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1<!DOCTYPE html>2<html lang="fr" data-theme="light">3<head>4<meta charset="utf-8">5<meta name="viewport" content="width=device-width, initial-scale=1, viewport-fit=cover">6<title>Séance 11 — Dépréciation fonctionnelle · IMM1033 — Méthodes du coût en évaluation immobilière</title>7<meta name="description" content="Séance 11 du cours IMM1033 (Méthodes du coût en évaluation immobilière) : Dépréciation fonctionnelle. Notes de cours complètes, explorateurs interactifs, exercices corrigés et quiz.">8<meta name="author" content="Simon-Pierre Boucher — Université du Québec en Outaouais">9<meta name="theme-color" content="#0f6180">10<meta property="og:site_name" content="IMM1033 — UQO">11<meta property="og:title" content="Séance 11 — Dépréciation fonctionnelle · IMM1033 — Méthodes du coût en évaluation immobilière">12<meta property="og:description" content="Séance 11 du cours IMM1033 (Méthodes du coût en évaluation immobilière) : Dépréciation fonctionnelle. 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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">Enregistrements</div><a href="/videos/"><span class="pastille" style="background:var(--rouge)">▶</span><span>Séances vidéo — enregistrements Zoom, transcription synchronisée</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><a class="nav-video" href="/videos/"><svg class="" aria-hidden="true"><use href="#i-video"/></svg> Vidéos</a><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="/videos/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-video"/></svg></span><span>Séances vidéo<span class="dd-desc">Enregistrements Zoom : chapitres, transcription, sous-titres</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 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class="readbar-fill"></div></div>94</header>9596<main id="main" class="chapter-page" data-chapter="11" data-title="Séance 11 — Dépréciation fonctionnelle" data-words="9020">97  98<header class="ch-hero">99  <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>100  <div class="watermark" aria-hidden="true">11</div>101  <div class="ch-hero-inner">102    <div class="eyebrow"><span class="part-chip">Partie IV</span> La dépréciation · Séance 11 · IMM1033</div>103    <h1>Dépréciation fonctionnelle</h1>104    <div class="ch-sub">Méthodes du coût en évaluation immobilière · Automne 2026 · Simon-Pierre Boucher · UQO</div>105    <div class="ch-meta">106      <span class="chip"><svg class="" aria-hidden="true"><use href="#i-list"/></svg> 7 sections</span>107      <span class="chip"><svg class="" aria-hidden="true"><use href="#i-book"/></svg> 6 définitions</span>108      <span class="chip"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg> 5 formules</span>109      <span class="chip"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg> 11 exemples</span>110      <span class="chip"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg> 6 exercices</span>111      <span class="chip"><svg class="" aria-hidden="true"><use href="#i-eye"/></svg> ≈ 50 min de lecture</span>112      113      114    </div>115    <div class="ch-tools">116      117      <a class="btn btn-ghost" href="/files/slides/seance11.pdf" target="_blank" rel="noopener"><svg class="" aria-hidden="true"><use href="#i-slides"/></svg> Diapositives (PDF)</a>118      <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>119      <button class="btn btn-ghost" type="button" data-action="tts"><svg class="" aria-hidden="true"><use href="#i-audio"/></svg> Écouter</button>120      <a class="btn btn-ghost" href="#quiz"><svg class="" aria-hidden="true"><use href="#i-quiz"/></svg> Quiz de la séance</a>121    </div>122  </div>123</header>124<div class="stepper-wrap"><nav class="stepper" aria-label="Sections"><a href="#s-11-1"><span class="n">1</span>Définition, sources et classification</a><a href="#s-11-2"><span class="n">2</span>La dépréciation fonctionnelle curable</a><a href="#s-11-3"><span class="n">3</span>La dépréciation fonctionnelle incurable</a><a href="#s-11-4"><span class="n">4</span>Reproduction ou remplacement : l'incidence du coût neuf</a><a href="#s-11-5"><span class="n">5</span>Le gabarit doctrinal et la synthèse du calcul</a><a href="#s-11-6"><span class="n">6</span>Cas intégrés</a><a href="#s-11-7"><span class="n">7</span>Exercices</a><span class="rem" id="read-remaining"></span></nav></div>125  <div class="ch-layout">126    127<aside class="ch-toc" aria-label="Sommaire de la séance">128  <div class="toc-progress"><div class="bar"><i></i></div><span>0 % lu</span></div>129  <h4>Dans cette séance</h4>130  <ol><li class="lvl2"><a href="#s-11-1"><span class="toc-num">11.1</span><span>Définition, sources et classification</span></a></li><li class="lvl3"><a href="#s-11-1-1"><span class="toc-num">11.1.1</span><span>Ce que mesure la dépréciation fonctionnelle</span></a></li><li class="lvl3"><a href="#s-11-1-2"><span class="toc-num">11.1.2</span><span>Les quatre familles de sources</span></a></li><li class="lvl3"><a href="#s-11-1-3"><span class="toc-num">11.1.3</span><span>Le test de curabilité et l'arbre de classification</span></a></li><li class="lvl2"><a href="#s-11-2"><span class="toc-num">11.2</span><span>La dépréciation fonctionnelle curable</span></a></li><li class="lvl3"><a href="#s-11-2-1"><span class="toc-num">11.2.1</span><span>Les déficiences requérant des ajouts</span></a></li><li class="lvl3"><a href="#s-11-2-2"><span class="toc-num">11.2.2</span><span>Les déficiences requérant des substitutions</span></a></li><li class="lvl2"><a href="#s-11-3"><span class="toc-num">11.3</span><span>La dépréciation fonctionnelle incurable</span></a></li><li class="lvl3"><a href="#s-11-3-1"><span class="toc-num">11.3.1</span><span>La superadéquation</span></a></li><li class="lvl3"><a href="#s-11-3-2"><span class="toc-num">11.3.2</span><span>L'obsolescence de conception</span></a></li><li class="lvl2"><a href="#s-11-4"><span class="toc-num">11.4</span><span>Reproduction ou remplacement : l'incidence du coût neuf</span></a></li><li class="lvl2"><a href="#s-11-5"><span class="toc-num">11.5</span><span>Le gabarit doctrinal et la synthèse du calcul</span></a></li><li class="lvl3"><a href="#s-11-5-1"><span class="toc-num">11.5.1</span><span>La procédure standard en cinq étapes</span></a></li><li class="lvl3"><a href="#s-11-5-2"><span class="toc-num">11.5.2</span><span>Le tableau récapitulatif et la formule globale</span></a></li><li class="lvl3"><a href="#s-11-5-3"><span class="toc-num">11.5.3</span><span>La carte des doubles comptages</span></a></li><li class="lvl2"><a href="#s-11-6"><span class="toc-num">11.6</span><span>Cas intégrés</span></a></li><li class="lvl3"><a href="#s-11-6-1"><span class="toc-num">11.6.1</span><span>Cas 1 — Bungalow de 1965, secteur Hull</span></a></li><li class="lvl3"><a href="#s-11-6-2"><span class="toc-num">11.6.2</span><span>Cas 2 — Immeuble de bureaux de 1980, Gatineau</span></a></li><li class="lvl2"><a href="#s-11-7"><span class="toc-num">11.7</span><span>Exercices</span></a></li></ol>131  <div class="toc-extra">132    <a href="#objectifs"><svg class="" aria-hidden="true"><use href="#i-target"/></svg> Objectifs d’apprentissage</a>133    <a href="#synthese"><svg class="" aria-hidden="true"><use href="#i-clipboard"/></svg> L’essentiel de la séance</a>134    <a href="#quiz"><svg class="" aria-hidden="true"><use href="#i-quiz"/></svg> Testez-vous</a>135    136    <a href="/fiches/?ch=11"><svg class="" aria-hidden="true"><use href="#i-cards"/></svg> Fiches de la séance</a>137    <a href="/entrainement/"><svg class="" aria-hidden="true"><use href="#i-dumbbell"/></svg> Entraînement</a>138    <a href="/aide-memoire/"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg> Aide-mémoire</a>139  </div>140  <h4 style="margin-top:14px">Raccourcis</h4>141  <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>142</aside>143    <div class="ch-body">144      <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>145      <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>146      <article class="prose" id="notes">147        <p id="p11-1">Un bâtiment peut être impeccablement entretenu et pourtant valoir nettement moins que son coût neuf déprécié physiquement. La cuisine fermée derrière un mur porteur, l'unique salle de bain d'une maison de quatre chambres, le chauffage au mazout, la piscine intérieure dans un quartier modeste : aucun de ces éléments n'est « usé », mais chacun réduit ce que le marché consent à payer. C'est le territoire de la <span class="motcle" data-term="dépréciation fonctionnelle">dépréciation fonctionnelle</span>, la perte de valeur attribuable aux défauts de conception, de plan, de style ou de fonctionnalité. Sa mesure est plus subtile que celle de la dépréciation physique : elle mobilise quatre catégories de calcul distinctes — ajouts, substitutions, superadéquation, obsolescence de conception — articulées autour d'un même test économique de curabilité. Ce chapitre développe chacune de ces catégories avec ses formules et ses exemples chiffrés, expose le gabarit doctrinal en cinq étapes qui les unifie, et cartographie les pièges de double comptage qui guettent l'évaluateur à la frontière du physique, du fonctionnel et de l'externe.</p>148<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-11-1" data-obj="obj-11-1"><span class="obj-text">Définir la dépréciation fonctionnelle et la distinguer des         dépréciations physique et externe;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-11-2" data-obj="obj-11-2"><span class="obj-text">Appliquer le <strong>test de curabilité</strong> (coût de correction contre         valeur ajoutée) à toute déficience fonctionnelle;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-11-3" data-obj="obj-11-3"><span class="obj-text">Calculer la dépréciation fonctionnelle curable par <strong>ajouts</strong>         et par <strong>substitutions</strong>;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-11-4" data-obj="obj-11-4"><span class="obj-text">Mesurer la dépréciation fonctionnelle incurable : la         <strong>superadéquation</strong> et l'<strong>obsolescence de conception</strong>         (capitalisation de la perte de revenus);</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-11-5" data-obj="obj-11-5"><span class="obj-text">Comprendre l'incidence du choix entre coût de <strong>reproduction</strong>         et coût de <strong>remplacement</strong> sur l'ampleur de l'obsolescence à         mesurer;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-11-6" data-obj="obj-11-6"><span class="obj-text">Appliquer le gabarit doctrinal en cinq étapes de <em>The Appraisal         of Real Estate</em>;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-11-7" data-obj="obj-11-7"><span class="obj-text">Éviter les quatre configurations classiques de <strong>double         comptage</strong> entre formes de dépréciation.</span></label></li></ul></div></section>149<h2 id="s-11-1" class="h-section"><span class="h-num">11.1</span><span class="h-text">Définition, sources et classification</span><a class="h-anchor" href="#s-11-1" aria-label="Lien vers cette section">#</a></h2>150<h3 id="s-11-1-1" class="h-subsection"><span class="h-num">11.1.1</span><span class="h-text">Ce que mesure la dépréciation fonctionnelle</span><a class="h-anchor" href="#s-11-1-1" aria-label="Lien vers cette section">#</a></h3>151<div class="box box-def" id="def-11-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 11.1</span><span class="box-title">— dépréciation fonctionnelle</span><a class="box-anchor" href="#def-11-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-9">La <strong>dépréciation fonctionnelle</strong> (ou <strong>obsolescence fonctionnelle</strong>) est la perte de valeur d'un bâtiment attribuable à des <strong>défauts de conception, de plan, de style ou de fonctionnalité</strong> qui réduisent son utilité ou son attrait par rapport aux attentes actuelles du marché.</p></div></div>152<p id="p11-10">Deux traits distinguent immédiatement cette forme de dépréciation. D'abord, elle est <strong>interne</strong> au bâtiment : elle provient de ses caractéristiques propres — son plan, ses équipements, sa conception — et non de facteurs extérieurs (ce qui la sépare de la dépréciation économique du chapitre 12). Ensuite, elle est <strong>indépendante de l'état physique</strong> : un bâtiment en parfait état matériel peut être lourdement déprécié fonctionnellement, parce que le marché a changé depuis sa construction. <label for="sn-11-1" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-11-1" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-repere">Fonctionnelle <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> interne au bâtiment, indépendante de l'usure.</span></p>153<p id="p11-11">Pourquoi cette forme de dépréciation existe-t-elle? Parce que le bâtiment est figé au moment de sa construction, alors que le marché, lui, ne cesse de bouger. Les normes techniques se resserrent (efficacité énergétique, capacité électrique, qualité de l'air), les modes de vie se transforment (le concept ouvert, le télétravail, la salle de bain attenante), les technologies déclassent des équipements entiers (le mazout, le simple vitrage, le panneau à fusibles). Chaque évolution creuse silencieusement l'écart entre ce que le bâtiment offre et ce que l'acheteur type attend — et le marché facture cet écart, que le propriétaire en soit conscient ou non. C'est pourquoi la dépréciation fonctionnelle est, des trois formes, celle qui exige la connaissance la plus fine du marché local : on ne peut pas mesurer un écart aux attentes sans savoir précisément ce que le marché attend, ici et maintenant. Le tableau <a class="xref" href="#tab-ch11-tab-troisformes">11.1</a> situe la dépréciation fonctionnelle entre ses deux voisines.</p>154<figure class="float-table" id="tab-ch11-tab-troisformes"><figcaption><span class="fig-label">Tableau 11.1</span> Physique, fonctionnelle, externe : la grille de distinction.</figcaption><div class="table-wrap"><table class="tbl"><thead><tr><th></th><th>Physique</th><th>Fonctionnelle</th><th>Externe</th></tr></thead><tbody><tr><td><strong>Cause</strong></td><td>Usure, détérioration, âge</td><td>Défauts de conception, plan, fonctionnalité</td><td>Facteurs extérieurs au bâtiment</td></tr><tr><td><strong>Origine</strong></td><td>Matériaux, composantes</td><td>Design, équipements, plan</td><td>Quartier, marché, réglementation</td></tr><tr><td><strong>Contrôle</strong></td><td>Propriétaire (entretien)</td><td>Propriétaire (rénovation)</td><td>Hors du contrôle du propriétaire</td></tr><tr><td><strong>Curable?</strong></td><td>Oui / non</td><td>Oui / non</td><td>Généralement non</td></tr></tbody></table></div></figure>155<h3 id="s-11-1-2" class="h-subsection"><span class="h-num">11.1.2</span><span class="h-text">Les quatre familles de sources</span><a class="h-anchor" href="#s-11-1-2" aria-label="Lien vers cette section">#</a></h3>156<p id="p11-12">D'où vient la perte fonctionnelle? De quatre familles de situations, que l'inspection et l'analyse de marché permettent d'identifier :</p>157<div class="center"><div class="tikz"><img src="/assets/fig/0b3b244e187efe88.svg" alt="Figure" width="509" height="81" style="width:min(100%,739px)" loading="lazy" decoding="async"></div></div>158<p id="p11-13"><label for="sn-11-2" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-11-2" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-terme"><strong class="sn-term">manque</strong> composante absente que le marché exige désormais</span> Le <strong>manque</strong> vise les composantes absentes que le marché exige désormais : équipements devenus standards, espaces requis par le mode de vie actuel, normes énergétiques non atteintes. L'<strong>inadéquation</strong> vise les éléments présents mais désuets ou obsolètes. L'<strong>excès</strong> — la superadéquation — vise les aménagements qui dépassent les besoins du marché. Le <strong>défaut de conception</strong> vise le plan et l'agencement eux-mêmes. En règle générale, le manque et l'inadéquation sont souvent <strong class="c-vert">curables</strong>; l'excès et les défauts de conception sont généralement <strong class="c-rouge">incurables</strong>.</p>159<h3 id="s-11-1-3" class="h-subsection"><span class="h-num">11.1.3</span><span class="h-text">Le test de curabilité et l'arbre de classification</span><a class="h-anchor" href="#s-11-1-3" aria-label="Lien vers cette section">#</a></h3>160<div class="box box-def" id="def-11-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 11.2</span><span class="box-title">— curabilité (dépréciation fonctionnelle)</span><a class="box-anchor" href="#def-11-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-14">Une déficience fonctionnelle est <strong>curable</strong> si le coût de sa correction est <strong>inférieur ou égal</strong> à la valeur ajoutée par cette correction; elle est <strong>incurable</strong> dans le cas contraire. Le test repose sur la <strong>rationalité économique</strong>, pas sur la faisabilité technique : un défaut peut être techniquement réparable mais économiquement incurable.</p></div></div>161<p id="p11-15">L'arbre complet de classification, qui gouverne tout le chapitre :</p>162<div class="center"><div class="tikz"><img src="/assets/fig/47c16c871ef1f34b.svg" alt="Figure" width="505" height="196" style="width:min(100%,733px)" loading="lazy" decoding="async"></div></div>163<div class="box box-qc" id="quebec-11-16"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-map"/></svg></span><span class="box-label">curable ou incurable : repères du marché québécois</span><a class="box-anchor" href="#quebec-11-16" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-17">Généralement <strong class="c-vert">curables</strong> (la valeur ajoutée excède le coût, à démontrer avec des données de marché) : ajouter une deuxième salle de bain manquante; remplacer le chauffage au mazout par une thermopompe; porter l'isolation aux normes et remplacer les fenêtres à simple vitrage; mettre à niveau le panneau électrique de 60 A à 200 A; moderniser une cuisine désuète. Généralement <strong class="c-rouge">incurables</strong> : piscine intérieure ou garage triple hors normes du quartier (superadéquation); plan fermé impossible à ouvrir (murs porteurs); trop peu de salles de bain pour le nombre de chambres; hauteur de plafond de 6 pi au sous-sol; domotique ultra-sophistiquée pour le marché visé. Dans ce dernier cas, le propriétaire <strong>subit</strong> la perte : la correction coûterait plus cher que le gain de valeur qu'elle produirait.</p></div></div>164<h2 id="s-11-2" class="h-section"><span class="h-num">11.2</span><span class="h-text">La dépréciation fonctionnelle curable</span><a class="h-anchor" href="#s-11-2" aria-label="Lien vers cette section">#</a></h2>165<p id="p11-18">La dépréciation fonctionnelle curable se décline en deux sous-catégories, selon que l'élément en cause est absent (ajout) ou présent mais inadéquat (substitution).</p>166<h3 id="s-11-2-1" class="h-subsection"><span class="h-num">11.2.1</span><span class="h-text">Les déficiences requérant des ajouts</span><a class="h-anchor" href="#s-11-2-1" aria-label="Lien vers cette section">#</a></h3>167<div class="box box-def" id="def-11-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 11.3</span><span class="box-title">— déficience par ajout</span><a class="box-anchor" href="#def-11-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-19">Une déficience par <strong>ajout</strong> vise un élément <strong>absent</strong> du bâtiment que le marché actuel considère comme nécessaire ou standard. Le bâtiment a été construit sans cet élément et il n'a jamais été ajouté; l'élément n'est donc <strong>pas inclus</strong> dans le coût neuf estimé.</p></div></div>168<p id="p11-20">Quatre caractéristiques structurent le calcul : l'élément n'est pas dans le coût neuf (aucune dépréciation n'a encore été comptée pour ce poste); le marché pénalise la propriété pour cette absence; l'ajout est économiquement justifiable (sinon la déficience serait incurable); et l'installation dans un bâtiment existant coûte généralement <strong>plus cher</strong> que dans une construction neuve.</p>169<div class="box box-form" id="form-11-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 11.1</span><span class="box-title">— dépréciation curable par ajout</span><a class="box-anchor" href="#form-11-1" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-11-1"><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><mtext>ajout</mtext></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><mrow><mtext>co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t d’installation de l’</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>l</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>ment dans le b</mtext><mover accent="true"><mtext>a</mtext><mo>ˆ</mo></mover><mtext>timent existant</mtext></mrow></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(11.1)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">D_{\text{ajout}} \;=\; \text{coût d&#x27;installation de l&#x27;élément dans le170bâtiment existant}\tag{11.1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">ajout</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:0.6944em;"></span><span class="mord text"><span class="mord">co</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">u</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˆ</span></span></span></span></span></span></span><span class="mord">t d’installation de l’</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">l</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">ment dans le b</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">a</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˆ</span></span></span></span></span></span></span><span class="mord">timent existant</span></span></span><span class="katex-tag"><span class="katex-strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">11.1</span></span><span class="mord">)</span></span></span></span></span></span></div></div></div>171<div class="box box-att" id="attention-11-21"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">le coût dans l'existant, pas la différence</span><a class="box-anchor" href="#attention-11-21" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-22">L'erreur classique consiste à retenir la <em>différence</em> entre le coût dans l'existant et le coût dans le neuf. C'est faux pour un ajout : puisque l'élément est <strong>exclu</strong> du coût neuf estimé, aucun montant n'a encore été compté pour ce poste, et la pénalité de marché correspond au <strong>coût complet</strong> d'ajouter l'élément maintenant. Tant que la correction n'est pas faite, cette dépréciation demeure — même si la correction est rentable.</p></div></div>172<p id="p11-23">Le raisonnement diffère de celui de la substitution (section suivante), où l'élément inadéquat <em>est</em> inclus au coût neuf : c'est cette présence ou absence au bordereau de coût neuf qui commande la formule. Parmi les éléments manquants typiques du marché québécois : la climatisation centrale (attendue dans une maison haut de gamme), la deuxième salle de bain complète (maison de trois chambres et plus), l'isolation aux normes énergétiques actuelles, le garage dans un quartier où il est standard, la hotte de cuisine exigée par le code, le rangement suffisant (walk-in, garde-robes), l'îlot de cuisine d'une maison familiale contemporaine, la buanderie au rez-de-chaussée plutôt qu'au sous-sol.</p>173<div class="box box-ex" id="ex-11-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 11.1</span><span class="box-title">— ajout d'une deuxième salle de bain</span><a class="box-anchor" href="#ex-11-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-24">Maison unifamiliale à Gatineau (1975), quatre chambres, une seule salle de bain; le marché en exige deux. Bordereau du coût d'installation dans l'existant :</p>174<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Poste (coût d'installation dans l'existant)</th><th class="al-r">Montant</th></tr></thead><tbody><tr><td>Plomberie (raccordements, tuyauterie)</td><td class="al-r">8 500 $</td></tr><tr><td>Électricité (ventilateur, prises, éclairage)</td><td class="al-r">2 200 $</td></tr><tr><td>Appareils (toilette, lavabo, bain/douche)</td><td class="al-r">4 500 $</td></tr><tr><td>Céramique, finitions, peinture</td><td class="al-r">5 800 $</td></tr><tr><td>Main-d'œuvre (démolition, construction)</td><td class="al-r">7 000 $</td></tr><tr class="rule-above"><td><strong>Dépréciation fonctionnelle curable (ajout)</strong></td><td class="al-r"><strong>28 000 $</strong></td></tr><tr><td><em>Référence : coût dans une construction neuve</em></td><td class="al-r"><em>18 000 $</em></td></tr></tbody></table></div></div>175<p id="p11-25">La dépréciation est le coût dans l'existant (<span class="num">28 000 $</span>), <strong class="c-rouge">pas</strong> la différence (<span class="num">10 000 $</span>). Vérification de curabilité : la valeur ajoutée estimée par le marché est de <span class="num">35 000 $</span>; comme <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>35</mn><mtext> </mtext><mn>000</mn><mo>&gt;</mo><mn>28</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">35\,000 &gt; 28\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6835em;vertical-align:-0.0391em;"></span><span class="mord">35</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">28</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span> (gain net de <span class="num">7000 $</span>), la déficience est bien <strong class="c-vert">curable</strong>. Et même rentable, la correction n'efface la dépréciation que lorsqu'elle est <em>réalisée</em> : au moment de l'évaluation, la perte de <span class="num">28 000 $</span> existe.</p></div></div>176<div class="box box-ex" id="ex-11-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 11.2</span><span class="box-title">— ajout de climatisation centrale</span><a class="box-anchor" href="#ex-11-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-26">Maison haut de gamme à Aylmer (Gatineau), construite en 1985, sans climatisation centrale. Coût dans l'existant : thermopompe centrale et unité extérieure <span class="num">6500 $</span>; conduits de ventilation (ajout et modification) <span class="num">5500 $</span>; électricité (circuit dédié, thermostat) <span class="num">1800 $</span>; main-d'œuvre et installation <span class="num">3200 $</span> — total <strong class="c-vert">17 000 $</strong> (contre <span class="num">9000 $</span> dans une construction neuve). Valeur ajoutée estimée par le marché : <span class="num">22 000 $</span>. Test de curabilité : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>22</mn><mtext> </mtext><mn>000</mn><mo>&gt;</mo><mn>17</mn><mtext> </mtext><mn>000</mn><mo>⇒</mo></mrow><annotation encoding="application/x-tex">22\,000 &gt; 17\,000 \Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6835em;vertical-align:-0.0391em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">17</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⇒</span></span></span></span> <strong class="c-vert">curable</strong>; dépréciation retenue : <span class="num">17 000 $</span>.</p></div></div>177<h3 id="s-11-2-2" class="h-subsection"><span class="h-num">11.2.2</span><span class="h-text">Les déficiences requérant des substitutions</span><a class="h-anchor" href="#s-11-2-2" aria-label="Lien vers cette section">#</a></h3>178<div class="box box-def" id="def-11-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 11.4</span><span class="box-title">— déficience par substitution</span><a class="box-anchor" href="#def-11-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-27">Une déficience par <strong>substitution</strong> vise un élément <strong>présent</strong> dans le bâtiment mais <strong>inadéquat, désuet ou obsolète</strong>, qui doit être remplacé par un élément conforme aux attentes actuelles du marché.</p></div></div>179<p id="p11-28">Trois différences avec l'ajout : l'élément existe déjà (il figure au coût neuf); il faut le <strong>retirer</strong> puis le remplacer (coûts de démolition, d'adaptation, de remise en état des surfaces); et l'élément retiré peut avoir une <strong>valeur résiduelle</strong> (revente, ferraille).</p>180<figure class="float-table" id="tab-ch11-tab-substitutions"><figcaption><span class="fig-label">Tableau 11.2</span> Substitutions typiques sur le marché québécois.</figcaption><div class="table-wrap"><table class="tbl"><thead><tr><th>Élément actuel</th><th>Remplacement requis</th><th>Raison</th></tr></thead><tbody><tr><td>Chauffage au mazout</td><td>Thermopompe / électrique</td><td>Obsolète, coûteux</td></tr><tr><td>Plomberie en plomb / fonte</td><td>Cuivre / PEX / PVC</td><td>Santé, normes</td></tr><tr><td>Panneau électrique 60 A</td><td>Panneau 200 A</td><td>Capacité insuffisante</td></tr><tr><td>Fenêtres à simple vitrage</td><td>Fenêtres thermos</td><td>Énergie, confort</td></tr><tr><td>Cuisine non fonctionnelle</td><td>Rénovation complète</td><td>Marché actuel</td></tr><tr><td>Salle de bain démodée</td><td>Modernisation</td><td>Attentes des acheteurs</td></tr><tr><td>Toiture en bardeaux d'amiante</td><td>Bardeaux d'asphalte</td><td>Sécurité, normes</td></tr></tbody></table></div></figure>181<div class="box box-form" id="form-11-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 11.2</span><span class="box-title">— dépréciation curable par substitution</span><a class="box-anchor" href="#form-11-2" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-11-2"><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><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><msub><mi>D</mi><mtext>subst</mtext></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><mrow></mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mrow><mtext>co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t d’installation du remplacement dans l’existant</mtext></mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>−</mo><mrow></mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mrow><mtext>co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t d’installation dans une construction neuve</mtext></mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>+</mo><mrow></mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mrow><mtext>co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t de d</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>molition / retrait de l’</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>l</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>ment actuel</mtext></mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>−</mo><mrow></mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mrow><mtext>valeur r</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>cup</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>r</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>e de l’</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>l</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>ment retir</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover></mrow></mrow></mstyle></mtd></mtr></mtable></mtd><mtd width="50%"></mtd><mtd><mtext>(11.2)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}D_{\text{subst}} \;=\;{} &amp; \text{coût d&#x27;installation du remplacement dans182l&#x27;existant} \\183{}-{} &amp; \text{coût d&#x27;installation dans une construction neuve} \\184{}+{} &amp; \text{coût de démolition / retrait de l&#x27;élément actuel} \\185{}-{} &amp; \text{valeur récupérée de l&#x27;élément retiré}\end{aligned}\tag{11.2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:5.7em;vertical-align:-2.6em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.1em;"><span style="top:-5.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">subst</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="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></span></span><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></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:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"></span></span></span><span style="top:-0.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.6em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.1em;"><span style="top:-5.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mord text"><span class="mord">co</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">u</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˆ</span></span></span></span></span></span></span><span class="mord">t d’installation du remplacement dans l’existant</span></span></span></span><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mord text"><span class="mord">co</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">u</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˆ</span></span></span></span></span></span></span><span class="mord">t d’installation dans une construction neuve</span></span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mord text"><span class="mord">co</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">u</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˆ</span></span></span></span></span></span></span><span class="mord">t de d</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">molition / retrait de l’</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">l</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">ment actuel</span></span></span></span><span style="top:-0.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mord text"><span class="mord">valeur r</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">cup</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">r</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">e de l’</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">l</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">ment retir</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><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.6em;"><span></span></span></span></span></span></span></span></span><span class="katex-tag"><span class="katex-strut" style="height:5.7em;vertical-align:-2.6em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">11.2</span></span><span class="mord">)</span></span></span></span></span></span></div></div></div>186<p id="p11-29">La logique de la formule mérite d'être décomposée, car elle éclaire tout le chapitre. Le marché ne pénalise pas le coût de l'élément moderne lui-même — cet élément, l'acheteur l'aurait payé de toute façon dans un bâtiment neuf, et l'élément désuet figure déjà au coût neuf estimé où il porte sa dépréciation physique. Ce que le marché pénalise, c'est le <strong>surcoût</strong> d'avoir à installer l'élément dans un bâtiment déjà construit (coût dans l'existant moins coût dans le neuf), augmenté du coût de <strong>retrait</strong> de l'ancien élément, et diminué du <strong>crédit de récupération</strong> éventuel. <label for="sn-11-3" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-11-3" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-repere">Substitution : la pénalité, c'est le surcoût de rénovation, pas le prix de l'équipement.</span></p>187<div class="box box-ex" id="ex-11-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 11.3</span><span class="box-title">— remplacement du chauffage au mazout</span><a class="box-anchor" href="#ex-11-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-30">Maison à Gatineau (1970), chauffage central au mazout; le marché exige l'électricité ou une thermopompe.</p>188<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Poste</th><th class="al-r">Montant</th></tr></thead><tbody><tr><td>Thermopompe centrale (achat et installation)</td><td class="al-r">12 000 $</td></tr><tr><td>Modification des conduits existants</td><td class="al-r">4 500 $</td></tr><tr><td>Électricité (nouveau circuit 240 V)</td><td class="al-r">1 800 $</td></tr><tr><td>Retrait du réservoir, décontamination et remise en état</td><td class="al-r">4 700 $</td></tr><tr><td><strong>Total — coût dans l'existant (retrait inclus)</strong></td><td class="al-r"><strong>23 000 $</strong></td></tr><tr class="rule-above"><td>Moins : coût dans une construction neuve (thermopompe)</td><td class="al-r">(8 500 $)</td></tr><tr><td>Moins : valeur récupérée (vieille fournaise, ferraille)</td><td class="al-r">(200 $)</td></tr><tr class="rule-above"><td><strong>Dépréciation fonctionnelle curable (substitution)</strong></td><td class="al-r"><strong>14 300 $</strong></td></tr></tbody></table></div></div>189<p id="p11-31">Vérification pas à pas :</p>190<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>D</mi><mo>=</mo><mn>23</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>8</mn><mtext> </mtext><mn>500</mn><mo>−</mo><mn>200</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">14</mn><mtext> </mtext><mn mathvariant="bold">300</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">D = 23\,000 - 8\,500 - 200 = \uqogreen{14\,300~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">23</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">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">200</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">14</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">300</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>191<p id="p11-32">Le retrait du réservoir étant déjà inclus dans le coût dans l'existant, la formule se réduit ici à trois termes. Ce montant représente la <strong>pénalité</strong> d'avoir aujourd'hui un système de chauffage obsolète.</p></div></div>192<div class="box box-ex" id="ex-11-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 11.4</span><span class="box-title">— panneau électrique 60 A vers 200 A</span><a class="box-anchor" href="#ex-11-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-33">Maison ancienne, panneau de 60 ampères à fusibles; le marché (et les assureurs) exigent 200 A avec disjoncteurs. Coût dans l'existant : panneau et disjoncteurs <span class="num">3800 $</span>; entrée électrique (mât, câble, compteur) <span class="num">4200 $</span>; main-d'œuvre de maître électricien, permis et inspection <span class="num">4000 $</span> — total <span class="num">12 000 $</span>. Moins le coût dans le neuf (<span class="num">5500 $</span>) et la valeur récupérée (nulle) :</p>193<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>D</mi><mo>=</mo><mn>12</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>5</mn><mtext> </mtext><mn>500</mn><mo>−</mo><mn>0</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">6</mn><mtext> </mtext><mn mathvariant="bold">500</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">D = 12\,000 - 5\,500 - 0 = \uqogreen{6\,500~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">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">5</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">0</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><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;">6</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">500</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span></span></div></div></div>194<div class="box box-ex" id="ex-11-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 11.5</span><span class="box-title">— fenêtres à simple vitrage vers thermos</span><a class="box-anchor" href="#ex-11-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-34">Bungalow de 1968, seize fenêtres d'origine à simple vitrage. Coût dans l'existant : fenêtres thermos Energy Star (achat, 16 unités) <span class="num">14 400 $</span>; retrait des anciennes fenêtres <span class="num">2400 $</span>; installation, calfeutrage et finitions <span class="num">9600 $</span> — total <span class="num">26 400 $</span>. Coût dans une construction neuve : <span class="num">16 800 $</span>; valeur récupérée : nulle.</p>195<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>D</mi><mo>=</mo><mn>26</mn><mtext> </mtext><mn>400</mn><mo>−</mo><mn>16</mn><mtext> </mtext><mn>800</mn><mo>−</mo><mn>0</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">9</mn><mtext> </mtext><mn mathvariant="bold">600</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">D = 26\,400 - 16\,800 - 0 = \uqogreen{9\,600~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">26</span><span class="mspace" style="margin-right:0.1667em;"></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:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.2222em;"></span><span 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">0</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><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;">9</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></span></div></div></div>196<div class="box box-terrain" id="terrain-11-35"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-hardhat"/></svg></span><span class="box-label">Sur le terrain</span><a class="box-anchor" href="#terrain-11-35" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-36">Dans les trois exemples, remarquez d'où viennent les chiffres : soumissions d'entrepreneurs pour le coût dans l'existant, guides de coûts <span class="citation">(<a class="cite" href="/bibliographie/#altus2026" data-cite="altus2026">Altus Group, 2026</a>; <a class="cite" href="/bibliographie/#rsmeans2025" data-cite="rsmeans2025">RSMeans, 2025</a>)</span> pour le coût dans le neuf, et jugement pour la valeur de récupération (souvent négligeable — <span class="num">200 $</span> de ferraille pour une fournaise — mais parfois substantielle : armoires de cuisine revendues, appareils récupérés). Documentez chaque terme séparément dans le dossier : c'est la décomposition, pas le total, que la contre-expertise attaquera.</p></div></div>197<p id="p11-37">En résumé du volet curable : <strong>ajout</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:0.3669em;"></span><span class="mrel">=</span></span></span></span> élément absent, dépréciation au coût complet dans l'existant; <strong>substitution</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:0.3669em;"></span><span class="mrel">=</span></span></span></span> élément inadéquat, dépréciation au surcoût (existant <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> neuf <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> démolition <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span> récupération). Dans les deux cas, le test de curabilité (coût <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≤</mo></mrow><annotation encoding="application/x-tex">\leq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mrel">≤</span></span></span></span> valeur ajoutée) doit être vérifié et documenté.</p>198<h2 id="s-11-3" class="h-section"><span class="h-num">11.3</span><span class="h-text">La dépréciation fonctionnelle incurable</span><a class="h-anchor" href="#s-11-3" aria-label="Lien vers cette section">#</a></h2>199<p id="p11-38">Lorsque le coût de correction dépasse la valeur ajoutée, la déficience est incurable : on ne mesure plus un coût de correction (que personne n'engagera rationnellement), mais la <strong>perte subie</strong>. Deux sous-catégories : la superadéquation et l'obsolescence de conception.</p>200<h3 id="s-11-3-1" class="h-subsection"><span class="h-num">11.3.1</span><span class="h-text">La superadéquation</span><a class="h-anchor" href="#s-11-3-1" aria-label="Lien vers cette section">#</a></h3>201<div class="box box-def" id="def-11-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 11.5</span><span class="box-title">— superadéquation</span><a class="box-anchor" href="#def-11-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-39">La <strong>superadéquation</strong> (<em>superadequacy</em>) survient lorsqu'un bâtiment contient des éléments ou des améliorations qui <strong>dépassent les attentes et les besoins du marché</strong> pour ce type de propriété dans ce secteur. Le principe fondamental : le marché <strong>ne paie pas pour l'excès de qualité</strong> — un acheteur typique ne verse pas de supplément pour un élément qu'il ne recherche pas.</p></div></div>202<p id="p11-40">D'où vient la superadéquation? Presque toujours d'une confusion, chez le propriétaire-constructeur, entre <em>coût</em> et <em>valeur</em>. Le propriétaire qui installe une piscine intérieure à <span class="num">80 000 $</span> raisonne en fonction de ses goûts personnels et croit « investir » dans sa propriété; le marché, lui, n'évalue l'élément qu'à travers les yeux de l'acheteur type du quartier, qui n'a pas demandé cette piscine, redoute ses coûts de chauffage et d'entretien, et n'acceptera d'en payer qu'une fraction. La superadéquation est ainsi la démonstration la plus éclatante du principe vu dès la séance 2 : le coût n'est pas la valeur. Elle rappelle aussi le principe de <strong>conformité</strong> — une propriété atteint sa valeur maximale lorsqu'elle s'harmonise avec son environnement, et tout écart vers le haut se paie autant qu'un écart vers le bas.</p>203<p id="p11-41"><label for="sn-11-4" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-11-4" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-terme"><strong class="sn-term">contribution au marché</strong> valeur qu'un élément ajoute réellement au prix de vente, estimée par comparables</span> L'économie du problème : l'élément a coûté cher à construire, mais sa <strong>contribution au marché</strong> — ce qu'il ajoute réellement au prix de vente, estimé par ventes comparables — est inférieure à ce coût. La différence est une perte fonctionnelle. S'y ajoute une subtilité : l'élément superadéquat subit aussi une dépréciation <strong>physique</strong>, qui doit être comptée <em>dans ce poste</em> et nulle part ailleurs.</p>204<p id="p11-42">Exemples québécois typiques : piscine intérieure dans un quartier de maisons à <span class="num">250 000 $</span>; domotique ultra-sophistiquée dans un marché moyen; finitions ultra-luxueuses en secteur de gamme moyenne; plancher chauffant généralisé là où il n'est pas valorisé; plafonds de 12 pi dans un bungalow standard; garage triple dans un quartier de garages simples; cuisine commerciale dans une résidence unifamiliale; ascenseur résidentiel dans un plain-pied; cave à vin tempérée dans une propriété d'entrée de gamme.</p>205<div class="box box-form" id="form-11-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 11.3</span><span class="box-title">— dépréciation par superadéquation</span><a class="box-anchor" href="#form-11-3" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-11-3"><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><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><msub><mi>D</mi><mtext>super</mtext></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><mrow></mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mrow><mtext>co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t de l’</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>l</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>ment superad</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>quat (dans le neuf)</mtext></mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>−</mo><mrow></mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mrow><mtext>d</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>pr</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>ciation physique sur cet </mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>l</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>ment</mtext></mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>−</mo><mrow></mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mrow><mtext>valeur ajout</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>e (contribution au march</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>)</mtext></mrow></mrow></mstyle></mtd></mtr></mtable></mtd><mtd width="50%"></mtd><mtd><mtext>(11.3)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}D_{\text{super}} \;=\;{} &amp; \text{coût de l&#x27;élément superadéquat (dans le neuf)}206\\207{}-{} &amp; \text{dépréciation physique sur cet élément} \\208{}-{} &amp; \text{valeur ajoutée (contribution au marché)}\end{aligned}\tag{11.3}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:4.2em;vertical-align:-1.85em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35em;"><span style="top:-4.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0278em;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">super</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 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:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></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:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"></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="mord text"><span class="mord">co</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">u</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˆ</span></span></span></span></span></span></span><span class="mord">t de l’</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">l</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">ment superad</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">quat (dans le neuf)</span></span></span></span><span style="top:-3.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mord text"><span class="mord">d</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">pr</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">ciation physique sur cet </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">l</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">ment</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="mord text"><span class="mord">valeur ajout</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">e (contribution au march</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><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 class="katex-tag"><span class="katex-strut" style="height:4.2em;vertical-align:-1.85em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">11.3</span></span><span class="mord">)</span></span></span></span></span></span></div>209<p id="p11-43">Autrement dit : <strong>coût neuf déprécié physiquement <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> contribution au marché</strong>.</p></div></div>210<div class="box box-ex" id="ex-11-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 11.6</span><span class="box-title">— piscine intérieure en quartier modeste</span><a class="box-anchor" href="#ex-11-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-44">Maison unifamiliale avec piscine intérieure, secteur Hull (Gatineau), quartier de 280 000 à 350 000 $. Hypothèses : âge effectif de l'élément 10 ans, vie économique 50 ans.</p>211<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Poste</th><th class="al-r">Montant</th></tr></thead><tbody><tr><td>Coût de la piscine intérieure dans une construction neuve</td><td class="al-r">80 000 $</td></tr><tr><td>Moins : dépréciation physique (10/50 <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> 20 %)</td><td class="al-r">(16 000 $)</td></tr><tr><td><strong>Coût déprécié physiquement</strong></td><td class="al-r"><strong>64 000 $</strong></td></tr><tr class="rule-above"><td>Moins : contribution au marché (valeur ajoutée estimée)</td><td class="al-r">(30 000 $)</td></tr><tr class="rule-above"><td><strong>Dépréciation fonctionnelle incurable (superadéquation)</strong></td><td class="al-r"><strong>34 000 $</strong></td></tr></tbody></table></div></div>212<p id="p11-45">Lecture : le coût neuf de <span class="num">80 000 $</span> se répartit en trois blocs — <span class="num">30 000 $</span> de contribution au marché (la seule part que l'acheteur paie), <span class="num">16 000 $</span> de dépréciation physique (l'usure de l'élément) et <strong class="c-rouge">34 000 $</strong> de perte fonctionnelle : le marché ne paie que <span class="num">30 000 $</span> pour un élément qui « vaut » <span class="num">64 000 $</span> déprécié.</p></div></div>213<div class="box box-ex" id="ex-11-7"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 11.7</span><span class="box-title">— garage triple en secteur de garages simples</span><a class="box-anchor" href="#ex-11-7" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-46">Quartier où la norme est le garage simple attaché; la maison sujet a un garage triple intégré. Hypothèses : âge effectif 15 ans, vie économique 50 ans. Ici, seule la <strong>portion excédentaire</strong> est superadéquate :</p>214<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Poste</th><th class="al-r">Montant</th></tr></thead><tbody><tr><td>Coût du garage triple dans une construction neuve</td><td class="al-r">75 000 $</td></tr><tr><td>Moins : coût d'un garage simple (standard du quartier)</td><td class="al-r">(28 000 $)</td></tr><tr><td><strong>Coût de la portion superadéquate</strong></td><td class="al-r"><strong>47 000 $</strong></td></tr><tr class="rule-above"><td>Moins : dépréciation physique (15/50 <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> 30 %)</td><td class="al-r">(14 100 $)</td></tr><tr><td><strong>Coût superadéquat déprécié</strong></td><td class="al-r"><strong>32 900 $</strong></td></tr><tr class="rule-above"><td>Moins : contribution au marché (2 places supplémentaires)</td><td class="al-r">(10 000 $)</td></tr><tr class="rule-above"><td><strong>Dépréciation par superadéquation</strong></td><td class="al-r"><strong>22 900 $</strong></td></tr></tbody></table></div></div>215<p id="p11-47">Le garage simple standard, lui, n'est pas superadéquat : il porte sa dépréciation physique normale dans la ventilation du chapitre 10.</p></div></div>216<div class="box box-rem" id="remarque-11-48"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pen"/></svg></span><span class="box-label">coûts d'exploitation excédentaires</span><a class="box-anchor" href="#remarque-11-48" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-49">La superadéquation peut infliger une pénalité additionnelle : les <strong>charges récurrentes</strong> de l'élément excédentaire (chauffer une piscine intérieure, entretenir des équipements spécialisés). Ces coûts d'exploitation excédentaires réduisent encore la valeur et peuvent être <strong>capitalisés</strong> comme pénalité supplémentaire — avec la même mécanique de capitalisation que l'obsolescence de conception ci-dessous.</p></div></div>217<div class="box box-att" id="attention-11-50"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">Attention</span><a class="box-anchor" href="#attention-11-50" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-51">Quatre points de vigilance sur la superadéquation : (1) elle est généralement incurable, car retirer l'élément coûterait plus que le gain; (2) la contribution au marché doit s'appuyer sur des <strong>ventes comparables</strong>, pas sur une intuition; (3) la dépréciation physique de l'élément est comptée <strong class="c-rouge">dans ce poste</strong>, jamais une seconde fois dans la ventilation physique générale; (4) si le coût neuf retenu est un coût de <em>remplacement</em> qui exclut déjà l'élément excédentaire, il n'y a rien à déduire (voir section <a class="xref" href="#s-11-4">11.4</a>).</p></div></div>218<h3 id="s-11-3-2" class="h-subsection"><span class="h-num">11.3.2</span><span class="h-text">L'obsolescence de conception</span><a class="h-anchor" href="#s-11-3-2" aria-label="Lien vers cette section">#</a></h3>219<div class="box box-def" id="def-11-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 11.6</span><span class="box-title">— obsolescence de conception</span><a class="box-anchor" href="#def-11-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-52">L'<strong>obsolescence de conception</strong> (<em>design obsolescence</em>) survient lorsque le <strong>plan, la configuration ou l'agencement</strong> du bâtiment ne correspond plus aux attentes et au mode de vie actuels des acheteurs ou des locataires, et qu'il est trop coûteux de modifier la structure pour y remédier.</p></div></div>220<p id="p11-53">Le problème est structurel : corriger exigerait de déplacer des murs porteurs ou de refaire la charpente, à un coût qui dépasse la valeur récupérable. La propriété génère alors moins de revenus — ou vaut moins — qu'avec un plan moderne, et c'est cette <strong>perte</strong> que l'on mesure, puisqu'aucun coût de correction ne sera engagé.</p>221<p id="p11-54">Au résidentiel : cuisine fermée (contre le concept ouvert), circulation inefficace (longs couloirs), trop de chambres pour trop peu de salles de bain, plafond de sous-sol sous 7 pi, absence de vestibule, escalier au centre de la maison, chambre principale sans salle de bain attenante, plan incompatible avec le télétravail. Au commercial : hauteur libre insuffisante (entrepôt), colonnes trop rapprochées (bureaux), quais de chargement mal positionnés, étages trop petits pour le marché, absence d'ascenseur dans un multi-étages, stationnement insuffisant, rapport plancher/terrain trop faible. Le trait commun : ces défauts se traduisent par des <strong>loyers inférieurs</strong> au marché — et c'est précisément cette perte de revenus qui sert de règle de mesure.</p>222<div class="box box-form" id="form-11-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 11.4</span><span class="box-title">— obsolescence de conception — capitalisation de la perte</span><a class="box-anchor" href="#form-11-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-55">Méthode privilégiée — capitalisation de la perte de revenus :</p>223<div class="eq" id="eq-11-4"><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><mtext>conception</mtext></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><mfrac><mtext>perte de loyer annuelle</mtext><mtext>TGA</mtext></mfrac><mtext>  </mtext><mo>−</mo><mtext>  </mtext><mtext>portion attribuable au terrain</mtext></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(11.4)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">D_{\text{conception}} \;=\;224\frac{\text{perte de loyer annuelle}}{\text{TGA}}225\;-\; \text{portion attribuable au terrain}\tag{11.4}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">conception</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="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 loyer 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 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><span class="katex-base"><span class="katex-strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord text"><span class="mord">portion attribuable au terrain</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">11.4</span></span><span class="mord">)</span></span></span></span></span></span></div>226<p id="p11-56">Méthode alternative — différence de valeur (ventes appariées) :</p>227<div class="eq" id="eq-11-5"><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><mtext>conception</mtext></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><mtext>valeur avec plan moderne</mtext><mtext>  </mtext><mo>−</mo><mtext>  </mtext><mtext>valeur avec plan actuel</mtext></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(11.5)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">D_{\text{conception}} \;=\; \text{valeur avec plan moderne}228\;-\; \text{valeur avec plan actuel}\tag{11.5}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">conception</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="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:0.8889em;vertical-align:-0.1944em;"></span><span class="mord text"><span class="mord">valeur avec plan moderne</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><span class="katex-base"><span class="katex-strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord text"><span class="mord">valeur avec plan actuel</span></span></span><span class="katex-tag"><span class="katex-strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">11.5</span></span><span class="mord">)</span></span></span></span></span></span></div></div></div>229<p id="p11-57"><label for="sn-11-5" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-11-5" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-terme"><strong class="sn-term">TGA</strong> taux global d'actualisation (capitalisation) du marché pour ce type de propriété</span> La capitalisation se déroule en cinq étapes : (1) estimer le loyer actuel du bâtiment avec son plan obsolète; (2) estimer le loyer d'un bâtiment similaire avec un plan moderne; (3) calculer la perte annuelle (différence mensuelle <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\times</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">×</span></span></span></span> 12); (4) capitaliser cette perte au TGA; (5) <strong>soustraire la portion terrain</strong>, car la dépréciation fonctionnelle ne s'applique qu'au bâtiment.</p>230<div class="box box-rem" id="remarque-11-58"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pen"/></svg></span><span class="box-label">la portion terrain — repères de marché</span><a class="box-anchor" href="#remarque-11-58" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-59">Portion 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:0.3669em;"></span><span class="mrel">=</span></span></span></span> perte capitalisée <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\times</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">×</span></span></span></span> (valeur du 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">\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 de la propriété). 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 de cas. Nous retrouverons exactement la même mécanique d'allocation au chapitre 12, appliquée cette fois à la dépréciation externe.</p></div></div>231<div class="box box-ex" id="ex-11-8"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 11.8</span><span class="box-title">— maison avec plan fermé — résidentiel</span><a class="box-anchor" href="#ex-11-8" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-60">Maison à Gatineau (1972), plan très compartimenté : cuisine fermée, pièces séparées, murs porteurs empêchant l'ouverture. Hypothèses : TGA de 6,0 % (2026); portion terrain de 20 %.</p>232<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Poste</th><th class="al-r">Montant</th></tr></thead><tbody><tr><td>Loyer mensuel estimé du bâtiment (plan actuel)</td><td class="al-r">1 800 $/mois</td></tr><tr><td>Loyer mensuel d'un bâtiment similaire (plan ouvert)</td><td class="al-r">2 050 $/mois</td></tr><tr><td><strong>Perte de loyer annuelle</strong> (250 $ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\times</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">×</span></span></span></span> 12)</td><td class="al-r"><strong>3 000 $/an</strong></td></tr><tr class="rule-above"><td>Perte capitalisée (TGA 6,0 %)</td><td class="al-r">50 000 $</td></tr><tr><td>Moins : portion terrain (20 %)</td><td class="al-r">(10 000 $)</td></tr><tr class="rule-above"><td><strong>Dépréciation fonctionnelle incurable (conception)</strong></td><td class="al-r"><strong>40 000 $</strong></td></tr></tbody></table></div></div>233<p id="p11-61">Pas à pas :</p>234<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Perte annuelle</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mo stretchy="false">(</mo><mn>2</mn><mtext> </mtext><mn>050</mn><mo>−</mo><mn>1</mn><mtext> </mtext><mn>800</mn><mo stretchy="false">)</mo><mo>×</mo><mn>12</mn><mo>=</mo><mn>3</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><mtext>an</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Perte capitalis</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>e</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>3</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>0,06</mn><mo>=</mo><mn>50</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Portion terrain</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>50</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>20</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mn>10</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>D</mi><mtext>conception</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>50</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>10</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">40</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{Perte annuelle} &amp;= (2\,050 - 1\,800) \times 12 = 3\,000\,\$/\text{an} \\235\text{Perte capitalisée} &amp;= 3\,000 \div 0{,}06 = 50\,000\,\$ \\236\text{Portion terrain} &amp;= 50\,000 \times 20\,\% = 10\,000\,\$ \\237D_{\text{conception}} &amp;= 50\,000 - 10\,000 = \uqogreen{40\,000~\$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:5.7em;vertical-align:-2.6em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.1em;"><span style="top:-5.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Perte annuelle</span></span></span></span><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Perte capitalis</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">e</span></span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Portion terrain</span></span></span></span><span style="top:-0.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">conception</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.6em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.1em;"><span style="top:-5.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mopen">(</span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">050</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">3</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 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">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">06</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-0.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></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;">40</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:2.6em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>238<p id="p11-62">La configuration fermée réduit la valeur des améliorations de <span class="num">40 000 $</span>, montant irrécupérable : déplacer les murs porteurs coûterait plus cher que le gain de valeur.</p></div></div>239<div class="box box-ex" id="ex-11-9"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 11.9</span><span class="box-title">— entrepôt industriel — hauteur libre insuffisante</span><a class="box-anchor" href="#ex-11-9" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-63">Entrepôt de 1985 dans un parc industriel de Gatineau : hauteur libre de 16 pi au lieu du standard actuel de 24 pi; <span class="num">20 000</span> pi<sup>2</sup>. Hypothèses : TGA de 8,0 % (2026); portion terrain de 15 %.</p>240<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Perte de loyer</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mo stretchy="false">(</mo><mn>8,50</mn><mo>−</mo><mn>7,00</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><mtext>pi²/an</mtext><mo>×</mo><mn>20</mn><mtext> </mtext><mn>000</mn><mtext> pi²</mtext><mo>=</mo><mn>30</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><mtext>an</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Perte capitalis</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>e</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>30</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>0,08</mn><mo>=</mo><mn>375</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Portion terrain (15</mtext><mtext> </mtext><mtext>%)</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>56</mn><mtext> </mtext><mn>250</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>D</mi><mtext>conception</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>375</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>56</mn><mtext> </mtext><mn>250</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">318</mn><mtext> </mtext><mn mathvariant="bold">750</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Perte de loyer} &amp;= (8{,}50 - 7{,}00)\,\$/\text{pi²/an}241   \times 20\,000~\text{pi²} = 30\,000\,\$/\text{an} \\242\text{Perte capitalisée} &amp;= 30\,000 \div 0{,}08 = 375\,000\,\$ \\243\text{Portion terrain (15\,\%)} &amp;= 56\,250\,\$ \\244D_{\text{conception}} &amp;= 375\,000 - 56\,250 = \uqogreen{318\,750~\$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:5.7em;vertical-align:-2.6em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.1em;"><span style="top:-5.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Perte de loyer</span></span></span></span><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Perte capitalis</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">e</span></span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Portion terrain (15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%)</span></span></span></span><span style="top:-0.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">conception</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.6em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.1em;"><span style="top:-5.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mopen">(</span><span class="mord">8</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">50</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">7</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">00</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$/</span><span class="mord text"><span class="mord">pi²/an</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord text"><span class="mord">pi²</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$/</span><span class="mord text"><span class="mord">an</span></span></span></span><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">08</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">375</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">56</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">250</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-0.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">375</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">56</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">250</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">318</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">750</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:2.6em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>245<p id="p11-64">L'ordre de grandeur est frappant : un seul défaut de conception structurel peut peser davantage que toute la dépréciation physique d'un bâtiment industriel — d'où l'importance, pour l'entrepôt, du standard de hauteur libre dans l'analyse du marché locatif.</p></div></div>246<h2 id="s-11-4" class="h-section"><span class="h-num">11.4</span><span class="h-text">Reproduction ou remplacement : l'incidence du coût neuf</span><a class="h-anchor" href="#s-11-4" aria-label="Lien vers cette section">#</a></h2>247<p id="p11-65">Le choix fait aux séances 5 et 6 entre coût de <span class="motcle" data-term="reproduction">reproduction</span> (réplique exacte du bâtiment, défauts inclus) et coût de <span class="motcle" data-term="remplacement">remplacement</span> (bâtiment à utilité équivalente, normes actuelles) rejaillit directement sur la dépréciation fonctionnelle à mesurer. <label for="sn-11-6" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-11-6" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-repere">Remplacement <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> certaines obsolescences sont déjà hors du coût neuf : ne pas les déduire deux fois.</span></p>248<p id="p11-66">Avec le coût de <strong>reproduction</strong>, la réplique inclut les défauts de conception et les matériaux désuets : <strong>toute</strong> la dépréciation fonctionnelle doit être calculée — plus de travail d'analyse. Avec le coût de <strong>remplacement</strong>, le bâtiment hypothétique aux normes actuelles élimine d'office certaines obsolescences (matériaux désuets, parfois le plan) : il y a moins de dépréciation fonctionnelle à calculer, ce qui explique que cette approche soit souvent préférée en pratique.</p>249<p id="p11-67">L'intuition à retenir est celle d'une <strong>comptabilité en partie double</strong> entre le coût neuf et la dépréciation. La valeur dépréciée visée est la même quel que soit le chemin : si le coût neuf retenu est plus « généreux » (la reproduction, qui paie pour reconstruire les défauts), la dépréciation à soustraire est plus lourde d'exactement la même quantité; si le coût neuf est plus « sobre » (le remplacement, qui ne reconstruit pas les défauts), la dépréciation correspondante disparaît avec eux. Les deux chemins doivent converger vers la même valeur — c'est d'ailleurs un excellent autocontrôle de dossier : si l'analyse par reproduction et l'analyse par remplacement divergent sensiblement, c'est presque toujours qu'une obsolescence a été comptée sur un chemin et pas sur l'autre, ou comptée deux fois sur l'un des deux. Le tableau <a class="xref" href="#tab-ch11-tab-reprod-rempl">11.3</a> détaille poste par poste ce que chaque choix laisse à calculer.</p>250<figure class="float-table" id="tab-ch11-tab-reprod-rempl"><figcaption><span class="fig-label">Tableau 11.3</span> Incidence du choix reproduction / remplacement sur l'analyse fonctionnelle. <sup>*</sup> Sauf si le coût de remplacement exclut déjà l'élément excédentaire.</figcaption><div class="table-wrap"><table class="tbl"><thead><tr><th>Déficience fonctionnelle</th><th>Coût reproduction</th><th>Coût remplacement</th></tr></thead><tbody><tr><td>Ajout manquant (2<sup>e</sup> salle de bain)</td><td>À calculer</td><td>À calculer</td></tr><tr><td>Substitution (mazout <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>→</mo></mrow><annotation encoding="application/x-tex">\rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">→</span></span></span></span> thermopompe)</td><td>À calculer</td><td>Déjà éliminée</td></tr><tr><td>Superadéquation</td><td>À calculer</td><td>À calculer<sup>*</sup></td></tr><tr><td>Obsolescence — plan fermé</td><td>À calculer</td><td>Éliminée si plan modernisé</td></tr><tr><td>Obsolescence — hauteur de plafond</td><td>À calculer</td><td>Dépend de l'approche</td></tr><tr><td>Matériaux désuets</td><td>À calculer</td><td>Déjà éliminée</td></tr></tbody></table></div></figure>251<div class="box box-att" id="attention-11-68"><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 — remplacement et fonctionnelle</span><a class="box-anchor" href="#attention-11-68" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-69">Avec le coût de remplacement, certaines obsolescences sont <strong class="c-rouge">déjà absentes du coût neuf</strong> : les soustraire une deuxième fois dans la dépréciation sous-évalue la propriété. Le rapport doit documenter clairement ce qui est <strong>inclus ou exclu</strong> du coût neuf retenu — c'est cette documentation qui protège contre le double comptage. Les <strong>ajouts manquants</strong> restent à calculer dans les deux cas (ils sont exclus des deux coûts neufs); la <strong>superadéquation</strong> reste généralement à calculer, sauf si le remplacement l'a explicitement exclue.</p></div></div>252<h2 id="s-11-5" class="h-section"><span class="h-num">11.5</span><span class="h-text">Le gabarit doctrinal et la synthèse du calcul</span><a class="h-anchor" href="#s-11-5" aria-label="Lien vers cette section">#</a></h2>253<h3 id="s-11-5-1" class="h-subsection"><span class="h-num">11.5.1</span><span class="h-text">La procédure standard en cinq étapes</span><a class="h-anchor" href="#s-11-5-1" aria-label="Lien vers cette section">#</a></h3>254<p id="p11-70">Les quatre formules du chapitre sont des applications d'un gabarit doctrinal unique, celui de <em>The Appraisal of Real Estate</em> <span class="citation">(<a class="cite" href="/bibliographie/#appraisal2026" data-cite="appraisal2026">Appraisal Institute, 2026</a>)</span>, applicable à tout élément porteur de perte fonctionnelle :</p>255<ol class="enum"><li><strong>Coût de l'élément existant</strong>, tel qu'inclus au coût neuf         estimé;</li><li><strong>Moins</strong> : dépréciation (physique) <strong>déjà comptée</strong> sur         cet élément;</li><li><strong>Plus</strong> : coût de correction (si curable) <strong>ou</strong> perte         capitalisée / coût de l'excédent (si incurable);</li><li><strong>Moins</strong> : coût de l'élément installé <strong>lors de la         construction</strong> (s'il est inclus au coût neuf);</li><li><strong>Égale</strong> : perte fonctionnelle attribuable à l'élément.</li></ol>256<div class="box box-rem" id="remarque-11-76"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pen"/></svg></span><span class="box-label">le lien avec les formules du cours</span><a class="box-anchor" href="#remarque-11-76" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-77">Pour un <strong>ajout</strong> exclu du coût neuf, les étapes 1, 2 et 4 sont nulles : la dépréciation se réduit au coût de correction dans l'existant — notre formule d'ajout. Pour une <strong>substitution</strong>, les étapes 1 et 2 neutralisent la valeur dépréciée de l'élément désuet (déjà porté au coût neuf), l'étape 3 apporte le coût de correction complet et l'étape 4 retranche ce que l'élément moderne aurait coûté au neuf : il reste le surcoût de rénovation, plus démolition, moins récupération — notre formule de substitution. La <strong>superadéquation</strong> et la <strong>capitalisation</strong> s'y raccordent de la même manière. Aux examens, l'une ou l'autre présentation (gabarit ou formule directe) est acceptée, pourvu que les termes soient identifiés.</p></div></div>257<h3 id="s-11-5-2" class="h-subsection"><span class="h-num">11.5.2</span><span class="h-text">Le tableau récapitulatif et la formule globale</span><a class="h-anchor" href="#s-11-5-2" aria-label="Lien vers cette section">#</a></h3>258<figure class="float-table" id="tab-ch11-tab-quatrecategories"><figcaption><span class="fig-label">Tableau 11.4</span> Les quatre catégories de dépréciation fonctionnelle.</figcaption><div class="table-wrap"><table class="tbl"><thead><tr><th>Catégorie</th><th>Type</th><th>Nature</th><th>Méthode de calcul</th></tr></thead><tbody><tr><td>Curable</td><td>Ajout</td><td>Élément absent</td><td>Coût d'installation dans l'existant</td></tr><tr><td>Curable</td><td>Substitution</td><td>Élément inadéquat</td><td>Coût existant <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> coût neuf <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> démolition <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span> récupération</td></tr><tr><td>Incurable</td><td>Superadéquation</td><td>Élément excédentaire</td><td>Coût déprécié physiquement <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> contribution au marché</td></tr><tr><td>Incurable</td><td>Obsol. de conception</td><td>Plan inadéquat</td><td>Capitalisation de la perte de revenus, moins la portion terrain</td></tr></tbody></table></div></figure>259<div class="box box-form" id="form-11-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 11.5</span><span class="box-title">— dépréciation fonctionnelle totale</span><a class="box-anchor" href="#form-11-5" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-11-6"><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><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><msub><mi>D</mi><mtext>fonctionnelle</mtext></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><mrow></mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><msub><mi>D</mi><mtext>curable (ajouts)</mtext></msub><mo>+</mo><msub><mi>D</mi><mtext>curable (substitutions)</mtext></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>+</mo><mrow></mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><msub><mi>D</mi><mrow><mtext>incurable (superad</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>quation)</mtext></mrow></msub><mo>+</mo><msub><mi>D</mi><mtext>incurable (conception)</mtext></msub></mrow></mstyle></mtd></mtr></mtable></mtd><mtd width="50%"></mtd><mtd><mtext>(11.6)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}D_{\text{fonctionnelle}} \;=\;{} &amp; D_{\text{curable (ajouts)}}260+ D_{\text{curable (substitutions)}} \\261{}+{} &amp; D_{\text{incurable (superadéquation)}}262+ D_{\text{incurable (conception)}}\end{aligned}\tag{11.6}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:2.7em;vertical-align:-1.1em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6em;"><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">fonctionnelle</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="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></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:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></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 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="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 mtight">curable (ajouts)</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:0.2222em;"></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 mtight">curable (substitutions)</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 style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></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 mtight">incurable (superad</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">quation)</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:0.2222em;"></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 mtight">incurable (conception)</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><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 class="katex-tag"><span class="katex-strut" style="height:2.7em;vertical-align:-1.1em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">11.6</span></span><span class="mord">)</span></span></span></span></span></span></div></div></div>263<p id="p11-78">Chaque poste est mesuré séparément, avec sa propre méthode; le total s'ajoute à la dépréciation physique (chapitre 10) et à la dépréciation externe (chapitre 12); et chaque estimation doit être <strong>appuyée par des données de marché</strong>. Dans le processus séquentiel global : coût neuf <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 physique <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> 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">\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> fonctionnelle incurable <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>→</mo></mrow><annotation encoding="application/x-tex">\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> 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">\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> valeur dépréciée des améliorations.</p>264<h3 id="s-11-5-3" class="h-subsection"><span class="h-num">11.5.3</span><span class="h-text">La carte des doubles comptages</span><a class="h-anchor" href="#s-11-5-3" aria-label="Lien vers cette section">#</a></h3>265<div class="box box-att" id="attention-11-79"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">les quatre configurations de double comptage</span><a class="box-anchor" href="#attention-11-79" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-80">Le double comptage — la même perte soustraite deux fois — est l'erreur la plus coûteuse du chapitre. Quatre configurations à surveiller :</p>266<ol class="enum"><li><strong class="c-rouge">Physique et fonctionnelle</strong> : un élément traité en         substitution fonctionnelle ne doit pas aussi être déprécié         physiquement dans la ventilation du chapitre 10 — la dépréciation         physique des composantes à courte vie ne s'applique qu'aux éléments         <em>non identifiés</em> comme obsolescences fonctionnelles.</li><li><strong class="c-rouge">Remplacement et fonctionnelle</strong> : ne pas soustraire des         obsolescences déjà éliminées du coût de remplacement         (section <a class="xref" href="#s-11-4">11.4</a>).</li><li><strong class="c-rouge">Superadéquation et physique</strong> : la dépréciation physique de         l'élément superadéquat se compte une seule fois, dans le poste         superadéquation.</li><li><strong class="c-rouge">Fonctionnelle et externe</strong> : séparer la perte de loyer due         à la conception (interne) de celle due au marché ou au voisinage         (externe, chapitre 12) — la même perte de revenus ne peut fonder         deux dépréciations.</li></ol></div></div>267<h2 id="s-11-6" class="h-section"><span class="h-num">11.6</span><span class="h-text">Cas intégrés</span><a class="h-anchor" href="#s-11-6" aria-label="Lien vers cette section">#</a></h2>268<h3 id="s-11-6-1" class="h-subsection"><span class="h-num">11.6.1</span><span class="h-text">Cas 1 — Bungalow de 1965, secteur Hull</span><a class="h-anchor" href="#s-11-6-1" aria-label="Lien vers cette section">#</a></h3>269<div class="box box-ex" id="ex-11-10"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 11.10</span><span class="box-title">— bungalow de 1965 : cinq déficiences fonctionnelles</span><a class="box-anchor" href="#ex-11-10" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-85"><strong>Description et hypothèses.</strong> Bungalow de <span class="num">1200</span> pi<sup>2</sup> (1965), trois chambres, une salle de bain, sous-sol non fini. Coût de remplacement : <span class="num">285 000 $</span>; terrain : <span class="num">85 000 $</span>. Hypothèses : portion terrain 23 % (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>85</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>370</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">\approx 85\,000 \div 370\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">85</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">370</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>); TGA de 6,0 % (2026).</p>270<p id="p11-86"><strong>Déficiences identifiées.</strong> (1) curable–ajout : absence d'une deuxième salle de bain; (2) curable–substitution : panneau électrique 60 A <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>→</mo></mrow><annotation encoding="application/x-tex">\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> 200 A; (3) curable–substitution : douze fenêtres à simple vitrage; (4) incurable–conception : cuisine fermée (mur porteur); (5) incurable–conception : hauteur du sous-sol de 6 pi 4 po.</p>271<p id="p11-87"><strong>Volet curable.</strong></p>272<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Poste</th><th class="al-r">Montant</th></tr></thead><tbody><tr><td>A) Ajout — 2<sup>e</sup> salle de bain : coût dans l'existant</td><td class="al-r">28 000 $</td></tr><tr><td>B) Substitution — panneau électrique : <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>5</mn><mtext> </mtext><mn>500</mn><mo>−</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">12\,000 - 5\,500 - 0</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">5</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">0</span></span></span></span></td><td class="al-r">6 500 $</td></tr><tr><td>B) Substitution — fenêtres (12) : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>21</mn><mtext> </mtext><mn>600</mn><mo>−</mo><mn>13</mn><mtext> </mtext><mn>200</mn><mo>−</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">21\,600 - 13\,200 - 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">21</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">13</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></td><td class="al-r">8 400 $</td></tr><tr class="rule-above"><td><strong>Sous-total curable</strong></td><td class="al-r"><strong>42 900 $</strong></td></tr></tbody></table></div></div>273<p id="p11-88">Chaque poste satisfait le test de curabilité (valeur ajoutée estimée supérieure au coût de correction, documentée par comparables).</p>274<p id="p11-89"><strong>Volet incurable (conception).</strong></p>275<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Poste</th><th class="al-r">Montant</th></tr></thead><tbody><tr><td>Cuisine fermée : perte 200 $/mois; <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>200</mn><mo>×</mo><mn>12</mn><mo stretchy="false">)</mo><mo>÷</mo><mn>0,06</mn><mo>=</mo><mn>40</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">(200 \times 12) \div 0{,}06276= 40\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">200</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">12</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">06</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">40</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>; moins terrain 23 % (9 200)</td><td class="al-r">30 800 $</td></tr><tr><td>Sous-sol 6 pi 4 po : perte 150 $/mois; <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>150</mn><mo>×</mo><mn>12</mn><mo stretchy="false">)</mo><mo>÷</mo><mn>0,06</mn><mo>=</mo><mn>30</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">(150 \times 12) \div 0{,}06277= 30\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">150</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">12</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">06</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>; <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo><mtext> </mtext><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mn>0,23</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\times\,(1 - 0{,}23)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">×</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="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">23</span><span class="mclose">)</span></span></span></span></td><td class="al-r">23 100 $</td></tr><tr class="rule-above"><td><strong>Sous-total incurable</strong></td><td class="al-r"><strong>53 900 $</strong></td></tr></tbody></table></div></div>278<p id="p11-90"><strong>Total de la dépréciation fonctionnelle :</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>42</mn><mtext> </mtext><mn>900</mn><mo>+</mo><mn>53</mn><mtext> </mtext><mn>900</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">96</mn><mtext> </mtext><mn mathvariant="bold">800</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">42\,900 + 53\,900 = \uqogreen{96\,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">42</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">900</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">53</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">900</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">96</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">800</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>, soit 34 % du coût de remplacement — lourd, mais plausible pour un plan de 1965 jamais modernisé.</p></div></div>279<h3 id="s-11-6-2" class="h-subsection"><span class="h-num">11.6.2</span><span class="h-text">Cas 2 — Immeuble de bureaux de 1980, Gatineau</span><a class="h-anchor" href="#s-11-6-2" aria-label="Lien vers cette section">#</a></h3>280<div class="box box-ex" id="ex-11-11"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 11.11</span><span class="box-title">— immeuble de bureaux : les quatre catégories réunies</span><a class="box-anchor" href="#ex-11-11" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-91"><strong>Description et hypothèses.</strong> Immeuble de bureaux de deux étages, <span class="num">8000</span> pi<sup>2</sup>, boulevard Maloney, construit en 1980, bon état physique. Coût de remplacement : <span class="num">1 200 000 $</span>; terrain : <span class="num">250 000 $</span>. Hypothèses : portion terrain 17 % (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>250</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>1</mn><mtext> </mtext><mn>450</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">\approx 250\,000 \div 1\,450\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">250</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">450</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>); TGA de 8,0 % (2026).</p>281<p id="p11-92"><strong>Déficiences identifiées.</strong> (1) curable–ajout : climatisation centrale adéquate absente; (2) curable–substitution : système CVAC désuet; (3) incurable–superadéquation : hall d'entrée surdimensionné en marbre; (4) incurable–conception : colonnes rapprochées limitant l'aménagement.</p>282<p id="p11-93"><strong>Calculs.</strong></p>283<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Poste</th><th class="al-r">Montant</th></tr></thead><tbody><tr><td>A) Ajout — climatisation : coût dans l'existant</td><td class="al-r">45 000 $</td></tr><tr><td>B) Substitution — CVAC : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>85</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>55</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>2</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">85\,000 - 55\,000 - 2\,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">85</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">55</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span> (récupération)</td><td class="al-r">28 000 $</td></tr><tr><td><strong>Sous-total curable</strong></td><td class="al-r"><strong>73 000 $</strong></td></tr><tr class="rule-above"><td>C) Superadéquation — hall en marbre : <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>24</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">120\,000 - 24\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">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">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span> (phys.) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mtext> </mtext><mn>45</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">-\,45\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">45</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span> (contribution)</td><td class="al-r">51 000 $</td></tr><tr><td>D) Conception — colonnes : perte <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><mtext>pi²/an</mtext><mo>×</mo><mn>8</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>16</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><mtext>an</mtext></mrow><annotation encoding="application/x-tex">2\,\$/\text{pi²/an} \times 8\,000 =28416\,000\,\$/\text{an}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$/</span><span class="mord text"><span class="mord">pi²/an</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">8</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></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><mn>16</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>0,08</mn><mo>=</mo><mn>200</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">16\,000 \div 0{,}08 = 200\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">08</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>; moins terrain 17 % (34 000)</td><td class="al-r">166 000 $</td></tr><tr><td><strong>Sous-total incurable</strong></td><td class="al-r"><strong>217 000 $</strong></td></tr><tr class="rule-above"><td><strong>TOTAL — dépréciation fonctionnelle</strong></td><td class="al-r"><strong>290 000 $</strong></td></tr></tbody></table></div></div>285<p id="p11-94">Près du quart du coût de remplacement, dans un immeuble pourtant en <em>bon état physique</em> : l'illustration parfaite de l'indépendance des deux formes de dépréciation.</p></div></div>286<p id="p11-95">Ces deux cas montrent ce que le chapitre 10 annonçait : la ventilation de la dépréciation est un exercice d'orfèvrerie où chaque perte doit être rangée dans un poste et un seul. Le bungalow de 1965 perd <span class="num">96 800 $</span> sans qu'aucune de ses composantes soit particulièrement usée; l'immeuble de bureaux perd <span class="num">290 000 $</span> en étant « en bon état ». Dans les deux cas, c'est l'analyse du marché — loyers comparés, contributions extraites des ventes, attentes du secteur — qui a fourni chaque chiffre. Il reste une troisième famille de pertes, la plus insaisissable : celles qui ne viennent ni de l'usure ni de la conception, mais de l'extérieur du bâtiment — l'autoroute qu'on prolonge, l'usine qui ferme, le zonage qui change. C'est l'objet du chapitre 12.</p>287<hr class="sep">288<div class="box box-ret" id="aretenir-11-96"><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-11-96" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-97">La dépréciation fonctionnelle naît de la <strong>conception</strong>, jamais de l'usure : interne au bâtiment, elle peut frapper de plein fouet un immeuble en parfait état matériel. Tout part du test économique de curabilité — curable si le coût de correction n'excède pas la valeur ajoutée — qui distribue les déficiences entre quatre méthodes de calcul. L'<strong>ajout</strong> (élément absent) se mesure au coût complet d'installation dans l'existant, jamais à la différence existant/neuf; la <strong>substitution</strong> (élément désuet) au surcoût de rénovation — coût dans l'existant, moins coût dans le neuf, plus démolition, moins récupération; la <strong>superadéquation</strong> au coût neuf de l'excédent déprécié physiquement, diminué de sa contribution au marché; et l'<strong>obsolescence de conception</strong> à la perte de loyer annuelle capitalisée au TGA, nette de la portion terrain. Le choix du coût neuf gouverne l'ampleur de l'analyse : la reproduction oblige à tout calculer, le remplacement élimine d'office certaines obsolescences — et impose de documenter ce que le coût neuf inclut. Restent les quatre doubles comptages à bannir absolument : physique/fonctionnelle, remplacement/fonctionnelle, superadéquation/physique et fonctionnelle/externe.</p></div></div>289<h2 id="s-11-7" class="h-section"><span class="h-num">11.7</span><span class="h-text">Exercices</span><a class="h-anchor" href="#s-11-7" aria-label="Lien vers cette section">#</a></h2>290<div class="box box-exo" id="exo-11-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 11.1</span><span class="box-title">— classification des déficiences</span><a class="box-anchor" href="#exo-11-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-98">Classez chaque situation dans l'une des quatre catégories (curable–ajout, curable–substitution, incurable–superadéquation, incurable–conception) et indiquez la méthode de calcul applicable.</p>291<ol class="enum"><li>Maison de 1970 sans hotte de cuisine; installation dans l'existant         <span class="num">1800 $</span>, valeur ajoutée <span class="num">2500 $</span>.</li><li>Spa intérieur avec solarium (<span class="num">95 000 $</span> à neuf) dans un         quartier de maisons à <span class="num">300 000 $</span>; contribution au marché         estimée à <span class="num">25 000 $</span>.</li><li>Plomberie en fonte d'origine; remplacement dans l'existant         <span class="num">18 000 $</span>, coût au neuf <span class="num">9000 $</span>, valeur ajoutée         <span class="num">22 000 $</span>.</li><li>Immeuble de bureaux dont les étages de <span class="num">2500</span> pi<sup>2</sup> sont trop         petits pour la demande locative (standard local :         <span class="num">5000</span> pi<sup>2</sup> et plus); loyers inférieurs de         1,50 $/pi<sup>2</sup>/an au marché.</li><li>Bungalow sans salle d'eau au rez-de-chaussée; ajout <span class="num">16 000 $</span>,         valeur ajoutée <span class="num">14 000 $</span>.</li></ol></div></div>292<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li><strong>Curable–ajout</strong> : élément absent, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mtext> </mtext><mn>800</mn><mo>≤</mo><mn>2</mn><mtext> </mtext><mn>500</mn></mrow><annotation encoding="application/x-tex">1\,800 \leq 2\,500</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7804em;vertical-align:-0.136em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span></span></span></span>;         dépréciation <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> <span class="num">1800 $</span> (coût dans l'existant).</li><li><strong>Incurable–superadéquation</strong> : excès de qualité pour le         secteur; coût neuf déprécié physiquement moins contribution         (<span class="num">25 000 $</span>).</li><li><strong>Curable–substitution</strong> : élément présent mais désuet,         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>18</mn><mtext> </mtext><mn>000</mn><mo>≤</mo><mn>22</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">18\,000 \leq 22\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7804em;vertical-align:-0.136em;"></span><span class="mord">18</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>; dépréciation <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>18</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>9</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">= 18\,000 - 9\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">18</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span> (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>         récupération, ici nulle) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> <span class="num">9000 $</span>.</li><li><strong>Incurable–conception</strong> : défaut structurel d'agencement;         capitalisation de la perte de loyer au TGA, moins la portion         terrain.</li><li><strong class="c-rouge">Piège</strong> : le test de curabilité échoue         (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>16</mn><mtext> </mtext><mn>000</mn><mo>&gt;</mo><mn>14</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">16\,000 &gt; 14\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6835em;vertical-align:-0.0391em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">14</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>). La déficience est <strong>incurable</strong> malgré         sa nature d'« ajout » : on ne retient pas le coût de correction; la         perte se mesure par la contribution manquante au marché (par ventes         appariées ou capitalisation), plafonnée ici à environ         <span class="num">14 000 $</span>.</li></ol></div></details>293<div class="box box-exo" id="exo-11-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 11.2</span><span class="box-title">— substitution complète</span><a class="box-anchor" href="#exo-11-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-109">Une maison de 1972 à Hull est chauffée par plinthes désuètes avec un panneau de 100 A. Le marché exige une thermopompe centrale et un panneau de 200 A. Données : thermopompe installée dans l'existant <span class="num">16 500 $</span> (dont modification des conduits <span class="num">3800 $</span>); retrait des plinthes et remise en état des murs <span class="num">2100 $</span>; valeur de récupération des plinthes <span class="num">150 $</span>; coût de la thermopompe dans une construction neuve <span class="num">9500 $</span>. Panneau : coût dans l'existant <span class="num">11 000 $</span>, au neuf <span class="num">5200 $</span>, récupération nulle. Valeurs ajoutées estimées : chauffage <span class="num">24 000 $</span>; panneau <span class="num">9000 $</span>.</p>294<ol class="enum"><li>Vérifiez la curabilité de chaque poste.</li><li>Calculez la dépréciation fonctionnelle curable totale.</li></ol></div></div>295<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>Chauffage : coût de correction complet         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>16</mn><mtext> </mtext><mn>500</mn><mo>+</mo><mn>2</mn><mtext> </mtext><mn>100</mn><mo>−</mo><mn>150</mn><mo>=</mo><mn>18</mn><mtext> </mtext><mn>450</mn><mo>≤</mo><mn>24</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">= 16\,500 + 2\,100 - 150 = 18\,450 \leq 24\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">100</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">150</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7804em;vertical-align:-0.136em;"></span><span class="mord">18</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">450</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span> <strong class="c-vert">curable</strong>. Panneau :         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>11</mn><mtext> </mtext><mn>000</mn><mo>≤</mo><mn>9</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">11\,000 \leq 9\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7804em;vertical-align:-0.136em;"></span><span class="mord">11</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>? Non — <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>11</mn><mtext> </mtext><mn>000</mn><mo>&gt;</mo><mn>9</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">11\,000 &gt; 9\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6835em;vertical-align:-0.0391em;"></span><span class="mord">11</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span> <strong class="c-rouge">incurable</strong> au sens strict du test. (Si         l'énoncé d'un examen retient une valeur ajoutée de <span class="num">12 000 $</span>,         il redevient curable : toujours dérouler le test explicitement.)</li><li>Seul le chauffage est curable :         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>subst</mtext></msub><mo>=</mo><mn>16</mn><mtext> </mtext><mn>500</mn><mo>−</mo><mn>9</mn><mtext> </mtext><mn>500</mn><mo>+</mo><mn>2</mn><mtext> </mtext><mn>100</mn><mo>−</mo><mn>150</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">8</mn><mtext> </mtext><mn mathvariant="bold">950</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">D_{\text{subst}} = 16\,500 - 9\,500 + 2\,100 - 150296        = \uqogreen{8\,950~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">subst</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">100</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">150</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">8</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">950</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>. Le panneau, incurable, se mesure par sa         contribution manquante (au plus <span class="num">9000 $</span>), non par son coût de         correction; il s'ajoute au volet incurable du dossier.</li></ol></div></details>297<div class="box box-exo" id="exo-11-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 11.3</span><span class="box-title">— superadéquation avec charges excédentaires</span><a class="box-anchor" href="#exo-11-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-114">Une résidence de Chelsea comprend une piscine intérieure : coût à neuf <span class="num">110 000 $</span>; âge effectif 12 ans, vie économique 40 ans; contribution au marché <span class="num">35 000 $</span>. Le chauffage et l'entretien de la piscine coûtent <span class="num">4200 $</span>/an de plus que ce que le marché accepte d'absorber; TGA de 6,0 %; portion terrain 25 %.</p>298<ol class="enum"><li>Calculez la dépréciation par superadéquation (volet coût).</li><li>Capitalisez la pénalité d'exploitation excédentaire.</li><li>Concluez la dépréciation fonctionnelle totale de l'élément.</li></ol></div></div>299<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>Dépréciation physique de l'élément : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>110</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>12</mn><mi mathvariant="normal">/</mi><mn>40</mn><mo>=</mo><mn>33</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">110\,000 \times 12/40 =300        33\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">110</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">12/40</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">33</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>. Coût déprécié : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>110</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>33</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>77</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">110\,000 - 33\,000 = 77\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">110</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">33</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">77</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>.         Superadéquation : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>77</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>35</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">42</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">77\,000 - 35\,000 = \uqogreen{42\,000~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">77</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">35</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">42</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</li><li>Perte capitalisée : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4</mn><mtext> </mtext><mn>200</mn><mo>÷</mo><mn>0,06</mn><mo>=</mo><mn>70</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">4\,200 \div 0{,}06 = 70\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">4</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">06</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">70</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>; portion         améliorations : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>70</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mn>0,25</mn><mo stretchy="false">)</mo><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">52</mn><mtext> </mtext><mn mathvariant="bold">500</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">70\,000 \times (1 - 0{,}25) =301        \uqogreen{52\,500~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">70</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">25</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">52</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">500</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</li><li>Total de l'élément : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>42</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>52</mn><mtext> </mtext><mn>500</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">94</mn><mtext> </mtext><mn mathvariant="bold">500</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">42\,000 + 52\,500 = \uqogreen{94\,500~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">42</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">52</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">94</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">500</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.         Vérification d'ordre de grandeur : la perte approche le coût neuf de         l'élément (<span class="num">110 000 $</span>) — cohérent pour un équipement que le         marché local ne valorise presque pas et qui coûte cher à exploiter.         Ne pas oublier : les <span class="num">33 000 $</span> de dépréciation physique de la         piscine sont comptés <em>ici</em> et doivent être exclus de la         ventilation physique générale.</li></ol></div></details>302<div class="box box-exo" id="exo-11-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 11.4</span><span class="box-title">— obsolescence de conception — commercial</span><a class="box-anchor" href="#exo-11-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-121">Un immeuble de bureaux de <span class="num">12 000</span> pi<sup>2</sup> à Gatineau souffre de deux défauts structurels : absence d'ascenseur (deux étages) et fenestration insuffisante au deuxième étage. Loyer obtenu : 14,50 $/pi<sup>2</sup>/an; loyer des immeubles comparables sans ces défauts : 16,25 $/pi<sup>2</sup>/an. Hypothèses : TGA de 7,5 %; valeur du terrain <span class="num">380 000 $</span>; valeur totale de la propriété (avant dépréciation fonctionnelle) <span class="num">2 100 000 $</span>.</p>303<ol class="enum"><li>Calculez la perte de loyer annuelle.</li><li>Calculez la dépréciation fonctionnelle incurable de conception.</li><li>Pourquoi ne pas plutôt chiffrer l'installation d'un ascenseur?</li></ol></div></div>304<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>16,25</mn><mo>−</mo><mn>14,50</mn><mo stretchy="false">)</mo><mo>×</mo><mn>12</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>1,75</mn><mo>×</mo><mn>12</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">21</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi><mi mathvariant="bold">/</mi><mi mathvariant="bold">a</mi><mi mathvariant="bold">n</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">(16{,}25 - 14{,}50) \times 12\,000 = 1{,}75 \times 12\,000 =305        \uqogreen{21\,000~\$/an}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">16</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">25</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">14</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">50</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">75</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">21</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$/an</span></span></span></span></span>.</li><li>Perte capitalisée : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>21</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>0,075</mn><mo>=</mo><mn>280</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">21\,000 \div 0{,}075 = 280\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">21</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">075</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">280</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>. Ratio         terrain : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>380</mn><mtext> </mtext><mn>000</mn><mo>÷</mo><mn>2</mn><mtext> </mtext><mn>100</mn><mtext> </mtext><mn>000</mn><mo>≈</mo><mn>18,1</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">380\,000 \div 2\,100\,000 \approx 18{,}1\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">380</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">100</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">18</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>; portion         terrain <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>280</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>18,1</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>≈</mo><mn>50</mn><mtext> </mtext><mn>667</mn></mrow><annotation encoding="application/x-tex">= 280\,000 \times 18{,}1\,\% \approx 50\,667</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">280</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">18</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">667</span></span></span></span>.         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>conception</mtext></msub><mo>=</mo><mn>280</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>50</mn><mtext> </mtext><mn>667</mn><mo>≈</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">229</mn><mtext> </mtext><mn mathvariant="bold">333</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">D_{\text{conception}} = 280\,000 - 50\,667 \approx306        \uqogreen{229\,333~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">conception</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">280</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">667</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">229</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">333</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</li><li>Parce que la déficience est présumée <strong>incurable</strong> : le coût         d'insérer un ascenseur et de refaire la fenestration dans la         structure existante excéderait la valeur ajoutée. On mesure donc la         perte subie (capitalisation), pas un coût de correction que nul         n'engagerait. Si une vérification montrait que la correction coûte         <em>moins</em> que la valeur ajoutée, la déficience basculerait en         curable–substitution et se mesurerait alors par le coût de         correction.</li></ol></div></details>307<div class="box box-exo" id="exo-11-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 11.5</span><span class="box-title">— cas intégrateur — maison d'Aylmer</span><a class="box-anchor" href="#exo-11-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-128">Maison à deux étages (1978), Aylmer (Gatineau) : trois chambres, une salle de bain, garage simple, secteur haut de gamme. Coût de remplacement : <span class="num">350 000 $</span>; terrain : <span class="num">110 000 $</span>. Hypothèses du cas : portion terrain 24 %; TGA de 5,5 % (2026).</p>308<ol class="enum"><li><strong>Ajout</strong> — salle d'eau au rez-de-chaussée : coût dans         l'existant <span class="num">15 000 $</span>; valeur ajoutée <span class="num">20 000 $</span>.</li><li><strong>Substitution</strong> — mazout <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>→</mo></mrow><annotation encoding="application/x-tex">\rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">→</span></span></span></span> thermopompe :         existant <span class="num">22 000 $</span>; neuf <span class="num">9000 $</span>; récupération         <span class="num">300 $</span>.</li><li><strong>Superadéquation</strong> — piscine creusée : coût neuf         <span class="num">65 000 $</span>; dépréciation physique 20 %; contribution         <span class="num">20 000 $</span>.</li><li><strong>Conception</strong> — cuisine fermée : perte de loyer de         175 $/mois.</li></ol>309<p id="p11-133">Calculez la dépréciation fonctionnelle totale et commentez l'ordre de grandeur.</p></div></div>310<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p11-134"><strong>Volet curable.</strong> Salle d'eau : test <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>20</mn><mtext> </mtext><mn>000</mn><mo>&gt;</mo><mn>15</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">20\,000 &gt; 15\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6835em;vertical-align:-0.0391em;"></span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span> curable; dépréciation <span class="num">15 000 $</span> (coût dans l'existant). Chauffage : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>22</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>9</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>300</mn><mo>=</mo><mn>12</mn><mtext> </mtext><mn>700</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">22\,000 - 9\,000 - 300 = 12\,700\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">300</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">700</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Sous-total curable : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">27</mn><mtext> </mtext><mn mathvariant="bold">700</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">\uqogreen{27\,700~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">27</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">700</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</p>311<p id="p11-135"><strong>Volet incurable.</strong> Piscine : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>65</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>13</mn><mtext> </mtext><mn>000</mn><mtext>  </mtext><mo stretchy="false">(</mo><mn>20</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo stretchy="false">)</mo><mo>−</mo><mn>20</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>32</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">65\,000 - 13\,000\;(20\,\%) - 20\,000 = 32\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">65</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">13</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mopen">(</span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">32</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Cuisine fermée : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>175</mn><mo>×</mo><mn>12</mn><mo stretchy="false">)</mo><mo>÷</mo><mn>0,055</mn><mo>=</mo><mn>38</mn><mtext> </mtext><mn>182</mn></mrow><annotation encoding="application/x-tex">(175 \times 12) \div 0{,}055 = 38\,182</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">175</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">12</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">055</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">38</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">182</span></span></span></span>; moins portion terrain 24 % (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>9</mn><mtext> </mtext><mn>164</mn></mrow><annotation encoding="application/x-tex">9\,164</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">164</span></span></span></span>) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>29</mn><mtext> </mtext><mn>018</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 29\,018\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">29</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">018</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Sous-total incurable : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">61</mn><mtext> </mtext><mn mathvariant="bold">018</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">\uqogreen{61\,018~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">61</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">018</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</p>312<p id="p11-136"><strong>Total :</strong></p>313<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><menclose notation="box"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mrow><msub><mi>D</mi><mtext>fonctionnelle</mtext></msub><mo>=</mo><mn>27</mn><mtext> </mtext><mn>700</mn><mo>+</mo><mn>61</mn><mtext> </mtext><mn>018</mn><mo>=</mo><mrow><mtext mathvariant="bold">88</mtext><mtext> </mtext><mtext mathvariant="bold">718</mtext><mtext> </mtext><mtext mathvariant="bold">$</mtext></mrow></mrow></mstyle></mstyle></mstyle></menclose></mrow><annotation encoding="application/x-tex">\boxed{D_{\text{fonctionnelle}} = 27\,700 + 61\,018 = \textbf{88\,718~\$}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.58em;vertical-align:-0.49em;"></span><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.09em;"><span style="top:-3.58em;"><span class="pstrut" style="height:3.58em;"></span><span class="boxpad"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">fonctionnelle</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">27</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">700</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">61</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">018</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord textbf">88</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">718</span><span class="mord textbf nobreak"> </span><span class="mord textbf">$</span></span></span></span></span></span><span style="top:-3.09em;"><span class="pstrut" style="height:3.58em;"></span><span class="katex-stretchy fbox" style="height:1.58em;border-style:solid;border-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.49em;"><span></span></span></span></span></span></span></span></span></span></div>314<p id="p11-137">Ordre de grandeur : environ 25 % du coût de remplacement (<span class="num">350 000 $</span>) — plausible pour une construction de 1978 au plan et aux équipements d'origine dans un secteur haut de gamme exigeant.</p></div></details>315<div class="box box-exo" id="exo-11-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 11.6</span><span class="box-title">— chasse au double comptage</span><a class="box-anchor" href="#exo-11-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-138">Un rapport d'évaluation contient les postes suivants pour une même maison (coût de <em>remplacement</em> retenu comme coût neuf) : (a) ventilation physique : incurable CT sur le système de chauffage au mazout (coût neuf <span class="num">12 000 $</span>, ratio 80 %, soit <span class="num">9600 $</span>); (b) fonctionnelle curable–substitution : remplacement du même chauffage au mazout, <span class="num">14 300 $</span>; (c) fonctionnelle : <span class="num">7500 $</span> pour « matériaux désuets » (revêtements intérieurs d'origine), alors que le coût de remplacement retenu est déjà fondé sur des matériaux modernes; (d) superadéquation d'un foyer de pierre : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>28</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>5</mn><mtext> </mtext><mn>600</mn></mrow><annotation encoding="application/x-tex">28\,000 - 5\,600</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">28</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span></span></span></span> (physique) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>12</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">- 12\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">12</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span> (contribution) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>10</mn><mtext> </mtext><mn>400</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 10\,400\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>, et la même dépréciation physique de <span class="num">5600 $</span> figure aussi dans la ventilation physique générale. Identifiez chaque double comptage et corrigez le total fonctionnel<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>physique en conséquence.</p></div></div>316<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li class="labeled"><span class="li-label">(a)<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>(b)</span><div class="li-body"><strong class="c-rouge">Physique et fonctionnelle</strong> : le chauffage traité         en substitution fonctionnelle ne doit pas aussi porter         <span class="num">9600 $</span> d'incurable CT. On retire <span class="num">9600 $</span> de la         ventilation physique (et l'assiette du long terme doit être         recalculée en conséquence).</div></li><li class="labeled"><span class="li-label">(c)</span><div class="li-body"><strong class="c-rouge">Remplacement et fonctionnelle</strong> : les matériaux         désuets sont déjà éliminés du coût de remplacement; les         <span class="num">7500 $</span> sont retirés.</div></li><li class="labeled"><span class="li-label">(d)</span><div class="li-body"><strong class="c-rouge">Superadéquation et physique</strong> : les <span class="num">5600 $</span> de         dépréciation physique du foyer se comptent une seule fois, dans le         poste superadéquation; on les retire de la ventilation physique         générale.</div></li></ol>317<p id="p11-142">Correction nette : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>9</mn><mtext> </mtext><mn>600</mn><mo>−</mo><mn>7</mn><mtext> </mtext><mn>500</mn><mo>−</mo><mn>5</mn><mtext> </mtext><mn>600</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mo>−</mo><mn mathvariant="bold">22</mn><mtext> </mtext><mn mathvariant="bold">700</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">-9\,600 - 7\,500 - 5\,600 = \uqogreen{-22\,700~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">9</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">7</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.0833em;"></span><span class="mord" style="color:#107C4E;"><span class="mord" style="color:#107C4E;">−</span><span class="mord mathbf" style="color:#107C4E;">22</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">700</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span> sur le total combiné (avant recalcul du long terme). Le rapport initial sous-évaluait la propriété d'au moins <span class="num">22 700 $</span> — l'ampleur typique que peuvent atteindre des doubles comptages non détectés.</p></div></details>318<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 due aux défauts de conception,         de plan, de style ou de fonctionnalité — interne au bâtiment,         indépendante de l'état physique.</li><li><strong>Quatre sources</strong> : manque (absent), inadéquation (désuet),         excès (superadéquation), défaut de conception (plan).</li><li><strong>Test de curabilité</strong> : économique — curable si coût de         correction <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≤</mo></mrow><annotation encoding="application/x-tex">\leq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mrel">≤</span></span></span></span> valeur ajoutée.</li><li><strong>Ajout</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo>=</mo></mrow><annotation encoding="application/x-tex">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:0.0278em;">D</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span></span></span></span> coût d'installation dans l'existant (élément         exclu du coût neuf <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> pénalité complète).</li><li><strong>Substitution</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo>=</mo></mrow><annotation encoding="application/x-tex">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:0.0278em;">D</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span></span></span></span> existant <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> neuf <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> démolition <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>         récupération (la pénalité est le surcoût de rénovation).</li><li><strong>Superadéquation</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo>=</mo></mrow><annotation encoding="application/x-tex">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:0.0278em;">D</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span></span></span></span> coût neuf de l'excédent <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>         dépréciation physique de l'élément <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> contribution au marché;         charges d'exploitation excédentaires capitalisables en sus.</li><li><strong>Conception</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo>=</mo></mrow><annotation encoding="application/x-tex">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:0.0278em;">D</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span></span></span></span> (perte de loyer 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:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span> portion terrain; ratios terrain usuels : banlieue 15–30 %,         urbain dense 30–50 %, industriel 5–15 %.</li><li><strong>Gabarit en 5 étapes</strong> (<em>The Appraisal of Real Estate</em>) :         coût de l'élément <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span> physique déjà comptée <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> correction ou perte         <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> coût au neuf <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> perte fonctionnelle.</li><li><strong>Reproduction vs remplacement</strong> : le remplacement élimine         d'office matériaux désuets et certaines obsolescences — documenter         ce que le coût neuf inclut.</li><li><strong>Formule globale</strong> : somme des quatre catégories, chacune         appuyée sur des données de marché.</li><li><strong>Pièges</strong> : retenir la différence au lieu du coût complet pour         un ajout; oublier la portion terrain dans la capitalisation; les         quatre doubles comptages (physique/fonctionnelle,         remplacement/fonctionnelle, superadéquation/physique,         fonctionnelle/externe).</li></ul></div></section>319      </article>320    </div>321  </div>322  <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>323  324<nav class="ch-pager" aria-label="Navigation entre les séances">325  <a class="prev" href="/seance/10/"><small>← Séance 10</small><b>Dépréciation physique</b></a>326  <a class="next" href="/seance/12/"><small>Séance 12 →</small><b>Dépréciation économique (externe)</b></a>327</nav>328  329<div class="read-tools" role="toolbar" aria-label="Outils de lecture">330  <button type="button" data-action="notes" data-tip="Mes notes et surlignages" aria-pressed="false"><svg class="" aria-hidden="true"><use href="#i-note"/></svg></button>331  <button type="button" data-action="tts" data-tip="Écouter la séance"><svg class="" aria-hidden="true"><use href="#i-audio"/></svg></button>332  <button type="button" data-action="revision" data-tip="Mode 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