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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 10 — Dépréciation physique · IMM1033 — Méthodes du coût en évaluation immobilière</title>7<meta name="description" content="Séance 10 du cours IMM1033 (Méthodes du coût en évaluation immobilière) : Dépréciation physique. 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 10 — Dépréciation physique · IMM1033 — Méthodes du coût en évaluation immobilière">12<meta property="og:description" content="Séance 10 du cours IMM1033 (Méthodes du coût en évaluation immobilière) : Dépréciation physique. 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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="10" data-title="Séance 10 — Dépréciation physique" data-words="9058">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">10</div>101  <div class="ch-hero-inner">102    <div class="eyebrow"><span class="part-chip">Partie IV</span> La dépréciation · Séance 10 · IMM1033</div>103    <h1>Dépréciation physique</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> 5 définitions</span>108      <span class="chip"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg> 6 formules</span>109      <span class="chip"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg> 6 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      <span class="chip"><svg class="" aria-hidden="true"><use href="#i-chart"/></svg> 1 explorateur interactif</span>113      <span class="chip">Annonce du TP3</span>114    </div>115    <div class="ch-tools">116      117      <a class="btn btn-ghost" href="/files/slides/seance10.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-10-1"><span class="n">1</span>La dépréciation physique : nature et causes</a><a href="#s-10-2"><span class="n">2</span>Curable ou incurable : la classification</a><a href="#s-10-3"><span class="n">3</span>La ventilation étape par étape</a><a href="#s-10-4"><span class="n">4</span>Les méthodes d'estimation comparées</a><a href="#s-10-5"><span class="n">5</span>L'inspection du bâtiment</a><a href="#s-10-6"><span class="n">6</span>Cas pratiques intégrés</a><a href="#s-10-7"><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-10-1"><span class="toc-num">10.1</span><span>La dépréciation physique : nature et causes</span></a></li><li class="lvl3"><a href="#s-10-1-1"><span class="toc-num">10.1.1</span><span>Position dans la méthode du coût</span></a></li><li class="lvl3"><a href="#s-10-1-2"><span class="toc-num">10.1.2</span><span>Les trois causes</span></a></li><li class="lvl2"><a href="#s-10-2"><span class="toc-num">10.2</span><span>Curable ou incurable : la classification</span></a></li><li class="lvl3"><a href="#s-10-2-1"><span class="toc-num">10.2.1</span><span>Le test économique de curabilité</span></a></li><li class="lvl3"><a href="#s-10-2-2"><span class="toc-num">10.2.2</span><span>Les trois catégories et l'ordre de calcul</span></a></li><li class="lvl2"><a href="#s-10-3"><span class="toc-num">10.3</span><span>La ventilation étape par étape</span></a></li><li class="lvl3"><a href="#s-10-3-1"><span class="toc-num">10.3.1</span><span>Étape 1 — La dépréciation curable (entretien différé)</span></a></li><li class="lvl3"><a href="#s-10-3-2"><span class="toc-num">10.3.2</span><span>Étape 2 — L'incurable à courte durée de vie</span></a></li><li class="lvl3"><a href="#s-10-3-3"><span class="toc-num">10.3.3</span><span>Étape 3 — L'incurable à longue durée de vie</span></a></li><li class="lvl3"><a href="#s-10-3-4"><span class="toc-num">10.3.4</span><span>Récapitulatif du fil rouge</span></a></li><li class="lvl2"><a href="#s-10-4"><span class="toc-num">10.4</span><span>Les méthodes d'estimation comparées</span></a></li><li class="lvl3"><a href="#s-10-4-1"><span class="toc-num">10.4.1</span><span>La méthode âge-vie simple</span></a></li><li class="lvl3"><a href="#s-10-4-2"><span class="toc-num">10.4.2</span><span>La méthode âge-vie modifiée</span></a></li><li class="lvl3"><a href="#s-10-4-3"><span class="toc-num">10.4.3</span><span>Le coût de remise en état et l'extraction du marché</span></a></li><li class="lvl3"><a href="#s-10-4-4"><span class="toc-num">10.4.4</span><span>Comparaison des résultats</span></a></li><li class="lvl2"><a href="#s-10-5"><span class="toc-num">10.5</span><span>L'inspection du bâtiment</span></a></li><li class="lvl3"><a href="#s-10-5-1"><span class="toc-num">10.5.1</span><span>Le fondement de toute estimation</span></a></li><li class="lvl3"><a href="#s-10-5-2"><span class="toc-num">10.5.2</span><span>La grille d'inspection par système</span></a></li><li class="lvl3"><a href="#s-10-5-3"><span class="toc-num">10.5.3</span><span>L'échelle de condition et l'âge effectif</span></a></li><li class="lvl3"><a href="#s-10-5-4"><span class="toc-num">10.5.4</span><span>La documentation photographique</span></a></li><li class="lvl2"><a href="#s-10-6"><span class="toc-num">10.6</span><span>Cas pratiques intégrés</span></a></li><li class="lvl3"><a href="#s-10-6-1"><span class="toc-num">10.6.1</span><span>Cas 1 — Bungalow de 1975, secteur Hull (Gatineau)</span></a></li><li class="lvl3"><a href="#s-10-6-2"><span class="toc-num">10.6.2</span><span>Cas 2 — Immeuble à revenus de 1990, Gatineau</span></a></li><li class="lvl2"><a href="#s-10-7"><span class="toc-num">10.7</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=10"><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="p10-1">La séance 9 a posé le vocabulaire de la dépréciation : vie économique, vie physique, âge effectif, distinction entre le curable et l'incurable. Nous entrons maintenant dans le premier des trois grands chantiers de mesure, celui de la <span class="motcle" data-term="dépréciation physique">dépréciation physique</span> — la perte de valeur causée par l'usure, le vieillissement et les intempéries. C'est la forme de dépréciation la plus intuitive : tout le monde comprend qu'une toiture de vingt ans vaut moins qu'une toiture neuve. C'est aussi, paradoxalement, celle où les erreurs de méthode sont les plus fréquentes, parce que sa mesure rigoureuse exige une discipline séquentielle stricte : d'abord le curable, ensuite l'incurable à courte durée de vie, enfin l'incurable à longue durée de vie, chaque étape retranchant sa part avant le calcul de la suivante. Ce chapitre développe cette mécanique en détail, la compare aux méthodes plus expéditives (âge-vie simple et modifiée), et l'ancre dans ce qui fonde toute estimation crédible : l'inspection minutieuse du bâtiment.</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-10-1" data-obj="obj-10-1"><span class="obj-text">Définir la dépréciation physique et en identifier les trois causes         (usure, vieillissement, intempéries), en tenant compte du climat         québécois;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-10-2" data-obj="obj-10-2"><span class="obj-text">Distinguer la dépréciation physique <strong>curable</strong> (entretien         différé) de la dépréciation <strong>incurable</strong>, à l'aide du test         économique de curabilité;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-10-3" data-obj="obj-10-3"><span class="obj-text">Classer les composantes d'un bâtiment selon leur durée de vie         (courte ou longue) et estimer leur âge effectif;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-10-4" data-obj="obj-10-4"><span class="obj-text">Appliquer la <strong>méthode de ventilation</strong> (<em>breakdown method</em>)         en trois étapes séquentielles, sans double comptage;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-10-5" data-obj="obj-10-5"><span class="obj-text">Appliquer la méthode <strong>âge-vie</strong> (simple et modifiée) et situer         ses résultats par rapport à ceux de la ventilation;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-10-6" data-obj="obj-10-6"><span class="obj-text">Conduire une <strong>inspection de bâtiment</strong> structurée aux fins de la         dépréciation et documenter les observations;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-10-7" data-obj="obj-10-7"><span class="obj-text">Résoudre des cas complets de dépréciation physique sur des propriétés         résidentielles et locatives québécoises.</span></label></li></ul></div></section>149<h2 id="s-10-1" class="h-section"><span class="h-num">10.1</span><span class="h-text">La dépréciation physique : nature et causes</span><a class="h-anchor" href="#s-10-1" aria-label="Lien vers cette section">#</a></h2>150<h3 id="s-10-1-1" class="h-subsection"><span class="h-num">10.1.1</span><span class="h-text">Position dans la méthode du coût</span><a class="h-anchor" href="#s-10-1-1" aria-label="Lien vers cette section">#</a></h3>151<p id="p10-9">Rappelons l'équation charpente du cours, celle que chaque séance vient raffiner d'un cran : <label for="sn-10-1" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-10-1" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-repere">La méthode du coût : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><msub><mi>V</mi><mi>T</mi></msub><mo>+</mo><mo stretchy="false">(</mo><mtext>CN</mtext><mo>−</mo><mi>D</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">V = V_T + (\text{CN} - D)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.1389em;">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord text"><span class="mord">CN</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="mclose">)</span></span></span></span>. La séance 10 mesure la première composante de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></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></span></span>.</span></p>152<div class="box box-form" id="form-10-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 10.1</span><span class="box-title">— formule fondamentale de la méthode du coût</span><a class="box-anchor" href="#form-10-1" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-10-1"><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><mi>V</mi><mtext>  </mtext><mo>=</mo><mtext>  </mtext><msub><mi>V</mi><mtext>terrain</mtext></msub><mtext>  </mtext><mo>+</mo><mtext>  </mtext><mo fence="true" stretchy="true" minsize="1.2em" maxsize="1.2em">(</mo><mrow><mtext>Co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t neuf</mtext></mrow><mo>−</mo><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 totale</mtext></mrow><mo fence="true" stretchy="true" minsize="1.2em" maxsize="1.2em">)</mo></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(10.1)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">V \;=\; V_{\text{terrain}} \;+\; \bigl(\text{Coût neuf} - \text{Dépréciation totale}\bigr)\tag{10.1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="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:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">terrain</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span 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:1.2em;vertical-align:-0.35em;"></span><span class="mopen"><span class="delimsizing size1">(</span></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 neuf</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.2em;vertical-align:-0.35em;"></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 totale</span></span><span class="mclose"><span class="delimsizing size1">)</span></span></span><span class="katex-tag"><span class="katex-strut" style="height:1.2em;vertical-align:-0.35em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">10.1</span></span><span class="mord">)</span></span></span></span></span></span></div>153<p id="p10-10">où la dépréciation totale se décompose en trois formes :</p>154<div class="eq" id="eq-10-2"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable width="100%"><mtr><mtd width="50%"></mtd><mtd><mrow><msub><mi>D</mi><mtext>totale</mtext></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><msub><mi>D</mi><mtext>physique</mtext></msub><mtext>  </mtext><mo>+</mo><mtext>  </mtext><msub><mi>D</mi><mtext>fonctionnelle</mtext></msub><mtext>  </mtext><mo>+</mo><mtext>  </mtext><msub><mi>D</mi><mrow><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>conomique</mtext></mrow></msub></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(10.2)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">D_{\text{totale}} \;=\; D_{\text{physique}} \;+\; D_{\text{fonctionnelle}} \;+\; D_{\text{économique}}\tag{10.2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">physique</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span 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:0.8333em;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">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:0.2222em;"></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:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord katex-accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight">e</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˊ</span></span></span></span></span></span></span><span class="mord mtight">conomique</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 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">10.2</span></span><span class="mord">)</span></span></span></span></span></span></div></div></div>155<p id="p10-11">La dépréciation physique est la première de ces trois formes, tant dans l'ordre pédagogique (séances 10, 11 et 12) que dans l'ordre de calcul professionnel : on mesure d'abord ce que le bâtiment a perdu par usure matérielle, avant de s'interroger sur ses défauts de conception (séance 11) puis sur les facteurs extérieurs qui l'affectent (séance 12). Cet ordre n'est pas arbitraire — nous verrons au chapitre 11 que la dépréciation fonctionnelle de certains éléments se calcule <em>nette</em> de leur dépréciation physique, ce qui impose de connaître celle-ci en premier.</p>156<div class="box box-def" id="def-10-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 10.1</span><span class="box-title">— dépréciation physique</span><a class="box-anchor" href="#def-10-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-12">La <strong>dépréciation physique</strong> est la perte de valeur des améliorations causée par l'<strong>usure</strong>, le <strong>vieillissement</strong> et l'action des <strong>intempéries</strong> sur les composantes d'un bâtiment. Elle traduit en dollars la détérioration matérielle du bien, indépendamment de sa conception (dépréciation fonctionnelle) et de son environnement (dépréciation économique).</p></div></div>157<p id="p10-13">Avant d'entrer dans la mécanique, il vaut la peine de comprendre ce que la dépréciation physique représente économiquement. Un bâtiment est un stock de capital qui se consomme : chaque année d'occupation transforme une fraction de ce capital en service rendu — abri, confort, revenus locatifs — et cette consommation a un prix que le marché réclame. L'acheteur type qui compare un bâtiment de vingt ans à la possibilité d'en construire un neuf raisonne exactement ainsi : il accepte de payer le coût neuf, <em>moins</em> tout ce qu'il devra débourser pour remettre l'existant à niveau, <em>moins</em> la part de vie déjà consommée des composantes qu'il ne remplacera pas tout de suite. La ventilation que nous allons dérouler n'est rien d'autre que la formalisation de ce raisonnement d'acheteur — c'est ce qui lui donne sa légitimité de marché, et c'est pourquoi ses trois étapes correspondent à trois attitudes de l'acheteur : ce que je répare immédiatement, ce que je remplacerai un jour, ce que je n'aurai jamais à remplacer.</p>158<p id="p10-14">Trois précisions découlent immédiatement de cette définition. Premièrement, la dépréciation physique n'affecte que les <span class="motcle" data-term="améliorations">améliorations</span> : le terrain ne s'use pas au sens de la méthode du coût. Deuxièmement, elle est mesurée par rapport au <strong>coût neuf</strong> estimé (reproduction ou remplacement, selon le choix fait aux séances 5 et 6) : c'est l'écart entre ce que coûterait le bâtiment neuf et ce que vaut le bâtiment usé. Troisièmement, un bâtiment peut être physiquement très déprécié tout en étant fonctionnellement adéquat — et inversement : les trois formes de dépréciation sont conceptuellement indépendantes et se mesurent séparément.</p>159<h3 id="s-10-1-2" class="h-subsection"><span class="h-num">10.1.2</span><span class="h-text">Les trois causes</span><a class="h-anchor" href="#s-10-1-2" aria-label="Lien vers cette section">#</a></h3>160<p id="p10-15"><label for="sn-10-2" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-10-2" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-terme"><strong class="sn-term">usure</strong> détérioration liée à l'utilisation du bâtiment</span> La première cause est l'<strong>usure</strong>, c'est-à-dire la détérioration liée à l'utilisation quotidienne des lieux : la fréquentation abrase les surfaces, les portes et les planchers subissent le frottement, les équipements mécaniques accumulent les heures de fonctionnement. L'usure est proportionnelle à l'intensité d'usage — un duplex loué à des familles s'use plus vite qu'une résidence occupée par un couple retraité, et les espaces communs d'un immeuble locatif plus vite que les logements eux-mêmes.</p>161<p id="p10-16"><label for="sn-10-3" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-10-3" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-terme"><strong class="sn-term">vieillissement</strong> dégradation naturelle des matériaux avec le temps</span> La deuxième cause est le <strong>vieillissement</strong> : même inutilisé, un bâtiment se dégrade. Les matériaux s'oxydent et se corrodent, les composés chimiques des membranes et des scellants se décomposent, les matériaux soumis à des cycles de charge finissent par se fatiguer. Le vieillissement court même lorsque l'usure est nulle — c'est pourquoi un chalet fermé dix ans n'est pas « comme neuf » à la réouverture.</p>162<p id="p10-17">La troisième cause, les <strong>intempéries</strong>, mérite un développement particulier au Québec.</p>163<div class="box box-qc" id="quebec-10-18"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-map"/></svg></span><span class="box-label">le climat québécois, accélérateur de dépréciation</span><a class="box-anchor" href="#quebec-10-18" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-19">Les conditions climatiques du Québec comptent parmi les plus exigeantes en Amérique du Nord pour les bâtiments : amplitude thermique de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>35</mn><mtext> </mtext><msup><mrow></mrow><mo lspace="0em" rspace="0em">∘</mo></msup></mrow><annotation encoding="application/x-tex">-35\,^{\circ}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7574em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">35</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6741em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∘</span></span></span></span></span></span></span></span></span></span></span></span>C à <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo><mn>35</mn><mtext> </mtext><msup><mrow></mrow><mo lspace="0em" rspace="0em">∘</mo></msup></mrow><annotation encoding="application/x-tex">+35\,^{\circ}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7574em;vertical-align:-0.0833em;"></span><span class="mord">+</span><span class="mord">35</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6741em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∘</span></span></span></span></span></span></span></span></span></span></span></span>C, jusqu'à 150 cycles de gel-dégel et plus par année, humidité estivale élevée, charges de neige, verglas et rayonnement UV. Les conséquences se lisent directement sur les grilles d'inspection : fissuration des fondations, dégradation des joints de maçonnerie et écaillage du béton, déformation des revêtements, infiltrations d'eau et moisissures. Concrètement, une même composante (bardeaux d'asphalte, calfeutrage, asphalte de stationnement) a souvent une durée de vie utile plus courte à Gatineau qu'à Vancouver : les tables de durées de vie publiées doivent être <strong>ajustées au climat local</strong>.</p></div></div>164<div class="box box-terrain" id="terrain-10-20"><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-10-20" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-21">Sur le terrain, les trois causes se combinent et se renforcent. Un calfeutrage vieilli (vieillissement) laisse entrer l'eau (intempéries), qui gèle et fissure la maçonnerie, laquelle laisse entrer plus d'eau encore — et le locataire qui claque la porte gonflée d'humidité (usure) achève la quincaillerie. L'évaluateur ne cherche pas à départager la part de chaque cause : il constate un état, estime un âge effectif et chiffre une perte. La décomposition causale sert surtout à <em>comprendre</em> pourquoi deux bâtiments jumeaux peuvent présenter des dépréciations très différentes.</p></div></div>165<h2 id="s-10-2" class="h-section"><span class="h-num">10.2</span><span class="h-text">Curable ou incurable : la classification</span><a class="h-anchor" href="#s-10-2" aria-label="Lien vers cette section">#</a></h2>166<h3 id="s-10-2-1" class="h-subsection"><span class="h-num">10.2.1</span><span class="h-text">Le test économique de curabilité</span><a class="h-anchor" href="#s-10-2-1" aria-label="Lien vers cette section">#</a></h3>167<p id="p10-22">Toute la mécanique de la ventilation repose sur une distinction unique, appliquée item par item : la déficience est-elle <span class="motcle" data-term="curable">curable</span> ou <span class="motcle" data-term="incurable">incurable</span>? <label for="sn-10-4" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-10-4" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-repere">Curable <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo mathvariant="normal">≠</mo></mrow><annotation encoding="application/x-tex">\neq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mrel"><span class="mrel"><span class="mord katex-vbox"><span class="katex-thinbox"><span class="rlap"><span class="katex-strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="katex-inner"><span class="mord"><span class="mrel"></span></span></span><span class="katex-fix"></span></span></span></span></span><span class="mspace nobreak"></span><span class="mrel">=</span></span></span></span></span> réparable. Le test est économique, pas technique.</span></p>168<div class="box box-def" id="def-10-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 10.2</span><span class="box-title">— curabilité (dépréciation physique)</span><a class="box-anchor" href="#def-10-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-23">Un item de dépréciation physique est <strong>curable</strong> lorsque le coût de sa réparation ou de son remplacement est <strong>inférieur ou égal</strong> à l'augmentation de valeur qui en résulterait. Il est <strong>incurable</strong> dans le cas contraire. Formellement :</p>169<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><mtext>Curable</mtext><mtext>  </mtext><mo>⟺</mo><mtext>  </mtext><mrow><mtext>Co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t de r</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>paration</mtext></mrow><mtext>  </mtext><mo>≤</mo><mtext>  </mtext><mrow><mtext>Valeur ajout</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>e r</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>sultante</mtext></mrow></mrow><annotation encoding="application/x-tex">\text{Curable} \iff \text{Coût de réparation} \;\leq\; \text{Valeur ajoutée résultante}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7184em;vertical-align:-0.024em;"></span><span class="mord text"><span class="mord">Curable</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">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 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">paration</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 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 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">sultante</span></span></span></span></span></span></div></div></div>170<div class="box box-att" id="attention-10-24"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">curable ne veut pas dire « réparable »</span><a class="box-anchor" href="#attention-10-24" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-25">Presque tout est techniquement réparable — on peut soulever une maison pour refaire ses fondations. Le test de curabilité est un test de <strong class="c-rouge">rationalité économique</strong> : un acheteur prudent procéderait-il à la réparation dès l'acquisition, parce que la valeur ajoutée égale ou excède le coût? Si oui, l'item est curable et se mesure au <strong>coût de réparation</strong>. Si non, l'item est incurable et se mesure par un <strong>ratio âge-vie</strong>. Aux examens, justifier la classification par ce critère économique, jamais par la seule faisabilité technique.</p></div></div>171<h3 id="s-10-2-2" class="h-subsection"><span class="h-num">10.2.2</span><span class="h-text">Les trois catégories et l'ordre de calcul</span><a class="h-anchor" href="#s-10-2-2" aria-label="Lien vers cette section">#</a></h3>172<p id="p10-26">La dépréciation physique se ventile en trois catégories, dont l'ordre de traitement est impératif :</p>173<div class="center"><div class="tikz"><img src="/assets/fig/f98fb00d32c327a1.svg" alt="Figure" width="418" height="139" style="width:min(100%,607px)" loading="lazy" decoding="async"></div></div>174<p id="p10-27"><label for="sn-10-5" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-10-5" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-terme"><strong class="sn-term">composante à courte vie</strong> élément qui s'use plus vite que le bâtiment (toiture, CVAC, chauffe-eau…)</span> Les composantes à <strong>courte durée de vie</strong> (<em>short-lived</em>) sont celles dont la vie utile est inférieure à celle du bâtiment : elles seront remplacées une ou plusieurs fois pendant la vie de l'immeuble (toiture, chauffe-eau, couvre-planchers, systèmes mécaniques). Les composantes à <strong>longue durée de vie</strong> (<em>long-lived</em>) durent aussi longtemps que le bâtiment lui-même et ne sont jamais remplacées séparément : fondations, charpente, dalle, murs porteurs, ossature du toit, maçonnerie structurale.</p>175<div class="box box-rem" id="remarque-10-28"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pen"/></svg></span><span class="box-label">pourquoi cet ordre est-il obligatoire?</span><a class="box-anchor" href="#remarque-10-28" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-29">Chaque étape retranche sa part de coût avant le calcul de la suivante. Les items curables sont retirés en premier parce que l'acheteur les corrigera immédiatement : les composantes visées ne doivent plus apparaître dans les calculs d'incurable. Les coûts neufs des composantes à courte vie sont ensuite isolés, de sorte que le ratio âge-vie du bâtiment ne s'applique qu'au <strong>résidu</strong> — les composantes structurales. Inverser l'ordre ou omettre une soustraction produit mécaniquement un double comptage.</p></div></div>176<div class="box box-att" id="attention-10-30"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">le piège de la composante en fin de vie</span><a class="box-anchor" href="#attention-10-30" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-31">Une composante à courte vie <strong>complètement usée</strong> (une toiture de 28 ans dont la vie utile était de 25 ans) n'est <em>pas</em> un incurable court terme à 100 % : elle est <strong class="c-rouge">curable</strong>, mesurée au coût de remplacement, parce qu'un acheteur la remplacerait dès l'acquisition. Le ratio âge/vie ne peut jamais excéder 100 % ; s'il l'atteint, l'item change de catégorie. Inversement, la même toiture à 8 ans (ratio <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>8</mn><mi mathvariant="normal">/</mi><mn>25</mn><mo>=</mo><mn>32</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">8/25 = 32\,\%</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">8/25</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">32</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>) est un incurable court terme. <strong class="c-rouge">Jamais les deux à la fois</strong> : c'est la première source de double comptage aux examens.</p></div></div>177<h2 id="s-10-3" class="h-section"><span class="h-num">10.3</span><span class="h-text">La ventilation étape par étape</span><a class="h-anchor" href="#s-10-3" aria-label="Lien vers cette section">#</a></h2>178<p id="p10-32">La <span class="motcle" data-term="méthode de ventilation">méthode de ventilation</span> (<em>breakdown method</em>) est le standard professionnel de mesure de la dépréciation physique : chaque catégorie est chiffrée séparément, avec ses propres données. Nous la déroulons ici sur un exemple fil rouge — un bungalow de <span class="num">1200</span> pi<sup>2</sup> construit en 1985 à Gatineau, coût de remplacement à neuf de <span class="num">350 000 $</span>, âge effectif de 20 ans, vie économique de 60 ans (hypothèse du cas, cohérente avec la table maîtresse de la séance 9 : résidentiel, 45 à 70 ans).</p>179<h3 id="s-10-3-1" class="h-subsection"><span class="h-num">10.3.1</span><span class="h-text">Étape 1 — La dépréciation curable (entretien différé)</span><a class="h-anchor" href="#s-10-3-1" aria-label="Lien vers cette section">#</a></h3>180<div class="box box-def" id="def-10-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 10.3</span><span class="box-title">— entretien différé</span><a class="box-anchor" href="#def-10-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-33">La dépréciation physique curable correspond à l'<strong>entretien différé</strong> (<em>deferred maintenance</em>) : l'ensemble des réparations et remplacements que l'acheteur type effectuerait immédiatement après l'acquisition, parce que leur coût est égal ou inférieur à la valeur qu'ils ajoutent. Elle se mesure au <strong>coût de réparation au prix du marché</strong>.</p></div></div>181<div class="box box-form" id="form-10-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 10.2</span><span class="box-title">— dépréciation physique curable</span><a class="box-anchor" href="#form-10-2" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-10-3"><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><mrow><msub><mi>D</mi><mtext>curable</mtext></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mrow><mtext>Co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t de r</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>paration</mtext></mrow><mi>i</mi></msub><mspace width="2em"/><mrow><mtext>(items d’entretien diff</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>)</mtext></mrow></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(10.3)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">D_{\text{curable}} \;=\; \sum_{i=1}^{n} \text{Coût de réparation}_i182\qquad \text{(items d&#x27;entretien différé)}\tag{10.3}</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">curable</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.9291em;vertical-align:-1.2777em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6514em;"><span style="top:-1.8723em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.05em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2777em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord text"><span class="mord">Co</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">u</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˆ</span></span></span></span></span></span></span><span class="mord">t de 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">paration</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2175em;"><span style="top:-2.4559em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:2em;"></span><span class="mord text"><span class="mord">(items d’entretien diff</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">)</span></span></span><span class="katex-tag"><span class="katex-strut" style="height:2.9291em;vertical-align:-1.2777em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">10.3</span></span><span class="mord">)</span></span></span></span></span></span></div></div></div>183<p id="p10-34">Les items curables sont visibles à l'inspection : peinture écaillée, bardeaux recroquevillés, fenêtres thermos embuées, robinetterie qui fuit, calfeutrage fissuré, gouttières déformées. Le tableau <a class="xref" href="#tab-ch10-tab-curables-typiques">10.1</a> donne les fourchettes de coûts observées pour une résidence unifamiliale type au Québec (main-d'œuvre et matériaux, 2025–2026).</p>184<figure class="float-table" id="tab-ch10-tab-curables-typiques"><figcaption><span class="fig-label">Tableau 10.1</span> Items d'entretien différé courants au Québec et fourchettes de coûts (résidence unifamiliale type, 2025–2026).</figcaption><div class="table-wrap"><table class="tbl"><thead><tr><th>Item d'entretien différé</th><th>Signe d'usure</th><th class="al-r">Coût estimé</th></tr></thead><tbody><tr><td>Peinture intérieure</td><td>Écaillage, jaunissement</td><td class="al-r">4 000 – 8 000 $</td></tr><tr><td>Toiture (bardeaux d'asphalte)</td><td>Bardeaux recroquevillés</td><td class="al-r">8 000 – 18 000 $</td></tr><tr><td>Fenêtres thermos embuées</td><td>Condensation entre vitres</td><td class="al-r">500 – 1 200 $/fen.</td></tr><tr><td>Robinetterie qui fuit</td><td>Gouttes, taches de rouille</td><td class="al-r">200 – 600 $/unité</td></tr><tr><td>Plancher usé</td><td>Rayures, décoloration</td><td class="al-r">3 – 8 $/pi<sup>2</sup></td></tr><tr><td>Calfeutrage extérieur</td><td>Fissures, décollement</td><td class="al-r">1 500 – 4 000 $</td></tr><tr><td>Revêtement extérieur dégradé</td><td>Écaillage, pourriture</td><td class="al-r">10 000 – 25 000 $</td></tr><tr><td>Gouttières endommagées</td><td>Fuites, déformation</td><td class="al-r">1 500 – 4 000 $</td></tr></tbody></table></div></figure>185<h5 class="para-title">L'estimation des coûts de réparation.</h5>186<p id="p10-35">Le coût retenu est le <strong>coût du marché</strong>, pas le coût de bricolage : il inclut la main-d'œuvre au taux courant, les matériaux, les frais connexes, les taxes applicables (TPS/TVQ) et les permis municipaux lorsque requis, avec un ajustement pour les conditions locales (les coûts de Gatineau ne sont pas ceux de Montréal). Les sources sont, par ordre de fiabilité décroissante pour un item précis : les soumissions d'entrepreneurs locaux, les guides de coûts publiés (RSMeans, Altus, Marshall &amp; Swift <span class="citation">(<a class="cite" href="/bibliographie/#rsmeans2025" data-cite="rsmeans2025">RSMeans, 2025</a>; <a class="cite" href="/bibliographie/#altus2026" data-cite="altus2026">Altus Group, 2026</a>; <a class="cite" href="/bibliographie/#marshallswift2025" data-cite="marshallswift2025">Marshall &amp;amp; Swift, 2025</a>)</span>), l'expérience professionnelle de l'évaluateur et les données historiques de réparation. <label for="sn-10-6" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-10-6" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-repere">Coût de réparation d'un item <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo mathvariant="normal">≠</mo></mrow><annotation encoding="application/x-tex">\neq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mrel"><span class="mrel"><span class="mord katex-vbox"><span class="katex-thinbox"><span class="rlap"><span class="katex-strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="katex-inner"><span class="mord"><span class="mrel"></span></span></span><span class="katex-fix"></span></span></span></span></span><span class="mspace nobreak"></span><span class="mrel">=</span></span></span></span></span> coût de remplacement à neuf de la composante complète.</span></p>187<div class="box box-att" id="attention-10-36"><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-10-36" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-37">Ne pas confondre le <strong>coût de réparation</strong> d'un item avec le <strong>coût de remplacement à neuf</strong> de la composante complète. Repeindre les murs coûte <span class="num">6500 $</span>; ce n'est pas le coût « peinture » complet du bordereau de coût neuf. La confusion gonfle artificiellement la dépréciation curable.</p></div></div>188<div class="box box-ex" id="ex-10-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 10.1</span><span class="box-title">— bungalow de Gatineau — entretien différé</span><a class="box-anchor" href="#ex-10-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-38">L'inspection du bungalow fil rouge (<span class="num">1200</span> pi<sup>2</sup>, 1985) révèle sept items d'entretien différé :</p>189<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th class="al-r">#</th><th>Item curable identifié</th><th class="al-r">Coût estimé</th></tr></thead><tbody><tr><td class="al-r">1</td><td>Peinture intérieure complète (murs et plafonds)</td><td class="al-r">6 500 $</td></tr><tr><td class="al-r">2</td><td>Remplacement des bardeaux de toiture</td><td class="al-r">12 000 $</td></tr><tr><td class="al-r">3</td><td>4 fenêtres thermos embuées (à 800 $/fen.)</td><td class="al-r">3 200 $</td></tr><tr><td class="al-r">4</td><td>Robinetterie cuisine et salle de bain</td><td class="al-r">1 800 $</td></tr><tr><td class="al-r">5</td><td>Plancher de cuisine (vinyle décollé, 120 pi<sup>2</sup>)</td><td class="al-r">1 440 $</td></tr><tr><td class="al-r">6</td><td>Calfeutrage extérieur portes et fenêtres</td><td class="al-r">2 200 $</td></tr><tr><td class="al-r">7</td><td>Gouttières et descentes pluviales</td><td class="al-r">2 500 $</td></tr><tr class="rule-above"><td class="al-r"></td><td><strong>Total dépréciation physique curable</strong></td><td class="al-r"><strong>29 640 $</strong></td></tr></tbody></table></div></div>190<p id="p10-39">Chaque item doit passer le test de curabilité. La vérification, appuyée sur les données de marché du secteur, confirme que la valeur ajoutée excède le coût pour chacun : peinture (<span class="num">8000 $</span> contre <span class="num">6500 $</span>), toiture (<span class="num">14 000 $</span> contre <span class="num">12 000 $</span>), fenêtres (<span class="num">4500 $</span> contre <span class="num">3200 $</span>), robinetterie (<span class="num">2000 $</span> contre <span class="num">1800 $</span>), plancher (<span class="num">2500 $</span> contre <span class="num">1440 $</span>), calfeutrage (<span class="num">3000 $</span> contre <span class="num">2200 $</span>), gouttières (<span class="num">3000 $</span> contre <span class="num">2500 $</span>). La dépréciation physique curable totale est donc de <strong class="c-vert">29 640 $</strong>.</p></div></div>191<p id="p10-40">Remarquez que la toiture, en fin de vie, est classée curable au coût de remplacement (<span class="num">12 000 $</span>) : elle ne réapparaîtra pas à l'étape 2. C'est l'application directe de la règle anti-double-comptage.</p>192<div class="widget" data-widget="ventilation"></div>193<h3 id="s-10-3-2" class="h-subsection"><span class="h-num">10.3.2</span><span class="h-text">Étape 2 — L'incurable à courte durée de vie</span><a class="h-anchor" href="#s-10-3-2" aria-label="Lien vers cette section">#</a></h3>194<div class="box box-def" id="def-10-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 10.4</span><span class="box-title">— dépréciation incurable court terme</span><a class="box-anchor" href="#def-10-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-41">La dépréciation incurable <strong>court terme</strong> (<em>short-lived</em>) frappe les composantes dont la durée de vie utile est <strong>inférieure</strong> à celle du bâtiment, mais dont le remplacement n'est <strong>pas encore économiquement justifiable</strong> au moment de l'évaluation : la composante n'est pas en fin de vie, elle est simplement partiellement consommée.</p></div></div>195<p id="p10-42">Quatre traits caractérisent ces composantes : elles ne sont pas en fin de vie (sinon elles seraient curables), leur durée de vie est déterminable et finie, elles s'usent plus vite que la structure principale, et leur dépréciation est proportionnelle au ratio « âge effectif sur durée de vie utile ».</p>196<div class="box box-form" id="form-10-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 10.3</span><span class="box-title">— incurable court terme, par composante</span><a class="box-anchor" href="#form-10-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-43">Pour chaque composante <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.854em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.0572em;">j</span></span></span></span> à courte durée de vie non classée curable :</p>197<div class="eq" id="eq-10-4"><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><mrow><mtext>CT</mtext><mo separator="true">,</mo><mi>j</mi></mrow></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><msub><mrow><mtext>Co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t neuf</mtext></mrow><mi>j</mi></msub><mo>×</mo><mfrac><msub><mrow><mover accent="true"><mtext>A</mtext><mo>ˆ</mo></mover><mtext>ge effectif</mtext></mrow><mi>j</mi></msub><msub><mrow><mtext>Dur</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>e de vie utile</mtext></mrow><mi>j</mi></msub></mfrac><mo separator="true">,</mo><mspace width="2em"/><mfrac><msub><mrow><mover accent="true"><mtext>A</mtext><mo>ˆ</mo></mover><mtext>ge effectif</mtext></mrow><mi>j</mi></msub><msub><mrow><mtext>Dur</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>e de vie</mtext></mrow><mi>j</mi></msub></mfrac><mo>≤</mo><mn>100</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(10.4)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">D_{\text{CT},j} \;=\; \text{Coût neuf}_j \times198\frac{\text{Âge effectif}_j}{\text{Durée de vie utile}_j},199\qquad \frac{\text{Âge effectif}_j}{\text{Durée de vie}_j} \leq 100\,\%\tag{10.4}</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:0.3283em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">CT</span></span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.0572em;">j</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:0.9805em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord text"><span class="mord">Co</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">u</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˆ</span></span></span></span></span></span></span><span class="mord">t neuf</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.0572em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.6891em;vertical-align:-0.9721em;"></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:1.717em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord text"><span class="mord">Dur</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 vie utile</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.0572em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.7702em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord text"><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9468em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">A</span></span><span style="top:-3.2523em;"><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">ge effectif</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2175em;"><span style="top:-2.4559em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.0572em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3802em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9721em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:2em;"></span><span class="mspace" style="margin-right:0.1667em;"></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:1.717em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord text"><span class="mord">Dur</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 vie</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.0572em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.7702em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord text"><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9468em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">A</span></span><span style="top:-3.2523em;"><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">ge effectif</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2175em;"><span style="top:-2.4559em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.0572em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3802em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9721em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">100</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span><span class="katex-tag"><span class="katex-strut" style="height:2.6891em;vertical-align:-0.9721em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">10.4</span></span><span class="mord">)</span></span></span></span></span></span></div></div></div>200<p id="p10-44">Le calcul exige donc, pour chaque composante : son <strong>coût neuf</strong> (tiré du bordereau des séances 6–8), sa <strong>durée de vie utile</strong> et son <strong>âge effectif</strong>. Le tableau <a class="xref" href="#tab-ch10-tab-durees-vie">10.2</a> rassemble les durées de vie typiques, ajustées pour le climat québécois.</p>201<figure class="float-table" id="tab-ch10-tab-durees-vie"><figcaption><span class="fig-label">Tableau 10.2</span> Durées de vie typiques des composantes à courte durée de vie (sources : tables d'espérance de vie Marshall &amp; Swift, SCHL, InterNACHI; durées ajustées pour le climat québécois).</figcaption><div class="table-wrap"><table class="tbl"><thead><tr><th>Composante</th><th class="al-c">Durée de vie (ans)</th><th>Catégorie</th></tr></thead><tbody><tr><td>Peinture intérieure</td><td class="al-c">5 – 10</td><td>Très courte</td></tr><tr><td>Chauffe-eau</td><td class="al-c">10 – 15</td><td>Courte</td></tr><tr><td>Couvre-plancher (tapis, vinyle)</td><td class="al-c">10 – 20</td><td>Courte</td></tr><tr><td>Système CVAC</td><td class="al-c">15 – 25</td><td>Moyenne</td></tr><tr><td>Toiture (bardeaux d'asphalte)</td><td class="al-c">20 – 30</td><td>Moyenne</td></tr><tr><td>Plomberie (accessoires)</td><td class="al-c">20 – 30</td><td>Moyenne</td></tr><tr><td>Cuisine et salle de bain</td><td class="al-c">20 – 30</td><td>Moyenne</td></tr><tr><td>Revêtement extérieur</td><td class="al-c">25 – 35</td><td>Longue</td></tr><tr><td>Fenêtres</td><td class="al-c">25 – 40</td><td>Longue</td></tr><tr><td>Système électrique</td><td class="al-c">30 – 40</td><td>Longue</td></tr></tbody></table></div></figure>202<h5 class="para-title">L'âge effectif des composantes.</h5>203<p id="p10-45"><label for="sn-10-7" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-10-7" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-terme"><strong class="sn-term">âge effectif</strong> âge apparent d'une composante compte tenu de son état et de son entretien, distinct de l'âge chronologique</span> L'âge effectif d'une composante peut différer de l'âge du bâtiment — et de son propre âge chronologique. Une composante rénovée ou remplacée a un âge effectif inférieur à l'âge du bâtiment; une composante mal entretenue peut avoir un âge effectif supérieur à son âge réel. Trois illustrations : un bâtiment de 40 ans dont la toiture a été refaite il y a 5 ans (âge effectif de la toiture : <strong>5 ans</strong>); un bâtiment de 20 ans au CVAC mal entretenu (âge effectif du CVAC : <strong>25 ans</strong>); un bâtiment de 30 ans à la cuisine rénovée il y a 8 ans (âge effectif de la cuisine : <strong>8 ans</strong>).</p>204<div class="box box-terrain" id="terrain-10-46"><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-10-46" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-47">L'historique des rénovations est aussi précieux que l'inspection elle-même : demandez systématiquement au propriétaire les <strong>reçus de travaux</strong> (toiture, chauffe-eau, fenêtres, rénovations de cuisine). Un reçu daté transforme une estimation d'âge effectif en donnée vérifiable — et protège l'évaluateur si son estimation est contestée. En l'absence de reçus, les plaques signalétiques des équipements (chauffe-eau, thermopompe, panneau électrique) donnent l'année de fabrication.</p></div></div>205<div class="box box-ex" id="ex-10-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 10.2</span><span class="box-title">— calcul pour une composante : le système CVAC</span><a class="box-anchor" href="#ex-10-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-48">Le CVAC du bungalow fil rouge a un coût neuf de <span class="num">18 000 $</span>, une durée de vie utile de 20 ans et un âge effectif de 12 ans.</p>206<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>D</mi><mtext>CVAC</mtext></msub><mo>=</mo><mn>18</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>×</mo><mfrac><mn>12</mn><mn>20</mn></mfrac><mo>=</mo><mn>18</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>×</mo><mn>0,60</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">10</mn><mtext> </mtext><mn mathvariant="bold">800</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">D_{\text{CVAC}} = 18\,000\,\$ \times \frac{12}{20}207              = 18\,000\,\$ \times 0{,}60 = \uqogreen{10\,800~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">CVAC</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.0833em;"></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:0.1667em;"></span><span class="mord">$</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">20</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">12</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.0833em;"></span><span class="mord">18</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">60</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">10</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">800</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span></span></div>208<p id="p10-49">Interprétation : 60 % de la vie utile est consommée, il reste 8 ans de vie. La valeur résiduelle de la composante est de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>18</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>10</mn><mtext> </mtext><mn>800</mn><mo>=</mo><mn>7200</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">18\,000 - 10\,800 =2097200\,\$</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">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">10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">7200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>.</p></div></div>210<p id="p10-50">Le même calcul, répété pour chacune des composantes à courte vie du bungalow (en excluant les items déjà classés curables à l'étape 1), donne le tableau <a class="xref" href="#tab-ch10-tab-ct-filrouge">10.3</a>.</p>211<figure class="float-table" id="tab-ch10-tab-ct-filrouge"><figcaption><span class="fig-label">Tableau 10.3</span> Ventilation, étape 2 — incurable court terme du bungalow fil rouge (montants arrondis au dollar; items curables de l'étape 1 exclus).</figcaption><div class="table-wrap"><table class="tbl table-wide"><thead><tr><th>Composante</th><th class="al-r">Coût neuf</th><th class="al-c">Âge / Vie</th><th class="al-r">%</th><th class="al-r">Dépréc.</th></tr></thead><tbody><tr><td>Toiture</td><td class="al-r">15 000 $</td><td class="al-c">8 / 25</td><td class="al-r">32,0</td><td class="al-r">4 800 $</td></tr><tr><td>Couvre-planchers</td><td class="al-r">12 000 $</td><td class="al-c">10 / 18</td><td class="al-r">55,6</td><td class="al-r">6 667 $</td></tr><tr><td>Peinture intérieure</td><td class="al-r">5 000 $</td><td class="al-c">4 / 8</td><td class="al-r">50,0</td><td class="al-r">2 500 $</td></tr><tr><td>Plomberie (accessoires)</td><td class="al-r">8 000 $</td><td class="al-c">12 / 25</td><td class="al-r">48,0</td><td class="al-r">3 840 $</td></tr><tr><td>Chauffe-eau</td><td class="al-r">3 500 $</td><td class="al-c">7 / 12</td><td class="al-r">58,3</td><td class="al-r">2 042 $</td></tr><tr><td>CVAC</td><td class="al-r">18 000 $</td><td class="al-c">12 / 20</td><td class="al-r">60,0</td><td class="al-r">10 800 $</td></tr><tr><td>Revêtement extérieur</td><td class="al-r">22 000 $</td><td class="al-c">12 / 30</td><td class="al-r">40,0</td><td class="al-r">8 800 $</td></tr><tr><td>Fenêtres</td><td class="al-r">20 000 $</td><td class="al-c">12 / 30</td><td class="al-r">40,0</td><td class="al-r">8 000 $</td></tr><tr><td>Cuisine / salle de bain</td><td class="al-r">25 000 $</td><td class="al-c">15 / 25</td><td class="al-r">60,0</td><td class="al-r">15 000 $</td></tr><tr><td>Système électrique</td><td class="al-r">10 000 $</td><td class="al-c">12 / 35</td><td class="al-r">34,3</td><td class="al-r">3 429 $</td></tr><tr class="rule-above"><td><strong>Total</strong></td><td class="al-r"><strong>138 500 $</strong></td><td class="al-c"></td><td class="al-r"></td><td class="al-r"><strong>65 878 $</strong></td></tr></tbody></table></div></figure>212<div class="box box-rem" id="remarque-10-51"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pen"/></svg></span><span class="box-label">pourquoi conserver deux totaux?</span><a class="box-anchor" href="#remarque-10-51" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-52">L'étape 2 produit <strong>deux</strong> totaux, et les deux servent : la <strong class="c-bleu">dépréciation court terme</strong> (<span class="num">65 878 $</span>) entre dans la dépréciation totale; le <strong class="c-bleu">total des coûts neufs des composantes CT</strong> (<span class="num">138 500 $</span>) sert à isoler le résidu de l'étape 3. Omettre le second total est l'erreur mécanique la plus fréquente dans les copies : le ratio long terme s'applique alors à une assiette trop large, et la dépréciation est surestimée.</p></div></div>213<p id="p10-53">Le lecteur attentif notera que la « toiture » figure à la fois dans l'exemple curable (remplacement à <span class="num">12 000 $</span>) et au tableau court terme (ratio <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>8</mn><mi mathvariant="normal">/</mi><mn>25</mn></mrow><annotation encoding="application/x-tex">8/25</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">8/25</span></span></span></span>). Il s'agit de <em>deux scénarios pédagogiques distincts</em> du même poste : dans un dossier réel, une composante est dans l'une <strong>ou</strong> l'autre catégorie, jamais les deux. Si la toiture réelle est en fin de vie, elle est curable et disparaît de l'étape 2; si elle a 8 ans, elle est en étape 2 et disparaît de l'étape 1.</p>214<h3 id="s-10-3-3" class="h-subsection"><span class="h-num">10.3.3</span><span class="h-text">Étape 3 — L'incurable à longue durée de vie</span><a class="h-anchor" href="#s-10-3-3" aria-label="Lien vers cette section">#</a></h3>215<div class="box box-def" id="def-10-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 10.5</span><span class="box-title">— dépréciation incurable long terme</span><a class="box-anchor" href="#def-10-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-54">La dépréciation incurable <strong>long terme</strong> (<em>long-lived</em>) frappe les composantes dont la durée de vie égale ou excède celle du bâtiment : les éléments structuraux et permanents (fondations, charpente, dalle, murs porteurs, colonnes et poutres, ossature du toit, isolation structurale, maçonnerie structurale). Ces composantes ne sont jamais remplacées séparément : elles durent aussi longtemps que le bâtiment lui-même.</p></div></div>216<div class="box box-form" id="form-10-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 10.4</span><span class="box-title">— incurable long terme — formule résiduelle</span><a class="box-anchor" href="#form-10-4" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-10-5"><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>LT</mtext></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><munder><munder><mrow><mo fence="true" stretchy="true" minsize="1.8em" maxsize="1.8em">(</mo><mrow><mtext>Co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t total</mtext></mrow><mo>−</mo><msub><mi>D</mi><mtext>curable</mtext></msub><mo>−</mo><mstyle scriptlevel="0" displaystyle="false"><mo>∑</mo><mrow><mtext>Co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>ts neufs CT</mtext></mrow><mo fence="true" stretchy="true" minsize="1.8em" maxsize="1.8em">)</mo></mstyle></mrow><mo stretchy="true">⏟</mo></munder><mrow><mtext>co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t r</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>siduel (composantes </mtext><mover accent="true"><mtext>a</mtext><mo>ˋ</mo></mover><mtext> longue vie)</mtext></mrow></munder><mo>×</mo><mfrac><msub><mrow><mover accent="true"><mtext>A</mtext><mo>ˆ</mo></mover><mtext>ge effectif</mtext></mrow><mrow><mtext>b</mtext><mover accent="true"><mtext>a</mtext><mo>ˆ</mo></mover><mtext>timent</mtext></mrow></msub><mrow><mtext>Dur</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>e de vie </mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>conomique</mtext></mrow></mfrac></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(10.5)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">D_{\text{LT}} \;=\; \underbrace{\Bigl(\text{Coût total} - D_{\text{curable}}217- \textstyle\sum \text{Coûts neufs CT}\Bigr)}_{\text{coût résiduel (composantes à longue vie)}}218\times \frac{\text{Âge effectif}_{\text{bâtiment}}}{\text{Durée de vie économique}}\tag{10.5}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">LT</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="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:3.348em;vertical-align:-2.198em;"></span><span class="minner munder"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.15em;"><span style="top:-1.127em;"><span class="pstrut" style="height:3.15em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">co</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">u</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˆ</span></span></span></span></span></span></span><span class="mord mtight">t r</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">siduel (composantes </span><span class="mord katex-accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight">a</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˋ</span></span></span></span></span></span></span><span class="mord mtight"> longue vie)</span></span></span></span></span><span style="top:-3.15em;"><span class="pstrut" style="height:3.15em;"></span><span class="minner munder"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.15em;"><span class="svg-align" style="top:-1.852em;"><span class="pstrut" style="height:3.15em;"></span><span class="katex-stretchy" style="height:0.548em;min-width:1.6em;"><span class="brace-left" style="height:0.548em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="0.548em" viewBox="0 0 400000 548" preserveAspectRatio="xMinYMin slice"><path d="M0 6l6-6h17c12.688 0 19.313.3 20 1 4 4 7.313 8.3 10 13219 35.313 51.3 80.813 93.8 136.5 127.5 55.688 33.7 117.188 55.8 184.5 66.5.688220 0 2 .3 4 1 18.688 2.7 76 4.3 172 5h399450v120H429l-6-1c-124.688-8-235-61.7221-331-161C60.687 138.7 32.312 99.3 7 54L0 41V6z"/></svg></span><span class="brace-center" style="height:0.548em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="0.548em" viewBox="0 0 400000 548" preserveAspectRatio="xMidYMin slice"><path d="M199572 214222c100.7 8.3 195.3 44 280 108 55.3 42 101.7 93 139 153l9 14c2.7-4 5.7-8.7 9-14223 53.3-86.7 123.7-153 211-199 66.7-36 137.3-56.3 212-62h199568v120H200432c-178.3224 11.7-311.7 78.3-403 201-6 8-9.7 12-11 12-.7.7-6.7 1-18 1s-17.3-.3-18-1c-1.3 0225-5-4-11-12-44.7-59.3-101.3-106.3-170-141s-145.3-54.3-229-60H0V214z"/></svg></span><span class="brace-right" style="height:0.548em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="0.548em" viewBox="0 0 400000 548" preserveAspectRatio="xMaxYMin slice"><path d="M399994 0l6 6v35l-6 11c-56 104-135.3 181.3-238 232-57.3226 28.7-117 45-179 50H-300V214h399897c43.3-7 81-15 113-26 100.7-33 179.7-91 237227-174 2.7-5 6-9 10-13 .7-1 7.3-1 20-1h17z"/></svg></span></span></span><span style="top:-3.15em;"><span class="pstrut" style="height:3.15em;"></span><span class="mord"><span class="mopen"><span class="delimsizing size2">(</span></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 total</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">curable</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="mspace" style="margin-right:0.1667em;"></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">ts neufs CT</span></span><span class="mclose"><span class="delimsizing size2">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.298em;"><span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.198em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.5042em;vertical-align:-0.8804em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6238em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Dur</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 vie </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">conomique</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"><span class="mord text"><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9468em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">A</span></span><span style="top:-3.2523em;"><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">ge effectif</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.242em;"><span style="top:-2.4559em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">b</span><span class="mord katex-accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight">a</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˆ</span></span></span></span></span></span></span><span class="mord mtight">timent</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="katex-tag"><span class="katex-strut" style="height:3.8218em;vertical-align:-2.198em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">10.5</span></span><span class="mord">)</span></span></span></span></span></span></div>228<p id="p10-55">L'âge effectif et la durée de vie sont ici ceux du <strong>bâtiment global</strong>, non d'une composante.</p></div></div>229<p id="p10-56">Le calcul en trois temps pour le bungalow fil rouge :</p>230<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t r</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>siduel</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>350</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>29</mn><mtext> </mtext><mn>640</mn><mo>−</mo><mn>138</mn><mtext> </mtext><mn>500</mn><mo>=</mo><mrow><mtext mathvariant="bold">181</mtext><mtext> </mtext><mtext mathvariant="bold">860</mtext><mtext> </mtext><mtext mathvariant="bold">$</mtext></mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>D</mi><mtext>LT</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>181</mn><mtext> </mtext><mn>860</mn><mo>×</mo><mfrac><mn>20</mn><mn>60</mn></mfrac><mo>=</mo><mrow><mtext mathvariant="bold">60</mtext><mtext> </mtext><mtext mathvariant="bold">620</mtext><mtext> </mtext><mtext mathvariant="bold">$</mtext></mrow></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Coût résiduel} &amp;= 350\,000 - 29\,640 - 138\,500 = \textbf{181\,860\,\$} \\231D_{\text{LT}} &amp;= 181\,860 \times \frac{20}{60} = \textbf{60\,620\,\$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:3.5074em;vertical-align:-1.5037em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0037em;"><span style="top:-4.4852em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord text"><span class="mord">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 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">siduel</span></span></span></span><span style="top:-2.5037em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">LT</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5037em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0037em;"><span style="top:-4.4852em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">350</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">29</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">640</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">138</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord textbf">181</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">860</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">$</span></span></span></span><span style="top:-2.5037em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">181</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">860</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">60</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">20</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord textbf">60</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">620</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">$</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5037em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>232<p id="p10-57">Le résidu de <span class="num">181 860 $</span> représente les fondations, la charpente et les autres éléments structuraux — tout ce qui n'a été ni réparé (étape 1) ni compté comme composante à courte vie (étape 2). Le ratio <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>20</mn><mi mathvariant="normal">/</mi><mn>60</mn></mrow><annotation encoding="application/x-tex">20/60</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">20/60</span></span></span></span> traduit le fait que le bâtiment, à 20 ans d'âge effectif sur une vie économique de 60 ans, a consommé le tiers de sa structure.</p>233<h3 id="s-10-3-4" class="h-subsection"><span class="h-num">10.3.4</span><span class="h-text">Récapitulatif du fil rouge</span><a class="h-anchor" href="#s-10-3-4" aria-label="Lien vers cette section">#</a></h3>234<div class="box box-ex" id="ex-10-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 10.3</span><span class="box-title">— dépréciation physique totale du bungalow fil rouge</span><a class="box-anchor" href="#ex-10-3" aria-label="Lien">#</a></div><div class="box-body"><div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Catégorie</th><th class="al-r">Montant</th><th class="al-r">% du coût</th></tr></thead><tbody><tr><td>Curable (entretien différé)</td><td class="al-r">29 640 $</td><td class="al-r">8,5 %</td></tr><tr><td>Incurable court terme</td><td class="al-r">65 878 $</td><td class="al-r">18,8 %</td></tr><tr><td>Incurable long terme</td><td class="al-r">60 620 $</td><td class="al-r">17,3 %</td></tr><tr class="rule-above"><td><strong>Dépréciation physique totale</strong></td><td class="al-r"><strong>156 138 $</strong></td><td class="al-r"><strong>44,6 %</strong></td></tr></tbody></table></div></div>235<p id="p10-58">La valeur dépréciée des améliorations, au titre de la seule dépréciation physique, est de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>350</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>156</mn><mtext> </mtext><mn>138</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">193</mn><mtext> </mtext><mn mathvariant="bold">862</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">350\,000 - 156\,138 = \uqogreen{193\,862~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">350</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">156</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">138</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: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;">193</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">862</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>. Restent à mesurer les dépréciations fonctionnelle (chapitre 11) et économique (chapitre 12) avant d'ajouter la valeur du terrain.</p></div></div>236<div class="center"><div class="tikz"><img src="/assets/fig/4ffb5b31228f3474.svg" alt="Figure" width="418" height="177" style="width:min(100%,607px)" loading="lazy" decoding="async"></div></div>237<h2 id="s-10-4" class="h-section"><span class="h-num">10.4</span><span class="h-text">Les méthodes d'estimation comparées</span><a class="h-anchor" href="#s-10-4" aria-label="Lien vers cette section">#</a></h2>238<p id="p10-59">La ventilation n'est pas la seule voie, et il serait naïf de croire que tout mandat justifie son déploiement complet : chiffrer composante par composante un bungalow pour une opinion préliminaire de financement, c'est facturer au client une précision qu'il n'a pas demandée. La pratique reconnaît quatre familles de méthodes, qui se distinguent par leur précision et leur coût d'analyse — et le choix entre elles est lui-même une décision professionnelle, qui doit être divulguée dans le rapport et proportionnée à l'usage prévu de l'évaluation. Le tableau <a class="xref" href="#tab-ch10-tab-methodes">10.4</a> les met en regard avant que nous les déroulions une à une sur le fil rouge, ce qui permettra de constater — chiffres à l'appui — que le choix de méthode peut déplacer la dépréciation de plus de dix points de pourcentage.</p>239<figure class="float-table" id="tab-ch10-tab-methodes"><figcaption><span class="fig-label">Tableau 10.4</span> Les méthodes d'estimation de la dépréciation physique.</figcaption><div class="table-wrap"><table class="tbl"><thead><tr><th>Méthode</th><th class="al-c">Précision</th><th class="al-c">Complexité</th><th>Usage</th></tr></thead><tbody><tr><td>Âge-vie (observation)</td><td class="al-c">Moyenne</td><td class="al-c">Faible</td><td>Estimation rapide, préliminaire</td></tr><tr><td>Ventilation (<em>breakdown</em>)</td><td class="al-c">Élevée</td><td class="al-c">Élevée</td><td>Analyse détaillée, standard professionnel</td></tr><tr><td>Coût de remise en état</td><td class="al-c">Variable</td><td class="al-c">Moyenne</td><td>Cas spécifiques, assurances</td></tr><tr><td>Extraction du marché</td><td class="al-c">Élevée</td><td class="al-c">Moyenne</td><td>Vérification croisée</td></tr></tbody></table></div></figure>240<h3 id="s-10-4-1" class="h-subsection"><span class="h-num">10.4.1</span><span class="h-text">La méthode âge-vie simple</span><a class="h-anchor" href="#s-10-4-1" aria-label="Lien vers cette section">#</a></h3>241<div class="box box-form" id="form-10-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 10.5</span><span class="box-title">— méthode âge-vie</span><a class="box-anchor" href="#form-10-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-60">Un ratio unique appliqué au coût de remplacement total :</p>242<div class="eq" id="eq-10-6"><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><mrow><msub><mi>D</mi><mtext>physique</mtext></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><mrow><mtext>Co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t neuf</mtext></mrow><mo>×</mo><mfrac><mrow><mover accent="true"><mtext>A</mtext><mo>ˆ</mo></mover><mtext>ge effectif</mtext></mrow><mrow><mtext>Dur</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>e de vie </mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>conomique</mtext></mrow></mfrac></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(10.6)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">D_{\text{physique}} \;=\; \text{Coût neuf} \times243\frac{\text{Âge effectif}}{\text{Durée de vie économique}}\tag{10.6}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">physique</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span 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:0.7778em;vertical-align:-0.0833em;"></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 neuf</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.5042em;vertical-align:-0.8804em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6238em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Dur</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 vie </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">conomique</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 katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9468em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">A</span></span><span style="top:-3.2523em;"><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">ge effectif</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="katex-tag"><span class="katex-strut" style="height:2.5042em;vertical-align:-0.8804em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">10.6</span></span><span class="mord">)</span></span></span></span></span></span></div></div></div>244<p id="p10-61">Sur le fil rouge : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo>=</mo><mn>350</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>20</mn><mi mathvariant="normal">/</mi><mn>60</mn><mo>=</mo><mn>116</mn><mtext> </mtext><mn>667</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">D = 350\,000 \times 20/60 = 116\,667\,\$</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">350</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">20/60</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">116</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">667</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. La ventilation donnait <span class="num">156 138 $</span> : l'âge-vie simple <strong class="c-rouge">sous-estime</strong> ici la dépréciation de près de 40 000 $. La raison est structurelle : le ratio unique suppose que toutes les composantes s'usent au rythme moyen du bâtiment, alors que les composantes à courte vie (toiture, CVAC, cuisine) sont proportionnellement bien plus consommées que la structure. Plus le bâtiment contient d'entretien différé et de composantes mécaniques âgées, plus l'écart se creuse.</p>245<h3 id="s-10-4-2" class="h-subsection"><span class="h-num">10.4.2</span><span class="h-text">La méthode âge-vie modifiée</span><a class="h-anchor" href="#s-10-4-2" aria-label="Lien vers cette section">#</a></h3>246<p id="p10-62">L'amélioration classique consiste à traiter l'entretien différé <strong>séparément</strong>, puis à appliquer le ratio âge-vie sur le solde :</p>247<div class="box box-form" id="form-10-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 10.6</span><span class="box-title">— méthode âge-vie modifiée</span><a class="box-anchor" href="#form-10-6" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-10-7"><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>totale</mtext></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><msub><mi>D</mi><mtext>curable</mtext></msub><mo>+</mo><mo fence="true" stretchy="true" minsize="1.2em" maxsize="1.2em">(</mo><mrow><mtext>Co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t neuf</mtext></mrow><mo>−</mo><msub><mi>D</mi><mtext>curable</mtext></msub><mo fence="true" stretchy="true" minsize="1.2em" maxsize="1.2em">)</mo><mo>×</mo><mfrac><mrow><mover accent="true"><mtext>A</mtext><mo>ˆ</mo></mover><mtext>ge effectif</mtext></mrow><mrow><mtext>Dur</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>e de vie </mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>conomique</mtext></mrow></mfrac></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(10.7)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">D_{\text{totale}} \;=\; D_{\text{curable}} +248\bigl(\text{Coût neuf} - D_{\text{curable}}\bigr) \times249\frac{\text{Âge effectif}}{\text{Durée de vie économique}}\tag{10.7}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="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:0.8333em;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">curable</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.2em;vertical-align:-0.35em;"></span><span class="mopen"><span class="delimsizing size1">(</span></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 neuf</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.2em;vertical-align:-0.35em;"></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">curable</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="mclose"><span class="delimsizing size1">)</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.5042em;vertical-align:-0.8804em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6238em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Dur</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 vie </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">conomique</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 katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9468em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">A</span></span><span style="top:-3.2523em;"><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">ge effectif</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="katex-tag"><span class="katex-strut" style="height:2.5042em;vertical-align:-0.8804em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">10.7</span></span><span class="mord">)</span></span></span></span></span></span></div></div></div>250<p id="p10-63">Sur le fil rouge : curable mesuré directement <span class="num">29 640 $</span>; solde <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>350</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>29</mn><mtext> </mtext><mn>640</mn><mo>=</mo><mn>320</mn><mtext> </mtext><mn>360</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">350\,000 - 29\,640 = 320\,360\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">350</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">29</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">640</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">320</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">360</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; incurable <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>320</mn><mtext> </mtext><mn>360</mn><mo>×</mo><mn>20</mn><mi mathvariant="normal">/</mi><mn>60</mn><mo>=</mo><mn>106</mn><mtext> </mtext><mn>787</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">320\,360 \times 20/60 =251106\,787\,\$</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">320</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">360</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">20/60</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">106</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">787</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; total <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>29</mn><mtext> </mtext><mn>640</mn><mo>+</mo><mn>106</mn><mtext> </mtext><mn>787</mn><mo>=</mo><mn>136</mn><mtext> </mtext><mn>427</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">29\,640 + 106\,787 = 136\,427\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">29</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">640</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">106</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">787</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">136</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">427</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Plus précise que l'âge-vie simple (l'entretien différé est mesuré, non moyenné), mais toujours en deçà de la ventilation, faute de distinguer les composantes à courte vie.</p>252<h3 id="s-10-4-3" class="h-subsection"><span class="h-num">10.4.3</span><span class="h-text">Le coût de remise en état et l'extraction du marché</span><a class="h-anchor" href="#s-10-4-3" aria-label="Lien vers cette section">#</a></h3>253<p id="p10-64">La méthode du <span class="motcle" data-term="coût de remise en état">coût de remise en état</span> estime le coût nécessaire pour remettre le bâtiment dans un état équivalent au neuf; la dépréciation physique correspond à ce coût. Intuitive, concrète, fondée sur des coûts réels et utile pour les assurances, elle bute sur les composantes structurales (que coûte la « remise à neuf » d'une fondation de 40 ans qui fonctionne parfaitement?), tend à surestimer la dépréciation et exige une expertise en construction; elle demeure peu utilisée en évaluation courante.</p>254<p id="p10-65">L'<span class="motcle" data-term="extraction du marché">extraction du marché</span>, que nous retrouverons au chapitre 12 sous la forme des ventes appariées, consiste à déduire la dépréciation observée des ventes de bâtiments comparables : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo>=</mo><mrow><mtext>Co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t neuf</mtext></mrow><mo>+</mo><msub><mi>V</mi><mtext>terrain</mtext></msub><mo>−</mo><mtext>Prix de vente</mtext></mrow><annotation encoding="application/x-tex">D = \text{Coût neuf} + V_{\text{terrain}}255- \text{Prix de vente}</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:0.7778em;vertical-align:-0.0833em;"></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 neuf</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">terrain</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6944em;"></span><span class="mord text"><span class="mord">Prix de vente</span></span></span></span></span>. Elle sert surtout de <strong>vérification croisée</strong> de la ventilation.</p>256<h3 id="s-10-4-4" class="h-subsection"><span class="h-num">10.4.4</span><span class="h-text">Comparaison des résultats</span><a class="h-anchor" href="#s-10-4-4" aria-label="Lien vers cette section">#</a></h3>257<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Méthode</th><th class="al-r">Dépréc. physique</th><th class="al-r">% du coût</th></tr></thead><tbody><tr><td>Âge-vie simple</td><td class="al-r">116 667 $</td><td class="al-r">33,3 %</td></tr><tr><td>Âge-vie modifiée</td><td class="al-r">136 427 $</td><td class="al-r">39,0 %</td></tr><tr><td>Ventilation (<em>breakdown</em>)</td><td class="al-r">156 138 $</td><td class="al-r">44,6 %</td></tr></tbody></table></div></div>258<div class="box box-att" id="attention-10-66"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">des écarts de 10 à 15 points</span><a class="box-anchor" href="#attention-10-66" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-67">Sur un même bâtiment, l'écart entre la méthode la plus simple et la plus détaillée atteint ici plus de 11 points de pourcentage — près de <span class="num">40 000 $</span>. Le choix de méthode n'est donc pas neutre : il doit être divulgué et justifié dans le rapport. L'OEAQ privilégie la <strong>ventilation</strong> en évaluation détaillée; l'âge-vie demeure acceptable en estimation préliminaire ou lorsque le mandat le justifie <span class="citation">(<a class="cite" href="/bibliographie/#oeaqNormes" data-cite="oeaqNormes">Ordre des évaluateurs agréés du Québec, 2024</a>)</span>.</p></div></div>259<div class="box box-qc" id="quebec-10-68"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-map"/></svg></span><span class="box-label">Contexte québécois</span><a class="box-anchor" href="#quebec-10-68" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-69">En évaluation municipale québécoise, les organismes évaluateurs travaillant sous la <em>Loi sur la fiscalité municipale</em> utilisent massivement des variantes calibrées de l'âge-vie (tables de classes de condition appliquées à des bordereaux normalisés), parce qu'il faut évaluer des dizaines de milliers d'unités. En mandat privé (financement, expropriation, litige), la ventilation détaillée s'impose : le client paie pour la précision, et le rapport doit résister à la contre-expertise.</p></div></div>260<h2 id="s-10-5" class="h-section"><span class="h-num">10.5</span><span class="h-text">L'inspection du bâtiment</span><a class="h-anchor" href="#s-10-5" aria-label="Lien vers cette section">#</a></h2>261<h3 id="s-10-5-1" class="h-subsection"><span class="h-num">10.5.1</span><span class="h-text">Le fondement de toute estimation</span><a class="h-anchor" href="#s-10-5-1" aria-label="Lien vers cette section">#</a></h3>262<p id="p10-70">Toutes les formules de ce chapitre consomment des données d'entrée — items curables, âges effectifs, états de composantes — qui proviennent d'une seule source : l'<span class="motcle" data-term="inspection">inspection</span>. Sans inspection minutieuse, la ventilation la plus élégante n'est qu'un exercice théorique. <label for="sn-10-8" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-10-8" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-repere">Pas de dépréciation crédible sans inspection documentée.</span></p>263<p id="p10-71">L'inspection poursuit quatre objectifs : déterminer l'<strong>état réel</strong> de chaque composante; identifier les items d'<strong>entretien différé</strong> et estimer les <strong>âges effectifs</strong>; détecter les <strong>problèmes cachés</strong> (infiltrations, moisissures); et <strong>documenter</strong> l'état par photographies.</p>264<p id="p10-72">Concrètement, une visite bien conduite suit toujours le même trajet. On commence par l'extérieur, en faisant le tour complet du bâtiment dans le sens des aiguilles d'une montre : les fondations d'abord (fissures, efflorescence, pente du terrain vers ou hors du bâtiment), puis l'enveloppe façade par façade, la toiture depuis le sol ou l'échelle, les gouttières, les balcons. On entre ensuite par le sous-sol — c'est là que le bâtiment avoue ses secrets : traces d'eau sur la dalle, cernes au bas des murs, odeur d'humidité, état de la structure apparente, plaques signalétiques du chauffe-eau et du panneau. On remonte enfin pièce par pièce, en ouvrant les robinets, en actionnant les fenêtres, en notant l'état des finitions. La visite d'un bungalow demande une heure à une heure et demie; celle d'un immeuble à revenus, une demi-journée avec l'accès aux logements. Le réflexe du débutant est de photographier ce qui est beau; celui du professionnel est de photographier ce qui coûtera de l'argent.</p>265<div class="box box-att" id="attention-10-73"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">responsabilité professionnelle</span><a class="box-anchor" href="#attention-10-73" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-74">L'évaluateur agréé a l'obligation déontologique de procéder à une inspection <strong>raisonnable</strong> et de rapporter ses observations dans le rapport d'évaluation. Une dépréciation estimée « du trottoir » expose l'évaluateur à la responsabilité professionnelle si la valeur conclue s'avère erronée en raison d'un vice qu'une inspection normale aurait révélé.</p></div></div>266<h3 id="s-10-5-2" class="h-subsection"><span class="h-num">10.5.2</span><span class="h-text">La grille d'inspection par système</span><a class="h-anchor" href="#s-10-5-2" aria-label="Lien vers cette section">#</a></h3>267<p id="p10-75">L'inspection se structure par systèmes du bâtiment; pour chaque élément, on note l'état sur une échelle simple (bon — acceptable — mauvais — critique) et on consigne les indices d'âge effectif.</p>268<figure class="float-table" id="tab-ch10-tab-grille"><figcaption><span class="fig-label">Tableau 10.5</span> Grille d'inspection synthétique par système.</figcaption><div class="table-wrap"><table class="tbl"><thead><tr><th>Système</th><th>Points de vérification</th></tr></thead><tbody><tr><td>Fondations</td><td>Fissures (largeur, direction, évolution); infiltrations au sous-sol; efflorescence (dépôts blancs); mouvement ou affaissement</td></tr><tr><td>Structure et dalle</td><td>Niveau des planchers (déflexion); état des poutres et colonnes; pourriture du bois; fissures et humidité de la dalle</td></tr><tr><td>Toiture</td><td>Revêtement (bardeaux, membrane); solins et étanchéité; ventilation de l'entretoit; gouttières et descentes pluviales</td></tr><tr><td>Enveloppe et isolation</td><td>Revêtement extérieur (brique, vinyle, bois); joints de maçonnerie et calfeutrage; portes et fenêtres; isolant, pare-vapeur, ponts thermiques</td></tr><tr><td>Plomberie et CVAC</td><td>Tuyauterie (matériau, fuites, corrosion); chauffe-eau (âge, capacité); chauffage et climatisation (type, âge, état); ventilation, échangeur d'air, conduits</td></tr><tr><td>Électricité</td><td>Panneau (capacité, état); câblage (cuivre ou aluminium); prises et interrupteurs; mise à la terre et protection</td></tr><tr><td>Finitions intérieures</td><td>Peinture, fissures, taches, moisissures; gypse (dommages d'eau); couvre-planchers (type, usure, niveau); cuisine et salle de bain (armoires, comptoirs, carrelage); portes et fenêtres (fonctionnement, étanchéité, quincaillerie)</td></tr></tbody></table></div></figure>269<div class="box box-att" id="attention-10-76"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">vigilance — bâtiments anciens</span><a class="box-anchor" href="#attention-10-76" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-77">Deux signaux exigent une attention immédiate dans le parc ancien québécois : le câblage en <strong class="c-rouge">aluminium</strong> (installations antérieures à 1977, risque d'échauffement aux connexions, assurabilité restreinte) et la tuyauterie en <strong class="c-rouge">plomb</strong> ou en <strong class="c-rouge">fonte</strong> (santé, obstructions, remplacement coûteux). Leur présence affecte à la fois la dépréciation physique et, souvent, la dépréciation fonctionnelle (substitution requise, chapitre 11). Porter aussi une attention particulière aux dommages des cycles gel-dégel sur la maçonnerie et le béton.</p></div></div>270<h3 id="s-10-5-3" class="h-subsection"><span class="h-num">10.5.3</span><span class="h-text">L'échelle de condition et l'âge effectif</span><a class="h-anchor" href="#s-10-5-3" aria-label="Lien vers cette section">#</a></h3>271<p id="p10-78">L'échelle de condition relie l'observation qualitative à l'estimation quantitative de l'âge effectif du bâtiment.</p>272<figure class="float-table" id="tab-ch10-tab-condition"><figcaption><span class="fig-label">Tableau 10.6</span> Échelle de condition du bâtiment et ratio âge effectif / âge chronologique.</figcaption><div class="table-wrap"><table class="tbl"><thead><tr><th class="al-c">Note</th><th>Condition</th><th class="al-c">Âge eff./chron.</th><th>Description</th></tr></thead><tbody><tr><td class="al-c">1</td><td>Excellent</td><td class="al-c"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>&lt;</mo></mrow><annotation encoding="application/x-tex">&lt;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">&lt;</span></span></span></span> 50 %</td><td>Neuf ou rénové récemment</td></tr><tr><td class="al-c">2</td><td>Bon</td><td class="al-c">50 – 75 %</td><td>Bien entretenu, usure mineure</td></tr><tr><td class="al-c">3</td><td>Moyen</td><td class="al-c">75 – 100 %</td><td>Usure normale, entretien adéquat</td></tr><tr><td class="al-c">4</td><td>Acceptable</td><td class="al-c">100 – 125 %</td><td>Entretien différé visible</td></tr><tr><td class="al-c">5</td><td>Médiocre</td><td class="al-c">125 – 175 %</td><td>Détérioration importante</td></tr><tr><td class="al-c">6</td><td>Mauvais</td><td class="al-c"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>&gt;</mo></mrow><annotation encoding="application/x-tex">&gt;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">&gt;</span></span></span></span> 175 %</td><td>Réparations majeures requises</td></tr></tbody></table></div></figure>273<div class="box box-ex" id="ex-10-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 10.4</span><span class="box-title">— de la condition à l'âge effectif</span><a class="box-anchor" href="#ex-10-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-79">Un bâtiment de 30 ans jugé en condition « excellent » (note 1, ratio inférieur à 50 %) pourrait se voir attribuer un âge effectif de seulement 15 ans; le même bâtiment en condition « acceptable » (note 4, ratio de 100 à 125 %) recevrait un âge effectif de 30 à 37 ans. L'échelle discipline le jugement : elle force l'évaluateur à relier son estimation d'âge effectif à des observations documentées plutôt qu'à une impression générale.</p></div></div>274<h3 id="s-10-5-4" class="h-subsection"><span class="h-num">10.5.4</span><span class="h-text">La documentation photographique</span><a class="h-anchor" href="#s-10-5-4" aria-label="Lien vers cette section">#</a></h3>275<p id="p10-80">La documentation visuelle appuie les conclusions de dépréciation dans le rapport. À l'extérieur : les quatre façades, la toiture (si accessible), les fondations visibles, l'aménagement et les structures annexes, et chaque déficience identifiée. À l'intérieur : chaque pièce, le sous-sol complet, les systèmes mécaniques (chauffage, chauffe-eau, CVAC), le panneau électrique et les plaques signalétiques des équipements, et chaque déficience notée.</p>276<div class="box box-terrain" id="terrain-10-81"><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-10-81" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-82">Prenez des photos <strong>datées</strong> et <strong>géolocalisées</strong>, et conservez les fichiers originaux au dossier d'évaluation. La plaque signalétique photographiée d'un chauffe-eau vaut mieux qu'une note manuscrite : elle établit l'année de fabrication sans contestation possible. En cas de litige — une contestation d'évaluation municipale, par exemple — le dossier photographique est souvent la pièce qui départage les experts.</p></div></div>277<h2 id="s-10-6" class="h-section"><span class="h-num">10.6</span><span class="h-text">Cas pratiques intégrés</span><a class="h-anchor" href="#s-10-6" aria-label="Lien vers cette section">#</a></h2>278<h3 id="s-10-6-1" class="h-subsection"><span class="h-num">10.6.1</span><span class="h-text">Cas 1 — Bungalow de 1975, secteur Hull (Gatineau)</span><a class="h-anchor" href="#s-10-6-1" aria-label="Lien vers cette section">#</a></h3>279<div class="box box-ex" id="ex-10-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 10.5</span><span class="box-title">— ventilation complète d'un bungalow de 1975</span><a class="box-anchor" href="#ex-10-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-83"><strong>Description.</strong> Bungalow de <span class="num">1100</span> pi<sup>2</sup> construit en 1975 (51 ans en 2026), sous-sol aménagé, terrain de <span class="num">8000</span> pi<sup>2</sup>, secteur Hull à Gatineau. Fondations en béton coulé, structure de bois (2<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>4), revêtement de brique, chauffage électrique, toiture refaite en 2014.</p>280<p id="p10-84"><strong>Données d'évaluation.</strong> Coût de remplacement à neuf : <span class="num">285 000 $</span>; âge chronologique : 51 ans; âge effectif estimé : <strong>30 ans</strong> (rénovations partielles); hypothèse du cas : vie économique de <strong>65 ans</strong> (cohérente avec la table maîtresse de la séance 9 : résidentiel, 45 à 70 ans selon le type de construction).</p>281<p id="p10-85"><strong>Étape 1 — curable.</strong> L'inspection identifie six items d'entretien différé :</p>282<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th class="al-r">#</th><th>Item curable</th><th class="al-r">Coût répar.</th></tr></thead><tbody><tr><td class="al-r">1</td><td>Peinture intérieure complète</td><td class="al-r">5 500 $</td></tr><tr><td class="al-r">2</td><td>Calfeutrage extérieur (portes et fenêtres)</td><td class="al-r">2 800 $</td></tr><tr><td class="al-r">3</td><td>Plancher du sous-sol (carreaux décollés, 500 pi<sup>2</sup>)</td><td class="al-r">3 000 $</td></tr><tr><td class="al-r">4</td><td>Robinetterie de salle de bain (2 robinets)</td><td class="al-r">900 $</td></tr><tr><td class="al-r">5</td><td>Gouttières arrière déformées</td><td class="al-r">1 200 $</td></tr><tr><td class="al-r">6</td><td>Joint de brique fissuré (façade sud)</td><td class="al-r">3 500 $</td></tr><tr class="rule-above"><td class="al-r"></td><td><strong>Total dépréciation curable</strong></td><td class="al-r"><strong>16 900 $</strong></td></tr></tbody></table></div></div>283<p id="p10-86"><strong>Étape 2 — incurable court terme.</strong> Dix composantes à courte vie, chacune au ratio âge effectif / durée de vie :</p>284<div class="center"><div class="table-wrap"><table class="tbl table-wide"><thead><tr><th>Composante</th><th class="al-r">Coût neuf</th><th class="al-c">Âge / Vie</th><th class="al-r">%</th><th class="al-r">Dépréc.</th></tr></thead><tbody><tr><td>Toiture (refaite 2014)</td><td class="al-r">14 000 $</td><td class="al-c">12 / 25</td><td class="al-r">48,0</td><td class="al-r">6 720 $</td></tr><tr><td>Couvre-planchers (RDC)</td><td class="al-r">8 500 $</td><td class="al-c">15 / 20</td><td class="al-r">75,0</td><td class="al-r">6 375 $</td></tr><tr><td>Peinture extérieure</td><td class="al-r">4 000 $</td><td class="al-c">6 / 10</td><td class="al-r">60,0</td><td class="al-r">2 400 $</td></tr><tr><td>Plomberie (accessoires)</td><td class="al-r">6 000 $</td><td class="al-c">20 / 25</td><td class="al-r">80,0</td><td class="al-r">4 800 $</td></tr><tr><td>Chauffe-eau</td><td class="al-r">2 800 $</td><td class="al-c">8 / 12</td><td class="al-r">66,7</td><td class="al-r">1 867 $</td></tr><tr><td>Chauffage électrique</td><td class="al-r">10 000 $</td><td class="al-c">18 / 25</td><td class="al-r">72,0</td><td class="al-r">7 200 $</td></tr><tr><td>Fenêtres</td><td class="al-r">18 000 $</td><td class="al-c">20 / 30</td><td class="al-r">66,7</td><td class="al-r">12 000 $</td></tr><tr><td>Panneau électrique</td><td class="al-r">8 000 $</td><td class="al-c">25 / 35</td><td class="al-r">71,4</td><td class="al-r">5 714 $</td></tr><tr><td>Cuisine (armoires, comptoirs)</td><td class="al-r">15 000 $</td><td class="al-c">20 / 25</td><td class="al-r">80,0</td><td class="al-r">12 000 $</td></tr><tr><td>Salle de bain</td><td class="al-r">10 000 $</td><td class="al-c">22 / 25</td><td class="al-r">88,0</td><td class="al-r">8 800 $</td></tr><tr class="rule-above"><td><strong>Total</strong></td><td class="al-r"><strong>96 300 $</strong></td><td class="al-c"></td><td class="al-r"></td><td class="al-r"><strong>67 876 $</strong></td></tr></tbody></table></div></div>285<p id="p10-87">Noter l'âge effectif de la toiture : 12 ans (refaite en 2014), et non 51 ans — illustration directe de l'utilité des reçus de travaux.</p>286<p id="p10-88"><strong>Étape 3 — incurable long terme.</strong></p>287<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t r</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>siduel</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>285</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>16</mn><mtext> </mtext><mn>900</mn><mo>−</mo><mn>96</mn><mtext> </mtext><mn>300</mn><mo>=</mo><mrow><mtext mathvariant="bold">171</mtext><mtext> </mtext><mtext mathvariant="bold">800</mtext><mtext> </mtext><mtext mathvariant="bold">$</mtext></mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>D</mi><mtext>LT</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>171</mn><mtext> </mtext><mn>800</mn><mo>×</mo><mfrac><mn>30</mn><mn>65</mn></mfrac><mo>=</mo><mn>171</mn><mtext> </mtext><mn>800</mn><mo>×</mo><mn>46,2</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mrow><mtext mathvariant="bold">79</mtext><mtext> </mtext><mtext mathvariant="bold">292</mtext><mtext> </mtext><mtext mathvariant="bold">$</mtext></mrow></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Coût résiduel} &amp;= 285\,000 - 16\,900 - 96\,300 = \textbf{171\,800\,\$} \\288D_{\text{LT}} &amp;= 171\,800 \times \frac{30}{65} = 171\,800 \times 46{,}2\,\%289             = \textbf{79\,292\,\$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:3.5074em;vertical-align:-1.5037em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0037em;"><span style="top:-4.4852em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord text"><span class="mord">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 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">siduel</span></span></span></span><span style="top:-2.5037em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">LT</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5037em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0037em;"><span style="top:-4.4852em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">285</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">900</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">96</span><span class="mspace" style="margin-right:0.1667em;"></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 class="mord text"><span class="mord textbf">171</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">$</span></span></span></span><span style="top:-2.5037em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">171</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">65</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">30</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">171</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">46</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span 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">79</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">292</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">$</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5037em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>290<p id="p10-89">Le résidu couvre les fondations, la charpente et les murs porteurs, l'ossature du toit, l'isolation structurale et la maçonnerie de brique.</p>291<p id="p10-90"><strong>Synthèse.</strong></p>292<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Catégorie</th><th class="al-r">Montant</th><th class="al-r">% du coût</th></tr></thead><tbody><tr><td>Curable (entretien différé)</td><td class="al-r">16 900 $</td><td class="al-r">5,9 %</td></tr><tr><td>Incurable court terme</td><td class="al-r">67 876 $</td><td class="al-r">23,8 %</td></tr><tr><td>Incurable long terme</td><td class="al-r">79 292 $</td><td class="al-r">27,8 %</td></tr><tr class="rule-above"><td><strong>Dépréciation physique totale</strong></td><td class="al-r"><strong>164 068 $</strong></td><td class="al-r"><strong>57,6 %</strong></td></tr></tbody></table></div></div>293<p id="p10-91">Valeur dépréciée des améliorations : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>285</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>164</mn><mtext> </mtext><mn>068</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">120</mn><mtext> </mtext><mn mathvariant="bold">932</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">285\,000 - 164\,068 =294\uqogreen{120\,932~\$}</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">285</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span 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">164</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">068</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: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;">120</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">932</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>. Contrôle de cohérence : 57,6 % de dépréciation physique est plausible pour un bâtiment de 51 ans (âge effectif 30 ans) dont la part long terme atteint 46,2 % (ratio 30/65).</p></div></div>295<h3 id="s-10-6-2" class="h-subsection"><span class="h-num">10.6.2</span><span class="h-text">Cas 2 — Immeuble à revenus de 1990, Gatineau</span><a class="h-anchor" href="#s-10-6-2" aria-label="Lien vers cette section">#</a></h3>296<div class="box box-ex" id="ex-10-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 10.6</span><span class="box-title">— immeuble de 6 logements — ventilation condensée</span><a class="box-anchor" href="#ex-10-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-92"><strong>Description et données.</strong> Immeuble de 6 logements construit en 1990 (36 ans en 2026), <span class="num">6000</span> pi<sup>2</sup> habitables, structure béton/acier, toiture membrane. Coût de remplacement : <span class="num">950 000 $</span>; âge effectif : 25 ans; entretien différé constaté : <span class="num">42 000 $</span>; coûts neufs des composantes à courte vie : <span class="num">310 000 $</span> (ratio moyen de dépréciation CT de 52 %); hypothèse du cas : vie économique de <strong>55 ans</strong> (cohérent avec la table maîtresse : multilogements, 45 à 65 ans).</p>297<p id="p10-93"><strong>Calcul par ventilation.</strong></p>298<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Curable</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mrow><mtext mathvariant="bold">42</mtext><mtext> </mtext><mtext mathvariant="bold">000</mtext><mtext> </mtext><mtext mathvariant="bold">$</mtext></mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Incurable CT</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>310</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,52</mn><mo>=</mo><mrow><mtext mathvariant="bold">161</mtext><mtext> </mtext><mtext mathvariant="bold">200</mtext><mtext> </mtext><mtext mathvariant="bold">$</mtext></mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>R</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>sidu LT</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>950</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>42</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>310</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>598</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Incurable LT</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>598</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mfrac><mn>25</mn><mn>55</mn></mfrac><mo>=</mo><mrow><mtext mathvariant="bold">271</mtext><mtext> </mtext><mtext mathvariant="bold">818</mtext><mtext> </mtext><mtext mathvariant="bold">$</mtext></mrow></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Curable} &amp;= \textbf{42\,000\,\$} \\299\text{Incurable CT} &amp;= 310\,000 \times 0{,}52 = \textbf{161\,200\,\$} \\300\text{Résidu LT} &amp;= 950\,000 - 42\,000 - 310\,000 = 598\,000\,\$ \\301\text{Incurable LT} &amp;= 598\,000 \times \frac{25}{55} = \textbf{271\,818\,\$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:6.5074em;vertical-align:-3.0037em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5037em;"><span style="top:-5.9852em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord text"><span class="mord">Curable</span></span></span></span><span style="top:-4.4852em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord text"><span class="mord">Incurable CT</span></span></span></span><span style="top:-2.9852em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord text"><span class="mord">R</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">sidu LT</span></span></span></span><span style="top:-1.0037em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord text"><span class="mord">Incurable LT</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.0037em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5037em;"><span style="top:-5.9852em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord textbf">42</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">$</span></span></span></span><span style="top:-4.4852em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">310</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</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">52</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord textbf">161</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">$</span></span></span></span><span style="top:-2.9852em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">950</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">42</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">310</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">598</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-1.0037em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">598</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">55</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">25</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord textbf">271</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">818</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">$</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.0037em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>302<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><menclose notation="box"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mrow><msub><mi>D</mi><mtext>totale</mtext></msub><mo>=</mo><mn>42</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>161</mn><mtext> </mtext><mn>200</mn><mo>+</mo><mn>271</mn><mtext> </mtext><mn>818</mn><mo>=</mo><mrow><mtext mathvariant="bold">475</mtext><mtext> </mtext><mtext mathvariant="bold">018</mtext><mtext> </mtext><mtext mathvariant="bold">$</mtext></mrow><mspace width="1em"/><mo stretchy="false">(</mo><mn>50,0</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo stretchy="false">)</mo></mrow></mstyle></mstyle></mstyle></menclose></mrow><annotation encoding="application/x-tex">\boxed{D_{\text{totale}} = 42\,000 + 161\,200 + 271\,818303     = \textbf{475\,018\,\$} \quad (50{,}0\,\%)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.68em;vertical-align:-0.59em;"></span><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.09em;"><span style="top:-3.68em;"><span class="pstrut" style="height:3.68em;"></span><span class="boxpad"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">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 class="mord">161</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">271</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">818</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord textbf">475</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">018</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">$</span></span><span class="mspace" style="margin-right:1em;"></span><span class="mopen">(</span><span class="mord">50</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mclose">)</span></span></span></span></span><span style="top:-3.09em;"><span class="pstrut" style="height:3.68em;"></span><span class="katex-stretchy fbox" style="height:1.68em;border-style:solid;border-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.59em;"><span></span></span></span></span></span></span></span></span></span></div></div></div>304<div class="box box-terrain" id="terrain-10-94"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-hardhat"/></svg></span><span class="box-label">particularités des immeubles à revenus</span><a class="box-anchor" href="#terrain-10-94" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-95">Les immeubles locatifs cumulent une usure accélérée (rotation des locataires, espaces communs très sollicités, entretien variable selon les occupants, vandalisme potentiel) et des composantes supplémentaires à inspecter (intercommunication, buanderie commune, stationnement asphalté, corridors et escaliers communs). Réflexe professionnel : <strong>confronter</strong> la dépréciation physique estimée par la méthode du coût aux indications de la <strong>méthode du revenu</strong> — si le coût déprécié s'écarte fortement de la valeur par capitalisation, l'une des deux analyses contient une erreur ou une dépréciation manquante.</p></div></div>305<p id="p10-96">Au terme de ce chapitre, la première des trois formes de dépréciation est maîtrisée — mais elle est rarement seule. Le bungalow fil rouge a perdu 44,6 % de son coût neuf par simple usure; il se peut qu'il souffre en outre d'un plan désuet, d'une seule salle de bain là où le marché en exige deux, ou d'un voisinage industriel qui décote tout le secteur. Ces pertes-là ne se voient pas à l'inspection des matériaux : elles se mesurent contre les attentes du marché, et c'est l'objet des deux prochaines séances. La rigueur séquentielle acquise ici — retrancher avant de calculer, ne jamais compter deux fois — y sera constamment sollicitée, car la dépréciation fonctionnelle se calcule précisément <em>nette</em> de la dépréciation physique déjà mesurée.</p>306<hr class="sep">307<div class="box box-ret" id="aretenir-10-97"><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-10-97" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-98">La dépréciation physique — usure, vieillissement, intempéries — n'affecte que les améliorations et se mesure toujours contre le coût neuf. Sa classification repose sur un test <strong>économique</strong> et non technique : un item est curable si son coût de réparation n'excède pas la valeur qu'il ajoute. La mesure professionnelle suit la ventilation en trois étapes <strong>séquentielles</strong> — le curable au coût de réparation, l'incurable court terme au ratio âge/vie de chaque composante, l'incurable long terme au ratio âge/vie économique du bâtiment appliqué au seul résidu — et l'étape 2 doit livrer ses <em>deux</em> totaux, la dépréciation <em>et</em> les coûts neufs des composantes courtes, faute de quoi le résidu de l'étape 3 est faux. Retenez enfin qu'une composante est curable <em>ou</em> incurable court terme, jamais les deux; que l'âge-vie simple sous-estime généralement la perte là où la ventilation fait référence (OEAQ); et qu'aucune de ces mécaniques n'a de valeur probante sans une inspection documentée — grilles par système, échelle de condition, photographies datées et reçus de travaux.</p></div></div>308<h2 id="s-10-7" class="h-section"><span class="h-num">10.7</span><span class="h-text">Exercices</span><a class="h-anchor" href="#s-10-7" aria-label="Lien vers cette section">#</a></h2>309<div class="box box-exo" id="exo-10-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 10.1</span><span class="box-title">— classification curable / incurable</span><a class="box-anchor" href="#exo-10-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-99">Pour chacune des situations suivantes (bâtiment résidentiel, marché de Gatineau), classez l'item : <strong>curable</strong>, <strong>incurable court terme</strong> ou <strong>incurable long terme</strong>. Justifiez en une phrase.</p>310<ol class="enum"><li>Toiture de bardeaux de 28 ans, durée de vie utile de 25 ans; coût de         remplacement <span class="num">14 000 $</span>, valeur ajoutée estimée <span class="num">16 000 $</span>.</li><li>Chauffe-eau de 6 ans (vie utile de 12 ans), fonctionnel.</li><li>Fissure structurale majeure de la fondation; coût de correction         <span class="num">85 000 $</span>, valeur ajoutée estimée <span class="num">40 000 $</span>.</li><li>Peinture intérieure défraîchie; coût <span class="num">5000 $</span>, valeur ajoutée         <span class="num">7000 $</span>.</li><li>Charpente saine d'un bâtiment de 35 ans (vie économique de 60 ans).</li></ol></div></div>311<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li><strong>Curable</strong> : la composante est en fin de vie (ratio plafonné à         100 %) et le test économique est satisfait         (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>14</mn><mtext> </mtext><mn>000</mn><mo>≤</mo><mn>16</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">14\,000 \leq 16\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7804em;vertical-align:-0.136em;"></span><span class="mord">14</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>); on la mesure au coût de remplacement.</li><li><strong>Incurable court terme</strong> : composante à courte vie en cours de         vie, ratio <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>6</mn><mi mathvariant="normal">/</mi><mn>12</mn><mo>=</mo><mn>50</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">6/12 = 50\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">6/12</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> appliqué à son coût neuf.</li><li><strong>Incurable</strong> : le coût de correction (<span class="num">85 000 $</span>) excède         la valeur ajoutée (<span class="num">40 000 $</span>); la déficience structurale se         reflète dans le long terme (âge effectif alourdi), non comme item         curable.</li><li><strong>Curable</strong> : entretien différé classique,         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn><mtext> </mtext><mn>000</mn><mo>≤</mo><mn>7</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">5\,000 \leq 7\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7804em;vertical-align:-0.136em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">7</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>.</li><li><strong>Incurable long terme</strong> : composante structurale saine,         dépréciée par le ratio âge/vie économique du bâtiment         (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>35</mn><mi mathvariant="normal">/</mi><mn>60</mn><mo>≈</mo><mn>58</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">35/60 \approx 58\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">35/60</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">58</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> sur le résidu).</li></ol></div></details>312<div class="box box-exo" id="exo-10-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 10.2</span><span class="box-title">— composante à courte vie</span><a class="box-anchor" href="#exo-10-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-110">Un système CVAC a un coût neuf de <span class="num">24 000 $</span> et une durée de vie utile de 20 ans. Le bâtiment a 15 ans, mais le CVAC a été remplacé il y a 6 ans; son entretien annuel est impeccable.</p>313<ol class="enum"><li>Quel âge effectif retenez-vous pour le CVAC?</li><li>Calculez sa dépréciation incurable court terme et sa valeur         résiduelle.</li><li>Qu'adviendrait-il du calcul si le CVAC, jamais entretenu, présentait         un âge effectif de 9 ans?</li></ol></div></div>314<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>L'âge effectif suit la composante, pas le bâtiment : <strong>6 ans</strong>         (remplacement documenté, entretien impeccable).</li><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo>=</mo><mn>24</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>6</mn><mi mathvariant="normal">/</mi><mn>20</mn><mo>=</mo><mn>24</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>30</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">7</mn><mtext> </mtext><mn mathvariant="bold">200</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">D = 24\,000 \times 6/20 = 24\,000 \times 30\,\% =315        \uqogreen{7\,200~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">6/20</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">7</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">200</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>; valeur résiduelle         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>24</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>7</mn><mtext> </mtext><mn>200</mn><mo>=</mo><mn>16</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 24\,000 - 7\,200 = 16\,800\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">7</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> (il reste 14 ans de vie         utile).</li><li>Avec un âge effectif de 9 ans : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo>=</mo><mn>24</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>9</mn><mi mathvariant="normal">/</mi><mn>20</mn><mo>=</mo><mn>10</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">D = 24\,000 \times 9/20 =316        10\,800\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">9/20</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>, valeur résiduelle <span class="num">13 200 $</span>. Le même         équipement, selon son entretien, porte une dépréciation qui varie de         <span class="num">3600 $</span> — d'où l'importance des observations d'inspection.</li></ol></div></details>317<div class="box box-exo" id="exo-10-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 10.3</span><span class="box-title">— cottage à Aylmer — ventilation complète</span><a class="box-anchor" href="#exo-10-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-117">Cottage de 2 étages, <span class="num">1500</span> pi<sup>2</sup>, construit en 1995 à Aylmer (Gatineau). Coût de remplacement à neuf : <span class="num">420 000 $</span>; âge effectif du bâtiment : 22 ans; hypothèse du cas : vie économique de 65 ans. Items curables constatés : peinture intérieure (<span class="num">7000 $</span>), gouttières (<span class="num">1800 $</span>), robinetterie (<span class="num">1200 $</span>). Composantes à courte vie :</p>318<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Composante</th><th class="al-r">Coût neuf</th><th class="al-c">Durée de vie</th><th class="al-c">Âge effectif</th></tr></thead><tbody><tr><td>Toiture</td><td class="al-r">18 000 $</td><td class="al-c">25 ans</td><td class="al-c">18 ans</td></tr><tr><td>CVAC</td><td class="al-r">22 000 $</td><td class="al-c">20 ans</td><td class="al-c">15 ans</td></tr><tr><td>Fenêtres</td><td class="al-r">25 000 $</td><td class="al-c">35 ans</td><td class="al-c">20 ans</td></tr><tr><td>Couvre-planchers</td><td class="al-r">15 000 $</td><td class="al-c">20 ans</td><td class="al-c">12 ans</td></tr><tr><td>Cuisine / salle de bain</td><td class="al-r">30 000 $</td><td class="al-c">25 ans</td><td class="al-c">18 ans</td></tr><tr><td>Système électrique</td><td class="al-r">12 000 $</td><td class="al-c">35 ans</td><td class="al-c">22 ans</td></tr><tr><td>Revêtement extérieur</td><td class="al-r">20 000 $</td><td class="al-c">30 ans</td><td class="al-c">20 ans</td></tr><tr><td>Plomberie</td><td class="al-r">8 000 $</td><td class="al-c">25 ans</td><td class="al-c">15 ans</td></tr></tbody></table></div></div>319<p id="p10-118">Calculez la dépréciation curable, l'incurable court terme (composante par composante), l'incurable long terme et la dépréciation physique totale, en pourcentage du coût neuf.</p></div></div>320<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p10-119"><strong>Étape 1 — curable :</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>7</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>1</mn><mtext> </mtext><mn>800</mn><mo>+</mo><mn>1</mn><mtext> </mtext><mn>200</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">10</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">7\,000 + 1\,800 + 1\,200 =321\uqogreen{10\,000~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">7</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">10</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">000</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>.</p>322<p id="p10-120"><strong>Étape 2 — incurable court terme :</strong></p>323<div class="center"><div class="table-wrap"><table class="tbl table-wide"><thead><tr><th>Composante</th><th class="al-r">Coût neuf</th><th class="al-c">Âge / Vie</th><th class="al-r">%</th><th class="al-r">Dépréc.</th></tr></thead><tbody><tr><td>Toiture</td><td class="al-r">18 000 $</td><td class="al-c">18 / 25</td><td class="al-r">72,0</td><td class="al-r">12 960 $</td></tr><tr><td>CVAC</td><td class="al-r">22 000 $</td><td class="al-c">15 / 20</td><td class="al-r">75,0</td><td class="al-r">16 500 $</td></tr><tr><td>Fenêtres</td><td class="al-r">25 000 $</td><td class="al-c">20 / 35</td><td class="al-r">57,1</td><td class="al-r">14 286 $</td></tr><tr><td>Couvre-planchers</td><td class="al-r">15 000 $</td><td class="al-c">12 / 20</td><td class="al-r">60,0</td><td class="al-r">9 000 $</td></tr><tr><td>Cuisine / salle de bain</td><td class="al-r">30 000 $</td><td class="al-c">18 / 25</td><td class="al-r">72,0</td><td class="al-r">21 600 $</td></tr><tr><td>Système électrique</td><td class="al-r">12 000 $</td><td class="al-c">22 / 35</td><td class="al-r">62,9</td><td class="al-r">7 543 $</td></tr><tr><td>Revêtement extérieur</td><td class="al-r">20 000 $</td><td class="al-c">20 / 30</td><td class="al-r">66,7</td><td class="al-r">13 333 $</td></tr><tr><td>Plomberie</td><td class="al-r">8 000 $</td><td class="al-c">15 / 25</td><td class="al-r">60,0</td><td class="al-r">4 800 $</td></tr><tr class="rule-above"><td><strong>Total CT</strong></td><td class="al-r"><strong>150 000 $</strong></td><td class="al-c"></td><td class="al-r"></td><td class="al-r"><strong>100 022 $</strong></td></tr></tbody></table></div></div>324<p id="p10-121"><strong>Étape 3 — incurable long terme :</strong></p>325<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>R</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>sidu</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>420</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>10</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>150</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>260</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>D</mi><mtext>LT</mtext></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>260</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mfrac><mn>22</mn><mn>65</mn></mfrac><mo>=</mo><mrow><mtext mathvariant="bold">88</mtext><mtext> </mtext><mtext mathvariant="bold">000</mtext><mtext> </mtext><mtext mathvariant="bold">$</mtext></mrow></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Résidu} &amp;= 420\,000 - 10\,000 - 150\,000 = 260\,000\,\$ \\326D_{\text{LT}} &amp;= 260\,000 \times \frac{22}{65} = \textbf{88\,000\,\$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:3.5074em;vertical-align:-1.5037em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0037em;"><span style="top:-4.4852em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord text"><span class="mord">R</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">sidu</span></span></span></span><span style="top:-2.5037em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">LT</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5037em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0037em;"><span style="top:-4.4852em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">150</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">260</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-2.5037em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">260</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">65</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">22</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord textbf">88</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">$</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5037em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>327<p id="p10-122"><strong>Total :</strong></p>328<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><menclose notation="box"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mrow><msub><mi>D</mi><mtext>totale</mtext></msub><mo>=</mo><mn>10</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>100</mn><mtext> </mtext><mn>022</mn><mo>+</mo><mn>88</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mrow><mtext mathvariant="bold">198</mtext><mtext> </mtext><mtext mathvariant="bold">022</mtext><mtext> </mtext><mtext mathvariant="bold">$</mtext></mrow><mspace width="1em"/><mo stretchy="false">(</mo><mn>47,1</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mrow><mtext> du co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t neuf</mtext></mrow><mo stretchy="false">)</mo></mrow></mstyle></mstyle></mstyle></menclose></mrow><annotation encoding="application/x-tex">\boxed{D_{\text{totale}} = 10\,000 + 100\,022 + 88\,000 = \textbf{198\,022\,\$}329\quad (47{,}1\,\% \text{ du coût neuf})}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.68em;vertical-align:-0.59em;"></span><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.09em;"><span style="top:-3.68em;"><span class="pstrut" style="height:3.68em;"></span><span class="boxpad"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">100</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">022</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">88</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord textbf">198</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">022</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord textbf">$</span></span><span class="mspace" style="margin-right:1em;"></span><span class="mopen">(</span><span class="mord">47</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mord text"><span class="mord"> du co</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">u</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˆ</span></span></span></span></span></span></span><span class="mord">t neuf</span></span><span class="mclose">)</span></span></span></span></span><span style="top:-3.09em;"><span class="pstrut" style="height:3.68em;"></span><span class="katex-stretchy fbox" style="height:1.68em;border-style:solid;border-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.59em;"><span></span></span></span></span></span></span></span></span></span></div>330<p id="p10-123">Le bâtiment a consommé près de la moitié de son coût neuf en dépréciation physique — lecture plausible pour 22 ans d'âge effectif avec des composantes mécaniques et de finition bien avancées dans leur vie utile.</p></div></details>331<div class="box box-exo" id="exo-10-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 10.4</span><span class="box-title">— comparaison des méthodes</span><a class="box-anchor" href="#exo-10-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-124">Reprenez les données du cottage d'Aylmer (exercice précédent). Calculez la dépréciation physique par la méthode âge-vie <strong>simple</strong>, puis par l'âge-vie <strong>modifiée</strong>, et comparez avec le résultat de la ventilation (<span class="num">198 022 $</span>). Expliquez la source des écarts et indiquez la méthode à privilégier dans un rapport détaillé.</p></div></div>332<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p10-125"><strong>Âge-vie simple :</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo>=</mo><mn>420</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>22</mn><mi mathvariant="normal">/</mi><mn>65</mn><mo>=</mo><mn>142</mn><mtext> </mtext><mn>154</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">D = 420\,000 \times 22/65 = 142\,154\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">22/65</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">142</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">154</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> (33,8 %).  <strong>Âge-vie modifiée :</strong> curable <span class="num">10 000 $</span>; solde <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>420</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>10</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>410</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">420\,000 - 10\,000 = 410\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">410</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>; incurable <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>410</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>22</mn><mi mathvariant="normal">/</mi><mn>65</mn><mo>=</mo><mn>138</mn><mtext> </mtext><mn>769</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">410\,000 \times 22/65 = 138\,769\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">410</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">22/65</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">138</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">769</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; total <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>148</mn><mtext> </mtext><mn>769</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\approx 148\,769\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">148</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">769</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> (35,4 %).  <strong>Ventilation :</strong> <span class="num">198 022 $</span> (47,1 %).  L'écart (11 à 13 points, soit 50 000 à 56 000 $) vient du fait que les ratios âge-vie appliquent le rythme moyen du bâtiment (22/65 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span></span></span></span> 34 %) à des composantes courtes déjà consommées à 57–75 % (toiture, CVAC, cuisine). Dans un rapport détaillé, la <strong>ventilation</strong> s'impose; l'âge-vie sert d'estimation préliminaire ou de contre-vérification d'ordre de grandeur.</p></div></details>333<div class="box box-exo" id="exo-10-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 10.5</span><span class="box-title">— erreur de double comptage</span><a class="box-anchor" href="#exo-10-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-126">Un étudiant remet la ventilation suivante pour un duplex (coût neuf <span class="num">380 000 $</span>, âge effectif 18 ans, vie économique 60 ans) : entretien différé <span class="num">22 000 $</span>, dont remplacement de la toiture en fin de vie <span class="num">15 000 $</span>; composantes à courte vie : toiture (coût neuf <span class="num">15 000 $</span>, ratio 100 %, dépréciation <span class="num">15 000 $</span>), autres composantes CT (coûts neufs <span class="num">105 000 $</span>, dépréciation <span class="num">52 000 $</span>); long terme : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>380</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>22</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>120</mn><mtext> </mtext><mn>000</mn><mo stretchy="false">)</mo><mo>×</mo><mn>18</mn><mi mathvariant="normal">/</mi><mn>60</mn><mo>=</mo><mn>71</mn><mtext> </mtext><mn>400</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">(380\,000 - 22\,000 - 120\,000) \times 18/60 =33471\,400\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">380</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">120</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">18/60</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">71</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. Total déclaré : <span class="num">160 400 $</span>. Identifiez l'erreur, corrigez la ventilation et recalculez le total.</p></div></div>335<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p10-127"><strong>L'erreur :</strong> la toiture en fin de vie est comptée <strong class="c-rouge">deux fois</strong> — une fois comme curable (<span class="num">15 000 $</span> dans l'entretien différé) et une fois comme incurable CT à 100 % (<span class="num">15 000 $</span>). Une composante complètement usée est <strong>curable seulement</strong>.  <strong>Correction :</strong> retirer la toiture de l'étape 2. Curable : <span class="num">22 000 $</span> (inchangé, la toiture y est à sa place). Incurable CT : <span class="num">52 000 $</span> sur coûts neufs CT de <span class="num">105 000 $</span>. Long terme : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>380</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>22</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>105</mn><mtext> </mtext><mn>000</mn><mo stretchy="false">)</mo><mo>×</mo><mn>18</mn><mi mathvariant="normal">/</mi><mn>60</mn><mo>=</mo><mn>253</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>30</mn><mtext> </mtext><mi mathvariant="normal">%</mi><mo>=</mo><mn>75</mn><mtext> </mtext><mn>900</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">(380\,000 - 22\,000 - 105\,000) \times 18/60 = 253\,000 \times 30\,\% =33675\,900\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">380</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">105</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">18/60</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">253</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">75</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">900</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>.  <strong>Total corrigé :</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>22</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>52</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>75</mn><mtext> </mtext><mn>900</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">149</mn><mtext> </mtext><mn mathvariant="bold">900</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">22\,000 + 52\,000 + 75\,900 =337\uqogreen{149\,900~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">52</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">75</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">900</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">149</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">900</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span> (au lieu de <span class="num">160 400 $</span> — l'erreur gonflait la dépréciation de <span class="num">10 500 $</span> : <span class="num">15 000 $</span> comptés en trop à l'étape 2, moins <span class="num">4500 $</span> de long terme calculé sur une assiette indûment réduite de <span class="num">15 000 $</span>).</p></div></details>338<div class="box box-exo" id="exo-10-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 10.6</span><span class="box-title">— mini-cas : sixplex avec historique de rénovations</span><a class="box-anchor" href="#exo-10-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p10-128">Un sixplex de 1988 à Hull présente : coût de remplacement <span class="num">820 000 $</span>; âge effectif global 24 ans; vie économique 55 ans; entretien différé <span class="num">31 000 $</span>. Composantes à courte vie (coûts neufs) : toitures et membranes <span class="num">48 000 $</span> (refaites il y a 10 ans, vie 25 ans); balcons et escaliers <span class="num">36 000 $</span> (âge effectif 20 ans, vie 30 ans); systèmes mécaniques <span class="num">94 000 $</span> (âge effectif 15 ans, vie 22 ans); finitions locatives <span class="num">72 000 $</span> (âge effectif 12 ans, vie 18 ans).</p>339<ol class="enum"><li>Calculez la dépréciation incurable court terme totale.</li><li>Calculez l'incurable long terme et la dépréciation physique totale.</li><li>Le propriétaire fournit ensuite des reçus montrant que les systèmes         mécaniques ont été remplacés il y a 8 ans (et non 15). Recalculez le         total et commentez l'impact d'un seul document sur la valeur.</li></ol></div></div>340<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><ol class="enum"><li>Incurable CT :         toitures <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>48</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>10</mn><mi mathvariant="normal">/</mi><mn>25</mn><mo>=</mo><mn>19</mn><mtext> </mtext><mn>200</mn></mrow><annotation encoding="application/x-tex">48\,000 \times 10/25 = 19\,200</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">48</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">10/25</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">19</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span></span></span></span>;         balcons <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>36</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>20</mn><mi mathvariant="normal">/</mi><mn>30</mn><mo>=</mo><mn>24</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">36\,000 \times 20/30 = 24\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">36</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">20/30</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>;         mécanique <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>94</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>15</mn><mi mathvariant="normal">/</mi><mn>22</mn><mo>=</mo><mn>64</mn><mtext> </mtext><mn>091</mn></mrow><annotation encoding="application/x-tex">94\,000 \times 15/22 = 64\,091</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">94</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">15/22</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">64</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">091</span></span></span></span>;         finitions <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>72</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>12</mn><mi mathvariant="normal">/</mi><mn>18</mn><mo>=</mo><mn>48</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">72\,000 \times 12/18 = 48\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">72</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">12/18</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">48</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>.         Total CT <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">155</mn><mtext> </mtext><mn mathvariant="bold">291</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= \uqogreen{155\,291~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">155</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">291</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span> sur coûts neufs CT de         <span class="num">250 000 $</span>.</li><li>Résidu <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>820</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>31</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>250</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>539</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">= 820\,000 - 31\,000 - 250\,000 = 539\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">820</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">31</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">250</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">539</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>;         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>LT</mtext></msub><mo>=</mo><mn>539</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>24</mn><mi mathvariant="normal">/</mi><mn>55</mn><mo>=</mo><mn>235</mn><mtext> </mtext><mn>200</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">D_{\text{LT}} = 539\,000 \times 24/55 = 235\,200\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">LT</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">539</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">24/55</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">235</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> (arrondi).         Total <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>31</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>155</mn><mtext> </mtext><mn>291</mn><mo>+</mo><mn>235</mn><mtext> </mtext><mn>200</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">421</mn><mtext> </mtext><mn mathvariant="bold">491</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= 31\,000 + 155\,291 + 235\,200 = \uqogreen{421\,491~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">31</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">155</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">291</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">235</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">421</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">491</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>         (51,4 % du coût neuf).</li><li>Mécanique corrigée : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>94</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>8</mn><mi mathvariant="normal">/</mi><mn>22</mn><mo>=</mo><mn>34</mn><mtext> </mtext><mn>182</mn></mrow><annotation encoding="application/x-tex">94\,000 \times 8/22 = 34\,182</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">94</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">8/22</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">34</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">182</span></span></span></span>, soit         <span class="num">29 909 $</span> de moins. Nouveau total CT <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>125</mn><mtext> </mtext><mn>382</mn></mrow><annotation encoding="application/x-tex">= 125\,382</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">125</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">382</span></span></span></span>; le long         terme est inchangé (mêmes coûts neufs CT). Total corrigé         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>31</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>125</mn><mtext> </mtext><mn>382</mn><mo>+</mo><mn>235</mn><mtext> </mtext><mn>200</mn><mo>=</mo><mstyle mathcolor="#107C4E"><mrow><mn mathvariant="bold">391</mn><mtext> </mtext><mn mathvariant="bold">582</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= 31\,000 + 125\,382 + 235\,200 = \uqogreen{391\,582~\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">31</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">125</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">382</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">235</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#107C4E;"><span class="mord mathbf" style="color:#107C4E;">391</span><span class="mspace" style="color:#107C4E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#107C4E;">582</span><span class="mspace nobreak" style="color:#107C4E;"><span style="color:#107C4E;"> </span></span><span class="mord mathbf" style="color:#107C4E;">$</span></span></span></span></span>. Un seul         jeu de reçus déplace la dépréciation de près de <span class="num">30 000 $</span>,         soit environ 3,6 % du coût neuf : la collecte documentaire n'est         pas une formalité, c'est de la valeur.</li></ol></div></details>341<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> : la dépréciation physique est la perte de valeur         causée par l'usure, le vieillissement et les intempéries; le climat         québécois (gel-dégel, amplitude thermique) l'accélère.</li><li><strong>Test de curabilité</strong> : curable si coût de réparation <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 — test économique, non technique.</li><li><strong>Curable</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> entretien différé, mesuré au coût de réparation         au prix du marché (taxes, permis, conditions locales inclus).</li><li><strong>Incurable CT</strong> : par composante,         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mo>=</mo><mrow><mtext>co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t neuf</mtext></mrow><mo>×</mo><mrow><mover accent="true"><mtext>a</mtext><mo>ˆ</mo></mover><mtext>ge effectif</mtext></mrow><mi mathvariant="normal">/</mi><mrow><mtext>dur</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>e de vie</mtext></mrow></mrow><annotation encoding="application/x-tex">D = \text{coût neuf} \times \text{âge effectif}/\text{durée de vie}</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:0.7778em;vertical-align:-0.0833em;"></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 neuf</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord text"><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">ge effectif</span></span><span class="mord">/</span><span class="mord text"><span class="mord">dur</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 vie</span></span></span></span></span>         (ratio plafonné à 100 %; en fin de vie <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).</li><li><strong>Incurable LT</strong> : sur le résidu         (coût total <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> curables <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> coûts neufs CT), ratio âge effectif /         vie économique <em>du bâtiment</em>.</li><li><strong>Total</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>physique</mtext></msub><mo>=</mo><msub><mi>D</mi><mtext>curable</mtext></msub><mo>+</mo><mo>∑</mo><msub><mi>D</mi><mtext>CT</mtext></msub><mo>+</mo><msub><mi>D</mi><mtext>LT</mtext></msub></mrow><annotation encoding="application/x-tex">D_{\text{physique}} = D_{\text{curable}} +342        \sum D_{\text{CT}} + D_{\text{LT}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">physique</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">curable</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">CT</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">LT</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>.</li><li><strong>Âge effectif</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo mathvariant="normal">≠</mo></mrow><annotation encoding="application/x-tex">\neq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mrel"><span class="mrel"><span class="mord katex-vbox"><span class="katex-thinbox"><span class="rlap"><span class="katex-strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="katex-inner"><span class="mord"><span class="mrel"></span></span></span><span class="katex-fix"></span></span></span></span></span><span class="mspace nobreak"></span><span class="mrel">=</span></span></span></span></span> âge chronologique : rénovations         (reçus!) et entretien le modulent, pour le bâtiment comme pour         chaque composante.</li><li><strong>Hiérarchie des méthodes</strong> : ventilation (standard OEAQ)         <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>&gt;</mo></mrow><annotation encoding="application/x-tex">&gt;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">&gt;</span></span></span></span> âge-vie modifiée <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>&gt;</mo></mrow><annotation encoding="application/x-tex">&gt;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">&gt;</span></span></span></span> âge-vie simple; écarts possibles de 10 à         15 points de pourcentage.</li><li><strong>Inspection</strong> : grilles par système, échelle de condition         (1 à 6), photos datées, plaques signalétiques, historique de         rénovations — le fondement probatoire de toute la ventilation.</li><li><strong>Pièges</strong> : double comptage curable/CT; oubli de soustraire         les coûts neufs CT du résidu; ratio CT appliqué au coût du bâtiment         entier; âge effectif copié sur l'âge chronologique.</li></ul></div></section>343      </article>344    </div>345  </div>346  <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>347  348<nav class="ch-pager" aria-label="Navigation entre les séances">349  <a class="prev" href="/seance/09/"><small>← Séance 9</small><b>Concepts de dépréciation</b></a>350  <a class="next" href="/seance/11/"><small>Séance 11 →</small><b>Dépréciation fonctionnelle</b></a>351</nav>352  353<div class="read-tools" role="toolbar" aria-label="Outils de lecture">354  <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>355  <button type="button" data-action="tts" data-tip="Écouter la séance"><svg class="" aria-hidden="true"><use 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