtext><mn>200</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">510\,000 \times (1 + 0{,}04202\times 6/12) = 510\,000 \times 1{,}02 = 520\,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">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="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">04</span><span class="mspace" style="margin-right:0.2222em;"></span><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">6/12</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">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:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">02</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">520</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">$</span></span></span></span>. Étape 5 (localisation, sur la base de marché) : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>520</mn><mtext> </mtext><mn>200</mn><mo>×</mo><mo stretchy="false">(</mo><mo>−</mo><mn>0,06</mn><mo stretchy="false">)</mo><mo>=</mo><mo>−</mo><mtext> </mtext><mn>31</mn><mtext> </mtext><mn>212</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">520\,200 \times (-0{,}06) =203-\,31\,212\,\$</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">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: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">06</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:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">31</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">212</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; base <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>488</mn><mtext> </mtext><mn>988</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 488\,988\,\$</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">488</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">988</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Étape 6 (garage) : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo><mtext> </mtext><mn>15</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">+\,15\,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">+</span><span class="mspace" style="margin-right:0.1667em;"></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:0.1667em;"></span><span class="mord">$</span></span></span></span>. <strong>Indication</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>488</mn><mtext> </mtext><mn>988</mn><mo>+</mo><mn>15</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>503</mn><mtext> </mtext><mn>988</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>≈</mo><mn>504</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 488\,988 + 15\,000 =204503\,988\,\$ \approx 504\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">488</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">988</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">503</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">988</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</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">504</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">$</span></span></span></span>. Contre-exemple du désordre : appliquer la localisation sur le prix brut (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>500</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mo>−</mo><mn>0,06</mn><mo>=</mo><mo>−</mo><mtext> </mtext><mn>30</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">500\,000 \times -0{,}06 =205-\,30\,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">500</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">−</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:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">30</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>) aurait sous-corrigé de <span class="num">1212 $</span> — l'erreur d'ordre est silencieuse mais systématique.</p></div></details>206<div class="box box-exo" id="exo-9-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 9.4</span><span class="box-title">— réconciliation complète</span><a class="box-anchor" href="#exo-9-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p9-87">Quatre comparables ajustés : A <span class="num">512 000 $</span> (net 2 %, vente de 2 mois); B <span class="num">498 000 $</span> (net 4 %, 5 mois); C <span class="num">535 000 $</span> (net 18 %, 4 mois); D <span class="num">489 000 $</span> (net 6 %, 13 mois). Attribuez un poids à chaque indication, proposez une fourchette et une valeur ponctuelle, et rédigez la justification en trois phrases.</p></div></div>207<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="p9-88"><strong>Poids.</strong> A : fort (net minimal, vente très récente). B : fort (net faible, délai raisonnable). C : faible ou écarté (net <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>18</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>></mo><mn>15</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">18\,\% > 15\,\%</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">18</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">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> — conserver à titre de balise haute seulement). D : moyen-faible (net correct mais vente de 13 mois : l'ajustement temporel domine son indication). <strong>Fourchette utile</strong> (A–B) : <span class="num">498 000 $</span>–<span class="num">512 000 $</span>. <strong>Conclusion : <span class="num">505 000 $</span></strong> (arrondie au <span class="num">5000 $</span>). <strong>Justification type :</strong> « Les indications les plus fiables (A et B), aux ajustements nets de 2 et 4 % et aux ventes les plus récentes, encadrent la conclusion. L'indication C, dont l'ajustement net excède le repère de 15 %, n'a servi que de balise supérieure; l'indication D corrobore le bas de la fourchette malgré son ancienneté. La valeur retenue de <span class="num">505 000 $</span> reflète le poids prépondérant accordé à A, la vente la plus récente et la plus semblable au sujet. »</p></div></details>208<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">— détecter les erreurs d'une grille</span><a class="box-anchor" href="#exo-9-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p9-89">Un étudiant remet la grille suivante pour un comparable vendu <span class="num">420 000 $</span> il y a 9 mois (marché <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo><mn>5</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">+5\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">+</span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>/an) : localisation inférieure au sujet : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mtext> </mtext><mn>12</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></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:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mspace" style="margin-right:0.1667em;"></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:0.1667em;"></span><span class="mord">$</span></span></span></span>; temps : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo><mtext> </mtext><mn>15</mn><mtext> </mtext><mn>750</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">+\,15\,750\,\$</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="mspace" style="margin-right:0.1667em;"></span><span class="mord">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">750</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> appliqué <em>après</em> les ajustements physiques; superficie du sujet supérieure de <span class="num">100</span> pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span> : ajustement au sujet de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo><mtext> </mtext><mn>10</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">+\,10\,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">+</span><span class="mspace" style="margin-right:0.1667em;"></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:0.1667em;"></span><span class="mord">$</span></span></span></span>; conclusion : moyenne des trois comparables. Relevez les quatre erreurs et corrigez la logique.</p></div></div>209<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p9-90">(1) <strong>Signe de localisation inversé</strong> : un comparable <em>inférieur</em> en localisation reçoit un ajustement <em>positif</em> (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>, pour le remonter au niveau du sujet), non <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mtext> </mtext><mn>12</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></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:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mspace" style="margin-right:0.1667em;"></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:0.1667em;"></span><span class="mord">$</span></span></span></span>. (2) <strong>Ordre violé</strong> : l'ajustement temporel est transactionnel et s'applique <em>avant</em> les ajustements physiques, sur le prix corrigé des étapes 1 à 3 (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>420</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,05</mn><mo>×</mo><mn>9</mn><mi mathvariant="normal">/</mi><mn>12</mn><mo>=</mo><mo>+</mo><mtext> </mtext><mn>15</mn><mtext> </mtext><mn>750</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">420\,000210\times 0{,}05 \times 9/12 = +\,15\,750\,\$</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:0.8389em;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:1em;vertical-align:-0.25em;"></span><span class="mord">9/12</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:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">+</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">750</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>, appliqué en premier). (3) <strong>Ajustement au sujet</strong> : on n'ajuste jamais le sujet; si le sujet a <span class="num">100</span> pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span> de plus, le comparable est inférieur et reçoit <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo><mtext> </mtext><mn>10</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">+\,10\,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">+</span><span class="mspace" style="margin-right:0.1667em;"></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:0.1667em;"></span><span class="mord">$</span></span></span></span> (à 100 $/pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><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>). (4) <strong>Moyenne en guise de réconciliation</strong> : la conclusion doit pondérer les indications selon leur fiabilité (nombre et ampleur des ajustements, similarité, date, qualité des données), avec justification écrite.</p></div></details>211<h2 class="h-section" id="s-10"><span class="h-num">10</span><span class="h-text">La méthode du coût</span></h2>212<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">— formule fondamentale</span><a class="box-anchor" href="#exo-10-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-102">Un bâtiment industriel léger présente un coût de remplacement à neuf de <span class="num">1 250 000 $</span>, une dépréciation totale estimée à 42 % du coût à neuf et un terrain évalué à <span class="num">310 000 $</span>. Calculez la valeur par la méthode du coût, puis indiquez deux raisons pour lesquelles cette méthode est particulièrement pertinente pour ce type de propriété.</p></div></div>213<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p10-103">Dépréciation en dollars : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo>=</mo><mn>1</mn><mtext> </mtext><mn>250</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,42</mn><mo>=</mo><mn>525</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">D = 1\,250\,000 \times 0{,}42 = 525\,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:0.0278em;">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">1</span><span class="mspace" style="margin-right:0.1667em;"></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:0.2222em;"></span><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">42</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">525</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">$</span></span></span></span>.</p>214<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mi>V</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><msub><mi>C</mi><mtext>neuf</mtext></msub><mo>−</mo><msub><mi>D</mi><mtext>totale</mtext></msub><mo>+</mo><msub><mi>V</mi><mtext>terrain</mtext></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>1</mn><mtext> </mtext><mn>250</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>525</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>310</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">1</mn><mtext> </mtext><mn mathvariant="bold">035</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}V &= C_{\text{neuf}} - D_{\text{totale}} + V_{\text{terrain}}\\215 &= 1\,250\,000 - 525\,000 + 310\,000 = \uqotitle{1\,035\,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></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:0.0715em;">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:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">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 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">1</span><span class="mspace" style="margin-right:0.1667em;"></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:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">525</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">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 class="mord" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">1</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">035</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">000</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</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>216<p id="p10-104">Valeur arrondie : environ <span class="num">1 035 000 $</span>. Pertinence pour l'industriel : (1) les ventes comparables d'immeubles industriels sont souvent rares (marché mince), ce qui affaiblit la méthode de comparaison; (2) plusieurs bâtiments industriels sont adaptés sur mesure à leur occupant (quasi-usage spécial), de sorte que ni les comparables ni les revenus ne reflètent bien leur valeur pour l'utilisateur.</p></div></details>217<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">— coût à neuf complet</span><a class="box-anchor" href="#exo-10-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-105">Un plain-pied de <span class="num">1350</span> pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><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> doit être évalué. Données : coût unitaire de 172 $/pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><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> (qualité moyenne), facteur de localisation de 1,04, garage simple de 280 pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><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> à 70 $/pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><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>, sous-sol fini de 900 pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><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> à 52 $/pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>. Hypothèses : coûts indirects de 14 % et profit de l'entrepreneur de 8 %, tous deux sur les coûts directs. Calculez le coût de remplacement à neuf complet.</p></div></div>218<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p10-106">Coûts directs :</p>219<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>R</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>sidence</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>1</mn><mtext> </mtext><mn>350</mn><mo>×</mo><mn>172</mn><mo>×</mo><mn>1,04</mn><mo>=</mo><mn>241</mn><mtext> </mtext><mn>488</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Garage</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>280</mn><mo>×</mo><mn>70</mn><mo>=</mo><mn>19</mn><mtext> </mtext><mn>600</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Sous-sol</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>900</mn><mo>×</mo><mn>52</mn><mo>=</mo><mn>46</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Total des co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>ts directs</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>241</mn><mtext> </mtext><mn>488</mn><mo>+</mo><mn>19</mn><mtext> </mtext><mn>600</mn><mo>+</mo><mn>46</mn><mtext> </mtext><mn>800</mn><mo>=</mo><mn>307</mn><mtext> </mtext><mn>888</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Résidence} &= 1\,350 \times 172 \times 1{,}04 = 241\,488\,\$\\220\text{Garage} &= 280 \times 70 = 19\,600\,\$\\221\text{Sous-sol} &= 900 \times 52 = 46\,800\,\$\\222\text{Total des coûts directs} &= 241\,488 + 19\,600 + 46\,800 = 307\,888\,\$\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:5.7em;vertical-align:-2.6em;"></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:3.1em;"><span style="top:-5.26em;"><span class="pstrut" style="height:3em;"></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">sidence</span></span></span></span><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Garage</span></span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Sous-sol</span></span></span></span><span style="top:-0.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Total des 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">ts directs</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.6em;"><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:3.1em;"><span style="top:-5.26em;"><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">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">350</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">172</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="mord"><span class="mpunct">,</span></span><span class="mord">04</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">241</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">488</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><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">280</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">70</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">19</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">$</span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">900</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">52</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">46</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-0.76em;"><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">241</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">488</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">19</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 class="mord">46</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 class="mord">307</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">888</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.6em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>223<p id="p10-107">Indirects et profit :</p>224<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>ts indirects (14</mtext><mtext> </mtext><mtext>%)</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>307</mn><mtext> </mtext><mn>888</mn><mo>×</mo><mn>0,14</mn><mo>=</mo><mn>43</mn><mtext> </mtext><mn>104</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Profit (8</mtext><mtext> </mtext><mtext>%)</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>307</mn><mtext> </mtext><mn>888</mn><mo>×</mo><mn>0,08</mn><mo>=</mo><mn>24</mn><mtext> </mtext><mn>631</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>C</mi><mtext>neuf</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>307</mn><mtext> </mtext><mn>888</mn><mo>+</mo><mn>43</mn><mtext> </mtext><mn>104</mn><mo>+</mo><mn>24</mn><mtext> </mtext><mn>631</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">375</mn><mtext> </mtext><mn mathvariant="bold">623</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Coûts indirects (14\,\%)} &= 307\,888 \times 0{,}14 = 43\,104\,\$\\225\text{Profit (8\,\%)} &= 307\,888 \times 0{,}08 = 24\,631\,\$\\226C_{\text{neuf}} &= 307\,888 + 43\,104 + 24\,631 = \uqotitle{375\,623\,\$}\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 text"><span class="mord">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">ts indirects (14</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%)</span></span></span></span><span style="top:-3.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Profit (8</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%)</span></span></span></span><span style="top:-1.51em;"><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><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">307</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">888</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">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 class="mord">43</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">104</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-3.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">307</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">888</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">08</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">631</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</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">307</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">888</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">43</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">104</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">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">631</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:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">375</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">623</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</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>227<p id="p10-108">Soit environ <span class="num">376 000 $</span>. Remarquez la structure du calcul : les pourcentages d'indirects et de profit s'appliquent aux coûts directs <em>totaux</em>, extras compris — pas seulement au coût de base de la résidence.</p></div></details>228<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">— âge/vie modifiée et ventilation</span><a class="box-anchor" href="#exo-10-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-109">Une résidence présente un coût de remplacement à neuf de <span class="num">520 000 $</span>. L'inspection révèle : toiture à remplacer (<span class="num">14 000 $</span>), peinture extérieure (<span class="num">6000 $</span>), salle de bain principale désuète dont la mise à jour est rentable (<span class="num">9000 $</span>), et des plafonds de sept pieds au sous-sol dont la perte de valeur au marché est estimée à <span class="num">11 000 $</span>. Le bâtiment a 24 ans d'âge chronologique, mais un entretien exemplaire lui confère un âge effectif de 15 ans; la vie utile économique retenue est de 60 ans. Aucune dépréciation externe. Calculez la dépréciation totale et le taux global de dépréciation.</p></div></div>229<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="p10-110">Classons d'abord chaque élément. La toiture (<span class="num">14 000 $</span>) et la peinture (<span class="num">6000 $</span>) relèvent de l'entretien différé — physique curable, pour un total de <span class="num">20 000 $</span>. La salle de bain (<span class="num">9000 $</span>) est une obsolescence de design dont la correction est rentable : fonctionnelle curable. Les plafonds bas (<span class="num">11 000 $</span>) sont une obsolescence de design impossible à corriger économiquement : fonctionnelle incurable. Aucune dépréciation économique n'est signalée.</p>230<p id="p10-111">Physique incurable par âge/vie modifiée — la base exclut l'entretien différé (mais pas la fonctionnelle, qui ne fait pas partie de l'usure physique) :</p>231<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Base</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>520</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>20</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>500</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>D</mi><mtext>phys. incurable</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mfrac><mn>15</mn><mn>60</mn></mfrac><mo>×</mo><mn>500</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>0,25</mn><mo>×</mo><mn>500</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>125</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Base} &= 520\,000 - 20\,000 = 500\,000\,\$\\232D_{\text{phys.\ incurable}} &= \frac{15}{60} \times 500\,000233 = 0{,}25 \times 500\,000 = 125\,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">Base</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:0.3361em;"><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. incurable</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></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">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">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 class="mord">500</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"><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">60</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">15</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="mord">500</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">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 class="mord">500</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">125</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">$</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.5037em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>234<p id="p10-112">Dépréciation totale :</p>235<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>D</mi><mtext>totale</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>20</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>125</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>9</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>11</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>0</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">165</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Taux global</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mfrac><mrow><mn>165</mn><mtext> </mtext><mn>000</mn></mrow><mrow><mn>520</mn><mtext> </mtext><mn>000</mn></mrow></mfrac><mo>=</mo><mn>31,7</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}D_{\text{totale}} &= 20\,000 + 125\,000 + 9\,000 + 11\,000 + 0236 = \uqotitle{165\,000\,\$}\\237\text{Taux global} &= \frac{165\,000}{520\,000} = 31{,}7\,\%\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"><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:-2.5037em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord text"><span class="mord">Taux global</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">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 class="mord">125</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">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 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 class="mord">0</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:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">165</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">000</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></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"><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">520</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</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">165</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</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">31</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><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>238<p id="p10-113">C'est bien l'âge <em>effectif</em> (15 ans) qui entre dans le ratio, et non l'âge chronologique (24 ans) : utiliser 24/60 aurait gonflé la dépréciation physique incurable à <span class="num">200 000 $</span>, soit une erreur de <span class="num">75 000 $</span>.</p></div></details>239<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">— valeur du terrain par extraction et répartition</span><a class="box-anchor" href="#exo-10-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-114">Dans un secteur où presque aucun terrain vacant ne se vend, vous relevez la vente récente d'une propriété bâtie à <span class="num">610 000 $</span>. Vous estimez le coût à neuf de son bâtiment à <span class="num">560 000 $</span> et sa dépréciation à 35 %. <strong>a)</strong> Estimez la valeur du terrain par extraction. <strong>b)</strong> Le rôle d'évaluation du secteur indique un ratio terrain/total typique de 28 % : vérifiez votre résultat par répartition et commentez l'écart.</p></div></div>240<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p10-115"><strong>a) Extraction.</strong></p>241<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>C</mi><mrow><mtext>b</mtext><mover accent="true"><mtext>a</mtext><mo>ˆ</mo></mover><mtext>timent d</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>pr</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>ci</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>560</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mn>0,35</mn><mo stretchy="false">)</mo><mo>=</mo><mn>364</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>V</mi><mi>T</mi></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>610</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>364</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">246</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}C_{\text{bâtiment déprécié}} &= 560\,000 \times (1 - 0{,}35) = 364\,000\,\$\\242V_T &= 610\,000 - 364\,000 = \uqotitle{246\,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:0.0715em;">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">b</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">a</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">ˆ</span></span></span></span></span></span></span><span class="mord mtight">timent d</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">pr</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">ci</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:0.2861em;"><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"><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:0.3283em;"><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 mathnormal mtight" style="margin-right:0.1389em;">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><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">560</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">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 class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">35</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">364</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:-2.26em;"><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">610</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">364</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:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">246</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">000</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.1em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>243<p id="p10-116"><strong>b) Répartition.</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>T</mi></msub><mo>=</mo><mn>610</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,28</mn><mo>=</mo><mn>170</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">V_T = 610\,000 \times 0{,}28 = 170\,800\,\$</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:0.3283em;"><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 mathnormal mtight" style="margin-right:0.1389em;">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:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">610</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">28</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">170</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>. L'écart est important (<span class="num">75 200 $</span>, soit environ 44 % de plus par extraction). Deux lectures possibles : soit la dépréciation de 35 % est sous-estimée (chaque point de dépréciation en plus réduit la valeur extraite du terrain de <span class="num">5600 $</span>), soit le ratio de 28 % du rôle est dépassé — fréquent dans les secteurs où la valeur des terrains monte plus vite que celle des bâtiments. L'évaluateur documenterait les deux hypothèses et chercherait une troisième indication (vente de terrain vacant même éloignée, méthode résiduelle) avant de conclure. L'exercice illustre la fragilité de l'extraction : elle hérite de toute l'incertitude de la dépréciation.</p></div></details>244<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">— cas intégrateur — méthode complète</span><a class="box-anchor" href="#exo-10-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-117">Un duplex de Gatineau (secteur Aylmer) doit être évalué par la méthode du coût au 1<sup>er</sup> septembre 2026. Données : superficie totale de <span class="num">2100</span> pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><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> à 178 $/pi<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8141em;"></span><span class="mord"><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> (facteur de localisation déjà inclus); aucun garage; coûts indirects de 15 % et profit de 10 % (sur les coûts directs); entretien différé de <span class="num">18 000 $</span>; âge effectif de 22 ans; vie utile de 55 ans; cuisine des deux logements à mettre à jour pour <span class="num">16 000 $</span> (rentable); proximité d'une voie ferrée dont l'analyse de paires indique un escompte de 4 % sur la valeur des propriétés du secteur, estimé ici à <span class="num">17 000 $</span>; terrain évalué à <span class="num">125 000 $</span> par comparaison directe. Calculez la valeur par la méthode du coût, en présentant le bordereau complet.</p></div></div>245<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p10-118"><strong>Étape 1 — Coût à neuf.</strong></p>246<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>ts directs</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>2</mn><mtext> </mtext><mn>100</mn><mo>×</mo><mn>178</mn><mo>=</mo><mn>373</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Indirects (15</mtext><mtext> </mtext><mtext>%)</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>373</mn><mtext> </mtext><mn>800</mn><mo>×</mo><mn>0,15</mn><mo>=</mo><mn>56</mn><mtext> </mtext><mn>070</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Profit (10</mtext><mtext> </mtext><mtext>%)</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>373</mn><mtext> </mtext><mn>800</mn><mo>×</mo><mn>0,10</mn><mo>=</mo><mn>37</mn><mtext> </mtext><mn>380</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><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>373</mn><mtext> </mtext><mn>800</mn><mo>+</mo><mn>56</mn><mtext> </mtext><mn>070</mn><mo>+</mo><mn>37</mn><mtext> </mtext><mn>380</mn><mo>=</mo><mn>467</mn><mtext> </mtext><mn>250</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Coûts directs} &= 2\,100 \times 178 = 373\,800\,\$\\247\text{Indirects (15\,\%)} &= 373\,800 \times 0{,}15 = 56\,070\,\$\\248\text{Profit (10\,\%)} &= 373\,800 \times 0{,}10 = 37\,380\,\$\\249C_{\text{neuf}} &= 373\,800 + 56\,070 + 37\,380 = 467\,250\,\$\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:5.7em;vertical-align:-2.6em;"></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:3.1em;"><span style="top:-5.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">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">ts directs</span></span></span></span><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Indirects (15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%)</span></span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Profit (10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%)</span></span></span></span><span style="top:-0.76em;"><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><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.6em;"><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:3.1em;"><span style="top:-5.26em;"><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">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 class="mord">178</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">373</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 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">373</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 class="mord">0</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 class="mord">56</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">070</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">373</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">10</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">37</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">380</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-0.76em;"><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">373</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 class="mord">56</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">070</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">37</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">380</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">467</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">250</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.6em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>250<p id="p10-119"><strong>Étape 2 — Dépréciation.</strong> Physique curable : <span class="num">18 000 $</span>. Physique incurable (âge/vie modifiée) :</p>251<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Base</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>467</mn><mtext> </mtext><mn>250</mn><mo>−</mo><mn>18</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>449</mn><mtext> </mtext><mn>250</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>D</mi><mtext>phys. incurable</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mfrac><mn>22</mn><mn>55</mn></mfrac><mo>×</mo><mn>449</mn><mtext> </mtext><mn>250</mn><mo>=</mo><mn>0,40</mn><mo>×</mo><mn>449</mn><mtext> </mtext><mn>250</mn><mo>=</mo><mn>179</mn><mtext> </mtext><mn>700</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Base} &= 467\,250 - 18\,000 = 449\,250\,\$\\252D_{\text{phys.\ incurable}} &= \frac{22}{55} \times 449\,250253 = 0{,}40 \times 449\,250 = 179\,700\,\$\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">Base</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:0.3361em;"><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. incurable</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></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">467</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 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 class="mord">449</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">250</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"><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">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:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">449</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 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 class="mord">449</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 class="mord">179</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><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>254<p id="p10-120">Fonctionnelle curable (cuisines) : <span class="num">16 000 $</span>. Économique (voie ferrée) : <span class="num">17 000 $</span>.</p>255<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>D</mi><mtext>totale</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>18</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>179</mn><mtext> </mtext><mn>700</mn><mo>+</mo><mn>16</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>17</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>230</mn><mtext> </mtext><mn>700</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}D_{\text{totale}} &= 18\,000 + 179\,700 + 16\,000 + 17\,000 = 230\,700\,\$\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.2em;vertical-align:-0.35em;"></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:0.85em;"><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><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.35em;"><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:0.85em;"><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">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 class="mord">179</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">16</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">17</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">230</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><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.35em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>256<p id="p10-121">Taux global : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>230</mn><mtext> </mtext><mn>700</mn><mi mathvariant="normal">/</mi><mn>467</mn><mtext> </mtext><mn>250</mn><mo>=</mo><mn>49,4</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">230\,700 / 467\,250 = 49{,}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="mord">230</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">700/467</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:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">49</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> — élevé mais plausible pour un bâtiment d'âge effectif 22/55 avec obsolescence et nuisance externe.</p>257<p id="p10-122"><strong>Étapes 3 et 4 — Terrain et conclusion.</strong></p>258<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><mn>467</mn><mtext> </mtext><mn>250</mn><mo>−</mo><mn>230</mn><mtext> </mtext><mn>700</mn><mo>+</mo><mn>125</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>361</mn><mtext> </mtext><mn>550</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}V &= 467\,250 - 230\,700 + 125\,000 = 361\,550\,\$\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.2em;vertical-align:-0.35em;"></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:0.85em;"><span style="top:-3.01em;"><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:0.35em;"><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:0.85em;"><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">467</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 class="mord">230</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">125</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">361</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">550</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.35em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>259<p id="p10-123"><strong>Valeur par la méthode du coût : environ 360 000 $</strong> (arrondie au 5 000 $). Dans un rapport réel, ce duplex — un immeuble à revenus — serait évalué principalement par la méthode du revenu (séances 11 et 12) et par comparaison; la méthode du coût jouerait le rôle de vérification.</p></div></details>260<h2 class="h-section" id="s-11"><span class="h-num">11</span><span class="h-text">La méthode du revenu — Partie 1 : du revenu brut au RNE</span></h2>261<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">— triangle valeur–RNE–TGA</span><a class="box-anchor" href="#exo-11-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-86"><strong>a)</strong> Un immeuble affiche un RNE stabilisé de <span class="num">84 500 $</span> et le marché indique un TGA de 6,2 % : quelle est sa valeur? <strong>b)</strong> Un immeuble s'est vendu <span class="num">1 450 000 $</span> avec un RNE de <span class="num">78 300 $</span> : quel TGA cette vente exprime-t-elle? <strong>c)</strong> Un acheteur exige un TGA de 5,75 % et dispose de <span class="num">900 000 $</span> : quel RNE minimal doit-il trouver?</p></div></div>262<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p11-87"><strong>a)</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mn>84</mn><mtext> </mtext><mn>500</mn><mi mathvariant="normal">/</mi><mn>0,062</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>362</mn><mtext> </mtext><mn>903</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>≈</mo><mn>1</mn><mtext> </mtext><mn>363</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">V = 84\,500 / 0{,}062 = 1\,362\,903\,\$ \approx2631\,363\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">84</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500/0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">062</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">362</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">903</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</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">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">363</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>.<br> <strong>b)</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>TGA</mtext><mo>=</mo><mn>78</mn><mtext> </mtext><mn>300</mn><mi mathvariant="normal">/</mi><mn>1</mn><mtext> </mtext><mn>450</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>0,0540</mn><mo>=</mo><mn>5,40</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">\text{TGA} = 78\,300 / 1\,450\,000 = 0{,}0540 = 5{,}40\,\%</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 text"><span class="mord">TGA</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">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">300/1</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:0.2778em;"></span><span 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">0540</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">40</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>.<br> <strong>c)</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>RNE</mtext><mo>=</mo><mi>V</mi><mo>×</mo><mtext>TGA</mtext><mo>=</mo><mn>900</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,0575</mn><mo>=</mo><mn>51</mn><mtext> </mtext><mn>750</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\text{RNE} = V \times \text{TGA} = 900\,000 \times 0{,}0575 =26451\,750\,\$</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 text"><span class="mord">RNE</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:0.7667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord text"><span class="mord">TGA</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">900</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">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">51</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">750</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> par année.<br> Les trois questions sont les trois faces du même triangle : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mtext>RNE</mtext><mi mathvariant="normal">/</mi><mtext>TGA</mtext></mrow><annotation encoding="application/x-tex">V =265\text{RNE}/\text{TGA}</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="mord text"><span class="mord">RNE</span></span><span class="mord">/</span><span class="mord text"><span class="mord">TGA</span></span></span></span></span>, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>TGA</mtext><mo>=</mo><mtext>RNE</mtext><mi mathvariant="normal">/</mi><mi>V</mi></mrow><annotation encoding="application/x-tex">\text{TGA} = \text{RNE}/V</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 text"><span class="mord">TGA</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 text"><span class="mord">RNE</span></span><span class="mord">/</span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span></span></span></span> et <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>RNE</mtext><mo>=</mo><mi>V</mi><mo>×</mo><mtext>TGA</mtext></mrow><annotation encoding="application/x-tex">\text{RNE} = V \times266\text{TGA}</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 text"><span class="mord">RNE</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:0.7667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord text"><span class="mord">TGA</span></span></span></span></span>.</p></div></details>267<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">— RBP et RBE d'un 8-plex</span><a class="box-anchor" href="#exo-11-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-88">Un 8-plex de Gatineau compte 4 logements de 4½ (loyer du marché : 1 175 $/mois) et 4 logements de 3½ (marché : 975 $/mois). Les baux en vigueur totalisent 8 150 $/mois. L'immeuble offre 6 places de stationnement à 70 $/mois et une buanderie rapportant environ <span class="num">1400 $</span>/an. Hypothèses : inoccupation de 3,0 %, mauvaises créances de 1,0 %. <strong>a)</strong> Calculez le RBP. <strong>b)</strong> Calculez le RBE. <strong>c)</strong> Chiffrez l'écart annuel contractuel–marché et donnez-en la cause probable.</p></div></div>268<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p11-89"><strong>a) RBP aux loyers du marché :</strong></p>269<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mn>4</mn><mo>×</mo><mn>1</mn><mtext> </mtext><mn>175</mn><mo>×</mo><mn>12</mn></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>56</mn><mtext> </mtext><mn>400</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mn>4</mn><mo>×</mo><mn>975</mn><mo>×</mo><mn>12</mn></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>46</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>RBP</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>56</mn><mtext> </mtext><mn>400</mn><mo>+</mo><mn>46</mn><mtext> </mtext><mn>800</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">103</mn><mtext> </mtext><mn mathvariant="bold">200</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}4 \times 1\,175 \times 12 &= 56\,400\,\$\\2704 \times 975 \times 12 &= 46\,800\,\$\\271\text{RBP} &= 56\,400 + 46\,800 = \uqotitle{103\,200\,\$}\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">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 class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></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 class="mord">12</span></span></span><span style="top:-3.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><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 class="mord">975</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">12</span></span></span><span style="top:-1.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">RBP</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 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">56</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">$</span></span></span><span style="top:-3.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">46</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span 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">56</span><span class="mspace" style="margin-right:0.1667em;"></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 class="mord">46</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 class="mord" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">103</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">200</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.85em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>272<p id="p11-90"><strong>b) RBE :</strong></p>273<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Inoccupation (3</mtext><mtext> </mtext><mtext>%)</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>103</mn><mtext> </mtext><mn>200</mn><mo>×</mo><mn>0,03</mn><mo>=</mo><mn>3</mn><mtext> </mtext><mn>096</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Mauvaises cr</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>ances (1</mtext><mtext> </mtext><mtext>%)</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>103</mn><mtext> </mtext><mn>200</mn><mo>×</mo><mn>0,01</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>032</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Stationnement</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>6</mn><mo>×</mo><mn>70</mn><mo>×</mo><mn>12</mn><mo>=</mo><mn>5</mn><mtext> </mtext><mn>040</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>RBE</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>103</mn><mtext> </mtext><mn>200</mn><mo>−</mo><mn>3</mn><mtext> </mtext><mn>096</mn><mo>−</mo><mn>1</mn><mtext> </mtext><mn>032</mn><mo>+</mo><mn>5</mn><mtext> </mtext><mn>040</mn><mo>+</mo><mn>1</mn><mtext> </mtext><mn>400</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">105</mn><mtext> </mtext><mn mathvariant="bold">512</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Inoccupation (3\,\%)} &= 103\,200 \times 0{,}03 = 3\,096\,\$\\274\text{Mauvaises créances (1\,\%)} &= 103\,200 \times 0{,}01 = 1\,032\,\$\\275\text{Stationnement} &= 6 \times 70 \times 12 = 5\,040\,\$\\276\text{RBE} &= 103\,200 - 3\,096 - 1\,032 + 5\,040 + 1\,400277 = \uqotitle{105\,512\,\$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:5.7em;vertical-align:-2.6em;"></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:3.1em;"><span style="top:-5.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Inoccupation (3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%)</span></span></span></span><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Mauvaises cr</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">ances (1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%)</span></span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Stationnement</span></span></span></span><span style="top:-0.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">RBE</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.6em;"><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:3.1em;"><span style="top:-5.26em;"><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">103</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">0</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 class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">096</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><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">103</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">0</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 class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">032</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">6</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">70</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">040</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-0.76em;"><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">103</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">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">096</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">032</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">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">040</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">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 class="mord" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">105</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">512</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.6em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>278<p id="p11-91"><strong>c)</strong> Loyers contractuels annuels : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>8</mn><mtext> </mtext><mn>150</mn><mo>×</mo><mn>12</mn><mo>=</mo><mn>97</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">8\,150 \times 12 = 97\,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">8</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">150</span><span class="mspace" style="margin-right:0.2222em;"></span><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:0.2778em;"></span><span 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">97</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">$</span></span></span></span>; écart : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>103</mn><mtext> </mtext><mn>200</mn><mo>−</mo><mn>97</mn><mtext> </mtext><mn>800</mn><mo>=</mo><mn>5400</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">103\,200 - 97\,800 = 5400\,\$</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">103</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">97</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">5400</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>/an (5,2 %). Cause probable : l'encadrement des loyers par le TAL, qui maintient sous le marché les loyers des locataires en place — l'écart se rattrapera au rythme du roulement.</p></div></details>279<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">— tri des dépenses admissibles</span><a class="box-anchor" href="#exo-11-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-92">L'état des résultats fourni par le propriétaire d'un 12-logements contient les postes suivants. Pour chacun, indiquez s'il entre dans les dépenses d'exploitation du RNE (tel quel, ajusté, ou exclu) et pourquoi : taxes foncières <span class="num">16 500 $</span>; assurances <span class="num">6800 $</span>; intérêts hypothécaires <span class="num">38 200 $</span>; amortissement <span class="num">21 000 $</span>; déneigement <span class="num">3500 $</span>; remplacement complet de la toiture <span class="num">34 000 $</span> (fait cette année); aucune gestion (autogéré); électricité des communs <span class="num">3600 $</span>.</p></div></div>280<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="p11-93">Les taxes foncières, les assurances, le déneigement et l'électricité des communs sont admissibles tels quels — total <span class="num">30 400 $</span> —, en validant taxes et assurances sur les documents officiels. Les intérêts hypothécaires (<span class="num">38 200 $</span>) sont <strong class="c-rouge">exclus</strong> : service de la dette, choix de financement du propriétaire. L'amortissement (<span class="num">21 000 $</span>) est <strong class="c-rouge">exclu</strong> : écriture comptable et fiscale, sans sortie de fonds d'exploitation. La toiture (<span class="num">34 000 $</span>) est <strong class="c-rouge">exclue comme dépense de l'année</strong> : dépense en capital non récurrente, elle entre <em>lissée</em> par la réserve pour remplacement (par exemple <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>34</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>22</mn></mrow><annotation encoding="application/x-tex">34\,000 / 22</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">34</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000/22</span></span></span></span> ans <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> 1 545 $/an dans la réserve globale). À l'inverse, la gestion est <strong class="c-vert">à ajouter</strong> même si l'immeuble est autogéré — environ 5 % du RBE, valeur de marché du travail de gestion — et il faudra <strong class="c-vert">ajouter</strong> une réserve pour remplacement complète si l'état n'en contient pas. L'exercice reproduit la reconstruction type : les états du propriétaire mélangent exploitation, financement, fiscalité et capital — le RNE économique ne garde que l'exploitation.</p></div></details>281<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">— reconstruction complète d'un RNE</span><a class="box-anchor" href="#exo-11-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-94">Reconstituez le RNE économique d'un 10-logements de Hull : 6 <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> 4½ au marché à 1 125 $/mois, 4 <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> 3½ au marché à 925 $/mois; 8 stationnements à 65 $/mois; buanderie <span class="num">1500 $</span>/an; inoccupation 3,0 %; mauvaises créances 1,0 %; taxes <span class="num">13 200 $</span>; assurances <span class="num">5400 $</span>; entretien 4,5 % du RBE; énergie des communs <span class="num">2600 $</span>; gestion 5,0 % du RBE; conciergerie <span class="num">3600 $</span>; déneigement <span class="num">3000 $</span>; paysager <span class="num">1200 $</span>; réserve <span class="num">6500 $</span>. Calculez RBP, RBE, dépenses totales, RNE, puis les ratios dépenses/RBE et RNE/RBE, et commentez leur vraisemblance.</p></div></div>282<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="p11-95"><strong>RBP :</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>6</mn><mo>×</mo><mn>1</mn><mtext> </mtext><mn>125</mn><mo>×</mo><mn>12</mn><mo>=</mo><mn>81</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">6 \times 1\,125 \times 12 = 81\,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:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">125</span><span class="mspace" style="margin-right:0.2222em;"></span><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:0.2778em;"></span><span 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">81</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><mn>4</mn><mo>×</mo><mn>925</mn><mo>×</mo><mn>12</mn><mo>=</mo><mn>44</mn><mtext> </mtext><mn>400</mn></mrow><annotation encoding="application/x-tex">4 \times 925 \times 12283= 44\,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">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:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">925</span><span class="mspace" style="margin-right:0.2222em;"></span><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:0.2778em;"></span><span 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">44</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span></span></span></span>; RBP <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">125</mn><mtext> </mtext><mn mathvariant="bold">400</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= \uqotitle{125\,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" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">125</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">400</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span>.<br> <strong>RBE :</strong></p>284<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Inoccupation</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>125</mn><mtext> </mtext><mn>400</mn><mo>×</mo><mn>0,03</mn><mo>=</mo><mn>3</mn><mtext> </mtext><mn>762</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Mauvaises cr</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>ances</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>125</mn><mtext> </mtext><mn>400</mn><mo>×</mo><mn>0,01</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>254</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Stationnement</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>8</mn><mo>×</mo><mn>65</mn><mo>×</mo><mn>12</mn><mo>=</mo><mn>6</mn><mtext> </mtext><mn>240</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>RBE</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>125</mn><mtext> </mtext><mn>400</mn><mo>−</mo><mn>3</mn><mtext> </mtext><mn>762</mn><mo>−</mo><mn>1</mn><mtext> </mtext><mn>254</mn><mo>+</mo><mn>6</mn><mtext> </mtext><mn>240</mn><mo>+</mo><mn>1</mn><mtext> </mtext><mn>500</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">128</mn><mtext> </mtext><mn mathvariant="bold">124</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Inoccupation} &= 125\,400 \times 0{,}03 = 3\,762\,\$\\285\text{Mauvaises créances} &= 125\,400 \times 0{,}01 = 1\,254\,\$\\286\text{Stationnement} &= 8 \times 65 \times 12 = 6\,240\,\$\\287\text{RBE} &= 125\,400 - 3\,762 - 1\,254 + 6\,240 + 1\,500288 = \uqotitle{128\,124\,\$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:5.7em;vertical-align:-2.6em;"></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:3.1em;"><span style="top:-5.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Inoccupation</span></span></span></span><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Mauvaises cr</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">ances</span></span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Stationnement</span></span></span></span><span style="top:-0.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">RBE</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.6em;"><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:3.1em;"><span style="top:-5.26em;"><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">125</span><span class="mspace" style="margin-right:0.1667em;"></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 class="mord">0</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 class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">762</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><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">125</span><span class="mspace" style="margin-right:0.1667em;"></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 class="mord">0</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 class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">254</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">8</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">65</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">6</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">240</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-0.76em;"><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">125</span><span class="mspace" style="margin-right:0.1667em;"></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 class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">762</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">254</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">6</span><span class="mspace" style="margin-right:0.1667em;"></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 class="mord">1</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 class="mord" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">128</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">124</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.6em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>289<p id="p11-96"><strong>Dépenses :</strong> entretien <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>128</mn><mtext> </mtext><mn>124</mn><mo>×</mo><mn>0,045</mn><mo>=</mo><mn>5</mn><mtext> </mtext><mn>766</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 128\,124 \times 0{,}045 = 5\,766\,\$</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">128</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">124</span><span class="mspace" style="margin-right:0.2222em;"></span><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">045</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">766</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; gestion <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>128</mn><mtext> </mtext><mn>124</mn><mo>×</mo><mn>0,05</mn><mo>=</mo><mn>6</mn><mtext> </mtext><mn>406</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 128\,124 \times 0{,}05 = 6\,406\,\$</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">128</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">124</span><span class="mspace" style="margin-right:0.2222em;"></span><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:0.2778em;"></span><span 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">406</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>;</p>290<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Total</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>13</mn><mtext> </mtext><mn>200</mn><mo>+</mo><mn>5</mn><mtext> </mtext><mn>400</mn><mo>+</mo><mn>5</mn><mtext> </mtext><mn>766</mn><mo>+</mo><mn>2</mn><mtext> </mtext><mn>600</mn><mo>+</mo><mn>6</mn><mtext> </mtext><mn>406</mn><mo>+</mo><mn>3</mn><mtext> </mtext><mn>600</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mspace width="1em"/><mo>+</mo><mn>3</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>1</mn><mtext> </mtext><mn>200</mn><mo>+</mo><mn>6</mn><mtext> </mtext><mn>500</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">47</mn><mtext> </mtext><mn mathvariant="bold">672</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Total} &= 13\,200 + 5\,400 + 5\,766 + 2\,600 + 6\,406 + 3\,600\\291&\quad + 3\,000 + 1\,200 + 6\,500 = \uqotitle{47\,672\,\$}\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 text"><span class="mord">Total</span></span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></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">13</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">5</span><span class="mspace" style="margin-right:0.1667em;"></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 class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">766</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">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 class="mord">6</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">406</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">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</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:1em;"></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">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 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">6</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 class="mord" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">47</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">672</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.1em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>292<p id="p11-97"><strong>RNE :</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>128</mn><mtext> </mtext><mn>124</mn><mo>−</mo><mn>47</mn><mtext> </mtext><mn>672</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">80</mn><mtext> </mtext><mn mathvariant="bold">452</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">128\,124 - 47\,672 = \uqotitle{80\,452\,\$}</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">128</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">124</span><span class="mspace" style="margin-right:0.2222em;"></span><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">47</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">672</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">80</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">452</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span>.<br> <strong>Ratios :</strong> dépenses/RBE <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>47</mn><mtext> </mtext><mn>672</mn><mi mathvariant="normal">/</mi><mn>128</mn><mtext> </mtext><mn>124</mn><mo>=</mo><mn>37,2</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">= 47\,672/128\,124 = 37{,}2\,\%</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">47</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">672/128</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">124</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">37</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>; RNE/RBE <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>62,8</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">=29362{,}8\,\%</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:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">62</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>. Pour un multilogements de 10 unités, chauffage aux locataires, la fourchette de marché est de 35–45 % : le calcul est vraisemblable. À un TGA de 5,5 %, la valeur indicative serait <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>80</mn><mtext> </mtext><mn>452</mn><mi mathvariant="normal">/</mi><mn>0,055</mn><mo>≈</mo><mn>1</mn><mtext> </mtext><mn>463</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">80\,452/0{,}055 \approx2941\,463\,000\,\$</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">80</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">452/0</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">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">463</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>.</p></div></details>295<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">— l'erreur du service de la dette</span><a class="box-anchor" href="#exo-11-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-98">Un étudiant évalue le 6-plex du chapitre en incluant l'hypothèque (2 800 $/mois) dans les dépenses d'exploitation. <strong>a)</strong> Recalculez son « RNE » et la « valeur » qu'il obtient à un TGA de 5,5 %. <strong>b)</strong> Chiffrez l'erreur de valeur. <strong>c)</strong> Expliquez en deux phrases pourquoi le raisonnement est fautif.</p></div></div>296<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p11-99"><strong>a)</strong> Dette annuelle : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mn>800</mn><mo>×</mo><mn>12</mn><mo>=</mo><mn>33</mn><mtext> </mtext><mn>600</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">2\,800 \times 12 = 33\,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">2</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">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">33</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">$</span></span></span></span>. « RNE » fautif : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>46</mn><mtext> </mtext><mn>807</mn><mo>−</mo><mn>33</mn><mtext> </mtext><mn>600</mn><mo>=</mo><mn>13</mn><mtext> </mtext><mn>207</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">46\,807 - 33\,600 = 13\,207\,\$</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">46</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">807</span><span class="mspace" style="margin-right:0.2222em;"></span><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">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">13</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">207</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; « valeur » : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>13</mn><mtext> </mtext><mn>207</mn><mi mathvariant="normal">/</mi><mn>0,055</mn><mo>=</mo><mn>240</mn><mtext> </mtext><mn>127</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>≈</mo><mn>240</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">13\,207 / 0{,}055 =297240\,127\,\$ \approx 240\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">13</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">207/0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">055</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">240</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">127</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</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">240</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">$</span></span></span></span>.<br> <strong>b)</strong> Erreur : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>851</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>240</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>611</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">851\,000 - 240\,000 = 611\,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">851</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">240</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">611</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> — la « valeur » fautive ne représente que 28 % de la vraie. La division par le taux transforme une erreur de dépense en catastrophe d'évaluation.<br> <strong>c)</strong> Le financement est un choix de l'investisseur, pas une caractéristique de l'immeuble : le même 6-plex génère le même RNE qu'il soit payé comptant ou financé à 80 %. Inclure la dette ferait dépendre la « valeur marchande » de la situation bancaire d'un propriétaire particulier, ce qui contredit la définition même de la valeur marchande.</p></div></details>298<h2 class="h-section" id="s-12"><span class="h-num">12</span><span class="h-text">La méthode du revenu — Partie 2 : le taux et le DCF</span></h2>299<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">— extraction directe</span><a class="box-anchor" href="#exo-12-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-69">Trois ventes récentes de multilogements comparables : un 8 logements vendu <span class="num">1 040 000 $</span> (RNE <span class="num">57 200 $</span>); un 12 logements vendu <span class="num">1 585 000 $</span> (RNE <span class="num">85 600 $</span>); un 10 logements vendu <span class="num">1 310 000 $</span> (RNE <span class="num">73 400 $</span>). <strong>a)</strong> Extrayez le TGA de chaque vente. <strong>b)</strong> Quel TGA retenez-vous pour un immeuble sujet semblable, et pourquoi? <strong>c)</strong> Appliquez-le à un RNE stabilisé de <span class="num">66 500 $</span>.</p></div></div>300<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="p12-70"><strong>a)</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>57</mn><mtext> </mtext><mn>200</mn><mi mathvariant="normal">/</mi><mn>1</mn><mtext> </mtext><mn>040</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>5,50</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">57\,200/1\,040\,000 = 5{,}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">57</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200/1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">040</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">5</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">50</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><mn>85</mn><mtext> </mtext><mn>600</mn><mi mathvariant="normal">/</mi><mn>1</mn><mtext> </mtext><mn>585</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>5,40</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">85\,600/1\,585\,000 = 5{,}40\,\%</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">85</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600/1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">585</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">5</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">40</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><mn>73</mn><mtext> </mtext><mn>400</mn><mi mathvariant="normal">/</mi><mn>1</mn><mtext> </mtext><mn>310</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>5,60</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">73\,400/1\,310\,000 = 5{,}60\,\%</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">73</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400/1</span><span class="mspace" style="margin-right:0.1667em;"></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">5</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">60</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>.<br> <strong>b)</strong> Fourchette de 5,40 à 5,60 %, médiane <strong>5,50 %</strong> : les trois indications sont serrées (20 points de base), donc fiables; on retient 5,50 %, en donnant éventuellement plus de poids à la vente la plus semblable au sujet.<br> <strong>c)</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mn>66</mn><mtext> </mtext><mn>500</mn><mi mathvariant="normal">/</mi><mn>0,055</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>209</mn><mtext> </mtext><mn>091</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>≈</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">1</mn><mtext> </mtext><mn mathvariant="bold">210</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">V = 66\,500 / 0{,}055 = 1\,209\,091\,\$ \approx301\uqotitle{1\,210\,000\,\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">66</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500/0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">055</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">209</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">091</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</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:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">1</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">210</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">000</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span>.</p></div></details>302<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">— bande d'investissement</span><a class="box-anchor" href="#exo-12-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-71">Le financement typique du marché : ratio prêt/valeur de 75 %, prêt à 5,0 % amorti sur 25 ans (constante hypothécaire <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mi>m</mi></msub><mo>=</mo><mn>6,97</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">R_m = 6{,}97\,\%</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:0.1514em;"><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">m</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">6</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">97</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>), rendement exigé sur les fonds propres de 8,5 %. <strong>a)</strong> Calculez le TGA par la bande d'investissement. <strong>b)</strong> Les ventes du secteur s'échangent à un TGA de 5,6 % : que concluez-vous? <strong>c)</strong> Recalculez le TGA si le taux hypothécaire monte et porte <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">R_m</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:0.1514em;"><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">m</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> à 7,9 % — commentez.</p></div></div>303<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="p12-72"><strong>a)</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>TGA</mtext><mo>=</mo><mn>0,75</mn><mo>×</mo><mn>0,0697</mn><mo>+</mo><mn>0,25</mn><mo>×</mo><mn>0,085</mn><mo>=</mo><mn>0,0523</mn><mo>+</mo><mn>0,0213</mn><mo>=</mo><mn>0,0736</mn><mo>≈</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">7,36</mn><mtext> </mtext><mi mathvariant="bold">%</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">\text{TGA} = 0{,}75 \times 0{,}0697 + 0{,}25 \times 0{,}085304= 0{,}0523 + 0{,}0213 = 0{,}0736 \approx \uqotitle{7{,}36\,\%}</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 text"><span class="mord">TGA</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:0.8389em;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:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0697</span><span class="mspace" style="margin-right:0.2222em;"></span><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:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">085</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">0523</span><span class="mspace" style="margin-right:0.2222em;"></span><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">0213</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">0736</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">7</span><span class="mord" style="color:#003E7E;"><span class="mpunct" style="color:#003E7E;">,</span></span><span class="mord mathbf" style="color:#003E7E;">36</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">%</span></span></span></span></span>.<br> <strong>b)</strong> Le marché paie des prix correspondant à 5,6 %, bien au-dessous du coût pondéré du capital (7,36 %) : le rendement courant ne couvre pas le financement — les acheteurs acceptent un levier défavorable à court terme en pariant sur la croissance des loyers et l'appréciation. Signal de prudence pour l'évaluateur : vérifier que les hypothèses de croissance justifient cet écart.<br> <strong>c)</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>TGA</mtext><mo>=</mo><mn>0,75</mn><mo>×</mo><mn>0,079</mn><mo>+</mo><mn>0,25</mn><mo>×</mo><mn>0,085</mn><mo>=</mo><mn>0,0593</mn><mo>+</mo><mn>0,0213</mn><mo>=</mo><mn>0,0806</mn><mo>≈</mo><mn>8,06</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">\text{TGA} = 0{,}75 \times 0{,}079 + 0{,}25 \times 0{,}085 =3050{,}0593 + 0{,}0213 = 0{,}0806 \approx 8{,}06\,\%</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 text"><span class="mord">TGA</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:0.8389em;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:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">079</span><span class="mspace" style="margin-right:0.2222em;"></span><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:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">085</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">0593</span><span class="mspace" style="margin-right:0.2222em;"></span><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">0213</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">0806</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">06</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>. Une hausse d'environ un point de la constante hypothécaire déplace le TGA de bande de 70 points de base : le canal par lequel les taux d'intérêt se transmettent aux valeurs immobilières est direct et rapide.</p></div></details>306<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">— réversion et part de la valeur</span><a class="box-anchor" href="#exo-12-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-73">Un immeuble affiche un RNE de <span class="num">95 000 $</span> à l'année 1, en croissance de 2,5 %/an. Détention de 5 ans, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi><mo>=</mo><mn>7,5</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">r = 7{,}5\,\%</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" style="margin-right:0.0278em;">r</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">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></span></span>, TGA de sortie de 6,0 %, frais de vente de 3,0 %. <strong>a)</strong> Calculez le RNE de l'année 6 et la valeur nette de réversion. <strong>b)</strong> Actualisez la réversion. <strong>c)</strong> La VA des cinq RNE s'élève à <span class="num">404 000 $</span> : concluez sur la valeur totale et sur la part de la réversion.</p></div></div>307<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p12-74"><strong>a)</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mtext>RNE</mtext><mn>6</mn></msub><mo>=</mo><mn>95</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mo stretchy="false">(</mo><mn>1,025</mn><msup><mo stretchy="false">)</mo><mn>5</mn></msup><mo>=</mo><mn>95</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>1,1314</mn><mo>=</mo><mn>107</mn><mtext> </mtext><mn>484</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\text{RNE}_6 = 95\,000 \times (1{,}025)^5 = 95\,000 \times3081{,}1314 = 107\,484\,\$</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 text"><span class="mord">RNE</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">6</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">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:1.0641em;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">025</span><span class="mclose"><span class="mclose">)</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">5</span></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">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:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">1314</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">107</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">484</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Valeur brute : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>107</mn><mtext> </mtext><mn>484</mn><mi mathvariant="normal">/</mi><mn>0,06</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>791</mn><mtext> </mtext><mn>400</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">107\,484 / 0{,}06 =3091\,791\,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="mord">107</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">484/0</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:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">791</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">$</span></span></span></span>; frais de vente : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mtext> </mtext><mn>791</mn><mtext> </mtext><mn>400</mn><mo>×</mo><mn>0,03</mn><mo>=</mo><mn>53</mn><mtext> </mtext><mn>742</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">1\,791\,400 \times 0{,}03 = 53\,742\,\$</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">791</span><span class="mspace" style="margin-right:0.1667em;"></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:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</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:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">53</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">742</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; réversion nette : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mtext> </mtext><mn>791</mn><mtext> </mtext><mn>400</mn><mo>−</mo><mn>53</mn><mtext> </mtext><mn>742</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">1</mn><mtext> </mtext><mn mathvariant="bold">737</mn><mtext> </mtext><mn mathvariant="bold">658</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">1\,791\,400 - 53\,742 = \uqotitle{1\,737\,658\,\$}</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">791</span><span class="mspace" style="margin-right:0.1667em;"></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">53</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">742</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">1</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">737</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">658</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span>.<br> <strong>b)</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>1,075</mn><msup><mo stretchy="false">)</mo><mn>5</mn></msup><mo>=</mo><mn>1,4356</mn></mrow><annotation encoding="application/x-tex">(1{,}075)^5 = 1{,}4356</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">075</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">4356</span></span></span></span>; VA <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>1</mn><mtext> </mtext><mn>737</mn><mtext> </mtext><mn>658</mn><mi mathvariant="normal">/</mi><mn>1,4356</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">1</mn><mtext> </mtext><mn mathvariant="bold">210</mn><mtext> </mtext><mn mathvariant="bold">405</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= 1\,737\,658 / 1{,}4356 =310\uqotitle{1\,210\,405\,\$}</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">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">737</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">658/1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">4356</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">1</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">210</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">405</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span>.<br> <strong>c)</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mn>404</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>1</mn><mtext> </mtext><mn>210</mn><mtext> </mtext><mn>405</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>614</mn><mtext> </mtext><mn>405</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>≈</mo><mn>1</mn><mtext> </mtext><mn>615</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">V = 404\,000 + 1\,210\,405 = 1\,614\,405\,\$ \approx3111\,615\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">404</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">210</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">405</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">614</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">405</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</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">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">615</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>. La réversion représente <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mtext> </mtext><mn>210</mn><mtext> </mtext><mn>405</mn><mi mathvariant="normal">/</mi><mn>1</mn><mtext> </mtext><mn>614</mn><mtext> </mtext><mn>405</mn><mo>=</mo><mn>75</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">1\,210\,405 / 1\,614\,405 =31275\,\%</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">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">210</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">405/1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">614</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">405</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">%</span></span></span></span> de la valeur : les hypothèses de sortie (TGA de sortie, frais de vente) dominent la conclusion — l'analyse de sensibilité doit porter d'abord sur elles.</p></div></details>313<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">— MRB, MRN et TGA</span><a class="box-anchor" href="#exo-12-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-75">Un triplex de Hull est offert à <span class="num">815 000 $</span>; son RBE est de <span class="num">58 000 $</span> et son RNE de <span class="num">36 500 $</span>. Les transactions récentes du segment indiquent des MRB de 12 à 14<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> et des TGA de 4,6 à 5,0 %. <strong>a)</strong> Calculez le MRB et le TGA implicites du prix demandé. <strong>b)</strong> Le prix demandé est-il dans le marché? <strong>c)</strong> Donnez la fourchette de valeurs impliquée par les TGA du marché et expliquez pourquoi elle prime sur celle du MRB.</p></div></div>314<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="p12-76"><strong>a)</strong> MRB <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>815</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>58</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>14,1</mn><mo>×</mo></mrow><annotation encoding="application/x-tex">= 815\,000 / 58\,000 = 14{,}1\times</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">815</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000/58</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">14</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">1</span><span class="mord">×</span></span></span></span>; TGA <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>36</mn><mtext> </mtext><mn>500</mn><mi mathvariant="normal">/</mi><mn>815</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>4,48</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">= 36\,500 /315815\,000 = 4{,}48\,\%</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">36</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500/815</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">4</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">48</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>.<br> <strong>b)</strong> Le MRB est à la limite haute (14<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>) et le TGA implicite (4,48 %) est <em>sous</em> la fourchette du marché (4,6–5,0 %) : le prix demandé est légèrement au-dessus du marché — l'acheteur paierait un rendement courant inférieur à ce que le segment offre.<br> <strong>c)</strong> Par les TGA : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mn>36</mn><mtext> </mtext><mn>500</mn><mi mathvariant="normal">/</mi><mn>0,050</mn><mo>=</mo><mn>730</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">V = 36\,500/0{,}050 = 730\,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:1em;vertical-align:-0.25em;"></span><span class="mord">36</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500/0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">050</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">730</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">$</span></span></span></span> à <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>36</mn><mtext> </mtext><mn>500</mn><mi mathvariant="normal">/</mi><mn>0,046</mn><mo>=</mo><mn>793</mn><mtext> </mtext><mn>478</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">36\,500/0{,}046 = 793\,478\,\$</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">36</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500/0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">046</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">793</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">478</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>, soit une fourchette d'environ <strong>730 000 à 795 000 $</strong>. Elle prime parce que le TGA intègre les dépenses réelles de l'immeuble, alors que le MRB suppose implicitement un ratio de dépenses identique à celui des comparables — une hypothèse jamais vérifiée. Le MRB filtre, le TGA conclut.</p></div></details>316<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 — l'exemple guidé mené à terme</span><a class="box-anchor" href="#exo-12-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-77">Complétez l'exemple guidé du 12 logements (section <a class="xref" href="/seance/12/#s-12-6">12.6</a>) : <strong>A)</strong> RNE et capitalisation directe; <strong>B)</strong> DCF sur 5 ans; <strong>C)</strong> réconciliation. Utilisez les données et hypothèses fournies (RBE déjà établi : <span class="num">159 360 $</span>).</p></div></div>317<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p12-78"><strong>A) Capitalisation directe.</strong> Gestion : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>159</mn><mtext> </mtext><mn>360</mn><mo>×</mo><mn>0,05</mn><mo>=</mo><mn>7</mn><mtext> </mtext><mn>968</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">159\,360 \times 0{,}05 =3187\,968\,\$</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">159</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">360</span><span class="mspace" style="margin-right:0.2222em;"></span><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:0.2778em;"></span><span 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">7</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">968</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Dépenses totales :</p>319<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right" columnspacing=""><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mn>16</mn><mtext> </mtext><mn>500</mn><mo>+</mo><mn>6</mn><mtext> </mtext><mn>800</mn><mo>+</mo><mn>7</mn><mtext> </mtext><mn>200</mn><mo>+</mo><mn>3</mn><mtext> </mtext><mn>600</mn><mo>+</mo><mn>7</mn><mtext> </mtext><mn>968</mn><mo>+</mo><mn>5</mn><mtext> </mtext><mn>400</mn><mo>+</mo><mn>3</mn><mtext> </mtext><mn>500</mn><mo>+</mo><mn>1</mn><mtext> </mtext><mn>800</mn><mo>+</mo><mn>8</mn><mtext> </mtext><mn>500</mn><mo>=</mo><mn>61</mn><mtext> </mtext><mn>268</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}16\,500 + 6\,800 + 7\,200 + 3\,600 + 7\,968 + 5\,400 + 3\,500 + 1\,800320 + 8\,500 = 61\,268\,\$\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.2em;vertical-align:-0.35em;"></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:0.85em;"><span style="top:-3.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><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 class="mord">6</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 class="mord">7</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">3</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 class="mord">7</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">968</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">5</span><span class="mspace" style="margin-right:0.1667em;"></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 class="mord">3</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 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 class="mord">8</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 class="mord">61</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">268</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.35em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>321<p id="p12-79">soit 38,4 % du RBE — dans la fourchette 35–45 % d'un multilogements.</p>322<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>RNE</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>159</mn><mtext> </mtext><mn>360</mn><mo>−</mo><mn>61</mn><mtext> </mtext><mn>268</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">98</mn><mtext> </mtext><mn mathvariant="bold">092</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>V</mi><mtext>cap</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mfrac><mrow><mn>98</mn><mtext> </mtext><mn>092</mn></mrow><mn>0,055</mn></mfrac><mo>=</mo><mn>1</mn><mtext> </mtext><mn>783</mn><mtext> </mtext><mn>491</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>≈</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">1</mn><mtext> </mtext><mn mathvariant="bold">785</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{RNE} &= 159\,360 - 61\,268 = \uqotitle{98\,092\,\$}\\323V_{\text{cap}} &= \frac{98\,092}{0{,}055} = 1\,783\,491\,\$324 \approx \uqotitle{1\,785\,000\,\$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:3.7019em;vertical-align:-1.6009em;"></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:2.1009em;"><span style="top:-4.5824em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord text"><span class="mord">RNE</span></span></span></span><span style="top:-2.6009em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><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:0.1514em;"><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">cap</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></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.6009em;"><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:2.1009em;"><span style="top:-4.5824em;"><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">159</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">360</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">268</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:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">98</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">092</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span><span style="top:-2.6009em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">055</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">98</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">092</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">783</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">491</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">1</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">785</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">000</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.6009em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>325<p id="p12-80"><strong>B) DCF sur 5 ans.</strong> RNE en croissance de 3,0 %/an, actualisation à 8,0 % :</p>326<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Année</th><th class="al-r">RNE</th><th class="al-r">Facteur</th><th class="al-r">VA</th></tr></thead><tbody><tr><td>1</td><td class="al-r">98 092 $</td><td class="al-r">0,9259</td><td class="al-r">90 825 $</td></tr><tr><td>2</td><td class="al-r">101 035 $</td><td class="al-r">0,8573</td><td class="al-r">86 620 $</td></tr><tr><td>3</td><td class="al-r">104 066 $</td><td class="al-r">0,7938</td><td class="al-r">82 610 $</td></tr><tr><td>4</td><td class="al-r">107 188 $</td><td class="al-r">0,7350</td><td class="al-r">78 786 $</td></tr><tr><td>5</td><td class="al-r">110 404 $</td><td class="al-r">0,6806</td><td class="al-r">75 139 $</td></tr><tr class="rule-above"><td colspan="3"><strong>VA des RNE</strong></td><td class="al-r"><strong>413 980 $</strong></td></tr></tbody></table></div></div>327<p id="p12-81">Réversion : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mtext>RNE</mtext><mn>6</mn></msub><mo>=</mo><mn>110</mn><mtext> </mtext><mn>404</mn><mo>×</mo><mn>1,03</mn><mo>=</mo><mn>113</mn><mtext> </mtext><mn>716</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\text{RNE}_6 = 110\,404 \times 1{,}03 = 113\,716\,\$</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 text"><span class="mord">RNE</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">6</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">110</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">404</span><span class="mspace" style="margin-right:0.2222em;"></span><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:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">113</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">716</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; valeur brute <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>113</mn><mtext> </mtext><mn>716</mn><mi mathvariant="normal">/</mi><mn>0,0575</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>977</mn><mtext> </mtext><mn>670</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 113\,716 / 0{,}0575 = 1\,977\,670\,\$</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">113</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">716/0</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">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">977</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">670</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; frais de vente (3 %) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>59</mn><mtext> </mtext><mn>330</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">=32859\,330\,\$</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">59</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">330</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; réversion nette <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>1</mn><mtext> </mtext><mn>918</mn><mtext> </mtext><mn>340</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 1\,918\,340\,\$</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">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">918</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">340</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; VA <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>1</mn><mtext> </mtext><mn>918</mn><mtext> </mtext><mn>340</mn><mi mathvariant="normal">/</mi><mn>1,4693</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>305</mn><mtext> </mtext><mn>614</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 1\,918\,340 /3291{,}4693 = 1\,305\,614\,\$</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">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">918</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">340/1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">4693</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">305</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">614</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>.</p>330<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>V</mi><mtext>DCF</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>413</mn><mtext> </mtext><mn>980</mn><mo>+</mo><mn>1</mn><mtext> </mtext><mn>305</mn><mtext> </mtext><mn>614</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>719</mn><mtext> </mtext><mn>594</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>≈</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">1</mn><mtext> </mtext><mn mathvariant="bold">720</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_{\text{DCF}} &= 413\,980 + 1\,305\,614 = 1\,719\,594\,\$331 \approx \uqotitle{1\,720\,000\,\$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.2em;vertical-align:-0.35em;"></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:0.85em;"><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:0.2222em;">V</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:-0.2222em;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">DCF</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:0.35em;"><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:0.85em;"><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">413</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">980</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">305</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">614</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">719</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">594</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 class="mord" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">1</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">720</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">000</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.35em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>332<p id="p12-82">(Selon les arrondis intermédiaires, un résultat entre 1 715 000 et 1 725 000 $ est acceptable.)<br> <strong>C) Réconciliation.</strong> Écart : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>1</mn><mtext> </mtext><mn>785</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>1</mn><mtext> </mtext><mn>720</mn><mtext> </mtext><mn>000</mn><mo stretchy="false">)</mo><mi mathvariant="normal">/</mi><mn>1</mn><mtext> </mtext><mn>785</mn><mtext> </mtext><mn>000</mn><mo>≈</mo><mn>3,6</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">(1\,785\,000 - 1\,720\,000) /3331\,785\,000 \approx 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">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">785</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">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">720</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mclose">)</span><span class="mord">/1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">785</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">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> — normal. Le TGA de marché (5,50 %) provient de ventes récentes et serrées, et l'immeuble est stabilisé (chauffage aux locataires, bon état, loyers proches du marché après reconstruction) : poids dominant à la capitalisation directe, le DCF servant de borne prudente. Conclusion type : <strong>valeur marchande d'environ 1 770 000 $</strong>, en expliquant la pondération (p. ex. deux tiers capitalisation directe, un tiers DCF). Toute pondération motivée par la fiabilité relative des données est recevable — une moyenne mécanique non justifiée ne l'est pas.</p></div></details>334<h2 class="h-section" id="s-13"><span class="h-num">13</span><span class="h-text">Le rapport d'évaluation</span></h2>335<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">— choix du type de rapport</span><a class="box-anchor" href="#exo-13-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p13-101">Pour chacune des situations suivantes, indiquez le type de rapport approprié et justifiez en une phrase : a) une banque finance l'achat d'un bungalow à Gatineau ; b) un propriétaire conteste son évaluation municipale devant le Tribunal administratif du Québec ; c) un gestionnaire immobilier veut une idée de la valeur d'un immeuble de son portefeuille avant de planifier son budget ; d) le ministère des Transports exproprie une bande de terrain.</p></div></div>336<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="p13-102">a) <strong>Rapport abrégé</strong> : financement hypothécaire résidentiel courant, format formulaire accepté par les prêteurs. b) <strong>Rapport complet</strong> : preuve d'expert devant un tribunal, le raisonnement intégral doit être exposé. c) <strong>Rapport restreint</strong> : usage interne, décision préliminaire, aucune diffusion à des tiers. d) <strong>Rapport complet</strong> : l'expropriation est un contexte contentieux exigeant le format narratif détaillé.</p></div></details>337<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">— dates</span><a class="box-anchor" href="#exo-13-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p13-103">Une évaluatrice inspecte une propriété le 3 novembre 2026, signe son rapport le 17 novembre 2026, et le mandat demande la valeur au 30 juin 2026 (date d'un décès, pour une succession). Identifiez la date d'inspection, la date du rapport et la date d'évaluation, puis expliquez pourquoi cette évaluation est dite « rétrospective ».</p></div></div>338<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="p13-104">Date d'inspection : 3 novembre 2026. Date du rapport : 17 novembre 2026. Date d'évaluation : <strong>30 juin 2026</strong>. L'évaluation est rétrospective parce que l'opinion de valeur s'applique à une date antérieure à celle de l'analyse : l'évaluatrice ne doit utiliser que les données de marché disponibles <em>au 30 juin 2026</em> (ventes antérieures à cette date), même si elle travaille en novembre.</p></div></details>339<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">— réconciliation argumentée</span><a class="box-anchor" href="#exo-13-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p13-105">Pour un duplex de Gatineau, vos indications sont : comparaison <span class="num">512 000 $</span>, coût <span class="num">540 000 $</span>, revenu <span class="num">505 000 $</span>. Le marché des duplex est actif (quatre ventes récentes très semblables), le bâtiment a 35 ans (dépréciation difficile à cerner) et les acheteurs de duplex dans ce secteur sont surtout des propriétaires-occupants. Proposez une pondération, calculez la conclusion et rédigez la justification en trois phrases.</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"><p id="p13-106">Pondération proposée : comparaison 60 %, revenu 30 %, coût 10 %.</p>341<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>512</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,60</mn><mo>+</mo><mn>505</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,30</mn><mo>+</mo><mn>540</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,10</mn><mo>=</mo><mn>307</mn><mtext> </mtext><mn>200</mn><mo>+</mo><mn>151</mn><mtext> </mtext><mn>500</mn><mo>+</mo><mn>54</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>512</mn><mtext> </mtext><mn>700</mn></mrow><annotation encoding="application/x-tex">512\,000 \times 0{,}60 + 505\,000 \times 0{,}30 + 540\,000 \times 0{,}10342= 307\,200 + 151\,500 + 54\,000 = 512\,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">512</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:0.2222em;"></span><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">505</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">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:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">540</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:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">307</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:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">151</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">54</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">512</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">700</span></span></span></span></span></div>343<p id="p13-107">Conclusion arrondie : <strong><span class="num">513 000 $</span></strong>. Justification : la méthode de comparaison domine car le marché est actif et les comparables excellents, ce qui reflète le comportement des propriétaires-occupants qui achètent par comparaison. La méthode du revenu conserve un poids significatif puisque le bien génère des loyers, mais les acheteurs types ne raisonnent pas d'abord en rendement. La méthode du coût reçoit un poids minimal : à 35 ans d'âge, l'estimation de la dépréciation est trop subjective pour être déterminante.</p></div></details>344<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">— déontologie</span><a class="box-anchor" href="#exo-13-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p13-108">Un client offre à un évaluateur des honoraires de <span class="num">2500 $</span>, « plus une prime de <span class="num">1000 $</span> si la valeur atteint <span class="num">800 000 $</span>, parce que mon refinancement en dépend ». L'évaluateur peut-il accepter : a) la totalité de l'offre ; b) les <span class="num">2500 $</span> en refusant la prime ; c) rien du tout? Justifiez au regard du Code de déontologie.</p></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"><p id="p13-109">Réponse : <strong>b)</strong>. Le Code de déontologie (C-26, r. 123) interdit tout honoraire conditionnel à la conclusion de valeur : la prime de <span class="num">1000 $</span> est donc irrecevable, et le seul fait de l'accepter compromettrait l'indépendance et l'impartialité de l'opinion. Rien n'interdit toutefois d'accepter le mandat à honoraires fixes de <span class="num">2500 $</span>, pourvu que l'évaluateur avise clairement le client que la conclusion découlera de l'analyse, quel que soit le besoin de refinancement. Si le client insiste sur la condition, l'évaluateur doit refuser le mandat.</p></div></details>346<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">— détection de non-conformités</span><a class="box-anchor" href="#exo-13-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p13-110">Relevez au moins cinq manquements dans la situation suivante : « Un évaluateur remet un rapport restreint pour un litige, sans y indiquer de restriction d'usage. La date d'évaluation n'apparaît nulle part ; la table des matières renvoie à des pages inexistantes. La réconciliation indique : "moyenne des deux méthodes". Le rapport mentionne que la superficie provient "du propriétaire". L'évaluateur a évalué le même immeuble il y a deux ans pour l'autre partie, sans le mentionner. Il détruit ses notes de travail après la remise. »</p></div></div>347<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="p13-111">(1) Type de rapport inadéquat : un litige exige un rapport <strong>complet</strong>, non restreint — et toute restriction d'usage devait de toute façon être écrite. (2) <strong>Date d'évaluation manquante</strong> : élément obligatoire de la page titre et de la certification. (3) Table des matières périmée : défaut de contrôle de qualité (forme). (4) Réconciliation par <strong>simple moyenne</strong> non argumentée : contraire aux normes. (5) Source de superficie non vérifiée présentée sans hypothèse explicite : il fallait une clause d'hypothèse ou une vérification (certificat de localisation, rôle). (6) <strong>Défaut de divulgation</strong> de l'évaluation antérieure du même bien (moins de trois ans). (7) Destruction des notes de travail : violation de l'obligation de <strong>conservation du dossier</strong> pendant au moins cinq ans.</p></div></details>348<div class="box box-exo" id="exo-13-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 13.6</span><span class="box-title">— rédaction professionnelle</span><a class="box-anchor" href="#exo-13-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p13-112">Réécrivez chacune des phrases suivantes dans le style attendu d'un rapport d'évaluation, en expliquant en une phrase ce qui clochait : a) « La cuisine est magnifique, refaite au goût du jour. » ; b) « Le vendeur nous a dit que le sous-sol n'a jamais eu d'infiltration. » ; c) « Vu le marché de fou actuellement, la valeur pourrait être plus haute dans six mois. »</p></div></div>349<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="p13-113">a) « Cuisine rénovée (armoires, comptoirs de quartz, électroménagers encastrés) ; qualité des matériaux supérieure à la moyenne du segment. » — l'original exprimait un jugement esthétique subjectif au lieu de faits observables. b) « Selon la déclaration du vendeur, aucune infiltration d'eau n'est survenue au sous-sol ; aucun indice contraire n'a été observé lors de l'inspection visuelle. Cette information n'a pas fait l'objet d'une vérification indépendante. » — l'original rapportait une déclaration de tiers comme un fait établi, sans réserve ni attribution. c) « La conclusion de valeur s'applique à la date d'évaluation du [date]. Le marché du segment affiche une tendance haussière (données Centris, T3) ; aucune opinion n'est émise quant à la valeur future. » — l'original spéculait sur une valeur future dans un registre familier, hors du mandat.</p></div></details>350<h2 class="h-section" id="s-14"><span class="h-num">14</span><span class="h-text">Révision générale et cas intégrateur</span></h2>351<div class="box box-exo" id="exo-14-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 14.1</span><span class="box-title">— capitalisation directe — 12 logements</span><a class="box-anchor" href="#exo-14-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p14-72">Un immeuble de 12 logements à Gatineau : 6 logements 4 ½ à <span class="num">1100 $</span>/mois et 6 logements 3 ½ à <span class="num">950 $</span>/mois ; inoccupation estimée à 4 % ; dépenses d'exploitation de 45 % du RBE ; TGA du marché de 5,5 %. Calculez la valeur par capitalisation directe.</p></div></div>352<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>RBP</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mo stretchy="false">(</mo><mn>6</mn><mo>×</mo><mn>1100</mn><mo>×</mo><mn>12</mn><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><mn>6</mn><mo>×</mo><mn>950</mn><mo>×</mo><mn>12</mn><mo stretchy="false">)</mo><mo>=</mo><mn>79</mn><mtext> </mtext><mn>200</mn><mo>+</mo><mn>68</mn><mtext> </mtext><mn>400</mn><mo>=</mo><mn>147</mn><mtext> </mtext><mn>600</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>RBE</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>147</mn><mtext> </mtext><mn>600</mn><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mn>0,04</mn><mo stretchy="false">)</mo><mo>=</mo><mn>141</mn><mtext> </mtext><mn>696</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>D</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>penses</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>141</mn><mtext> </mtext><mn>696</mn><mo>×</mo><mn>0,45</mn><mo>=</mo><mn>63</mn><mtext> </mtext><mn>763</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>RNE</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>141</mn><mtext> </mtext><mn>696</mn><mo>−</mo><mn>63</mn><mtext> </mtext><mn>763</mn><mo>=</mo><mn>77</mn><mtext> </mtext><mn>933</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mi>V</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mfrac><mrow><mn>77</mn><mtext> </mtext><mn>933</mn></mrow><mn>0,055</mn></mfrac><mo>=</mo><mn>1</mn><mtext> </mtext><mn>416</mn><mtext> </mtext><mn>964</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>≈</mo><mrow><mn mathvariant="bold">1</mn><mtext> </mtext><mn mathvariant="bold">417</mn><mtext> </mtext><mn mathvariant="bold">000</mn></mrow><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{RBP} &= (6 \times 1100 \times 12) + (6 \times 950 \times 12)353 = 79\,200 + 68\,400 = 147\,600\,\$ \\354\text{RBE} &= 147\,600 \times (1 - 0{,}04) = 141\,696\,\$ \\355\text{Dépenses} &= 141\,696 \times 0{,}45 = 63\,763\,\$ \\356\text{RNE} &= 141\,696 - 63\,763 = 77\,933\,\$ \\357V &= \frac{77\,933}{0{,}055} = 1\,416\,964\,\$ \approx \mathbf{1\,417\,000}\,\$\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:8.2019em;vertical-align:-3.8509em;"></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:4.3509em;"><span style="top:-6.8324em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord text"><span class="mord">RBP</span></span></span></span><span style="top:-5.3324em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord text"><span class="mord">RBE</span></span></span></span><span style="top:-3.8324em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord text"><span class="mord">D</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">penses</span></span></span></span><span style="top:-2.3324em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord text"><span class="mord">RNE</span></span></span></span><span style="top:-0.3509em;"><span class="pstrut" style="height:3.3214em;"></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:3.8509em;"><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:4.3509em;"><span style="top:-6.8324em;"><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="mopen">(</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 class="mord">1100</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">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 class="mopen">(</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 class="mord">950</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">12</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">79</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">68</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 class="mord">147</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 style="top:-5.3324em;"><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">147</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 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 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 class="mord">141</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">696</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-3.8324em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">141</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">696</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">45</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">63</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">763</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-2.3324em;"><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">141</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">696</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">63</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">763</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">77</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">933</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-0.3509em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">055</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">77</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">933</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">416</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">964</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"><span class="mord mathbf">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathbf">417</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathbf">000</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:3.8509em;"><span></span></span></span></span></span></span></span></span></span></span></span></div></div></details>358<div class="box box-exo" id="exo-14-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 14.2</span><span class="box-title">— méthode du coût — bâtiment commercial</span><a class="box-anchor" href="#exo-14-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p14-73">Un bâtiment commercial à Gatineau : coût de remplacement à neuf de <span class="num">1 800 000 $</span> ; âge effectif de 15 ans et vie utile économique de 45 ans ; dépréciation fonctionnelle de <span class="num">40 000 $</span> (système CVAC inadéquat) ; dépréciation économique de <span class="num">25 000 $</span> (route en construction) ; valeur du terrain de <span class="num">250 000 $</span>. Calculez la valeur par la méthode du coût.</p></div></div>359<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>D</mi><mtext>physique</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>1</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mfrac><mn>15</mn><mn>45</mn></mfrac><mo>=</mo><mn>600</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</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>600</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>40</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>25</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>665</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>V</mi><mrow><mtext>am</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>liorations</mtext></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>1</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>665</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>135</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</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>1</mn><mtext> </mtext><mn>135</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>250</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mrow><mn mathvariant="bold">1</mn><mtext> </mtext><mn mathvariant="bold">385</mn><mtext> </mtext><mn mathvariant="bold">000</mn></mrow><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}D_{\text{physique}} &= 1\,800\,000 \times \frac{15}{45} = 600\,000\,\$ \\360D_{\text{totale}} &= 600\,000 + 40\,000 + 25\,000 = 665\,000\,\$ \\361V_{\text{améliorations}} &= 1\,800\,000 - 665\,000 = 1\,135\,000\,\$ \\362V &= 1\,135\,000 + 250\,000 = \mathbf{1\,385\,000}\,\$\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:6.5074em;vertical-align:-3.0037em;"></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:3.5037em;"><span style="top:-5.5037em;"><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:0.3361em;"><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">physique</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></span><span style="top:-3.6777em;"><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:0.3361em;"><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:-2.1777em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><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:0.3361em;"><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">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">liorations</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:-0.6777em;"><span class="pstrut" style="height:3.3214em;"></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:3.0037em;"><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:3.5037em;"><span style="top:-5.5037em;"><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">1</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">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">45</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">15</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">600</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:-3.6777em;"><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">600</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">40</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:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">665</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">$</span></span></span><span style="top:-2.1777em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">665</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">135</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-0.6777em;"><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">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">135</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">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 class="mord"><span class="mord mathbf">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathbf">385</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathbf">000</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:3.0037em;"><span></span></span></span></span></span></span></span></span></span></span></span></div></div></details>363<div class="box box-exo" id="exo-14-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 14.3</span><span class="box-title">— ajustement de comparables</span><a class="box-anchor" href="#exo-14-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p14-74">Unifamiliale à Gatineau. Un comparable vendu <span class="num">425 000 $</span> il y a 8 mois présente les différences suivantes par rapport au sujet : garage double (sujet : simple) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>→</mo><mo>−</mo><mn>20</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\rightarrow -20\,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">−</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:0.1667em;"></span><span class="mord">$</span></span></span></span> ; terrain de 600 m<sup>2</sup> (sujet : 750 m<sup>2</sup>) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>→</mo><mo>+</mo><mn>15</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\rightarrow +15\,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">+</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:0.1667em;"></span><span class="mord">$</span></span></span></span> ; sous-sol non aménagé (sujet : aménagé) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>→</mo><mo>+</mo><mn>25</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\rightarrow +25\,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">+</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:0.1667em;"></span><span class="mord">$</span></span></span></span> ; marché en hausse de 0,5 % par mois. Calculez la valeur ajustée du comparable, puis vérifiez les seuils d'ajustement net et brut.</p></div></div>364<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="p14-75">Ajustement temporel : <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>0,005</mn><mo>×</mo><mn>8</mn><mo>=</mo><mo>+</mo><mn>17</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">425\,000 \times 0{,}005 \times 8 = +17\,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" 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">005</span><span class="mspace" style="margin-right:0.2222em;"></span><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">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">+</span><span class="mord">17</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span> $. Total des ajustements : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>20</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>15</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>17</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>25</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mo>+</mo><mn>37</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">-20\,000 + 15\,000 + 17\,000 + 25\,000365= +37\,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">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:0.7278em;vertical-align:-0.0833em;"></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:0.2222em;"></span><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">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:0.6444em;"></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:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">+</span><span class="mord">37</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span> $. Valeur ajustée : <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>37</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mrow><mn mathvariant="bold">462</mn><mtext> </mtext><mn mathvariant="bold">000</mn></mrow></mrow><annotation encoding="application/x-tex">425\,000 + 37\,000 =366\mathbf{462\,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" 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">37</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"><span class="mord mathbf">462</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathbf">000</span></span></span></span></span> $. Vérification des seuils : ajustement brut <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>20</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>15</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>17</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>25</mn><mtext> </mtext><mn>000</mn><mo stretchy="false">)</mo><mi mathvariant="normal">/</mi><mn>425</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>77</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>425</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>18,1</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">= (20\,000+15\,000+17\,000+25\,000) / 425\,000 =36777\,000/425\,000 = 18{,}1\,\%</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">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:0.7278em;vertical-align:-0.0833em;"></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:0.2222em;"></span><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">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:1em;vertical-align:-0.25em;"></span><span class="mord">25</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mclose">)</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:0.2778em;"></span><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="mspace" style="margin-right:0.1667em;"></span><span class="mord">000/425</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> (<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> ✓) ; ajustement net <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>37</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>425</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>8,7</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">= 37\,000/425\,000 = 8{,}7\,\%</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">37</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000/425</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">8</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> (<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><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">\leq 15\,\%</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">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> ✓). Le comparable est utilisable.</p></div></details>368<div class="box box-exo" id="exo-14-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 14.4</span><span class="box-title">— réconciliation complète</span><a class="box-anchor" href="#exo-14-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p14-76">Reprenez le cas intégrateur du chapitre, mais supposez qu'une vérification tardive révèle que le RNE du sujet est en réalité de <span class="num">78 000 $</span> (bail commercial renégocié à la baisse). Recalculez l'indication par le revenu (TGA inchangé à 5,20 %), puis la conclusion pondérée (mêmes poids : 40 % comparaison à <span class="num">1 580 000 $</span>, 15 % coût à <span class="num">1 610 000 $</span>, 45 % revenu). Que remarquez-vous sur la sensibilité de la conclusion?</p></div></div>369<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="p14-77">Nouvelle indication par le revenu : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>78</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>0,052</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>500</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">78\,000 / 0{,}052 = 1\,500\,000</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">78</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">052</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">500</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span> $. Conclusion pondérée :</p>370<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mi>V</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mtext> </mtext><mn>580</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,40</mn><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><mn>1</mn><mtext> </mtext><mn>610</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,15</mn><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><mn>1</mn><mtext> </mtext><mn>500</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,45</mn><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>632</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>241</mn><mtext> </mtext><mn>500</mn><mo>+</mo><mn>675</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>548</mn><mtext> </mtext><mn>500</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>≈</mo><mrow><mn mathvariant="bold">1</mn><mtext> </mtext><mn mathvariant="bold">550</mn><mtext> </mtext><mn mathvariant="bold">000</mn></mrow><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}V &= (1\,580\,000 \times 0{,}40) + (1\,610\,000 \times 0{,}15)371 + (1\,500\,000 \times 0{,}45) \\372 &= 632\,000 + 241\,500 + 675\,000 = 1\,548\,500\,\$373 \approx \mathbf{1\,550\,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></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="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">580</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">40</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 class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">610</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">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 class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</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">45</span><span class="mclose">)</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">632</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">241</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 class="mord">675</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">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">548</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</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 class="mord"><span class="mord mathbf">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathbf">550</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathbf">000</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</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>374<p id="p14-78">Une baisse de 5,1 % du RNE fait reculer la conclusion d'environ 2,2 % (<span class="num">36 500 $</span>) : parce que la méthode du revenu pèse 45 %, toute variation du RNE se transmet presque à moitié dans la conclusion. D'où l'importance de <strong>normaliser et vérifier les revenus</strong> avant de capitaliser — et de réexaminer la pondération si une donnée dominante devient incertaine.</p></div></details>375<div class="box box-exo" id="exo-14-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 14.5</span><span class="box-title">— utilisation optimale et choix des méthodes</span><a class="box-anchor" href="#exo-14-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p14-79">Un client vous demande d'évaluer un ancien cinéma de quartier à Gatineau, vacant depuis trois ans, zoné commercial, dans un secteur où la demande porte sur les espaces de bureaux et les commerces de services. Le bâtiment de 1962 nécessiterait des travaux majeurs pour tout usage. a) Décrivez la démarche d'utilisation optimale que vous mèneriez (les deux volets et les quatre tests). b) Indiquez laquelle ou lesquelles des trois méthodes seraient applicables et avec quelles difficultés. c) Formulez en deux phrases la mise en garde que vous inscririez au mandat.</p></div></div>376<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="p14-80">a) Analyse en deux volets. <em>Comme si vacant</em> : le terrain commercial supporterait vraisemblablement un usage de bureaux ou de commerce de services — on applique les quatre tests (légalement permis par le zonage, physiquement possible sur ce lot, financièrement faisable au vu des loyers du secteur, maximalement productif parmi les usages admissibles). <em>Telle qu'améliorée</em> : on compare la valeur du bien converti (moins les coûts de conversion) à la valeur du terrain nu (moins la démolition) ; si la seconde l'emporte, l'utilisation optimale est la démolition-reconstruction. b) La comparaison est fragile : les ventes d'anciens cinémas sont rarissimes — on élargirait aux bâtiments commerciaux à convertir. Le revenu ne s'applique qu'au bien <em>après</em> conversion, en déduisant coûts et risques du projet (approche résiduelle). Le coût est pertinent pour le volet terrain (valeur du terrain moins démolition) mais la dépréciation d'un bâtiment de 1962 vacant est massive et difficile à ventiler. c) Mise en garde type : « L'évaluation repose sur une analyse d'utilisation optimale dont la conclusion (conversion ou démolition) détermine la valeur ; toute hypothèse relative aux coûts de conversion et à l'obtention des permis constitue une hypothèse extraordinaire divulguée au rapport. »</p></div></details>377<div class="box box-exo" id="exo-14-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 14.6</span><span class="box-title">— mini-DCF</span><a class="box-anchor" href="#exo-14-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p14-81">Un investisseur exige un rendement de 8 % sur un immeuble dont le RNE de l'année 1 est de <span class="num">132 000 $</span>, croissant de 3 % par année. Il prévoit revendre à la fin de l'année 3. Calculez : a) le RNE de l'année 3 ; b) sa valeur actualisée ; c) la valeur de revente à la fin de l'année 3 si le TGA de sortie est de 5,75 % (appliqué au RNE de l'année 4), avant frais de vente.</p></div></div>378<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="p14-82">a) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mtext>RNE</mtext><mn>3</mn></msub><mo>=</mo><mn>132</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mo stretchy="false">(</mo><mn>1,03</mn><msup><mo stretchy="false">)</mo><mn>2</mn></msup><mo>=</mo><mn>140</mn><mtext> </mtext><mn>039</mn></mrow><annotation encoding="application/x-tex">\text{RNE}_3 = 132\,000 \times (1{,}03)^2 = 140\,039</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 text"><span class="mord">RNE</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;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 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">132</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:1.0641em;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">03</span><span class="mclose"><span class="mclose">)</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 class="mspace" style="margin-right:0.2778em;"></span><span 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">140</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">039</span></span></span></span> $. b) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mtext>VA</mtext><mn>3</mn></msub><mo>=</mo><mn>140</mn><mtext> </mtext><mn>039</mn><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><mn>1,08</mn><msup><mo stretchy="false">)</mo><mn>3</mn></msup><mo>=</mo><mn>140</mn><mtext> </mtext><mn>039</mn><mi mathvariant="normal">/</mi><mn>1,2597</mn><mo>=</mo><mn>111</mn><mtext> </mtext><mn>167</mn></mrow><annotation encoding="application/x-tex">\text{VA}_3 = 140\,039 / (1{,}08)^3 = 140\,039 / 1{,}2597 =379111\,167</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 text"><span class="mord">VA</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;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 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:1.0641em;vertical-align:-0.25em;"></span><span class="mord">140</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">039/</span><span class="mopen">(</span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">08</span><span class="mclose"><span class="mclose">)</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">3</span></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">140</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">039/1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">2597</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">111</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">167</span></span></span></span> $. c) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mtext>RNE</mtext><mn>4</mn></msub><mo>=</mo><mn>140</mn><mtext> </mtext><mn>039</mn><mo>×</mo><mn>1,03</mn><mo>=</mo><mn>144</mn><mtext> </mtext><mn>240</mn></mrow><annotation encoding="application/x-tex">\text{RNE}_4 = 140\,039 \times 1{,}03 = 144\,240</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 text"><span class="mord">RNE</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">4</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">140</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">039</span><span class="mspace" style="margin-right:0.2222em;"></span><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:0.6444em;"></span><span class="mord">144</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">240</span></span></span></span> $ ; valeur de revente <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>144</mn><mtext> </mtext><mn>240</mn><mi mathvariant="normal">/</mi><mn>0,0575</mn><mo>=</mo><mn>2</mn><mtext> </mtext><mn>508</mn><mtext> </mtext><mn>522</mn></mrow><annotation encoding="application/x-tex">= 144\,240 / 0{,}0575 = 2\,508\,522</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">144</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">240/0</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:0.6444em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">508</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">522</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><mn mathvariant="bold">2</mn><mtext> </mtext><mn mathvariant="bold">509</mn><mtext> </mtext><mn mathvariant="bold">000</mn></mrow></mrow><annotation encoding="application/x-tex">\approx380\mathbf{2\,509\,000}</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:0.6444em;"></span><span class="mord"><span class="mord mathbf">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathbf">509</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathbf">000</span></span></span></span></span> $ (avant frais de vente). Pour obtenir la valeur nette, on déduirait ensuite les frais de vente, puis on actualiserait à <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>1,08</mn><msup><mo stretchy="false">)</mo><mn>3</mn></msup></mrow><annotation encoding="application/x-tex">(1{,}08)^3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.0641em;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">08</span><span class="mclose"><span class="mclose">)</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">3</span></span></span></span></span></span></span></span></span></span></span>.</p></div></details>381</article><aside class="side"><h4>Séances</h4><ol><li class="lvl2"><a href="#s-1">1 Introduction à l'évaluation immobilière</a></li><li class="lvl2"><a href="#s-2">2 Le cadre professionnel au Québec</a></li><li class="lvl2"><a href="#s-3">3 Les principes fondamentaux de l'évaluation</a></li><li class="lvl2"><a href="#s-4">4 La valeur : concepts et types</a></li><li class="lvl2"><a href="#s-5">5 Le marché immobilier québécois</a></li><li class="lvl2"><a href="#s-6">6 Collecte et analyse des données</a></li><li class="lvl2"><a href="#s-7">7 Examen mi-session : révision des blocs 1 et 2</a></li><li class="lvl2"><a href="#s-8">8 La méthode de comparaison — Partie 1 : principes et sélection des comparables</a></li><li class="lvl2"><a href="#s-9">9 La méthode de comparaison — Partie 2 : ajustements et réconciliation</a></li><li class="lvl2"><a href="#s-10">10 La méthode du coût</a></li><li class="lvl2"><a href="#s-11">11 La méthode du revenu — Partie 1 : du revenu brut au RNE</a></li><li class="lvl2"><a href="#s-12">12 La méthode du revenu — Partie 2 : le taux et le DCF</a></li><li class="lvl2"><a href="#s-13">13 Le rapport d'évaluation</a></li><li class="lvl2"><a href="#s-14">14 Révision générale et cas intégrateur</a></li></ol></aside></div></main>382<footer class="site-footer">383 <div class="footer-inner">384 <div class="footer-brand">385 <img src="/assets/brand/uqo-logo-white.png" alt="UQO" width="140" height="59" style="width:140px;height:auto;margin-bottom:10px">386 <div class="brand-code">IMM1003</div>387 <div>Éléments d’évaluation immobilière</div>388 <div style="opacity:.7;margin-top:6px;font-size:.85rem">Automne 2026 · 3 crédits · premier cycle · 14 séances</div>389 <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>390 </div>391 <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>392 <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>393 <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-imm1033.app" rel="noopener">IMM1033 — Méthodes du coût en évaluation immobilière</a></div>394 </div>395 <div class="footer-legal"><div><span>© 2026 Simon-Pierre Boucher — Université du Québec en Outaouais. 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