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20H2"/></symbol>72  <symbol id="i-network" viewBox="0 0 24 24"><circle cx="12" cy="12" r="3" fill="none" stroke="currentColor" stroke-width="2"/><circle cx="4" cy="6" r="2" fill="none" stroke="currentColor" stroke-width="2"/><circle cx="20" cy="6" r="2" fill="none" stroke="currentColor" stroke-width="2"/><circle cx="4" cy="18" r="2" fill="none" stroke="currentColor" stroke-width="2"/><circle cx="20" cy="18" r="2" fill="none" stroke="currentColor" stroke-width="2"/><path stroke="currentColor" stroke-width="2" d="M6 7l4 3M18 7l-4 3M6 17l4-3M18 17l-4-3"/></symbol>73  <symbol id="i-report" viewBox="0 0 24 24"><path fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" d="M14 2H6a2 2 0 0 0-2 2v16a2 2 0 0 0 2 2h12a2 2 0 0 0 2-2V8zM14 2v6h6M8 17l3-4 2 2 3-5"/></symbol>74</svg>7576<a class="skip" href="#main">Aller au contenu</a>77<header class="topbar">78  <div class="topbar-inner">79    <a class="brand" href="/" aria-label="IMM1033 — accueil"><img class="brand-logo" src="/assets/brand/uqo-logo.png" alt="UQO" width="568" height="238"><span class="brand-sep"></span><span class="brand-text"><span class="brand-code">IMM1033</span><span class="brand-title">Méthodes du coût en évaluation immobilière</span></span></a>80    <nav class="topnav" aria-label="Navigation principale"><div class="dd current"><button type="button" aria-expanded="false" aria-haspopup="true">Séances <span class="caret" aria-hidden="true">▾</span></button><div class="dd-menu wide"><div class="dd-part"><i style="background:#2976bb"></i>Partie I — Fondements de la méthode du coût</div><a href="/seance/01/" data-ch="01"><span class="pastille" style="background:#2976bb">1</span><span>Introduction à la méthode du coût</span></a><a href="/seance/02/" data-ch="02"><span class="pastille" style="background:#2976bb">2</span><span>Cadre conceptuel et terminologie</span></a><div class="dd-part"><i style="background:#0f8b8d"></i>Partie II — Évaluation du terrain</div><a href="/seance/03/" data-ch="03"><span class="pastille" style="background:#0f8b8d">3</span><span>Méthodes d'évaluation du terrain</span></a><a href="/seance/04/" data-ch="04"><span class="pastille" style="background:#0f8b8d">4</span><span>Analyse du terrain et ajustements</span></a><div class="dd-part"><i style="background:#cca424"></i>Partie III — Coût de construction</div><a href="/seance/05/" data-ch="05"><span class="pastille" style="background:#cca424">5</span><span>Coût de reproduction et coût de remplacement</span></a><a href="/seance/06/" data-ch="06"><span class="pastille" style="background:#cca424">6</span><span>Méthodes d'estimation des coûts</span></a><a href="/seance/07/" data-ch="07"><span class="pastille" style="background:#cca424">7</span><span>Coûts directs de construction</span></a><a href="/seance/08/" data-ch="08"><span class="pastille" style="background:#cca424">8</span><span>Coûts indirects et profit entrepreneurial</span></a><div class="dd-part"><i style="background:#6b4fbb"></i>Partie IV — La dépréciation</div><a href="/seance/09/" data-ch="09"><span class="pastille" style="background:#6b4fbb">9</span><span>Concepts de dépréciation</span></a><a href="/seance/10/" data-ch="10"><span class="pastille" style="background:#6b4fbb">10</span><span>Dépréciation physique</span></a><a href="/seance/11/" data-ch="11"><span class="pastille" style="background:#6b4fbb">11</span><span>Dépréciation fonctionnelle</span></a><a href="/seance/12/" data-ch="12"><span class="pastille" style="background:#6b4fbb">12</span><span>Dépréciation économique (externe)</span></a><div class="dd-part"><i style="background:#107c4e"></i>Partie V — Applications et intégration</div><a href="/seance/13/" data-ch="13"><span class="pastille" style="background:#107c4e">13</span><span>Applications spécialisées</span></a><a href="/seance/14/" data-ch="14"><span class="pastille" style="background:#107c4e">14</span><span>Synthèse et révision</span></a><div class="dd-part">Annexes</div><a href="/aide-memoire/"><span class="pastille">A</span><span>Aide-mémoire des formules</span></a><a href="/glossaire/"><span class="pastille">B</span><span>Glossaire</span></a><a href="/rapport/"><span class="pastille" style="background:var(--teal)">R</span><span>Rapport — Le marché de l’habitation au Québec</span></a></div></div><div class="dd"><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  <div class="readbar"><div class="readbar-fill"></div></div>88</header>8990<main id="main" class="chapter-page" data-chapter="12" data-title="Séance 12 — Dépréciation économique (externe)" data-words="8496">91  92<header class="ch-hero">93  <svg class="deco" viewBox="0 0 1200 300" preserveAspectRatio="xMaxYMin slice" aria-hidden="true"><circle cx="1090" cy="20" r="110"/><circle cx="1160" cy="110" r="160"/><circle class="gold" cx="990" cy="170" r="45"/></svg>94  <div class="watermark" aria-hidden="true">12</div>95  <div class="ch-hero-inner">96    <div class="eyebrow"><span class="part-chip">Partie IV</span> La dépréciation · Séance 12 · IMM1033</div>97    <h1>Dépréciation économique (externe)</h1>98    <div class="ch-sub">Méthodes du coût en évaluation immobilière · Hiver 2026 · Simon-Pierre Boucher · UQO</div>99    <div class="ch-meta">100      <span class="chip"><svg class="" aria-hidden="true"><use href="#i-list"/></svg> 8 sections</span>101      <span class="chip"><svg class="" aria-hidden="true"><use href="#i-book"/></svg> 2 définitions</span>102      <span class="chip"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg> 3 formules</span>103      <span class="chip"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg> 10 exemples</span>104      <span class="chip"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg> 6 exercices</span>105      <span class="chip"><svg class="" aria-hidden="true"><use href="#i-eye"/></svg> ≈ 47 min de lecture</span>106      <span class="chip"><svg class="" aria-hidden="true"><use href="#i-chart"/></svg> 1 explorateur interactif</span>107      108    </div>109    <div class="ch-tools">110      <a class="btn btn-ghost" href="/files/slides/seance12.pdf" target="_blank" rel="noopener"><svg class="" aria-hidden="true"><use href="#i-slides"/></svg> Diapositives (PDF)</a>111      <button class="btn btn-ghost" type="button" data-action="revision" aria-pressed="false"><svg class="" aria-hidden="true"><use href="#i-eye"/></svg> Mode révision</button>112      <button class="btn btn-ghost" type="button" data-action="tts"><svg class="" aria-hidden="true"><use href="#i-audio"/></svg> Écouter</button>113      <a class="btn btn-ghost" href="#quiz"><svg class="" aria-hidden="true"><use href="#i-quiz"/></svg> Quiz de la séance</a>114    </div>115  </div>116</header>117<div class="stepper-wrap"><nav class="stepper" aria-label="Sections"><a href="#s-12-1"><span class="n">1</span>Définition et caractéristiques</a><a href="#s-12-2"><span class="n">2</span>Les causes liées à la localisation</a><a href="#s-12-3"><span class="n">3</span>Réglementation, quartier et marché</a><a href="#s-12-4"><span class="n">4</span>Mesurer : capitalisation de la perte de revenus</a><a href="#s-12-5"><span class="n">5</span>Mesurer : l'extraction du marché (ventes appariées)</a><a href="#s-12-6"><span class="n">6</span>L'allocation terrain / améliorations</a><a href="#s-12-7"><span class="n">7</span>Cas québécois et intégration finale</a><a href="#s-12-8"><span class="n">8</span>Exercices</a><span class="rem" id="read-remaining"></span></nav></div>118  <div class="ch-layout">119    120<aside class="ch-toc" aria-label="Sommaire de la séance">121  <div class="toc-progress"><div class="bar"><i></i></div><span>0 % lu</span></div>122  <h4>Dans cette séance</h4>123  <ol><li class="lvl2"><a href="#s-12-1"><span class="toc-num">12.1</span><span>Définition et caractéristiques</span></a></li><li class="lvl3"><a href="#s-12-1-1"><span class="toc-num">12.1.1</span><span>Ce n'est pas le bâtiment, c'est son environnement</span></a></li><li class="lvl3"><a href="#s-12-1-2"><span class="toc-num">12.1.2</span><span>Portée des chiffres présentés dans ce chapitre</span></a></li><li class="lvl2"><a href="#s-12-2"><span class="toc-num">12.2</span><span>Les causes liées à la localisation</span></a></li><li class="lvl3"><a href="#s-12-2-1"><span class="toc-num">12.2.1</span><span>Autoroutes et voies ferrées</span></a></li><li class="lvl3"><a href="#s-12-2-2"><span class="toc-num">12.2.2</span><span>Pylônes et lignes à haute tension</span></a></li><li class="lvl3"><a href="#s-12-2-3"><span class="toc-num">12.2.3</span><span>Dépotoirs, sites d'enfouissement et contamination</span></a></li><li class="lvl2"><a href="#s-12-3"><span class="toc-num">12.3</span><span>Réglementation, quartier et marché</span></a></li><li class="lvl3"><a href="#s-12-3-1"><span class="toc-num">12.3.1</span><span>Les causes réglementaires</span></a></li><li class="lvl3"><a href="#s-12-3-2"><span class="toc-num">12.3.2</span><span>La détérioration du quartier</span></a></li><li class="lvl3"><a href="#s-12-3-3"><span class="toc-num">12.3.3</span><span>Les facteurs économiques et de marché</span></a></li><li class="lvl2"><a href="#s-12-4"><span class="toc-num">12.4</span><span>Mesurer : capitalisation de la perte de revenus</span></a></li><li class="lvl2"><a href="#s-12-5"><span class="toc-num">12.5</span><span>Mesurer : l'extraction du marché (ventes appariées)</span></a></li><li class="lvl2"><a href="#s-12-6"><span class="toc-num">12.6</span><span>L'allocation terrain / améliorations</span></a></li><li class="lvl3"><a href="#s-12-6-1"><span class="toc-num">12.6.1</span><span>Pourquoi allouer?</span></a></li><li class="lvl3"><a href="#s-12-6-2"><span class="toc-num">12.6.2</span><span>Les trois erreurs courantes</span></a></li><li class="lvl2"><a href="#s-12-7"><span class="toc-num">12.7</span><span>Cas québécois et intégration finale</span></a></li><li class="lvl3"><a href="#s-12-7-1"><span class="toc-num">12.7.1</span><span>Cas 1 — Autoroute 50 à Gatineau (ventes appariées)</span></a></li><li class="lvl3"><a href="#s-12-7-2"><span class="toc-num">12.7.2</span><span>Cas 2 — Fermeture d'usine en Outaouais (capitalisation)</span></a></li><li class="lvl3"><a href="#s-12-7-3"><span class="toc-num">12.7.3</span><span>Cas 3 — Contamination d'un site voisin</span></a></li><li class="lvl3"><a href="#s-12-7-4"><span class="toc-num">12.7.4</span><span>La formule complète de la méthode du coût</span></a></li><li class="lvl2"><a href="#s-12-8"><span class="toc-num">12.8</span><span>Exercices</span></a></li></ol>124  <div class="toc-extra">125    <a href="#objectifs"><svg class="" aria-hidden="true"><use href="#i-target"/></svg> Objectifs d’apprentissage</a>126    <a href="#synthese"><svg class="" aria-hidden="true"><use href="#i-clipboard"/></svg> L’essentiel de la séance</a>127    <a href="#quiz"><svg class="" aria-hidden="true"><use href="#i-quiz"/></svg> Testez-vous</a>128    <a href="/fiches/?ch=12"><svg class="" aria-hidden="true"><use href="#i-cards"/></svg> Fiches de la séance</a>129    <a href="/entrainement/"><svg class="" aria-hidden="true"><use href="#i-dumbbell"/></svg> Entraînement</a>130    <a href="/aide-memoire/"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg> Aide-mémoire</a>131  </div>132  <h4 style="margin-top:14px">Raccourcis</h4>133  <div style="font-size:.76rem;color:var(--gris)"><kbd>←</kbd> <kbd>→</kbd> séance précédente / suivante · <kbd>⌘K</kbd> recherche · sélectionnez un passage pour le surligner</div>134</aside>135    <div class="ch-body">136      <div class="revision-banner"><svg class="" aria-hidden="true"><use href="#i-eye"/></svg><span><strong>Mode révision</strong> — seuls les définitions, formules, mises en garde, « À retenir », notes marginales et la fiche synthèse sont affichés.</span><button class="btn btn-sm btn-ghost" type="button" data-action="revision-off">Quitter</button></div>137      <div style="display:flex;justify-content:flex-end;margin-bottom:8px"><button class="btn btn-sm btn-ghost" type="button" data-action="toggle-solutions">Révéler toutes les solutions</button></div>138      <article class="prose" id="notes">139        <p id="p12-1">Il arrive qu'un bâtiment n'ait rien à se reprocher — ni usure anormale, ni défaut de conception — et que sa valeur baisse quand même : une autoroute se prolonge à cent mètres, l'usine qui faisait vivre le quartier ferme, un règlement de zonage retire au terrain son potentiel de développement. C'est la <span class="motcle" data-term="dépréciation économique">dépréciation économique</span>, aussi appelée <span class="motcle" data-term="obsolescence externe">obsolescence externe</span> : la perte de valeur causée par des facteurs extérieurs à la propriété, sur lesquels le propriétaire n'a aucun contrôle. Troisième et dernière forme de dépréciation de la méthode du coût, elle possède deux propriétés qui la distinguent radicalement des deux premières : elle est <strong>toujours incurable</strong>, et elle frappe <strong>à la fois le terrain et les améliorations</strong> — ce qui impose une opération d'<strong>allocation</strong> que les chapitres précédents n'exigeaient pas. Ce chapitre recense les causes (localisation, réglementation, quartier, marché), développe les deux méthodes de mesure (capitalisation de la perte de revenus et ventes appariées), détaille la mécanique d'allocation et referme la boucle : la formule complète de la méthode du coût, avec ses trois dépréciations en place.</p>140<section class="box box-obj" id="objectifs"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-target"/></svg></span><span class="box-label">Objectifs d’apprentissage</span><span class="obj-progress" aria-live="polite"></span></div><div class="box-body"><ul><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-12-1" data-obj="obj-12-1"><span class="obj-text">Définir la dépréciation économique et la distinguer des dépréciations         physique et fonctionnelle;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-12-2" data-obj="obj-12-2"><span class="obj-text">Identifier les quatre familles de causes externes : localisation,         réglementation, détérioration du quartier et facteurs de marché;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-12-3" data-obj="obj-12-3"><span class="obj-text">Appliquer la méthode de <strong>capitalisation de la perte de         revenus</strong>;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-12-4" data-obj="obj-12-4"><span class="obj-text">Appliquer la méthode d'<strong>extraction du marché</strong> (ventes         appariées) et en apprécier la fiabilité statistique;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-12-5" data-obj="obj-12-5"><span class="obj-text"><strong>Allouer</strong> la dépréciation externe entre le terrain et les         améliorations, sans double comptage;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-12-6" data-obj="obj-12-6"><span class="obj-text">Distinguer les conditions de marché <strong>cycliques</strong> (temporaires)         des changements <strong>structurels</strong> (permanents);</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-12-7" data-obj="obj-12-7"><span class="obj-text">Intégrer les trois formes de dépréciation dans la formule finale de         la méthode du coût, à l'aide de cas québécois.</span></label></li></ul></div></section>141<h2 id="s-12-1" class="h-section"><span class="h-num">12.1</span><span class="h-text">Définition et caractéristiques</span><a class="h-anchor" href="#s-12-1" aria-label="Lien vers cette section">#</a></h2>142<h3 id="s-12-1-1" class="h-subsection"><span class="h-num">12.1.1</span><span class="h-text">Ce n'est pas le bâtiment, c'est son environnement</span><a class="h-anchor" href="#s-12-1-1" aria-label="Lien vers cette section">#</a></h3>143<div class="box box-def" id="def-12-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 12.1</span><span class="box-title">— dépréciation économique (obsolescence externe)</span><a class="box-anchor" href="#def-12-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-9">La <strong>dépréciation économique</strong> est la perte de valeur d'une propriété causée par des <strong>facteurs extérieurs</strong> à la propriété elle-même, sur lesquels le propriétaire n'a <strong>aucun contrôle</strong> : environnement physique, économique, réglementaire ou social.</p></div></div>144<p id="p12-10">En d'autres mots : ce n'est pas le bâtiment qui a un problème — c'est son <strong>environnement</strong> qui nuit à sa valeur. Cette origine externe emporte trois caractéristiques structurantes. <label for="sn-12-1" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-12-1" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-repere">Externe <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> hors du contrôle du propriétaire, toujours incurable, frappe terrain ET améliorations.</span></p>145<p id="p12-11">Premièrement, les <strong>facteurs sont externes</strong> : ils naissent au-delà des limites du terrain et du bâtiment. Deuxièmement, la dépréciation est <strong>toujours incurable</strong> : le propriétaire ne peut ni contrôler ni modifier l'autoroute, le zonage ou la conjoncture — il n'existe pas de « coût de correction » à comparer à une valeur ajoutée, et le test de curabilité des chapitres 10 et 11 n'a simplement pas d'objet. Troisièmement — et c'est la nouveauté opérationnelle du chapitre — elle affecte <strong class="c-rouge">le terrain <strong>et</strong> les améliorations</strong>, alors que les dépréciations physique et fonctionnelle ne touchent que les améliorations. C'est cette troisième propriété qui rendra l'<strong>allocation</strong> indispensable (section <a class="xref" href="#s-12-6">12.6</a>).</p>146<p id="p12-12">L'économiste reconnaîtra ici la notion d'<strong>externalité</strong> : le voisinage impose à la propriété des coûts (bruit, risque, stigmate) ou lui retire des bénéfices (accès, vue, services) sans qu'aucune transaction ne les compense. Le marché immobilier a ceci de particulier qu'il <em>internalise</em> ces externalités dans les prix : chaque vente incorpore, silencieusement, la prime du parc voisin et la décote de l'autoroute. Le travail de l'évaluateur consiste précisément à <strong>extraire</strong> cette composante du prix — à isoler, dans l'écart entre deux ventes, la part attribuable au facteur externe. C'est pourquoi les deux méthodes de mesure de ce chapitre sont toutes deux des méthodes <em>de marché</em> : la capitalisation lit l'externalité dans les loyers, les ventes appariées la lisent dans les prix. Aucune table, aucun barème ne peut s'y substituer, car l'externalité n'existe qu'à travers la réaction des acheteurs locaux.</p>147<figure class="float-table" id="tab-ch12-tab-synthese3"><figcaption><span class="fig-label">Tableau 12.1</span> Les trois formes de dépréciation — tableau synthèse du cours.</figcaption><div class="table-wrap"><table class="tbl"><thead><tr><th>Critère</th><th>Physique (ch. 10)</th><th>Fonctionnelle (ch. 11)</th><th>Économique (ch. 12)</th></tr></thead><tbody><tr><td>Origine</td><td>Usure, âge, intempéries</td><td>Conception, plan, style</td><td>Environnement extérieur</td></tr><tr><td>Curabilité</td><td>Curable ou incurable</td><td>Curable ou incurable</td><td><strong>Toujours incurable</strong></td></tr><tr><td>Affecte</td><td>Améliorations seulement</td><td>Améliorations seulement</td><td><strong>Terrain <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> améliorations</strong></td></tr><tr><td>Contrôle</td><td>Propriétaire peut agir</td><td>Propriétaire peut agir</td><td>Hors de contrôle</td></tr><tr><td>Exemples</td><td>Toiture usée, fondation fissurée</td><td>Plan obsolète, superadéquation</td><td>Autoroute, fermeture d'usine</td></tr><tr><td>Méthodes</td><td>Âge-vie, ventilation</td><td>Coût de correction, capitalisation</td><td>Capitalisation, ventes appariées</td></tr></tbody></table></div></figure>148<h3 id="s-12-1-2" class="h-subsection"><span class="h-num">12.1.2</span><span class="h-text">Portée des chiffres présentés dans ce chapitre</span><a class="h-anchor" href="#s-12-1-2" aria-label="Lien vers cette section">#</a></h3>149<div class="box box-att" id="attention-12-13"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">mise en garde méthodologique</span><a class="box-anchor" href="#attention-12-13" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-14">Les fourchettes d'impact en pourcentage présentées dans ce chapitre (autoroutes, lignes électriques, dépotoirs, contamination, rezonage, fermetures d'usines, etc.) sont des <strong class="c-rouge">ordres de grandeur illustratifs</strong> compilés de la littérature. Elles servent à <strong>structurer l'analyse</strong>, pas à remplacer la preuve de marché : en pratique, chaque impact doit être <strong>mesuré sur le marché local</strong>, par ventes appariées ou par capitalisation de la perte de revenus. L'ampleur réelle varie selon le secteur, le type de propriété et la période — et devant un tribunal, seule une <strong>démonstration chiffrée locale</strong> est recevable.</p></div></div>150<h2 id="s-12-2" class="h-section"><span class="h-num">12.2</span><span class="h-text">Les causes liées à la localisation</span><a class="h-anchor" href="#s-12-2" aria-label="Lien vers cette section">#</a></h2>151<p id="p12-15">La <strong>proximité de nuisances</strong> ou la <strong>perte d'aménités</strong> réduit la valeur d'une propriété indépendamment de sa qualité intrinsèque. Du côté des nuisances : autoroutes et routes achalandées, voies ferrées (bruit, vibrations), zones industrielles, pylônes et lignes à haute tension, dépotoirs et lieux d'enfouissement technique, stations d'épuration, aéroports. Du côté des aménités perdues : vue ou ensoleillement, fermeture d'un parc, démantèlement de services de transport, perte d'accès à un plan d'eau, réduction de l'intimité.</p>152<h3 id="s-12-2-1" class="h-subsection"><span class="h-num">12.2.1</span><span class="h-text">Autoroutes et voies ferrées</span><a class="h-anchor" href="#s-12-2-1" aria-label="Lien vers cette section">#</a></h3>153<p id="p12-16">Les impacts mesurables combinent le <strong>bruit</strong> (niveaux de décibels réduisant l'attrait), les <strong>vibrations</strong> (trains de marchandises, camionnage lourd), la <strong>pollution atmosphérique</strong> (particules fines), la <strong>sécurité</strong> perçue et l'<strong>esthétique</strong> (vue dégradée). La littérature rapporte des pertes de <strong>5 à 15 %</strong> de la valeur pour des propriétés à moins de 200 mètres d'une autoroute — ordre de grandeur à valider par ventes appariées sur le marché local. L'effet est <strong>dégressif avec la distance</strong> :</p>154<div class="center"><div class="tikz"><img src="/assets/fig/e74e524d5a4e16d3.svg" alt="Figure" width="494" height="164" style="width:min(100%,717px)" loading="lazy" decoding="async"></div></div>155<p id="p12-17">Grille pédagogique illustrative : l'impact réel dépend du bruit effectif, de la topographie et des écrans (murs antibruit, végétation).</p>156<p id="p12-18">Deux subtilités méritent l'attention. D'abord, l'effet d'une infrastructure de transport n'est pas uniformément négatif : la même autoroute qui décote les résidences riveraines <em>bonifie</em> les terrains commerciaux et industriels qui vivent de l'accessibilité et de la visibilité. Le signe de l'externalité dépend de l'usage — c'est pourquoi l'analyse commence toujours par l'utilisation optimale, jamais par la nuisance elle-même. Ensuite, le moment compte : le marché anticipe. La décote apparaît souvent dès l'<em>annonce</em> du projet routier, des années avant la première pelletée de terre, puis s'ajuste à mesure que l'incertitude se résorbe. L'évaluateur qui compare des ventes doit donc situer chacune par rapport au calendrier du projet, sous peine de mélanger des prix « avant annonce », « pendant l'incertitude » et « après mise en service » qui ne mesurent pas la même chose.</p>157<h3 id="s-12-2-2" class="h-subsection"><span class="h-num">12.2.2</span><span class="h-text">Pylônes et lignes à haute tension</span><a class="h-anchor" href="#s-12-2-2" aria-label="Lien vers cette section">#</a></h3>158<p id="p12-19"><label for="sn-12-2" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-12-2" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-terme"><strong class="sn-term">servitude</strong> restriction d'usage du terrain dans l'emprise d'une ligne ou d'une infrastructure</span> Les lignes de transport d'électricité cumulent les impacts <strong>visuels</strong> (pylônes dans le paysage), les <strong>servitudes</strong> (restrictions d'usage dans l'emprise), les préoccupations de <strong>santé perçues</strong> (champs électromagnétiques), le <strong>bruit</strong> (grésillement par temps humide) et une <strong>perception négative</strong> du marché, surtout en résidentiel. L'effet est dégressif avec la distance et dépend fortement de la <strong>visibilité</strong> des lignes depuis la propriété.</p>159<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Type de ligne (Hydro-Québec)</th><th class="al-c">Impact indicatif</th></tr></thead><tbody><tr><td>735 kV (transport)</td><td class="al-c"><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>15 à 20 %</td></tr><tr><td>315 kV (transport)</td><td class="al-c"><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>10 à 15 %</td></tr><tr><td>120 kV (répartition)</td><td class="al-c"><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>5 à 10 %</td></tr><tr><td>25 kV (distribution)</td><td class="al-c"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>2 à 5 %</td></tr></tbody></table></div></div>160<p id="p12-20">Grille illustrative; l'impact maximal frappe les lignes de 735 kV adjacentes au résidentiel. En pratique : mesurer par <strong>ventes appariées</strong> dans le secteur visé.</p>161<h3 id="s-12-2-3" class="h-subsection"><span class="h-num">12.2.3</span><span class="h-text">Dépotoirs, sites d'enfouissement et contamination</span><a class="h-anchor" href="#s-12-2-3" aria-label="Lien vers cette section">#</a></h3>162<p id="p12-21">Les sites problématiques pour le voisinage incluent les lieux d'enfouissement technique (LET, anciennement « dépotoirs »), les sites d'entreposage de matières dangereuses, les stations d'épuration, les sites inscrits au <strong>Répertoire des terrains contaminés</strong> du MELCCFP et les usines à émissions atmosphériques. Impacts sur le voisinage : odeurs et gaz, contamination potentielle des eaux, nuisances visuelles, circulation de camions lourds, perception de risque sanitaire. Ordres de grandeur illustratifs : pertes de <strong>10 à 30 % et plus</strong> selon la proximité.</p>163<div class="box box-qc" id="quebec-12-22"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-map"/></svg></span><span class="box-label">l'encadrement québécois</span><a class="box-anchor" href="#quebec-12-22" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-23">Le voisinage de ces sites est encadré par la <em>Loi sur la qualité de l'environnement</em> (LQE) <span class="citation">(<a class="cite" href="/bibliographie/#lqe" data-cite="lqe">Québec, 1972</a>)</span>, les audiences publiques du <strong>BAPE</strong> pour les grands projets, le répertoire des terrains contaminés du <strong>MELCCFP</strong> et la réglementation municipale (usages, distances séparatrices). Distinction cruciale pour l'évaluateur : la contamination du <strong class="c-rouge">propre terrain</strong> du sujet est un facteur <strong>physique</strong> de la propriété; c'est la contamination du terrain <strong class="c-rouge">voisin</strong> qui constitue une dépréciation <strong>externe</strong>.</p></div></div>164<div class="box box-ex" id="ex-12-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 12.1</span><span class="box-title">— facteurs de localisation — trois situations illustratives</span><a class="box-anchor" href="#ex-12-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-24">Trois situations types illustrent le raisonnement (chiffres illustratifs, non sourcés). Le <strong>prolongement d'une autoroute</strong> du type de l'A-50 à Gatineau frappe d'abord les propriétés situées à moins de 150 m du nouveau tracé : le bruit et les vibrations leur infligent une dépréciation de l'ordre de <strong>8 à 12 %</strong>, dégressive à mesure que l'on s'éloigne de l'emprise. Une <strong>ligne de 735 kV</strong> en Outaouais pèse plus lourd encore sur les terrains résidentiels directement adjacents — <strong>10 à 18 %</strong> — parce qu'aux nuisances objectives s'ajoute la perception du risque. Enfin, un <strong>ancien site d'enfouissement</strong> montre le phénomène de <strong>stigmatisation</strong> : même après la fermeture et la réhabilitation du site, une dépréciation résiduelle de <strong>5 à 8 %</strong> persiste, mémoire du marché qui survit à la nuisance elle-même. Dans les trois cas, les pourcentages ne se transposent jamais d'un secteur à l'autre sans analyse de marché locale.</p></div></div>165<p id="p12-25"><label for="sn-12-3" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-12-3" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-terme"><strong class="sn-term">stigmatisation</strong> perte de valeur résiduelle qui persiste après la disparition de la nuisance elle-même</span></p>166<h2 id="s-12-3" class="h-section"><span class="h-num">12.3</span><span class="h-text">Réglementation, quartier et marché</span><a class="h-anchor" href="#s-12-3" aria-label="Lien vers cette section">#</a></h2>167<h3 id="s-12-3-1" class="h-subsection"><span class="h-num">12.3.1</span><span class="h-text">Les causes réglementaires</span><a class="h-anchor" href="#s-12-3-1" aria-label="Lien vers cette section">#</a></h3>168<p id="p12-26">Les <strong>changements réglementaires</strong> créent une dépréciation économique lorsqu'ils réduisent le <strong>potentiel d'utilisation</strong> ou la valeur d'usage d'une propriété : dézonage (de commercial à résidentiel), restrictions de densité (étages permis réduits), nouvelles marges de recul, limites d'usage, moratoires de développement. Le cadre québécois : la <em>Loi sur l'aménagement et l'urbanisme</em> (LAU) <span class="citation">(<a class="cite" href="/bibliographie/#lau" data-cite="lau">Québec, 1979</a>)</span>, les règlements d'urbanisme municipaux, les schémas d'aménagement des MRC, les plans d'urbanisme révisés et les règlements sur les usages conditionnels.</p>169<div class="box box-qc" id="quebec-12-27"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-map"/></svg></span><span class="box-label">la CPTAQ et la zone agricole</span><a class="box-anchor" href="#quebec-12-27" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-28">La <strong>Commission de protection du territoire agricole du Québec</strong> protège la zone agricole en vertu de la <em>Loi sur la protection du territoire et des activités agricoles</em> (LPTAA) <span class="citation">(<a class="cite" href="/bibliographie/#lptaa" data-cite="lptaa">Québec, 1978</a>)</span> : interdiction de morcellement, restrictions sur les usages non agricoles, limitation de la construction résidentielle. Exemple chiffré illustratif : un terrain <strong>en zone blanche</strong> (développable) à 25 $/pi<sup>2</sup> ne vaut plus que 0,50 à 2,00 $/pi<sup>2</sup> <strong>en zone verte</strong> (agricole) — un écart potentiel de <strong>plus de 90 %</strong>. L'inclusion en zone agricole est l'une des dépréciations économiques les plus massives du droit québécois de l'aménagement.</p></div></div>170<p id="p12-29">S'y ajoutent les contraintes environnementales : <strong>bandes riveraines</strong> (protection des cours d'eau, 10–15 m minimum), <strong>milieux humides</strong> (la loi de 2017 sur la conservation des milieux humides et hydriques retire la constructibilité des portions visées), <strong>zones inondables</strong> et habitats d'espèces menacées.</p>171<div class="box box-qc" id="quebec-12-30"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-map"/></svg></span><span class="box-label">zones inondables — le cadre de 2026</span><a class="box-anchor" href="#quebec-12-30" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-31">Un nouveau cadre réglementaire est en vigueur au Québec depuis le <strong>1<sup>er</sup> mars 2026</strong> <span class="citation">(<a class="cite" href="/bibliographie/#zonesInond2026" data-cite="zonesInond2026">Gouvernement du Québec, 2026</a>)</span> : il remplace les anciennes zones « 0–20 ans » et « 20–100 ans » par <strong>quatre classes de risque</strong> (très élevé, élevé, modéré, faible), avec des cartes graduelles publiées progressivement depuis le printemps 2026. Conséquences pour la valeur : restrictions de construction et de reconstruction, assurabilité réduite, obligations de divulgation. Impact indicatif (illustratif) : de <strong><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>20 %</strong> (risque faible) à <strong><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>60 % et plus</strong> (risque très élevé), selon la classe, l'historique d'inondation et l'assurabilité — à mesurer par ventes appariées dans chaque secteur.</p></div></div>172<div class="box box-att" id="attention-12-32"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">double comptage réglementaire</span><a class="box-anchor" href="#attention-12-32" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-33">Si la valeur du terrain est déjà estimée <strong class="c-rouge">en tenant compte de ces contraintes</strong> (comparables eux-mêmes en zone inondable, terrain évalué comme non développable), ne pas déduire une dépréciation économique une deuxième fois. Ce réflexe de vérification reviendra à l'allocation (section <a class="xref" href="#s-12-6">12.6</a>).</p></div></div>173<div class="box box-ex" id="ex-12-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 12.2</span><span class="box-title">— facteurs réglementaires — trois situations illustratives</span><a class="box-anchor" href="#ex-12-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-34">Un <strong>rezonage</strong> du type de ceux qu'a connus Gatineau montre l'ampleur possible de la perte : un terrain commercial (C-2) rezoné résidentiel de faible densité (R-1) voit son potentiel passer de 15 logements à 3 unifamiliales, soit une perte estimée de <strong>40 à 60 %</strong> de la valeur du terrain — l'usage optimal d'hier n'est plus légalement permis. Le <strong>reclassement en zone inondable</strong> sous le cadre de 2026 produit le même mécanisme par la voie cartographique : une propriété nouvellement classée en risque élevé ou très élevé subit une dépréciation indicative de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>20 à <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>60 % et plus, selon la classe, l'historique et l'assurabilité. Quant aux <strong>milieux humides</strong>, ils amputent la superficie utile plutôt que l'usage : sur un terrain de <span class="num">5000</span> m<sup>2</sup> dont <span class="num">2000</span> m<sup>2</sup> sont identifiés comme milieu humide d'intérêt, seuls <span class="num">3000</span> m<sup>2</sup> demeurent développables, et la valeur se réduit en proportion de l'assiette perdue.</p></div></div>174<h3 id="s-12-3-2" class="h-subsection"><span class="h-num">12.3.2</span><span class="h-text">La détérioration du quartier</span><a class="h-anchor" href="#s-12-3-2" aria-label="Lien vers cette section">#</a></h3>175<p id="p12-35">Le <strong>déclin d'un quartier</strong> déprécie même les propriétés bien entretenues. Indicateurs de déclin : vieillissement généralisé du parc immobilier, hausse des logements vacants, criminalité et vandalisme, dégradation des infrastructures publiques, entretien négligé chez les voisins. Pertes de services : fermetures de commerces de proximité et d'écoles, réduction du transport en commun, départ des services de santé, perte d'institutions culturelles. Le processus est typiquement <strong>cumulatif et auto-renforçant</strong> :</p>176<div class="center"><div class="tikz"><img src="/assets/fig/55a3b883a2f4cf50.svg" alt="Figure" width="510" height="180" style="width:min(100%,740px)" loading="lazy" decoding="async"></div></div>177<div class="box box-ex" id="ex-12-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 12.3</span><span class="box-title">— deux quartiers, une même maison</span><a class="box-anchor" href="#ex-12-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-36">Scénario A — quartier stable : maison de trois chambres, <span class="num">1200</span> pi<sup>2</sup>, rénovée; écoles, parcs et commerces à proximité; taux de vacance faible; valeur <span class="num">350 000 $</span>. Scénario B — quartier en déclin : la <em>même</em> maison, même qualité; fermetures commerciales, vandalisme, vacance en hausse, infrastructures dégradées; valeur <span class="num">280 000 $</span>. Dépréciation économique (données fictives à des fins pédagogiques) :</p>178<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>350</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>280</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">70</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle><mspace width="1em"/><mo stretchy="false">(</mo><mn>20</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">350\,000 - 280\,000 = \uqogreen{70\,000~\$} \quad (20\,\%)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">350</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">280</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">70</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span><span class="mspace" style="margin-right:1em;"></span><span class="mopen">(</span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mclose">)</span></span></span></span></span></div>179<p id="p12-37">La maison est identique — seul l'<strong>environnement</strong> a changé. C'est la définition même de l'obsolescence externe, et déjà, en filigrane, la logique des ventes appariées.</p></div></div>180<h3 id="s-12-3-3" class="h-subsection"><span class="h-num">12.3.3</span><span class="h-text">Les facteurs économiques et de marché</span><a class="h-anchor" href="#s-12-3-3" aria-label="Lien vers cette section">#</a></h3>181<p id="p12-38">Côté macroéconomique : récession locale ou régionale, hausse des taux d'intérêt (pouvoir d'achat), suroffre sur le marché local, changements démographiques (dépopulation, vieillissement), obsolescence économique d'un type de propriété. Côté sectoriel : fermeture d'un <strong>employeur majeur</strong> (usine, mine, base militaire), délocalisations, fin de contrats gouvernementaux, déclin d'une industrie régionale.</p>182<figure class="float-table" id="tab-ch12-tab-employeurs"><figcaption><span class="fig-label">Tableau 12.2</span> Fermetures d'employeurs majeurs — grille pédagogique illustrative (non sourcée). La perte d'un employeur majeur entraîne aussi des pertes d'emplois <em>indirects</em> (sous-traitants, commerces, services) qui amplifient l'impact immobilier.</figcaption><div class="table-wrap"><table class="tbl"><thead><tr><th>Événement</th><th>Région</th><th>Emplois perdus</th><th>Impact indicatif</th></tr></thead><tbody><tr><td>Fermeture de papetière</td><td>Outaouais</td><td>300–500</td><td>Baisse 10–15 % locale</td></tr><tr><td>Fermeture de mine</td><td>Abitibi</td><td>500–1 000</td><td>Baisse 15–25 % (ville)</td></tr><tr><td>Départ de siège social</td><td>Montréal</td><td>Variable</td><td>Impact sectoriel</td></tr><tr><td>Fermeture de base militaire</td><td>Plusieurs</td><td>200–800</td><td>Baisse 10–20 % locale</td></tr></tbody></table></div></figure>183<div class="box box-att" id="attention-12-39"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">cyclique ou structurel : la question clé</span><a class="box-anchor" href="#attention-12-39" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-40">La suroffre et les conditions défavorables sont souvent <strong class="c-rouge">temporaires</strong> : taux de vacance élevé, délais de vente prolongés, inventaire gonflé, ratio inscriptions/ventes défavorable, baisse des mises en chantier. Question clé de l'évaluateur : la condition est-elle <strong>cyclique</strong> (temporaire) ou <strong>structurelle</strong> (permanente)? Seuls les changements <strong class="c-rouge">structurels</strong> justifient une dépréciation économique dans la méthode du coût — et attention au double comptage si la baisse cyclique est déjà reflétée dans les comparables.</p></div></div>184<div class="box box-rem" id="remarque-12-41"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pen"/></svg></span><span class="box-label">taux d'intérêt et valeur — le mécanisme, et le contexte 2026</span><a class="box-anchor" href="#remarque-12-41" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-42">Le mécanisme d'une hausse de taux : hausse des taux hypothécaires <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> baisse du pouvoir d'achat des emprunteurs <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> réduction de la demande <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> pression à la baisse sur les prix <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> hausse des taux de capitalisation (TGA). La relation valeur–taux est inverse : à revenu net constant, <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 = \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>, de sorte qu'un TGA passant hypothétiquement de 5,0 à 6,5 % ampute la valeur d'environ 23 %. Contexte 2026 : le taux directeur de la Banque du Canada est passé de 5,00 % (2023) à <strong>2,25 %</strong> à la fin de 2025, niveau maintenu en 2026 <span class="citation">(<a class="cite" href="/bibliographie/#bdcTaux2026" data-cite="bdcTaux2026">Banque du Canada, 2026</a>)</span>. Les fluctuations de taux sont généralement <strong>cycliques</strong> : vérifier si leur effet est déjà reflété dans les comparables avant de conclure à une dépréciation économique distincte.</p></div></div>185<h2 id="s-12-4" class="h-section"><span class="h-num">12.4</span><span class="h-text">Mesurer : capitalisation de la perte de revenus</span><a class="h-anchor" href="#s-12-4" aria-label="Lien vers cette section">#</a></h2>186<p id="p12-43">Deux méthodes mesurent la dépréciation économique : la <strong>capitalisation de la perte de revenus</strong> (propriétés locatives) et l'<strong>extraction du marché</strong> par ventes appariées (tous types de propriétés). Dans les deux cas, le résultat est une dépréciation <strong>totale</strong> — terrain et améliorations confondus — qu'il faudra ensuite <strong>allouer</strong>.</p>187<div class="box box-form" id="form-12-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 12.1</span><span class="box-title">— capitalisation de la perte de revenus</span><a class="box-anchor" href="#form-12-1" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-12-1"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable width="100%"><mtr><mtd width="50%"></mtd><mtd><mrow><msub><mi>D</mi><mrow><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>co totale</mtext></mrow></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><mfrac><mtext>Perte de revenu net annuelle</mtext><mtext>TGA</mtext></mfrac></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(12.1)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">D_{\text{éco totale}} \;=\;188\frac{\text{Perte de revenu net annuelle}}{\text{TGA}}\tag{12.1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord 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">co totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.0574em;vertical-align:-0.686em;"></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:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">TGA</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Perte de revenu net annuelle</span></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><span class="katex-tag"><span class="katex-strut" style="height:2.0574em;vertical-align:-0.686em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">12.1</span></span><span class="mord">)</span></span></span></span></span></span></div>189<p id="p12-44">où la perte de revenu <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> revenu normal (sans le facteur externe) <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> revenu réel (avec le facteur), après dépenses, et où le TGA est le taux global d'actualisation du marché pour ce type de propriété.</p></div></div>190<p id="p12-45">La méthode se déroule en cinq étapes : (1) estimer le <strong>revenu normal</strong> à partir de loyers de comparables <strong>non affectés</strong> par la nuisance; (2) estimer le <strong>revenu réel</strong> sur la propriété ou des comparables affectés, vacance additionnelle comprise; (3) calculer la <strong>perte annuelle de revenu net</strong> (après dépenses); (4) <strong>capitaliser</strong> la perte au TGA pour obtenir la dépréciation totale; (5) <strong>allouer</strong> entre terrain et améliorations selon le ratio de valeurs. <label for="sn-12-4" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-12-4" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-repere">Capitalisation <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> dépréciation TOTALE. L'allocation vient après.</span></p>191<div class="box box-ex" id="ex-12-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 12.4</span><span class="box-title">— immeuble locatif près d'une autoroute</span><a class="box-anchor" href="#ex-12-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-46">Immeuble de huit logements à proximité de l'autoroute 50 à Gatineau (données fictives à des fins pédagogiques). Loyer <strong>normal</strong> (sans autoroute) : 1 100 $/mois par logement; loyer <strong>réel</strong> : 950 $/mois; ratio de dépenses : 40 % du revenu brut effectif. Hypothèses du cas : TGA de 5,5 % (2026); ratio terrain/propriété de 25 %.</p>192<p id="p12-47"><strong>Étape par étape :</strong></p>193<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Étape</th><th class="al-r">Montant</th></tr></thead><tbody><tr><td>1. Revenu brut normal : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mtext> </mtext><mn>100</mn><mo>×</mo><mn>12</mn><mo>×</mo><mn>8</mn></mrow><annotation encoding="application/x-tex">1\,100 \times 12 \times 8</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">100</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">8</span></span></span></span></td><td class="al-r">105 600 $/an</td></tr><tr><td>2. Revenu brut réel : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>950</mn><mo>×</mo><mn>12</mn><mo>×</mo><mn>8</mn></mrow><annotation encoding="application/x-tex">950 \times 12 \times 8</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">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><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">8</span></span></span></span></td><td class="al-r">91 200 $/an</td></tr><tr><td>3. Perte brute : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>105</mn><mtext> </mtext><mn>600</mn><mo>−</mo><mn>91</mn><mtext> </mtext><mn>200</mn></mrow><annotation encoding="application/x-tex">105\,600 - 91\,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">105</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">91</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span></span></span></span></td><td class="al-r">14 400 $/an</td></tr><tr><td>4. Perte nette (après dépenses 40 %) : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>14</mn><mtext> </mtext><mn>400</mn><mo>×</mo><mn>0,60</mn></mrow><annotation encoding="application/x-tex">14\,400 \times 0{,}60</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">14</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">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">60</span></span></span></span></td><td class="al-r">8 640 $/an</td></tr><tr><td>5. Capitalisation : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>8</mn><mtext> </mtext><mn>640</mn><mo>÷</mo><mn>0,055</mn></mrow><annotation encoding="application/x-tex">8\,640 \div 0{,}055</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">640</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">055</span></span></span></span></td><td class="al-r"><strong>157 091 $</strong></td></tr><tr class="rule-above"><td>Portion terrain (25 %) — reflétée dans la valeur du terrain</td><td class="al-r">39 273 $</td></tr><tr><td>Portion améliorations (75 %) — déduite du coût neuf</td><td class="al-r"><strong>117 818 $</strong></td></tr></tbody></table></div></div>194<p id="p12-48">Seuls les <span class="num">117 818 $</span> de la portion améliorations seront soustraits du coût neuf; les <span class="num">39 273 $</span> de la portion terrain se refléteront dans la valeur du terrain (si elle ne les reflète pas déjà).</p></div></div>195<div class="box box-rem" id="remarque-12-49"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pen"/></svg></span><span class="box-label">forces et limites de la capitalisation</span><a class="box-anchor" href="#remarque-12-49" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-50"><strong>Avantages</strong> : méthode directe et logique, facile à expliquer, bien adaptée aux immeubles locatifs, quantification précise, données de loyers souvent disponibles. <strong>Limites</strong> : réservée aux propriétés générant des revenus; exige des comparables fiables des deux côtés (affectés et non affectés); sensible au calibrage du TGA et du ratio de dépenses; et surtout, difficulté d'<strong class="c-rouge">isoler l'unique cause</strong> de la perte de revenu — si le loyer inférieur tient à la fois au bruit de l'autoroute (externe) et à un plan désuet (fonctionnel), il faut ventiler la perte entre les deux formes, sous peine de double comptage avec le chapitre 11.</p></div></div>196<h2 id="s-12-5" class="h-section"><span class="h-num">12.5</span><span class="h-text">Mesurer : l'extraction du marché (ventes appariées)</span><a class="h-anchor" href="#s-12-5" aria-label="Lien vers cette section">#</a></h2>197<div class="box box-def" id="def-12-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 12.2</span><span class="box-title">— ventes appariées</span><a class="box-anchor" href="#def-12-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-51">La méthode des <strong>ventes appariées</strong> (<em>paired sales analysis</em>) compare des propriétés <strong>similaires</strong> dont certaines sont <strong>affectées</strong> par le facteur externe et d'autres <strong>non</strong> : la différence de prix, une fois les autres écarts ajustés, isole la dépréciation économique.</p></div></div>198<p id="p12-52">Le principe tient en une image : propriété A, non affectée, vendue <span class="num">350 000 $</span>; propriété B, comparable en tous points mais affectée, vendue <span class="num">310 000 $</span>; différence de <span class="num">40 000 $</span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> dépréciation économique. La force probante de la méthode dépend de six conditions idéales : (1) propriétés similaires (type, taille, âge, qualité); (2) ventes récentes, même période de marché; (3) même secteur géographique; (4) conditions de vente normales (ni vente forcée ni lien de dépendance); (5) <strong>un seul facteur différent</strong> — celui qu'on étudie; (6) plusieurs paires (idéalement trois et plus) pour confirmer la tendance. Les paires parfaites étant rares, l'évaluateur procède en pratique à des ajustements préalables — le processus complet : identifier les ventes affectées, identifier les ventes non affectées comparables, <strong>ajuster</strong> toutes les différences sauf le facteur étudié, calculer la différence de prix (dépréciation totale), puis <strong>allouer</strong>.</p>199<div class="box box-ex" id="ex-12-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 12.5</span><span class="box-title">— maisons près de lignes à haute tension</span><a class="box-anchor" href="#ex-12-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-53">Quatre paires de ventes dans un même secteur (données fictives à des fins pédagogiques) :</p>200<div class="center"><div class="table-wrap"><table class="tbl table-wide"><thead><tr><th>Paire</th><th class="al-r">Non affectée</th><th class="al-r">Affectée (HT)</th><th class="al-r">Différence</th><th class="al-r">Perte (%)</th></tr></thead><tbody><tr><td>Paire 1</td><td class="al-r">385 000 $</td><td class="al-r">340 000 $</td><td class="al-r">45 000 $</td><td class="al-r">11,7 %</td></tr><tr><td>Paire 2</td><td class="al-r">410 000 $</td><td class="al-r">355 000 $</td><td class="al-r">55 000 $</td><td class="al-r">13,4 %</td></tr><tr><td>Paire 3</td><td class="al-r">365 000 $</td><td class="al-r">320 000 $</td><td class="al-r">45 000 $</td><td class="al-r">12,3 %</td></tr><tr><td>Paire 4</td><td class="al-r">395 000 $</td><td class="al-r">345 000 $</td><td class="al-r">50 000 $</td><td class="al-r">12,7 %</td></tr><tr class="rule-above"><td><strong>Moyenne</strong></td><td class="al-r"></td><td class="al-r"></td><td class="al-r"><strong>48 750 $</strong></td><td class="al-r"><strong>12,5 %</strong></td></tr></tbody></table></div></div>201<p id="p12-54">Conclusion : la proximité des lignes à haute tension crée dans ce secteur une dépréciation économique d'environ <strong>12,5 %</strong> de la valeur (48 750 $ en moyenne). L'analyse statistique renforce la fiabilité : moyenne 12,5 %, médiane 12,5 %, écart-type d'environ 0,7 point — la faible dispersion suggère un résultat robuste. Pour aller plus loin : régression (prix hédoniques) pour isoler le facteur, test <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi></mrow><annotation encoding="application/x-tex">t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6151em;"></span><span class="mord mathnormal">t</span></span></span></span> de Student pour la significativité.</p></div></div>202<div class="box box-att" id="attention-12-55"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">petits échantillons</span><a class="box-anchor" href="#attention-12-55" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-56">Un échantillon de moins de cinq paires limite la fiabilité, et des ajustements nombreux réduisent la précision : privilégier la <strong>cohérence</strong> des résultats (dispersion faible, signe constant) plutôt que la seule moyenne. Une moyenne de 12 % tirée de paires oscillant entre <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>2 et <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>25 % ne prouve rien.</p></div></div>203<div class="box box-rem" id="remarque-12-57"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pen"/></svg></span><span class="box-label">forces et limites des ventes appariées</span><a class="box-anchor" href="#remarque-12-57" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-58"><strong>Avantages</strong> : fondée sur des données de marché réelles, applicable à tous les types de propriétés, mesure directe de l'impact sur les prix, bien acceptée par les tribunaux, résultat vérifiable. <strong>Limites</strong> : paires parfaites rares, échantillon suffisant requis, ajustements multiples, difficulté d'isoler un facteur unique, et recherche coûteuse en temps sur un marché peu actif.</p></div></div>204<h2 id="s-12-6" class="h-section"><span class="h-num">12.6</span><span class="h-text">L'allocation terrain / améliorations</span><a class="h-anchor" href="#s-12-6" aria-label="Lien vers cette section">#</a></h2>205<h3 id="s-12-6-1" class="h-subsection"><span class="h-num">12.6.1</span><span class="h-text">Pourquoi allouer?</span><a class="h-anchor" href="#s-12-6-1" aria-label="Lien vers cette section">#</a></h3>206<p id="p12-59">Dans la méthode du coût, la valeur du <strong>terrain</strong> est estimée séparément (par comparaison directe, séances 3 et 4), tandis que la <strong>dépréciation</strong> se déduit du coût neuf des <strong>améliorations</strong>. Or la dépréciation économique frappe les deux. Il faut donc <strong>répartir</strong> la dépréciation totale mesurée (par capitalisation ou par ventes appariées) entre ses deux assiettes — sinon, on déduit du coût neuf une perte qui appartient en partie au terrain.</p>207<div class="box box-form" id="form-12-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 12.2</span><span class="box-title">— allocation par la méthode du ratio</span><a class="box-anchor" href="#form-12-2" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-12-2"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable width="100%"><mtr><mtd width="50%"></mtd><mtd><mrow><msub><mi>D</mi><mrow><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>co, am</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>liorations</mtext></mrow></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><msub><mi>D</mi><mrow><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>co, totale</mtext></mrow></msub><mo>×</mo><mfrac><mrow><mtext>Valeur des am</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>liorations</mtext></mrow><mrow><mtext>Valeur totale de la propri</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>t</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover></mrow></mfrac></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(12.2)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">D_{\text{éco, améliorations}} \;=\; D_{\text{éco, totale}} \times208\frac{\text{Valeur des améliorations}}{\text{Valeur totale de la propriété}}\tag{12.2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord 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">co, 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:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord 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">co, totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.2519em;vertical-align:-0.8804em;"></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:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Valeur totale de la propri</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">t</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></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 text"><span class="mord">Valeur des am</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">liorations</span></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><span class="katex-tag"><span class="katex-strut" style="height:2.2519em;vertical-align:-0.8804em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">12.2</span></span><span class="mord">)</span></span></span></span></span></span></div>209<p id="p12-60">Le ratio se calcule sur les valeurs <strong>avant</strong> dépréciation économique; le complément (portion terrain) est reflété dans la valeur du terrain.</p></div></div>210<div class="box box-rem" id="remarque-12-61"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pen"/></svg></span><span class="box-label">ratios terrain/propriété usuels — référence du cours</span><a class="box-anchor" href="#remarque-12-61" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-62">Fourchettes usuelles du ratio terrain/propriété : <strong>résidentiel de banlieue 15–30 %</strong>; <strong>urbain dense 30–50 %</strong>; <strong>industriel 5–15 %</strong>. C'est une <strong>donnée de marché à documenter</strong> dans chaque mandat; les exercices du cours énoncent chacun leur « hypothèse du cas ». Ce sont les mêmes repères que ceux utilisés au chapitre 11 pour la portion terrain de l'obsolescence de conception — la mécanique est identique.</p></div></div>211<div class="box box-ex" id="ex-12-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 12.6</span><span class="box-title">— allocation — exemple chiffré</span><a class="box-anchor" href="#ex-12-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-63">Dépréciation économique totale mesurée : <span class="num">60 000 $</span>. Valeur du terrain (avant dépréciation économique) : <span class="num">150 000 $</span>; coût neuf des améliorations (avant toute dépréciation) : <span class="num">350 000 $</span>; valeur totale : <span class="num">500 000 $</span> (hypothèse du cas : ratio terrain 30 %).</p>212<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Ratio am</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>liorations</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>350</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>500</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>70</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>D</mi><mrow><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>co, am</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>liorations</mtext></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>60</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>70</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">42</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>D</mi><mrow><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>co, terrain</mtext></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>60</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>30</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">18</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{Ratio améliorations} &amp;= 350\,000 \div 500\,000 = 70\,\% \\213D_{\text{éco, améliorations}} &amp;= 60\,000 \times 70\,\% = \uqogreen{42\,000~\$} \\214D_{\text{éco, terrain}} &amp;= 60\,000 \times 30\,\% = \uqogreen{18\,000~\$}\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">Ratio am</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">liorations</span></span></span></span><span style="top:-3.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord 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">co, 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:0.2861em;"><span></span></span></span></span></span></span></span></span><span style="top:-1.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><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 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">co, terrain</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:1.85em;"><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">350</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span><span 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">70</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">60</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">70</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:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">42</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span><span 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">60</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">18</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span><span 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>215<p id="p12-64">Seuls les <span class="num">42 000 $</span> se déduisent du coût neuf; les <span class="num">18 000 $</span> appartiennent à la valeur du terrain.</p></div></div>216<div class="widget" data-widget="allocation"></div>217<h3 id="s-12-6-2" class="h-subsection"><span class="h-num">12.6.2</span><span class="h-text">Les trois erreurs courantes</span><a class="h-anchor" href="#s-12-6-2" aria-label="Lien vers cette section">#</a></h3>218<div class="box box-att" id="attention-12-65"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">erreur 1 — le double comptage</span><a class="box-anchor" href="#attention-12-65" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-66">Si les comparables ayant servi à évaluer le terrain sont <strong class="c-rouge">déjà dans la zone affectée</strong>, leur prix reflète déjà la dépréciation externe du terrain : la déduire à nouveau la compte deux fois. <strong>Règle d'or</strong> : toujours vérifier si la valeur du terrain a déjà été ajustée pour le facteur externe avant d'appliquer l'allocation. Comparables non affectés <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> allouer; comparables affectés <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> ne déduire que la portion améliorations, le terrain étant déjà net.</p></div></div>219<div class="box box-att" id="attention-12-67"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">erreur 2 — tout imputer aux améliorations</span><a class="box-anchor" href="#attention-12-67" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-68">La dépréciation économique affecte <strong class="c-rouge">aussi le terrain</strong> : attribuer 100 % de la perte aux seules améliorations les sous-évalue et fausse le rapprochement final avec le marché.</p></div></div>220<div class="box box-att" id="attention-12-69"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">erreur 3 — le ratio inapproprié</span><a class="box-anchor" href="#attention-12-69" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-70">Un ratio qui ne reflète pas les valeurs <strong class="c-rouge">avant dépréciation</strong> fausse l'allocation. Le ratio doit être fondé sur les valeurs de départ, documentées sur le marché — pas sur les valeurs déjà amputées de la perte qu'on cherche justement à répartir.</p></div></div>221<h2 id="s-12-7" class="h-section"><span class="h-num">12.7</span><span class="h-text">Cas québécois et intégration finale</span><a class="h-anchor" href="#s-12-7" aria-label="Lien vers cette section">#</a></h2>222<h3 id="s-12-7-1" class="h-subsection"><span class="h-num">12.7.1</span><span class="h-text">Cas 1 — Autoroute 50 à Gatineau (ventes appariées)</span><a class="h-anchor" href="#s-12-7-1" aria-label="Lien vers cette section">#</a></h3>223<div class="box box-ex" id="ex-12-7"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 12.7</span><span class="box-title">— bungalow près du prolongement de l'autoroute 50</span><a class="box-anchor" href="#ex-12-7" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-71"><strong>Contexte</strong> (données fictives à des fins pédagogiques) : bungalow de <span class="num">1100</span> pi<sup>2</sup>, terrain de <span class="num">6000</span> pi<sup>2</sup>, à 120 m du prolongement de l'autoroute 50. Coût de remplacement déprécié (avant dépréciation externe) : <span class="num">220 000 $</span>; valeur du terrain (comparables <strong>non affectés</strong>) : <span class="num">80 000 $</span>.</p>224<p id="p12-72"><strong>Mesure par ventes appariées :</strong></p>225<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th></th><th class="al-r">Non affectée</th><th class="al-r">Affectée</th><th class="al-r">Différence</th></tr></thead><tbody><tr><td>Paire 1</td><td class="al-r">295 000 $</td><td class="al-r">262 000 $</td><td class="al-r">33 000 $</td></tr><tr><td>Paire 2</td><td class="al-r">310 000 $</td><td class="al-r">275 000 $</td><td class="al-r">35 000 $</td></tr><tr><td>Paire 3</td><td class="al-r">285 000 $</td><td class="al-r">252 000 $</td><td class="al-r">33 000 $</td></tr><tr class="rule-above"><td><strong>Moyenne</strong></td><td class="al-r"></td><td class="al-r"></td><td class="al-r"><strong>33 667 $ (<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> 11 %)</strong></td></tr></tbody></table></div></div>226<p id="p12-73"><strong>Allocation</strong> (dépréciation retenue : <span class="num">33 000 $</span>, arrondi) : valeur totale avant dépréciation externe <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>80</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>220</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>300</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 80\,000 + 220\,000 =227300\,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">80</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">220</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">300</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; ratio terrain <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>80</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>300</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>26,7</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">= 80\,000 \div 300\,000 = 26{,}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:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">80</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">300</span><span class="mspace" style="margin-right:0.1667em;"></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">26</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>; ratio améliorations <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>73,3</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">= 73{,}3\,\%</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">73</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>.</p>228<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>terrain</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>33</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>26,7</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mn>8</mn><mtext> </mtext><mn>811</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>D</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>33</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>73,3</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mn>24</mn><mtext> </mtext><mn>189</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}D_{\text{terrain}} &amp;= 33\,000 \times 26{,}7\,\% = 8\,811\,\$ \\229D_{\text{améliorations}} &amp;= 33\,000 \times 73{,}3\,\% = 24\,189\,\$\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:2.7em;vertical-align:-1.1em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6em;"><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">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 class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">am</span><span class="mord katex-accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight">e</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˊ</span></span></span></span></span></span></span><span class="mord mtight">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><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">33</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">26</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 class="mord">8</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">811</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">33</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">73</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 class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">189</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.1em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>230<p id="p12-74"><strong>Valeur finale :</strong> terrain <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>80</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>8</mn><mtext> </mtext><mn>811</mn><mo>=</mo><mn>71</mn><mtext> </mtext><mn>189</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">80\,000 - 8\,811 = 71\,189\,\$</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:0.1667em;"></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">811</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">71</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">189</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; améliorations <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>220</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>24</mn><mtext> </mtext><mn>189</mn><mo>=</mo><mn>195</mn><mtext> </mtext><mn>811</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">220\,000 - 24\,189 = 195\,811\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">220</span><span class="mspace" style="margin-right:0.1667em;"></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">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">189</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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">195</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">811</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>;</p>231<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>V</mi><mo>=</mo><mn>71</mn><mtext> </mtext><mn>189</mn><mo>+</mo><mn>195</mn><mtext> </mtext><mn>811</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">267</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">V = 71\,189 + 195\,811 = \uqogreen{267\,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">71</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">189</span><span class="mspace" style="margin-right:0.2222em;"></span><span 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">195</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">811</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">267</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span></span></div>232<p id="p12-75">La déduction du terrain est légitime ici parce que sa valeur venait de comparables <em>non affectés</em> : sans cet ajustement, le terrain aurait été surévalué de <span class="num">8811 $</span>.</p></div></div>233<h3 id="s-12-7-2" class="h-subsection"><span class="h-num">12.7.2</span><span class="h-text">Cas 2 — Fermeture d'usine en Outaouais (capitalisation)</span><a class="h-anchor" href="#s-12-7-2" aria-label="Lien vers cette section">#</a></h3>234<div class="box box-ex" id="ex-12-8"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 12.8</span><span class="box-title">— immeuble de 12 logements après la fermeture d'une papetière</span><a class="box-anchor" href="#ex-12-8" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-76"><strong>Contexte</strong> (données fictives) : fermeture d'une papetière employant 400 personnes; immeuble de 12 logements à évaluer. Hypothèses du cas : TGA de 6,0 % (2026); ratio terrain de 20 %.</p>235<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Élément</th><th class="al-r">Montant</th></tr></thead><tbody><tr><td>Revenu brut potentiel (avant fermeture)</td><td class="al-r">172 800 $/an</td></tr><tr><td>Revenu brut potentiel (après fermeture, hausse de vacance)</td><td class="al-r">144 000 $/an</td></tr><tr><td>Perte de revenu brut</td><td class="al-r">28 800 $/an</td></tr><tr><td>Perte de revenu net (ratio de dépenses 42 %)</td><td class="al-r">16 704 $/an</td></tr><tr class="rule-above"><td><strong>Dépréciation économique totale</strong> (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>16</mn><mtext> </mtext><mn>704</mn><mo>÷</mo><mn>0,06</mn></mrow><annotation encoding="application/x-tex">16\,704 \div 0{,}06</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">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">704</span><span class="mspace" style="margin-right:0.2222em;"></span><span 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></span></span>)</td><td class="al-r"><strong>278 400 $</strong></td></tr><tr><td>Portion améliorations (80 %)</td><td class="al-r"><strong>222 720 $</strong></td></tr><tr><td>Portion terrain (20 %)</td><td class="al-r"><strong>55 680 $</strong></td></tr></tbody></table></div></div>236<p id="p12-77">L'ampleur (278 000 $ sur un immeuble de douze logements) illustre le poids d'un choc structurel d'emploi sur l'immobilier locatif d'une petite ville mono-industrielle — et rappelle l'exigence préalable : vérifier que la perte de vacance est bien <em>structurelle</em>, pas un creux cyclique.</p></div></div>237<h3 id="s-12-7-3" class="h-subsection"><span class="h-num">12.7.3</span><span class="h-text">Cas 3 — Contamination d'un site voisin</span><a class="h-anchor" href="#s-12-7-3" aria-label="Lien vers cette section">#</a></h3>238<div class="box box-ex" id="ex-12-9"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 12.9</span><span class="box-title">— stigmatisation par contamination du voisin</span><a class="box-anchor" href="#ex-12-9" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-78"><strong>Contexte</strong> : contamination aux hydrocarbures sur le terrain <strong>voisin</strong> (inscrit au Répertoire des terrains contaminés du MELCCFP); la propriété évaluée est un immeuble commercial sur terrain <strong>non</strong> contaminé. Impacts mesurés (ordres de grandeur illustratifs) : ventes appariées montrant des propriétés adjacentes vendues <strong>15 à 25 %</strong> de moins; <strong>stigmatisation</strong> résiduelle de 5 à 10 % persistant même après décontamination; impact maximal à proximité immédiate (moins de 50 m). Distinction essentielle : la contamination du <em>propre</em> terrain du sujet serait un facteur <strong>physique</strong> de la propriété; ici, c'est le voisin qui est contaminé — dépréciation <strong>externe</strong>.</p></div></div>239<h3 id="s-12-7-4" class="h-subsection"><span class="h-num">12.7.4</span><span class="h-text">La formule complète de la méthode du coût</span><a class="h-anchor" href="#s-12-7-4" aria-label="Lien vers cette section">#</a></h3>240<p id="p12-79">Avec la troisième forme de dépréciation en place, la formule du cours prend sa forme définitive :</p>241<div class="box box-form" id="form-12-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 12.3</span><span class="box-title">— formule complète de la méthode du coût</span><a class="box-anchor" href="#form-12-3" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-12-3"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable width="100%"><mtr><mtd width="50%"></mtd><mtd><menclose notation="box"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>  </mtext><mi>V</mi><mtext>  </mtext><mo>=</mo><mtext>  </mtext><msub><mi>V</mi><mi>T</mi></msub><mtext>  </mtext><mo>+</mo><mtext>  </mtext><mo fence="true" stretchy="true" minsize="1.8em" maxsize="1.8em">[</mo><mtext> </mtext><msub><mi>C</mi><mi>N</mi></msub><mo>−</mo><msub><mi>D</mi><mtext>phys</mtext></msub><mo>−</mo><msub><mi>D</mi><mtext>fonc</mtext></msub><mo>−</mo><msub><mi>D</mi><mrow><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>co(am</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>l.)</mtext></mrow></msub><mtext> </mtext><mo fence="true" stretchy="true" minsize="1.8em" maxsize="1.8em">]</mo><mtext>  </mtext></mrow></mstyle></mstyle></mstyle></menclose></mtd><mtd width="50%"></mtd><mtd><mtext>(12.3)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">\boxed{\;V \;=\; V_T \;+\;242\Bigl[\, C_N - D_{\text{phys}} - D_{\text{fonc}} - D_{\text{éco(amél.)}} \,\Bigr]\;}\tag{12.3}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:2.48em;vertical-align:-0.99em;"></span><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.49em;"><span style="top:-4.48em;"><span class="pstrut" style="height:4.48em;"></span><span class="boxpad"><span class="mord"><span class="mord"><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">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="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen"><span class="delimsizing size2">[</span></span><span class="mspace" style="margin-right:0.1667em;"></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:0.3283em;"><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 mathnormal mtight" style="margin-right:0.109em;">N</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">phys</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></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">fonc</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></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:0.3448em;"><span style="top:-2.5198em;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 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">co(am</span><span class="mord katex-accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight">e</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˊ</span></span></span></span></span></span></span><span class="mord mtight">l.)</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3552em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mclose"><span class="delimsizing size2">]</span></span><span class="mspace" style="margin-right:0.2778em;"></span></span></span></span></span><span style="top:-3.49em;"><span class="pstrut" style="height:4.48em;"></span><span class="katex-stretchy fbox" style="height:2.48em;border-style:solid;border-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.99em;"><span></span></span></span></span></span></span><span class="katex-tag"><span class="katex-strut" style="height:2.48em;vertical-align:-0.99em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">12.3</span></span><span class="mord">)</span></span></span></span></span></span></div>243<p id="p12-80">où <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi></mrow><annotation encoding="application/x-tex">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 mathnormal" style="margin-right:0.2222em;">V</span></span></span></span> est la valeur estimée de la propriété; <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></mrow><annotation encoding="application/x-tex">V_T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">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> la valeur du terrain (déjà ajustée pour la dépréciation économique, s'il y a lieu); <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mi>N</mi></msub></mrow><annotation encoding="application/x-tex">C_N</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><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 mathnormal mtight" style="margin-right:0.109em;">N</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> le coût neuf (reproduction ou remplacement); <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>phys</mtext></msub></mrow><annotation encoding="application/x-tex">D_{\text{phys}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">phys</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span> et <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>fonc</mtext></msub></mrow><annotation encoding="application/x-tex">D_{\text{fonc}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">fonc</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> les dépréciations physique et fonctionnelle (curable <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> incurable); et <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mrow><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>co(am</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>l.)</mtext></mrow></msub></mrow><annotation encoding="application/x-tex">D_{\text{éco(amél.)}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.0385em;vertical-align:-0.3552em;"></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:0.3448em;"><span style="top:-2.5198em;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 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">co(am</span><span class="mord katex-accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight">e</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˊ</span></span></span></span></span></span></span><span class="mord mtight">l.)</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3552em;"><span></span></span></span></span></span></span></span></span></span> la dépréciation économique, <strong>portion améliorations seulement</strong> — la portion terrain étant reflétée dans <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></mrow><annotation encoding="application/x-tex">V_T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">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>.</p></div></div>244<p id="p12-81">Le processus séquentiel complet de déduction, illustré sur un coût neuf de <span class="num">500 000 $</span> :</p>245<div class="center"><div class="tikz"><img src="/assets/fig/a9ad241a3dec97a2.svg" alt="Figure" width="418" height="243" style="width:min(100%,607px)" loading="lazy" decoding="async"></div></div>246<div class="box box-ex" id="ex-12-10"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 12.10</span><span class="box-title">— exemple intégrateur — les trois dépréciations réunies</span><a class="box-anchor" href="#ex-12-10" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-82"><strong>Données</strong> (fictives à des fins pédagogiques) : immeuble à revenus de six logements à Gatineau; coût de remplacement neuf <span class="num">480 000 $</span>; valeur du terrain (comparables non affectés) <span class="num">120 000 $</span>; dépréciation économique totale (extraction du marché) <span class="num">36 000 $</span>; hypothèse du cas : ratio terrain/propriété 20 % (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>120</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>600</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">120\,000 \div 600\,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">120</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">600</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>).</p>247<p id="p12-83"><strong>Les dépréciations :</strong></p>248<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Type</th><th class="al-r">Montant</th><th>Détail</th></tr></thead><tbody><tr><td>Physique curable</td><td class="al-r">12 000 $</td><td>Entretien différé</td></tr><tr><td>Physique incurable</td><td class="al-r">72 000 $</td><td>Âge-vie : 15 % du coût neuf</td></tr><tr><td>Fonctionnelle curable</td><td class="al-r">8 000 $</td><td>Ajout de climatisation</td></tr><tr><td>Fonctionnelle incurable</td><td class="al-r">18 000 $</td><td>Plan obsolète</td></tr><tr><td>Économique (totale)</td><td class="al-r">36 000 $</td><td>Extraction du marché</td></tr><tr><td>&emsp; Portion terrain (20 %)</td><td class="al-r">7 200 $</td><td>Reflétée dans la valeur du terrain</td></tr><tr><td>&emsp; Portion améliorations (80 %)</td><td class="al-r">28 800 $</td><td>Déduite du coût neuf</td></tr></tbody></table></div></div>249<p id="p12-84">Total déduit des améliorations : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>12</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>72</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>8</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>18</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>28</mn><mtext> </mtext><mn>800</mn><mo>=</mo><mn>138</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">12\,000 + 72\,000 + 8\,000 + 18\,000 + 28\,800 = 138\,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">12</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">72</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></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:0.2222em;"></span><span 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">18</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">28</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">138</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">$</span></span></span></span>.</p>250<p id="p12-85"><strong>Conclusion de valeur :</strong></p>251<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Am</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>liorations</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>480</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>138</mn><mtext> </mtext><mn>800</mn><mo>=</mo><mn>341</mn><mtext> </mtext><mn>200</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Terrain (ajust</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>)</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>120</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>7</mn><mtext> </mtext><mn>200</mn><mo>=</mo><mn>112</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mi>V</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>112</mn><mtext> </mtext><mn>800</mn><mo>+</mo><mn>341</mn><mtext> </mtext><mn>200</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">454</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Améliorations} &amp;= 480\,000 - 138\,800 = 341\,200\,\$ \\252\text{Terrain (ajusté)} &amp;= 120\,000 - 7\,200 = 112\,800\,\$ \\253V &amp;= 112\,800 + 341\,200 = \uqogreen{454\,000~\$}\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">Am</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">liorations</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">Terrain (ajust</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">)</span></span></span></span><span style="top:-1.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.85em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35em;"><span style="top:-4.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">480</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">138</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">341</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">$</span></span></span><span style="top:-3.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">120</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">7</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">112</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</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">112</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">341</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 class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">454</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span><span 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></div></div>254<p id="p12-86">Avec ce cas, la boucle ouverte à la séance 1 se referme : l'équation <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><msub><mi>V</mi><mi>T</mi></msub><mo>+</mo><mo stretchy="false">(</mo><msub><mi>C</mi><mi>N</mi></msub><mo>−</mo><mi>D</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">V = V_T + (C_N - D)</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:0.8333em;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:0.2222em;"></span><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 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:0.3283em;"><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 mathnormal mtight" style="margin-right:0.109em;">N</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><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="mclose">)</span></span></span></span> n'a plus une seule inconnue. Nous savons estimer le terrain (séances 3 et 4), chiffrer le coût neuf (séances 5 à 8) et ventiler la dépréciation dans ses trois formes (séances 9 à 12) — en respectant l'ordre, en documentant chaque poste et en traquant les doubles comptages à chaque frontière. Les deux dernières séances mettront cette mécanique complète au service de cas réels : les bâtiments à usage spécial où la méthode du coût est souvent la seule praticable (séance 13), puis la synthèse générale et la préparation à l'examen final (séance 14).</p>255<hr class="sep">256<div class="box box-ret" id="aretenir-12-87"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-star"/></svg></span><span class="box-label">À retenir</span><a class="box-anchor" href="#aretenir-12-87" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-88">La dépréciation économique provient de facteurs <strong>externes</strong> — localisation, réglementation, quartier, marché — entièrement hors du contrôle du propriétaire : elle est de ce fait <strong>toujours incurable</strong>, et elle frappe à la fois le terrain et les améliorations. Sa mesure passe par deux voies : la <strong>capitalisation de la perte de revenus</strong> (perte nette divisée par le TGA, indiquée pour les immeubles locatifs) et les <strong>ventes appariées</strong> (applicables à tous les types et bien reçues par les tribunaux). Dans les deux cas, le résultat est une dépréciation <strong>totale</strong> de la propriété : c'est l'<strong>allocation</strong> par le ratio terrain/améliorations — calculé sur les valeurs <em>avant</em> dépréciation — qui isole la seule portion déductible du coût neuf, la part terrain étant censée se refléter dans la valeur du terrain elle-même. D'où le réflexe systématique : vérifier si la valeur de terrain retenue reflète déjà le facteur externe (comparables eux-mêmes affectés), sans quoi la perte serait comptée deux fois. Rappelez-vous enfin que le cyclique n'est pas le structurel — seuls les changements durables fondent une dépréciation économique — et que tout le chapitre se condense dans la formule finale <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><msub><mi>V</mi><mi>T</mi></msub><mo>+</mo><mo stretchy="false">[</mo><mtext> </mtext><msub><mi>C</mi><mi>N</mi></msub><mo>−</mo><msub><mi>D</mi><mtext>phys</mtext></msub><mo>−</mo><msub><mi>D</mi><mtext>fonc</mtext></msub><mo>−</mo><msub><mi>D</mi><mrow><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>co(am</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>l.)</mtext></mrow></msub><mtext> </mtext><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">V = V_T + [\,C_N - D_{\text{phys}} - D_{\text{fonc}}257- D_{\text{éco(amél.)}}\,]</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:0.8333em;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:0.2222em;"></span><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="mspace" style="margin-right:0.1667em;"></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:0.3283em;"><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 mathnormal mtight" style="margin-right:0.109em;">N</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><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">phys</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">fonc</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1052em;vertical-align:-0.3552em;"></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:0.3448em;"><span style="top:-2.5198em;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 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">co(am</span><span class="mord katex-accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight">e</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˊ</span></span></span></span></span></span></span><span class="mord mtight">l.)</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3552em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mclose">]</span></span></span></span>.</p></div></div>258<h2 id="s-12-8" class="h-section"><span class="h-num">12.8</span><span class="h-text">Exercices</span><a class="h-anchor" href="#s-12-8" aria-label="Lien vers cette section">#</a></h2>259<div class="box box-exo" id="exo-12-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 12.1</span><span class="box-title">— qualifier la dépréciation</span><a class="box-anchor" href="#exo-12-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-89">Pour chaque situation, dites s'il s'agit d'une dépréciation <strong>économique (externe)</strong>, <strong>fonctionnelle</strong>, <strong>physique</strong> — ou d'aucune dépréciation au sens de la méthode du coût. Justifiez brièvement.</p>260<ol class="enum"><li>Le terrain du sujet est contaminé aux hydrocarbures.</li><li>Le terrain voisin du sujet est contaminé et inscrit au répertoire du         MELCCFP.</li><li>La Ville rezone le secteur : le potentiel passe de 15 logements à         3 unifamiliales.</li><li>Le marché locatif local traverse un creux cyclique de 18 mois lié à         une suroffre temporaire de condos.</li><li>L'immeuble n'a qu'une salle de bain pour quatre chambres.</li><li>Une papetière, principal employeur de la ville, ferme         définitivement.</li></ol></div></div>261<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li><strong>Physique</strong> (de la propriété) : la contamination du propre         terrain du sujet est un état de la propriété, pas un facteur         externe.</li><li><strong>Économique</strong> : facteur extérieur, hors du contrôle du         propriétaire (stigmatisation de voisinage).</li><li><strong>Économique</strong> (réglementaire) : perte de potentiel imposée de         l'extérieur, toujours incurable.</li><li><strong class="c-rouge">Aucune</strong> : condition <strong>cyclique</strong> temporaire; seuls         les changements structurels fondent une dépréciation économique —         et l'effet du creux est probablement déjà dans les comparables.</li><li><strong>Fonctionnelle</strong> : défaut interne de conception (chapitre 11).</li><li><strong>Économique</strong> (facteur de marché structurel) : perte         d'employeur majeur, mesurable par capitalisation ou ventes         appariées.</li></ol></div></details>262<div class="box box-exo" id="exo-12-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 12.2</span><span class="box-title">— capitalisation de la perte de revenus</span><a class="box-anchor" href="#exo-12-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-102">Un immeuble de dix logements à Buckingham borde une nouvelle voie de camionnage lourd. Loyer normal des comparables non affectés : 1 250 $/mois par logement; loyer réel obtenu : 1 120 $/mois; ratio de dépenses : 38 % du revenu brut. Hypothèses du cas : TGA de 5,75 %; ratio terrain/propriété de 22 % (valeur du terrain issue de comparables non affectés).</p>263<ol class="enum"><li>Calculez la perte de revenu net annuelle.</li><li>Calculez la dépréciation économique totale.</li><li>Allouez entre terrain et améliorations, et indiquez le montant à         déduire du coût neuf.</li></ol></div></div>264<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>Perte brute <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mtext> </mtext><mn>250</mn><mo>−</mo><mn>1</mn><mtext> </mtext><mn>120</mn><mo stretchy="false">)</mo><mo>×</mo><mn>12</mn><mo>×</mo><mn>10</mn><mo>=</mo><mn>15</mn><mtext> </mtext><mn>600</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><mtext>an</mtext></mrow><annotation encoding="application/x-tex">= (1\,250 - 1\,120) \times 12 \times 10 =265        15\,600\,\$/\text{an}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">250</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">120</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$/</span><span class="mord text"><span class="mord">an</span></span></span></span></span>; perte nette         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>15</mn><mtext> </mtext><mn>600</mn><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mn>0,38</mn><mo stretchy="false">)</mo><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">9</mn><mtext> </mtext><mn mathvariant="bold">672</mn><mtext> </mtext><mi mathvariant="bold">$</mi><mi mathvariant="bold">/</mi><mi mathvariant="bold">a</mi><mi mathvariant="bold">n</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= 15\,600 \times (1 - 0{,}38) = \uqogreen{9\,672~\$/an}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">38</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">9</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">672</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$/an</span></span></span></span></span>.</li><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>totale</mtext></msub><mo>=</mo><mn>9</mn><mtext> </mtext><mn>672</mn><mo>÷</mo><mn>0,0575</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">168</mn><mtext> </mtext><mn mathvariant="bold">209</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">D_{\text{totale}} = 9\,672 \div 0{,}0575 =266        \uqogreen{168\,209~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">672</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0575</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">168</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">209</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</li><li>Portion terrain <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>168</mn><mtext> </mtext><mn>209</mn><mo>×</mo><mn>22</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mn>37</mn><mtext> </mtext><mn>006</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 168\,209 \times 22\,\% = 37\,006\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">168</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">209</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">37</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">006</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> (reflétée         dans la valeur du terrain, puisque les comparables de terrain sont         non affectés); portion améliorations         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>168</mn><mtext> </mtext><mn>209</mn><mo>×</mo><mn>78</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">131</mn><mtext> </mtext><mn mathvariant="bold">203</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= 168\,209 \times 78\,\% = \uqogreen{131\,203~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">168</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">209</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">131</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">203</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span> — seul ce         montant se déduit du coût neuf.</li></ol></div></details>267<div class="box box-exo" id="exo-12-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 12.3</span><span class="box-title">— ventes appariées et fiabilité</span><a class="box-anchor" href="#exo-12-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-109">Pour mesurer l'impact d'un poste de transformation électrique, un évaluateur réunit cinq paires de ventes : différences de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>28 000, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>31 000, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>26 000, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>34 000 et <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>29 000 $ sur des propriétés non affectées se vendant en moyenne <span class="num">310 000 $</span>.</p>268<ol class="enum"><li>Calculez la dépréciation moyenne en dollars et en pourcentage.</li><li>La médiane et la dispersion appuient-elles la conclusion?</li><li>Un collègue propose plutôt une seule « super-paire » très propre         montrant <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>52 000 $. Que lui répondez-vous?</li></ol></div></div>269<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>Moyenne <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mo stretchy="false">(</mo><mn>28</mn><mo>+</mo><mn>31</mn><mo>+</mo><mn>26</mn><mo>+</mo><mn>34</mn><mo>+</mo><mn>29</mn><mo stretchy="false">)</mo><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>5</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">29</mn><mtext> </mtext><mn mathvariant="bold">600</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= (28 + 31 + 26 + 34 + 29)\,000 \div 5 =270        \uqogreen{29\,600~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">28</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">31</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">26</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">34</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">29</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">29</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">600</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>, soit <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>29</mn><mtext> </mtext><mn>600</mn><mo>÷</mo><mn>310</mn><mtext> </mtext><mn>000</mn><mo>≈</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">9,5</mn><mtext> </mtext><mi mathvariant="bold">%</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">29\,600 \div 310\,000 \approx271        \uqogreen{9{,}5\,\%}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">29</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">310</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">9</span><span class="mord" style="color:#107C4E;"><span class="mpunct" style="color:#107C4E;">,</span></span><span class="mord mathbf" style="color:#107C4E;">5</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">%</span></span></span></span></span>.</li><li>Médiane <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>29</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 29\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">29</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>, proche de la moyenne; étendue de 26 000 à         34 000 (dispersion modérée, signe constant) : la conclusion         d'environ 9 à 10 % est <strong>robuste</strong> — cinq paires         cohérentes valent mieux qu'une moyenne isolée.</li><li>Une paire unique, si « propre » soit-elle, ne permet ni de mesurer         la dispersion ni d'exclure un facteur idiosyncratique (vente         pressée, rénovation cachée). L'écart de la super-paire         (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>52 000 $, soit près de 17 %) s'éloigne nettement du faisceau         des cinq autres : elle mérite d'être examinée, pas de gouverner la         conclusion. Privilégier la <strong>cohérence</strong> de l'échantillon.</li></ol></div></details>272<div class="box box-exo" id="exo-12-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 12.4</span><span class="box-title">— allocation et double comptage</span><a class="box-anchor" href="#exo-12-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-116">Une maison borde une emprise ferroviaire. Dépréciation économique totale mesurée par ventes appariées : <span class="num">45 000 $</span>. Coût de remplacement déprécié (physique et fonctionnelle déjà déduites) : <span class="num">265 000 $</span>.</p>273<ol class="enum"><li><strong>Scénario A</strong> : la valeur du terrain (<span class="num">90 000 $</span>)         provient de comparables <strong>non affectés</strong> par la voie ferrée.         Calculez l'allocation et la valeur finale.</li><li><strong>Scénario B</strong> : la valeur du terrain (<span class="num">78 500 $</span>)         provient de comparables <strong>eux-mêmes bordant la voie ferrée</strong>.         Que change ce fait? Calculez la valeur finale.</li></ol></div></div>274<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>Valeur totale avant dépréciation externe         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>90</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>265</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>355</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 90\,000 + 265\,000 = 355\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">90</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">265</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">355</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; ratio terrain         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>90</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>355</mn><mtext> </mtext><mn>000</mn><mo>≈</mo><mn>25,4</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">= 90\,000 \div 355\,000 \approx 25{,}4\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">90</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">355</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">25</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">4</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>. Portion terrain         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>45</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>25,4</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>≈</mo><mn>11</mn><mtext> </mtext><mn>430</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 45\,000 \times 25{,}4\,\% \approx 11\,430\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">45</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">25</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">4</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">11</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">430</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; portion         améliorations <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>33</mn><mtext> </mtext><mn>570</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\approx 33\,570\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">33</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">570</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Valeur finale : terrain         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>90</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>11</mn><mtext> </mtext><mn>430</mn><mo>=</mo><mn>78</mn><mtext> </mtext><mn>570</mn></mrow><annotation encoding="application/x-tex">90\,000 - 11\,430 = 78\,570</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">90</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">11</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">430</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">570</span></span></span></span>; améliorations         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>265</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>33</mn><mtext> </mtext><mn>570</mn><mo>=</mo><mn>231</mn><mtext> </mtext><mn>430</mn></mrow><annotation encoding="application/x-tex">265\,000 - 33\,570 = 231\,430</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">265</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">33</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">570</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">231</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">430</span></span></span></span>;         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>≈</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">310</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">V \approx \uqogreen{310\,000~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">310</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</li><li>Les comparables affectés reflètent <strong>déjà</strong> la portion terrain         de la dépréciation (d'ailleurs <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>78</mn><mtext> </mtext><mn>500</mn><mo>≈</mo><mn>78</mn><mtext> </mtext><mn>570</mn></mrow><annotation encoding="application/x-tex">78\,500 \approx 78\,570</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">570</span></span></span></span> du         scénario A). Déduire de nouveau la portion terrain serait un         <strong class="c-rouge">double comptage</strong>. On ne déduit que la portion         améliorations (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>33</mn><mtext> </mtext><mn>570</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\approx 33\,570\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">33</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">570</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>) :         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mn>78</mn><mtext> </mtext><mn>500</mn><mo>+</mo><mo stretchy="false">(</mo><mn>265</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>33</mn><mtext> </mtext><mn>570</mn><mo stretchy="false">)</mo><mo>=</mo><mn>78</mn><mtext> </mtext><mn>500</mn><mo>+</mo><mn>231</mn><mtext> </mtext><mn>430</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">309</mn><mtext> </mtext><mn mathvariant="bold">930</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">V = 78\,500 + (265\,000 - 33\,570) = 78\,500 + 231\,430 =275        \uqogreen{309\,930~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">265</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">33</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">570</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">231</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">430</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">309</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">930</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span> — même conclusion, deux chemins. L'erreur         (déduire deux fois) aurait amputé la valeur d'environ         <span class="num">11 400 $</span>.</li></ol></div></details>276<div class="box box-exo" id="exo-12-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 12.5</span><span class="box-title">— cas intégrateur — entreposage de matières résiduelles</span><a class="box-anchor" href="#exo-12-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-121">Un immeuble commercial de trois étages à Gatineau se trouve à 100 m d'un nouveau site d'entreposage de matières résiduelles (données fictives). Revenu net : <span class="num">95 000 $</span>/an avant la nuisance, <span class="num">78 000 $</span>/an après. Hypothèse du cas : TGA de 6,5 % (2026). Coût de remplacement (après dépréciations physique et fonctionnelle) : <span class="num">650 000 $</span>; valeur du terrain (comparables non affectés) : <span class="num">200 000 $</span>.</p>277<ol class="enum"><li>Calculez la dépréciation économique totale.</li><li>Déterminez la portion améliorations.</li><li>Calculez la valeur finale de la propriété.</li></ol></div></div>278<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>Perte de revenu net <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>95</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>78</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>17</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><mtext>an</mtext></mrow><annotation encoding="application/x-tex">= 95\,000 - 78\,000 = 17\,000\,\$/\text{an}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">95</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">17</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$/</span><span class="mord text"><span class="mord">an</span></span></span></span></span>;         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>totale</mtext></msub><mo>=</mo><mn>17</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>0,065</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">261</mn><mtext> </mtext><mn mathvariant="bold">538</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">D_{\text{totale}} = 17\,000 \div 0{,}065 =279        \uqogreen{261\,538~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">17</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">065</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">261</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">538</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</li><li>Ratio améliorations <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>650</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>850</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>76,5</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">= 650\,000 \div 850\,000 = 76{,}5\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">650</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">850</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">76</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> :         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mrow><mtext>am</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>l.</mtext></mrow></msub><mo>=</mo><mn>261</mn><mtext> </mtext><mn>538</mn><mo>×</mo><mn>650</mn><mi mathvariant="normal">/</mi><mn>850</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">200</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">D_{\text{amél.}} = 261\,538 \times 650/850 =280        \uqogreen{200\,000~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">am</span><span class="mord katex-accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight">e</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˊ</span></span></span></span></span></span></span><span class="mord mtight">l.</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">261</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">538</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">650/850</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">200</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>; portion terrain         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>261</mn><mtext> </mtext><mn>538</mn><mo>×</mo><mn>200</mn><mi mathvariant="normal">/</mi><mn>850</mn><mo>=</mo><mn>61</mn><mtext> </mtext><mn>538</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 261\,538 \times 200/850 = 61\,538\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">261</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">538</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">200/850</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">61</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">538</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>.</li><li>Améliorations : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>650</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>200</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>450</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">650\,000 - 200\,000 = 450\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">650</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">450</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; terrain :         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>200</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>61</mn><mtext> </mtext><mn>538</mn><mo>=</mo><mn>138</mn><mtext> </mtext><mn>462</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">200\,000 - 61\,538 = 138\,462\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">61</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">538</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">138</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">462</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>;         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">588</mn><mtext> </mtext><mn mathvariant="bold">462</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle><mo>≈</mo><mn>588</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">V = \uqogreen{588\,462~\$} \approx 588\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">588</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">462</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">588</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>.</li></ol></div></details>281<div class="box box-exo" id="exo-12-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 12.6</span><span class="box-title">— synthèse du bloc dépréciation</span><a class="box-anchor" href="#exo-12-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p12-128">Un cottage de 1982 à Hull présente : coût de remplacement neuf <span class="num">390 000 $</span>; valeur du terrain <span class="num">95 000 $</span> (comparables non affectés). Dépréciations mesurées : physique curable <span class="num">14 000 $</span>; physique incurable <span class="num">88 000 $</span>; fonctionnelle curable <span class="num">11 000 $</span>; fonctionnelle incurable <span class="num">21 000 $</span>; dépréciation économique totale <span class="num">29 000 $</span> (nuisance de circulation, ventes appariées). Hypothèse : ratio terrain/propriété de 19,6 % (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>95</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>485</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">95\,000 \div 485\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">95</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">485</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>).</p>282<ol class="enum"><li>Allouez la dépréciation économique.</li><li>Dressez le tableau séquentiel complet des déductions et concluez la         valeur par la méthode du coût.</li><li>Quel pourcentage du coût neuf la dépréciation totale des         améliorations représente-t-elle?</li></ol></div></div>283<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>Portion terrain <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>29</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>19,6</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>≈</mo><mn>5</mn><mtext> </mtext><mn>684</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 29\,000 \times 19{,}6\,\% \approx 5\,684\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">29</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">19</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">6</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">684</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>;         portion améliorations <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>29</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>5</mn><mtext> </mtext><mn>684</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">23</mn><mtext> </mtext><mn mathvariant="bold">316</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= 29\,000 - 5\,684 =284        \uqogreen{23\,316~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">29</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">684</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">23</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">316</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</li><li>Déductions sur les améliorations :         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>14</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>88</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>11</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>21</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>23</mn><mtext> </mtext><mn>316</mn><mo>=</mo><mn>157</mn><mtext> </mtext><mn>316</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">14\,000 + 88\,000 + 11\,000 + 21\,000 + 23\,316 = 157\,316\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">14</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">88</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">11</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">21</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">23</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">316</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">157</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">316</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>.         Améliorations : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>390</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>157</mn><mtext> </mtext><mn>316</mn><mo>=</mo><mn>232</mn><mtext> </mtext><mn>684</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">390\,000 - 157\,316 = 232\,684\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">390</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">157</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">316</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">232</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">684</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Terrain         ajusté : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>95</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>5</mn><mtext> </mtext><mn>684</mn><mo>=</mo><mn>89</mn><mtext> </mtext><mn>316</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">95\,000 - 5\,684 = 89\,316\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">95</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">684</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">89</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">316</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>.</p>285<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>V</mi><mo>=</mo><mn>89</mn><mtext> </mtext><mn>316</mn><mo>+</mo><mn>232</mn><mtext> </mtext><mn>684</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">322</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">V = 89\,316 + 232\,684 = \uqogreen{322\,000~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">89</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">316</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">232</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">684</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">322</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span></span></div>286<p id="p12-134">•  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>157</mn><mtext> </mtext><mn>316</mn><mo>÷</mo><mn>390</mn><mtext> </mtext><mn>000</mn><mo>≈</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">40,3</mn><mtext> </mtext><mi mathvariant="bold">%</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">157\,316 \div 390\,000 \approx \uqogreen{40{,}3\,\%}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">157</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">316</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">390</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">40</span><span class="mord" style="color:#107C4E;"><span class="mpunct" style="color:#107C4E;">,</span></span><span class="mord mathbf" style="color:#107C4E;">3</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">%</span></span></span></span></span> —         plausible pour un cottage de 44 ans portant les trois formes de         dépréciation. Réflexe final de l'évaluateur : confronter ces         <span class="num">322 000 $</span> aux indications des méthodes de comparaison et du         revenu avant de conclure le rapport.</li></ol></div></details>287<section class="box box-synth" id="synthese"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-clipboard"/></svg></span><span class="box-label">L’essentiel de la séance</span></div><div class="box-body"><ul><li><strong>Définition</strong> : perte de valeur causée par des facteurs         extérieurs (localisation, réglementation, quartier, marché), hors du         contrôle du propriétaire.</li><li><strong>Deux propriétés distinctives</strong> : toujours incurable; frappe         terrain <em>et</em> améliorations (d'où l'allocation).</li><li><strong>Causes de localisation</strong> : autoroutes (<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>5 à 15 %         indicatif), lignes HT (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>2 à 20 % selon le voltage), LET et         contamination du voisinage (<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>10 à 30 %), avec stigmatisation         résiduelle — ordres de grandeur illustratifs, preuve locale         exigée.</li><li><strong>Causes réglementaires</strong> : rezonage, CPTAQ/zone verte (écarts         de plus de 90 %), milieux humides, cadre 2026 des zones         inondables (quatre classes de risque).</li><li><strong>Quartier et marché</strong> : cycle de détérioration         auto-renforçant; fermetures d'employeurs majeurs; distinguer         cyclique (rien à déduire) et structurel (dépréciation).</li><li><strong>Capitalisation</strong> : perte de revenu net annuelle <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">\div</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> TGA         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> dépréciation totale.</li><li><strong>Ventes appariées</strong> : différence de prix entre propriétés         affectées et non affectées, 3 paires et plus, cohérence avant         moyenne.</li><li><strong>Allocation</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mrow><mtext>am</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>l.</mtext></mrow></msub><mo>=</mo><msub><mi>D</mi><mtext>totale</mtext></msub><mo>×</mo></mrow><annotation encoding="application/x-tex">D_{\text{amél.}} = D_{\text{totale}} \times</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">am</span><span class="mord katex-accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight">e</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˊ</span></span></span></span></span></span></span><span class="mord mtight">l.</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">×</span></span></span></span>         (valeur améliorations <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">\div</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> valeur totale), ratios sur valeurs         <em>avant</em> dépréciation; repères terrain : banlieue 15–30 %,         urbain dense 30–50 %, industriel 5–15 %.</li><li><strong>Trois erreurs d'allocation</strong> : double comptage (terrain déjà         ajusté), 100 % aux améliorations, ratio calculé sur valeurs         dépréciées.</li><li><strong>Formule finale</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><msub><mi>V</mi><mi>T</mi></msub><mo>+</mo><mo stretchy="false">[</mo><mtext> </mtext><msub><mi>C</mi><mi>N</mi></msub><mo>−</mo><msub><mi>D</mi><mtext>phys</mtext></msub><mo>−</mo><msub><mi>D</mi><mtext>fonc</mtext></msub><mo>−</mo><msub><mi>D</mi><mrow><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>co(am</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>l.)</mtext></mrow></msub><mtext> </mtext><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">V = V_T + [\,C_N - D_{\text{phys}} -288        D_{\text{fonc}} - D_{\text{éco(amél.)}}\,]</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:0.8333em;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:0.2222em;"></span><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="mspace" style="margin-right:0.1667em;"></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:0.3283em;"><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 mathnormal mtight" style="margin-right:0.109em;">N</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><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">phys</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">fonc</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1052em;vertical-align:-0.3552em;"></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:0.3448em;"><span style="top:-2.5198em;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 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">co(am</span><span class="mord katex-accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight">e</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˊ</span></span></span></span></span></span></span><span class="mord mtight">l.)</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3552em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mclose">]</span></span></span></span> — la portion terrain         de la dépréciation externe vit dans <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></mrow><annotation encoding="application/x-tex">V_T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">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>, jamais dans la déduction.</li></ul></div></section>289      </article>290    </div>291  </div>292  <section class="ch-quiz" id="quiz"><div class="ch-quiz-inner"><div id="quiz-app"><p class="gl-count">Chargement du quiz…</p></div></div></section>293  294<nav class="ch-pager" aria-label="Navigation entre les séances">295  <a class="prev" href="/seance/11/"><small>← Séance 11</small><b>Dépréciation fonctionnelle</b></a>296  <a class="next" href="/seance/13/"><small>Séance 13 →</small><b>Applications spécialisées</b></a>297</nav>298  299<div class="read-tools" role="toolbar" aria-label="Outils de lecture">300  <button 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