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id="i-network" viewBox="0 0 24 24"><circle cx="12" cy="12" r="3" fill="none" stroke="currentColor" stroke-width="2"/><circle cx="4" cy="6" r="2" fill="none" stroke="currentColor" stroke-width="2"/><circle cx="20" cy="6" r="2" fill="none" stroke="currentColor" stroke-width="2"/><circle cx="4" cy="18" r="2" fill="none" stroke="currentColor" stroke-width="2"/><circle cx="20" cy="18" r="2" fill="none" stroke="currentColor" stroke-width="2"/><path stroke="currentColor" stroke-width="2" d="M6 7l4 3M18 7l-4 3M6 17l4-3M18 17l-4-3"/></symbol>73 <symbol id="i-report" viewBox="0 0 24 24"><path fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" d="M14 2H6a2 2 0 0 0-2 2v16a2 2 0 0 0 2 2h12a2 2 0 0 0 2-2V8zM14 2v6h6M8 17l3-4 2 2 3-5"/></symbol>74</svg>7576<a class="skip" href="#main">Aller au contenu</a>77<header class="topbar">78 <div class="topbar-inner">79 <a class="brand" href="/" aria-label="IMM1033 — accueil"><img class="brand-logo" src="/assets/brand/uqo-logo.png" alt="UQO" width="568" height="238"><span class="brand-sep"></span><span class="brand-text"><span class="brand-code">IMM1033</span><span class="brand-title">Méthodes du coût en évaluation immobilière</span></span></a>80 <nav class="topnav" aria-label="Navigation principale"><div class="dd current"><button type="button" aria-expanded="false" aria-haspopup="true">Séances <span class="caret" aria-hidden="true">▾</span></button><div class="dd-menu wide"><div class="dd-part"><i style="background:#2976bb"></i>Partie I — Fondements de la méthode du coût</div><a href="/seance/01/" data-ch="01"><span class="pastille" style="background:#2976bb">1</span><span>Introduction à la méthode du coût</span></a><a href="/seance/02/" data-ch="02"><span class="pastille" style="background:#2976bb">2</span><span>Cadre conceptuel et terminologie</span></a><div class="dd-part"><i style="background:#0f8b8d"></i>Partie II — Évaluation du terrain</div><a href="/seance/03/" data-ch="03"><span class="pastille" style="background:#0f8b8d">3</span><span>Méthodes d'évaluation du terrain</span></a><a href="/seance/04/" data-ch="04"><span class="pastille" style="background:#0f8b8d">4</span><span>Analyse du terrain et ajustements</span></a><div class="dd-part"><i style="background:#cca424"></i>Partie III — Coût de construction</div><a href="/seance/05/" data-ch="05"><span class="pastille" style="background:#cca424">5</span><span>Coût de reproduction et coût de remplacement</span></a><a href="/seance/06/" data-ch="06"><span class="pastille" style="background:#cca424">6</span><span>Méthodes d'estimation des coûts</span></a><a href="/seance/07/" data-ch="07"><span class="pastille" style="background:#cca424">7</span><span>Coûts directs de construction</span></a><a href="/seance/08/" data-ch="08"><span class="pastille" style="background:#cca424">8</span><span>Coûts indirects et profit entrepreneurial</span></a><div class="dd-part"><i style="background:#6b4fbb"></i>Partie IV — La dépréciation</div><a href="/seance/09/" data-ch="09"><span class="pastille" style="background:#6b4fbb">9</span><span>Concepts de dépréciation</span></a><a href="/seance/10/" data-ch="10"><span class="pastille" style="background:#6b4fbb">10</span><span>Dépréciation physique</span></a><a href="/seance/11/" data-ch="11"><span class="pastille" style="background:#6b4fbb">11</span><span>Dépréciation fonctionnelle</span></a><a href="/seance/12/" data-ch="12"><span class="pastille" style="background:#6b4fbb">12</span><span>Dépréciation économique (externe)</span></a><div class="dd-part"><i style="background:#107c4e"></i>Partie V — Applications et intégration</div><a href="/seance/13/" data-ch="13"><span class="pastille" style="background:#107c4e">13</span><span>Applications spécialisées</span></a><a href="/seance/14/" data-ch="14"><span class="pastille" style="background:#107c4e">14</span><span>Synthèse et révision</span></a><div class="dd-part">Annexes</div><a href="/aide-memoire/"><span class="pastille">A</span><span>Aide-mémoire des formules</span></a><a href="/glossaire/"><span class="pastille">B</span><span>Glossaire</span></a><a href="/rapport/"><span class="pastille" style="background:var(--teal)">R</span><span>Rapport — Le marché de l’habitation au Québec</span></a></div></div><div class="dd"><button type="button" aria-expanded="false" aria-haspopup="true">Réviser <span class="caret" aria-hidden="true">▾</span></button><div class="dd-menu "><a href="/aide-memoire/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span>Aide-mémoire<span class="dd-desc">Toutes les formules commentées</span></span></a><a href="/glossaire/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span>Glossaire<span class="dd-desc">Termes du métier, équivalents anglais</span></span></a><a href="/definitions/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-list"/></svg></span><span>Toutes les définitions<span class="dd-desc">Les formulations attendues aux examens</span></span></a><a href="/fiches/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-cards"/></svg></span><span>Fiches de révision<span class="dd-desc">Recto-verso, suivi d’acquisition</span></span></a><a href="/carte/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-network"/></svg></span><span>Carte du cours<span class="dd-desc">Les 14 séances et leurs objectifs en un coup d’œil</span></span></a><a href="/exercices/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span>Banque d’exercices<span class="dd-desc">Tous les exercices corrigés</span></span></a></div></div><div class="dd"><button type="button" aria-expanded="false" aria-haspopup="true">S’exercer <span class="caret" aria-hidden="true">▾</span></button><div class="dd-menu "><a href="/quiz/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-quiz"/></svg></span><span>Quiz et examens blancs<span class="dd-desc">QCM avec rétroaction, chronomètre</span></span></a><a href="/entrainement/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-dumbbell"/></svg></span><span>Entraînement<span class="dd-desc">Problèmes à données aléatoires, corrigés pas à pas</span></span></a><a href="/jeux/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-game"/></svg></span><span>Jeux de révision<span class="dd-desc">Association, vrai ou faux, remise en ordre</span></span></a><a href="/outils/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-calc"/></svg></span><span>Calculateurs<span class="dd-desc">Les formules en interactif</span></span></a><a href="/progression/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-progress"/></svg></span><span>Ma progression<span class="dd-desc">Lecture, quiz, objectifs, notes</span></span></a></div></div><div class="dd"><button type="button" aria-expanded="false" aria-haspopup="true">Ressources <span class="caret" aria-hidden="true">▾</span></button><div class="dd-menu "><a href="/diapositives/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-slides"/></svg></span><span>Diapositives<span class="dd-desc">Les 14 présentations en ligne</span></span></a><a href="/ressources/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-download"/></svg></span><span>Téléchargements<span class="dd-desc">Manuel, plan, TP, gabarits Excel</span></span></a><a href="/rapport/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-report"/></svg></span><span>Rapport marché QC<span class="dd-desc">Indices de prix, macro, abordabilité — 26 sections, 67 figures</span></span></a><a href="/bibliographie/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-bib"/></svg></span><span>Bibliographie<span class="dd-desc">Références citées</span></span></a><a href="/recherche/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-search"/></svg></span><span>Recherche<span class="dd-desc">Tout le manuel indexé</span></span></a></div></div></nav>81 <div class="topbar-actions">82 <button class="icon-btn search-btn" type="button" data-action="search" aria-label="Rechercher"><svg class="" aria-hidden="true"><use href="#i-search"/></svg><span>Rechercher</span><kbd>⌘K</kbd></button>83 <button class="icon-btn" type="button" data-action="theme" aria-label="Thème clair ou sombre" title="Thème"><svg class="" aria-hidden="true"><use href="#i-sun"/></svg></button>84 <button class="icon-btn menu-btn" type="button" aria-label="Menu" aria-expanded="false"><svg class="" aria-hidden="true"><use href="#i-menu"/></svg></button>85 </div>86 </div>87 <div class="readbar"><div class="readbar-fill"></div></div>88</header>8990<main id="main" class="chapter-page" data-chapter="06" data-title="Séance 6 — Méthodes d'estimation des coûts" data-words="7041">91 92<header class="ch-hero">93 <svg class="deco" viewBox="0 0 1200 300" preserveAspectRatio="xMaxYMin slice" aria-hidden="true"><circle cx="1090" cy="20" r="110"/><circle cx="1160" cy="110" r="160"/><circle class="gold" cx="990" cy="170" r="45"/></svg>94 <div class="watermark" aria-hidden="true">06</div>95 <div class="ch-hero-inner">96 <div class="eyebrow"><span class="part-chip">Partie III</span> Coût de construction · Séance 6 · IMM1033</div>97 <h1>Méthodes d'estimation des coûts</h1>98 <div class="ch-sub">Méthodes du coût en évaluation immobilière · Hiver 2026 · Simon-Pierre Boucher · UQO</div>99 <div class="ch-meta">100 <span class="chip"><svg class="" aria-hidden="true"><use href="#i-list"/></svg> 9 sections</span>101 <span class="chip"><svg class="" aria-hidden="true"><use href="#i-book"/></svg> 3 définitions</span>102 <span class="chip"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg> 3 formules</span>103 <span class="chip"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg> 8 exemples</span>104 <span class="chip"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg> 6 exercices</span>105 <span class="chip"><svg class="" aria-hidden="true"><use href="#i-eye"/></svg> ≈ 39 min de lecture</span>106 107 108 </div>109 <div class="ch-tools">110 <a class="btn btn-ghost" href="/files/slides/seance06.pdf" target="_blank" rel="noopener"><svg class="" aria-hidden="true"><use href="#i-slides"/></svg> Diapositives (PDF)</a>111 <button class="btn btn-ghost" type="button" data-action="revision" aria-pressed="false"><svg class="" aria-hidden="true"><use href="#i-eye"/></svg> Mode révision</button>112 <button class="btn btn-ghost" type="button" data-action="tts"><svg class="" aria-hidden="true"><use href="#i-audio"/></svg> Écouter</button>113 <a class="btn btn-ghost" href="#quiz"><svg class="" aria-hidden="true"><use href="#i-quiz"/></svg> Quiz de la séance</a>114 </div>115 </div>116</header>117<div class="stepper-wrap"><nav class="stepper" aria-label="Sections"><a href="#s-6-1"><span class="n">1</span>Vue d'ensemble des quatre méthodes</a><a href="#s-6-2"><span class="n">2</span>La méthode comparative</a><a href="#s-6-3"><span class="n">3</span>La méthode par quantité et prix unitaires (Quantity Survey)</a><a href="#s-6-4"><span class="n">4</span>La méthode par composantes (Unit-in-Place)</a><a href="#s-6-5"><span class="n">5</span>La méthode du coût indexé (Trended Cost)</a><a href="#s-6-6"><span class="n">6</span>Choisir et réconcilier : les quatre méthodes face à face</a><a href="#s-6-7"><span class="n">7</span>Les facteurs d'ajustement transversaux</a><a href="#s-6-8"><span class="n">8</span>Les erreurs classiques de l'estimation des coûts</a><a href="#s-6-9"><span class="n">9</span>Exercices</a><span class="rem" id="read-remaining"></span></nav></div>118 <div class="ch-layout">119 120<aside class="ch-toc" aria-label="Sommaire de la séance">121 <div class="toc-progress"><div class="bar"><i></i></div><span>0 % lu</span></div>122 <h4>Dans cette séance</h4>123 <ol><li class="lvl2"><a href="#s-6-1"><span class="toc-num">6.1</span><span>Vue d'ensemble des quatre méthodes</span></a></li><li class="lvl2"><a href="#s-6-2"><span class="toc-num">6.2</span><span>La méthode comparative</span></a></li><li class="lvl3"><a href="#s-6-2-1"><span class="toc-num">6.2.1</span><span>Sélection des comparables de coût</span></a></li><li class="lvl3"><a href="#s-6-2-2"><span class="toc-num">6.2.2</span><span>Les six ajustements</span></a></li><li class="lvl3"><a href="#s-6-2-3"><span class="toc-num">6.2.3</span><span>Exemple résidentiel complet</span></a></li><li class="lvl2"><a href="#s-6-3"><span class="toc-num">6.3</span><span>La méthode par quantité et prix unitaires (Quantity Survey)</span></a></li><li class="lvl3"><a href="#s-6-3-1"><span class="toc-num">6.3.1</span><span>La main-d'œuvre : le cadre de la CCQ</span></a></li><li class="lvl3"><a href="#s-6-3-2"><span class="toc-num">6.3.2</span><span>Bordereau complet — résidence de <span class="num">1450</span> pi<sup>2</sup></span></a></li><li class="lvl3"><a href="#s-6-3-3"><span class="toc-num">6.3.3</span><span>Récapitulatif et structure des coûts</span></a></li><li class="lvl3"><a href="#s-6-3-4"><span class="toc-num">6.3.4</span><span>La leçon de la portée des coûts</span></a></li><li class="lvl2"><a href="#s-6-4"><span class="toc-num">6.4</span><span>La méthode par composantes (Unit-in-Place)</span></a></li><li class="lvl3"><a href="#s-6-4-1"><span class="toc-num">6.4.1</span><span>Coûts installés types</span></a></li><li class="lvl3"><a href="#s-6-4-2"><span class="toc-num">6.4.2</span><span>Exemple complet</span></a></li><li class="lvl2"><a href="#s-6-5"><span class="toc-num">6.5</span><span>La méthode du coût indexé (Trended Cost)</span></a></li><li class="lvl2"><a href="#s-6-6"><span class="toc-num">6.6</span><span>Choisir et réconcilier : les quatre méthodes face à face</span></a></li><li class="lvl3"><a href="#s-6-6-1"><span class="toc-num">6.6.1</span><span>Exercice intégrateur — un duplex, trois méthodes</span></a></li><li class="lvl2"><a href="#s-6-7"><span class="toc-num">6.7</span><span>Les facteurs d'ajustement transversaux</span></a></li><li class="lvl3"><a href="#s-6-7-1"><span class="toc-num">6.7.1</span><span>Économies d'échelle</span></a></li><li class="lvl3"><a href="#s-6-7-2"><span class="toc-num">6.7.2</span><span>Forme et périmètre</span></a></li><li class="lvl3"><a href="#s-6-7-3"><span class="toc-num">6.7.3</span><span>Hauteur</span></a></li><li class="lvl3"><a href="#s-6-7-4"><span class="toc-num">6.7.4</span><span>Qualité</span></a></li><li class="lvl2"><a href="#s-6-8"><span class="toc-num">6.8</span><span>Les erreurs classiques de l'estimation des coûts</span></a></li><li class="lvl2"><a href="#s-6-9"><span class="toc-num">6.9</span><span>Exercices</span></a></li></ol>124 <div class="toc-extra">125 <a href="#objectifs"><svg class="" aria-hidden="true"><use href="#i-target"/></svg> Objectifs d’apprentissage</a>126 <a href="#synthese"><svg class="" aria-hidden="true"><use href="#i-clipboard"/></svg> L’essentiel de la séance</a>127 <a href="#quiz"><svg class="" aria-hidden="true"><use href="#i-quiz"/></svg> Testez-vous</a>128 <a href="/fiches/?ch=06"><svg class="" aria-hidden="true"><use href="#i-cards"/></svg> Fiches de la séance</a>129 <a href="/entrainement/"><svg class="" aria-hidden="true"><use href="#i-dumbbell"/></svg> Entraînement</a>130 <a href="/aide-memoire/"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg> Aide-mémoire</a>131 </div>132 <h4 style="margin-top:14px">Raccourcis</h4>133 <div style="font-size:.76rem;color:var(--gris)"><kbd>←</kbd> <kbd>→</kbd> séance précédente / suivante · <kbd>⌘K</kbd> recherche · sélectionnez un passage pour le surligner</div>134</aside>135 <div class="ch-body">136 <div class="revision-banner"><svg class="" aria-hidden="true"><use href="#i-eye"/></svg><span><strong>Mode révision</strong> — seuls les définitions, formules, mises en garde, « À retenir », notes marginales et la fiche synthèse sont affichés.</span><button class="btn btn-sm btn-ghost" type="button" data-action="revision-off">Quitter</button></div>137 <div style="display:flex;justify-content:flex-end;margin-bottom:8px"><button class="btn btn-sm btn-ghost" type="button" data-action="toggle-solutions">Révéler toutes les solutions</button></div>138 <article class="prose" id="notes">139 <p id="p6-1">La séance 5 a répondu à la question « quel coût estimer? » (reproduction ou remplacement, à la date d'évaluation). La présente séance répond à la question « comment l'estimer? ». Quatre familles de méthodes s'offrent à l'évaluateur, du plus simple au plus détaillé : la <span class="motcle" data-term="méthode comparative">méthode comparative</span> (coût au pied carré), la <span class="motcle" data-term="méthode par quantité et prix unitaires">méthode par quantité et prix unitaires</span> (<em>Quantity Survey</em>), la <span class="motcle" data-term="méthode par composantes">méthode par composantes</span> (<em>Unit-in-Place</em>) et la <span class="motcle" data-term="méthode du coût indexé">méthode du coût indexé</span> (<em>Trended Cost</em>). Aucune n'est supérieure dans l'absolu : le choix dépend du bâtiment, des données disponibles, du temps alloué et de la précision requise. Ce chapitre développe chacune avec un bordereau chiffré complet, puis les confronte sur un même bâtiment — l'occasion de découvrir la leçon la plus importante du bloc : on ne compare jamais des coûts sans en vérifier la <strong class="c-bleu">portée</strong>.</p>140<section class="box box-obj" id="objectifs"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-target"/></svg></span><span class="box-label">Objectifs d’apprentissage</span><span class="obj-progress" aria-live="polite"></span></div><div class="box-body"><ul><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-6-1" data-obj="obj-6-1"><span class="obj-text">Appliquer la méthode comparative (coût au pi<sup>2</sup> ou au m<sup>2</sup>) avec ses ajustements de taille, de date, de qualité, de localisation, de hauteur et de forme;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-6-2" data-obj="obj-6-2"><span class="obj-text">Construire un bordereau détaillé par quantité et prix unitaires (<em>Quantity Survey</em>) et connaître le cadre de main-d'œuvre de la CCQ;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-6-3" data-obj="obj-6-3"><span class="obj-text">Décomposer un bâtiment en composantes à coûts installés (<em>Unit-in-Place</em>) selon l'approche Marshall & Swift;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-6-4" data-obj="obj-6-4"><span class="obj-text">Appliquer la méthode du coût indexé, y compris en présence de rénovations datées;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-6-5" data-obj="obj-6-5"><span class="obj-text">Comparer les quatre méthodes, choisir la bonne selon le contexte et réconcilier leurs résultats;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-6-6" data-obj="obj-6-6"><span class="obj-text">Appliquer les facteurs d'ajustement transversaux : économies d'échelle, périmètre, hauteur, qualité;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-6-7" data-obj="obj-6-7"><span class="obj-text">Diagnostiquer les écarts de <em>portée</em> entre coûts directs, coût de construction et coût complet de projet.</span></label></li></ul></div></section>141<h2 id="s-6-1" class="h-section"><span class="h-num">6.1</span><span class="h-text">Vue d'ensemble des quatre méthodes</span><a class="h-anchor" href="#s-6-1" aria-label="Lien vers cette section">#</a></h2>142<div class="center"><div class="tikz"><img src="/assets/fig/7625028ca17377c6.svg" alt="Figure" width="543" height="92" style="width:min(100%,788px)" loading="lazy" decoding="async"></div></div>143<p id="p6-9">Le niveau de détail croît de la comparative au <em>Quantity Survey</em>; le temps requis aussi<label for="sn-6-1" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-6-1" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-repere">Comparative : 1–2 h. Composantes : 4–8 h. Quantity Survey : 20–40 h. Indexée : moins d'une heure.</span>. En pratique professionnelle, la plupart des mandats s'appuient sur la comparative ou la méthode par composantes, validées par le coût indexé; le <em>Quantity Survey</em> est réservé aux litiges et aux bâtiments spéciaux.</p>144<p id="p6-10">Le choix de la méthode est d'abord une décision économique de l'évaluateur lui-même. Un mandat résidentiel courant facturé quelques centaines de dollars ne peut absorber quarante heures de bordereau détaillé : la comparative, correctement documentée, y suffit amplement et le client n'en attend pas davantage. À l'autre extrême, une expertise devant le Tribunal administratif du Québec, où chaque poste de coût sera contre-interrogé par l'expert de la partie adverse, exige la traçabilité poste par poste du <em>Quantity Survey</em>. Entre les deux, l'évaluateur d'un immeuble commercial de taille moyenne combinera le plus souvent deux méthodes : l'une comme estimation principale, l'autre comme contre-vérification. Cette redondance délibérée n'est pas du zèle — c'est elle qui transforme une estimation en opinion défendable, car deux méthodes indépendantes qui convergent valent mieux qu'une seule méthode poussée à trois décimales.</p>145<p id="p6-11">Une seconde considération guide le choix : ce que l'on fera du résultat <em>ensuite</em>. Si l'estimation du coût neuf n'est qu'une étape vers une ventilation fine de la dépréciation — ce qui est le propre du bloc 4 —, la méthode par composantes s'impose presque d'elle-même, puisqu'elle produit d'emblée le coût de chaque composante que la dépréciation viendra éroder. Estimer le coût neuf en bloc par la comparative, puis devoir le redécomposer pour ventiler la dépréciation, revient à faire le travail deux fois.</p>146<h2 id="s-6-2" class="h-section"><span class="h-num">6.2</span><span class="h-text">La méthode comparative</span><a class="h-anchor" href="#s-6-2" aria-label="Lien vers cette section">#</a></h2>147<div class="box box-def" id="def-6-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 6.1</span><span class="box-title">— méthode comparative</span><a class="box-anchor" href="#def-6-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-12">Estimer le coût neuf en multipliant la superficie du bâtiment par un coût unitaire dérivé de constructions récentes comparables :</p>148<div class="eq" id="eq-6-1"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable width="100%"><mtr><mtd width="50%"></mtd><mtd><mrow><msub><mi>C</mi><mtext>neuf</mtext></msub><mtext> </mtext><mo>=</mo><mtext> </mtext><mi>S</mi><mo>×</mo><msub><mi>c</mi><mrow><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>2</mn></msup></mrow></msub><mi mathvariant="normal">.</mi></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(6.1)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">C_{\text{neuf}} \;=\; S \times c_{\$/\text{pi}^2}.\tag{6.1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">neuf</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></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:0.7667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.0576em;">S</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8035em;vertical-align:-0.3729em;"></span><span class="mord"><span class="mord mathnormal">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.5021em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">$/</span><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7753em;"><span style="top:-2.815em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="katex-sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.3729em;"><span></span></span></span></span></span></span><span class="mord">.</span></span><span class="katex-tag"><span class="katex-strut" style="height:1.1229em;vertical-align:-0.3729em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">6.1</span></span><span class="mord">)</span></span></span></span></span></span></div></div></div>149<p id="p6-13">C'est la méthode la plus couramment utilisée : rapide, fondée sur le principe de substitution, alimentée par les constructions récentes locales, les guides de coûts (Altus, Marshall & Swift, RSMeans) et les données d'entrepreneurs. Toute sa rigueur repose sur deux piliers : la <strong class="c-bleu">sélection</strong> des comparables et la <strong class="c-bleu">cohérence</strong> des ajustements.</p>150<h3 id="s-6-2-1" class="h-subsection"><span class="h-num">6.2.1</span><span class="h-text">Sélection des comparables de coût</span><a class="h-anchor" href="#s-6-2-1" aria-label="Lien vers cette section">#</a></h3>151<p id="p6-14">La sélection des comparables de coût obéit à la même discipline que celle des comparables de vente, mais avec ses critères propres. Le comparable doit être du <strong class="c-bleu">même type de bâtiment</strong> — on n'estime pas une maison à étages avec des coûts de bungalow, la répartition fondations/enveloppe différant trop. Sa <strong class="c-bleu">qualité de construction</strong> doit être similaire, faute de quoi l'ajustement de qualité, le plus puissant de tous, dominera la grille. Sa <strong class="c-bleu">taille</strong> doit rester dans un rayon d'environ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>±</mo></mrow><annotation encoding="application/x-tex">\pm</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">±</span></span></span></span>20 % pour contenir l'effet des économies d'échelle. Sa <strong class="c-bleu">date de construction</strong> doit être récente — moins de trois ans —, car au-delà l'indexation introduit sa propre incertitude. Il doit provenir de la <strong class="c-bleu">même région</strong> de coûts, et présenter des <strong class="c-bleu">composantes similaires</strong> : nombre d'étages, sous-sol, garage. Au Québec, ces comparables se dénichent dans les permis de construction municipaux, le rôle d'évaluation, les données de la SCHL, auprès des entrepreneurs généraux, et dans le <em>Canadian Cost Guide</em> d'Altus.</p>152<div class="box box-att" id="attention-6-15"><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-6-15" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-16">Avant tout calcul, vérifier la <strong class="c-rouge">portée</strong> du coût rapporté par chaque source : coûts directs seulement? coût du contrat de construction? coût complet du projet incluant honoraires, financement et profit du promoteur? Mélanger les portées dans une même grille produit des écarts de 30 à 45 % qui n'ont rien à voir avec le bâtiment (voir la section <a class="xref" href="#s-6-3-4">6.3.4</a>).</p></div></div>153<h3 id="s-6-2-2" class="h-subsection"><span class="h-num">6.2.2</span><span class="h-text">Les six ajustements</span><a class="h-anchor" href="#s-6-2-2" aria-label="Lien vers cette section">#</a></h3>154<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Facteur</th><th>Description</th><th>Direction</th></tr></thead><tbody><tr><td>Taille</td><td>Économies d'échelle</td><td>Plus grand <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> coût/pi<sup>2</sup> <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">\downarrow</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></span></span></span></td></tr><tr><td>Qualité</td><td>Matériaux et finitions</td><td>Qualité sup. <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> coût <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>↑</mo></mrow><annotation encoding="application/x-tex">\uparrow</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></span></span></span></td></tr><tr><td>Date</td><td>Inflation des coûts</td><td>Plus récent <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> coût <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>↑</mo></mrow><annotation encoding="application/x-tex">\uparrow</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></span></span></span></td></tr><tr><td>Localisation</td><td>Main-d'œuvre et transport</td><td>Région éloignée <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> coût <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>↑</mo></mrow><annotation encoding="application/x-tex">\uparrow</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></span></span></span></td></tr><tr><td>Hauteur</td><td>Complexité structurale</td><td>Plus d'étages <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> coût <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>↑</mo></mrow><annotation encoding="application/x-tex">\uparrow</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></span></span></span></td></tr><tr><td>Forme</td><td>Rapport périmètre/superficie</td><td>Irrégulière <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> coût <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>↑</mo></mrow><annotation encoding="application/x-tex">\uparrow</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></span></span></span></td></tr></tbody></table></div></div>155<h5 class="para-title">Taille.</h5>156<p id="p6-17">Règle empirique : environ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>2 à <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>5 % de coût unitaire par tranche de 20 % de superficie supplémentaire. Un comparable de <span class="num">1200</span> pi<sup>2</sup> à 185 $/pi<sup>2</sup>, utilisé pour un sujet de <span class="num">1600</span> pi<sup>2</sup>, reçoit un facteur d'échelle d'environ 0,95 : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>185</mn><mo>×</mo><mn>0,95</mn><mo>=</mo><mn>175,75</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">185 \times 0{,}95 = 175{,}75~\$/\text{pi}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">185</span><span class="mspace" style="margin-right:0.2222em;"></span><span 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">95</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1219em;vertical-align:-0.25em;"></span><span class="mord">175</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">75</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>.</p>157<h5 class="para-title">Date.</h5>158<p id="p6-18">Indexation par ratio d'indices (éq. <a class="xref" href="/seance/05/#form-5-2">5.2</a> du chapitre <a class="xref" href="/seance/05/">5</a>) : un comparable de 2023 à 175 $/pi<sup>2</sup> (indice 100,0) vaut, en 2025 (indice 105,5), <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>175</mn><mo>×</mo><mn>1,055</mn><mo>=</mo><mn>184,63</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">175 \times 1{,}055 = 184{,}63~\$/\text{pi}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">175</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">055</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1219em;vertical-align:-0.25em;"></span><span class="mord">184</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">63</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>.</p>159<h5 class="para-title">Qualité.</h5>160<p id="p6-19">Les classes de qualité portent des indices relatifs : économique 0,75–0,85; standard 1,00; bon 1,10–1,20; supérieur 1,25–1,45; luxe 1,50–2,00<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>. On évalue la classe à l'inspection : revêtements, fenêtration, équipements mécaniques, finitions.</p>161<h5 class="para-title">Localisation.</h5>162<p id="p6-20">Facteurs régionaux indicatifs sur base Montréal <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> 1,00 : Québec 0,97; Gatineau/Outaouais 0,98; Sherbrooke 0,94; Trois-Rivières 0,93; Saguenay 0,95; régions éloignées 1,05–1,15. <label for="sn-6-2" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-6-2" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-repere">En région éloignée, le coût de <em>construction</em> est plus élevé même si le coût de la <em>vie</em> y est plus bas.</span></p>163<h5 class="para-title">Hauteur et forme.</h5>164<p id="p6-21">Traités en détail à la section <a class="xref" href="#s-6-7">6.7</a>.</p>165<h3 id="s-6-2-3" class="h-subsection"><span class="h-num">6.2.3</span><span class="h-text">Exemple résidentiel complet</span><a class="h-anchor" href="#s-6-2-3" aria-label="Lien vers cette section">#</a></h3>166<div class="box box-ex" id="ex-6-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 6.1</span><span class="box-title">— maison unifamiliale, Gatineau, <span class="num">1450</span> pi<sup>2</sup></span><a class="box-anchor" href="#ex-6-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-22">Sujet : unifamiliale de qualité standard, 2 étages. Trois comparables récents dont le <em>coût complet</em> par pi<sup>2</sup> est connu :</p>167<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th></th><th class="al-r">Comp. 1</th><th class="al-r">Comp. 2</th><th class="al-r">Comp. 3</th></tr></thead><tbody><tr><td>Superficie (pi<sup>2</sup>)</td><td class="al-r"><span class="num">1300</span></td><td class="al-r"><span class="num">1550</span></td><td class="al-r"><span class="num">1400</span></td></tr><tr><td>Coût/pi<sup>2</sup> brut</td><td class="al-r">195,00 $</td><td class="al-r">185,00 $</td><td class="al-r">189,00 $</td></tr><tr><td>Ajust. taille</td><td class="al-r"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>2 %</td><td class="al-r"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>1 %</td><td class="al-r">0 %</td></tr><tr><td>Ajust. date</td><td class="al-r"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>3 %</td><td class="al-r">0 %</td><td class="al-r"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>1,5 %</td></tr><tr><td>Ajust. qualité</td><td class="al-r">0 %</td><td class="al-r"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>5 %</td><td class="al-r">0 %</td></tr><tr><td>Ajust. localisation</td><td class="al-r">0 %</td><td class="al-r"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>2 %</td><td class="al-r"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>1 %</td></tr><tr class="rule-above"><td><strong>Coût/pi<sup>2</sup> ajusté</strong></td><td class="al-r"><strong>196,95 $</strong></td><td class="al-r"><strong>192,40 $</strong></td><td class="al-r"><strong>193,73 $</strong></td></tr></tbody></table></div></div>168<p id="p6-23">Moyenne <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> 194,36 $/pi<sup>2</sup>, d'où</p>169<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>C</mi><mtext>neuf</mtext></msub><mo>=</mo><mn>1</mn><mtext> </mtext><mn>450</mn><mo>×</mo><mn>194,36</mn><mo>≈</mo><mrow><mtext>281</mtext><mtext> </mtext><mtext>822</mtext><mtext> </mtext><mtext>$</mtext></mrow><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">C_{\text{neuf}} = 1\,450 \times 194{,}36 \approx \text{281\,822\,\$}.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">neuf</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">450</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">194</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">36</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord text"><span class="mord">281</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">822</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span><span class="mord">.</span></span></span></span></span></div>170<p id="p6-24">Les trois valeurs ajustées convergent à moins de 2,5 % — signe d'une grille saine. Les coûts observés étant des coûts complets (directs <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> indirects <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> profit), aucun ajout n'est requis.</p></div></div>171<p id="p6-25">Il vaut la peine de s'attarder à la lecture de cette grille, car elle illustre la discipline de la méthode. Les ajustements individuels sont tous modestes — aucun ne dépasse 5 % — parce que les comparables ont été <em>bien choisis</em> en amont : tailles voisines, construction récente, même région. Si l'un des comparables avait exigé un ajustement de qualité de 20 %, la bonne réaction n'aurait pas été de le calculer avec plus de soin, mais de le remplacer. La convergence finale à 2,5 % n'est donc pas un coup de chance : c'est le produit de la sélection. On retrouve ici, transposée aux coûts, la règle d'or des grilles de terrain du chapitre <a class="xref" href="/seance/04/">4</a> — la qualité des intrants prime le raffinement du traitement.</p>172<div class="box box-ex" id="ex-6-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 6.2</span><span class="box-title">— immeuble de bureaux, Gatineau, <span class="num">8500</span> pi<sup>2</sup></span><a class="box-anchor" href="#ex-6-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-26">Sujet : bureaux de bonne qualité, 3 étages. Deux comparables :</p>173<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th></th><th class="al-r">Comp. A</th><th class="al-r">Comp. B</th></tr></thead><tbody><tr><td>Superficie (pi<sup>2</sup>)</td><td class="al-r"><span class="num">7200</span></td><td class="al-r"><span class="num">9800</span></td></tr><tr><td>Coût/pi<sup>2</sup> brut</td><td class="al-r">245,00 $</td><td class="al-r">228,00 $</td></tr><tr><td>Ajust. taille</td><td class="al-r"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>3 %</td><td class="al-r"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>2 %</td></tr><tr><td>Ajust. date (2024 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>→</mo></mrow><annotation encoding="application/x-tex">\rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">→</span></span></span></span> 2025)</td><td class="al-r"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>4 %</td><td class="al-r"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>2 %</td></tr><tr><td>Ajust. qualité</td><td class="al-r"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>5 %</td><td class="al-r"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>3 %</td></tr><tr><td>Ajust. hauteur (2 ét. <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> 3)</td><td class="al-r"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>4 %</td><td class="al-r">0 %</td></tr><tr class="rule-above"><td><strong>Coût/pi<sup>2</sup> ajusté</strong></td><td class="al-r"><strong>245,00 $</strong></td><td class="al-r"><strong>243,96 $</strong></td></tr></tbody></table></div></div>174<p id="p6-27">Moyenne <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> 244,48 $/pi<sup>2</sup> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>8</mn><mtext> </mtext><mn>500</mn><mo>×</mo><mn>244,48</mn><mo>≈</mo><mrow><mtext>2</mtext><mtext> </mtext><mtext>078</mtext><mtext> </mtext><mtext>080</mtext><mtext> </mtext><mtext>$</mtext></mrow></mrow><annotation encoding="application/x-tex">8\,500 \times 244{,}48 \approx \text{2\,078\,080\,\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">8</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">244</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">48</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord text"><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">078</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">080</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span></span>.</p></div></div>175<div class="box box-rem" id="remarque-6-28"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pen"/></svg></span><span class="box-label">avantages et limites</span><a class="box-anchor" href="#remarque-6-28" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-29"><strong>Pour</strong> : rapide, simple, données disponibles, bien comprise des clients, reflète le marché. <strong>Contre</strong> : moins précise, difficile pour les bâtiments atypiques, ajustements parfois subjectifs, sensible au choix des comparables. Idéale pour les bâtiments standards et les évaluations courantes.</p></div></div>176<h2 id="s-6-3" class="h-section"><span class="h-num">6.3</span><span class="h-text">La méthode par quantité et prix unitaires (Quantity Survey)</span><a class="h-anchor" href="#s-6-3" aria-label="Lien vers cette section">#</a></h2>177<div class="box box-def" id="def-6-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 6.2</span><span class="box-title">— Quantity Survey</span><a class="box-anchor" href="#def-6-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-30">Décomposer la construction en chacun de ses postes de travail, quantifier les matériaux et la main-d'œuvre, puis appliquer les prix unitaires courants :</p>178<div class="eq" id="eq-6-2"><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>C</mi><mtext>neuf</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><mi>Q</mi><mi>i</mi></msub><mo>×</mo><msub><mi>P</mi><mi>i</mi></msub><mtext> </mtext><mo>+</mo><mtext> </mtext><msub><mi>C</mi><mtext>indirects</mtext></msub><mtext> </mtext><mo>+</mo><mtext> </mtext><mtext>Profit</mtext></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(6.2)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">C_{\text{neuf}} \;=\; \sum_{i=1}^{n} Q_i \times P_i179\;+\; C_{\text{indirects}} \;+\; \text{Profit}\tag{6.2}</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:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">neuf</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></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 mathnormal">Q</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-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</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:0.1389em;">P</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-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</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:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">indirects</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:0.6944em;"></span><span class="mord text"><span class="mord">Profit</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">6.2</span></span><span class="mord">)</span></span></span></span></span></span></div>180<p id="p6-31">où <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">Q_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">Q</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-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</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> est la quantité du poste <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6595em;"></span><span class="mord mathnormal">i</span></span></span></span> et <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">P_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.1389em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</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> son prix unitaire.</p></div></div>181<p id="p6-32">C'est la méthode de l'estimateur professionnel et de l'entrepreneur — l'équivalent d'une soumission détaillée. La décomposition suit l'ordre chronologique du chantier : excavation et terrassement; fondations et dalle; structure; enveloppe (toiture, murs extérieurs); mécanique (CVAC, plomberie); électricité; finitions intérieures; aménagements extérieurs. Les quantités se calculent à partir des plans et devis, des relevés de terrain, des exigences du Code de construction du Québec et de ratios standards pour les composantes cachées : volumes de béton (m<sup>3</sup>) et d'armature (kg), bois de charpente (pmp), tuyauterie (pi linéaires), points électriques (unités), surfaces de gypse et de peinture (pi<sup>2</sup>).</p>182<p id="p6-33">La force de la méthode — son exhaustivité — est aussi sa vulnérabilité : un poste omis est un poste à zéro dollar, et l'erreur est silencieuse. L'estimateur expérimenté se protège par une liste de contrôle systématique et par les postes que les débutants oublient presque toujours : la mobilisation et la démobilisation du chantier, les échafaudages et la location d'équipement, la gestion des débris et les conteneurs, le déneigement ou le chauffage temporaire selon la saison, les essais et la mise en service des systèmes, et le nettoyage final. Il ajoute enfin une <strong class="c-bleu">contingence</strong> de 5 à 10 % des coûts directs, non pour masquer son imprécision, mais parce que l'expérience démontre qu'aucun bordereau, si soigné soit-il, ne capture la totalité des aléas d'un chantier réel.</p>183<h3 id="s-6-3-1" class="h-subsection"><span class="h-num">6.3.1</span><span class="h-text">La main-d'œuvre : le cadre de la CCQ</span><a class="h-anchor" href="#s-6-3-1" aria-label="Lien vers cette section">#</a></h3>184<div class="box box-qc" id="quebec-6-34"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-map"/></svg></span><span class="box-label">loi R-20 et conventions collectives</span><a class="box-anchor" href="#quebec-6-34" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-35">Au Québec, les relations de travail dans la construction sont encadrées par la <strong class="c-bleu">loi R-20</strong> (relations du travail, formation et gestion de la main-d'œuvre dans l'industrie de la construction). Les conventions collectives <strong>2025–2029</strong> couvrent quatre secteurs : résidentiel, institutionnel-commercial (IC), industriel, génie civil et voirie — avec des hausses d'environ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>5 % au 26 avril 2026 selon le secteur. Les taux de base varient selon le métier, le statut (apprenti ou compagnon), le secteur et parfois la région; la source officielle est l'outil « Salaire et taux » de la <span class="motcle" data-term="CCQ">CCQ</span> (Commission de la construction du Québec — à ne pas confondre avec le <em>Code de construction du Québec</em>, toujours écrit en toutes lettres dans ce cours).</p></div></div>185<p id="p6-36">La main-d'œuvre représente typiquement 40 à 50 % des coûts directs d'un bâtiment résidentiel, et le contexte québécois lui donne un relief particulier : les taux étant fixés par conventions collectives sectorielles, ils sont publics, uniformes et prévisibles — un avantage rare pour l'estimateur, qui n'a pas à deviner le salaire du marché comme dans les provinces voisines. La contrepartie est une mécanique de charges sociales parmi les plus lourdes du continent, qu'il faut impérativement intégrer au calcul : c'est l'objet de la notion de coût « chargé ».</p>186<div class="box box-form" id="form-6-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 6.1</span><span class="box-title">— du taux de base au coût employeur « chargé »</span><a class="box-anchor" href="#form-6-1" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-6-3"><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><mrow><mtext>Co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>t horaire charg</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover></mrow><mtext> </mtext><mo>≈</mo><mtext> </mtext><mtext>Taux de base</mtext><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mn>0,45</mn><mtext> </mtext><mover accent="true"><mtext>a</mtext><mo>ˋ</mo></mover><mtext> </mtext><mn>0,60</mn><mo stretchy="false">)</mo></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(6.3)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">\text{Coût horaire chargé} \;\approx\; \text{Taux de base} \times187(1 + 0{,}45~\text{à}~0{,}60)\tag{6.3}</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="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 horaire charg</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span></span><span 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">Taux de base</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">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">45</span><span class="mspace nobreak"> </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">ˋ</span></span></span></span></span></span></span></span><span class="mspace nobreak"> </span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">60</span><span class="mclose">)</span></span><span class="katex-tag"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">6.3</span></span><span class="mord">)</span></span></span></span></span></span></div>188<p id="p6-37">Les charges (avantages sociaux, cotisations CCQ et CNESST, congés payés) ajoutent environ 45 à 60 % au taux de base.</p></div></div>189<div class="box box-ex" id="ex-6-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 6.3</span><span class="box-title">— coût chargé de deux métiers (secteur IC, janvier 2026)</span><a class="box-anchor" href="#ex-6-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-38">Électricien compagnon : taux de base <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> 50,67 $/h <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> coût chargé <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> 73 à 81 $/h. Charpentier-menuisier compagnon : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span></span></span></span> 47,77 $/h <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><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> 69 à 76 $/h. Dans un estimé, on utilise <strong class="c-rouge">toujours le coût chargé</strong>, jamais le taux de base seul — l'oublier sous-estime la main-d'œuvre de moitié.</p></div></div>190<h3 id="s-6-3-2" class="h-subsection"><span class="h-num">6.3.2</span><span class="h-text">Bordereau complet — résidence de <span class="num">1450</span> pi<sup>2</sup></span><a class="h-anchor" href="#s-6-3-2" aria-label="Lien vers cette section">#</a></h3>191<p id="p6-39">Les tableaux suivants déroulent un <em>Quantity Survey</em> complet (prix installés indicatifs 2025–2026, matériaux <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> main-d'œuvre, à valider sur guides et soumissions).</p>192<div class="center"><div class="table-wrap"><table class="tbl table-wide"><thead><tr><th>Fondations</th><th>Unité</th><th class="al-r">Qté</th><th class="al-r">P.U.</th><th class="al-r">Total</th></tr></thead><tbody><tr><td>Excavation</td><td>m<sup>3</sup></td><td class="al-r">85</td><td class="al-r">18,50 $</td><td class="al-r">1 572 $</td></tr><tr><td>Semelles de béton</td><td>m<sup>3</sup></td><td class="al-r">4,2</td><td class="al-r">310,00 $</td><td class="al-r">1 302 $</td></tr><tr><td>Coffrage des murs</td><td>pi<sup>2</sup></td><td class="al-r">640</td><td class="al-r">6,75 $</td><td class="al-r">4 320 $</td></tr><tr><td>Béton des murs (30 MPa)</td><td>m<sup>3</sup></td><td class="al-r">12,5</td><td class="al-r">245,00 $</td><td class="al-r">3 063 $</td></tr><tr><td>Armature #15</td><td>kg</td><td class="al-r">680</td><td class="al-r">1,85 $</td><td class="al-r">1 258 $</td></tr><tr><td>Imperméabilisation</td><td>pi<sup>2</sup></td><td class="al-r">640</td><td class="al-r">3,50 $</td><td class="al-r">2 240 $</td></tr><tr><td>Drain français</td><td>pi lin.</td><td class="al-r">130</td><td class="al-r">12,00 $</td><td class="al-r">1 560 $</td></tr><tr><td>Dalle sur sol (4 po)</td><td>pi<sup>2</sup></td><td class="al-r">900</td><td class="al-r">5,25 $</td><td class="al-r">4 725 $</td></tr><tr><td>Remblayage</td><td>m<sup>3</sup></td><td class="al-r">55</td><td class="al-r">14,00 $</td><td class="al-r">770 $</td></tr><tr class="rule-above"><td class="al-r" colspan="4"><strong>Sous-total fondations</strong></td><td class="al-r"><strong>20 810 $</strong></td></tr></tbody></table></div></div>193<div class="center"><div class="table-wrap"><table class="tbl table-wide"><thead><tr><th>Structure et enveloppe</th><th>Unité</th><th class="al-r">Qté</th><th class="al-r">P.U.</th><th class="al-r">Total</th></tr></thead><tbody><tr><td>Solives de plancher 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>10</td><td>pi lin.</td><td class="al-r"><span class="num">1200</span></td><td class="al-r">2,15 $</td><td class="al-r">2 580 $</td></tr><tr><td>Montants de murs 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>6</td><td>pi lin.</td><td class="al-r"><span class="num">2400</span></td><td class="al-r">0,95 $</td><td class="al-r">2 280 $</td></tr><tr><td>Fermes de toit</td><td>unité</td><td class="al-r">24</td><td class="al-r">285,00 $</td><td class="al-r">6 840 $</td></tr><tr><td>Contreplaqué de plancher</td><td>pi<sup>2</sup></td><td class="al-r"><span class="num">1450</span></td><td class="al-r">1,85 $</td><td class="al-r">2 683 $</td></tr><tr class="rule-above"><td class="al-r" colspan="4"><em>Sous-total structure</em></td><td class="al-r"><em>14 383 $</em></td></tr><tr class="rule-above"><td>Revêtement extérieur vinyle</td><td>pi<sup>2</sup></td><td class="al-r"><span class="num">1800</span></td><td class="al-r">4,50 $</td><td class="al-r">8 100 $</td></tr><tr><td>Isolation des murs R-24</td><td>pi<sup>2</sup></td><td class="al-r"><span class="num">1800</span></td><td class="al-r">1,45 $</td><td class="al-r">2 610 $</td></tr><tr><td>Fenêtres PVC</td><td>unité</td><td class="al-r">14</td><td class="al-r">650,00 $</td><td class="al-r">9 100 $</td></tr><tr><td>Toiture en bardeaux</td><td>carré</td><td class="al-r">18</td><td class="al-r">285,00 $</td><td class="al-r">5 130 $</td></tr><tr class="rule-above"><td class="al-r" colspan="4"><em>Sous-total enveloppe</em></td><td class="al-r"><em>24 940 $</em></td></tr></tbody></table></div></div>194<div class="center"><div class="table-wrap"><table class="tbl table-wide"><thead><tr><th>Mécanique, électricité, finitions</th><th>Unité</th><th class="al-r">Qté</th><th class="al-r">P.U.</th><th class="al-r">Total</th></tr></thead><tbody><tr><td>Tuyauterie d'alimentation</td><td>pi lin.</td><td class="al-r">180</td><td class="al-r">14,50 $</td><td class="al-r">2 610 $</td></tr><tr><td>Tuyauterie d'évacuation</td><td>pi lin.</td><td class="al-r">120</td><td class="al-r">18,75 $</td><td class="al-r">2 250 $</td></tr><tr><td>Appareils sanitaires</td><td>unité</td><td class="al-r">8</td><td class="al-r">425,00 $</td><td class="al-r">3 400 $</td></tr><tr><td>Fournaise électrique</td><td>unité</td><td class="al-r">1</td><td class="al-r">3 200,00 $</td><td class="al-r">3 200 $</td></tr><tr><td>Conduits et registres</td><td>pi lin.</td><td class="al-r">220</td><td class="al-r">12,50 $</td><td class="al-r">2 750 $</td></tr><tr><td>Panneau 200 A</td><td>unité</td><td class="al-r">1</td><td class="al-r">2 800,00 $</td><td class="al-r">2 800 $</td></tr><tr><td>Câblage et prises</td><td>point</td><td class="al-r">65</td><td class="al-r">185,00 $</td><td class="al-r">12 025 $</td></tr><tr><td>Luminaires</td><td>unité</td><td class="al-r">22</td><td class="al-r">145,00 $</td><td class="al-r">3 190 $</td></tr><tr class="rule-above"><td class="al-r" colspan="4"><em>Sous-total mécanique/électricité</em></td><td class="al-r"><em>32 225 $</em></td></tr><tr class="rule-above"><td>Gypse (murs et plafonds)</td><td>pi<sup>2</sup></td><td class="al-r"><span class="num">5200</span></td><td class="al-r">2,85 $</td><td class="al-r">14 820 $</td></tr><tr><td>Peinture</td><td>pi<sup>2</sup></td><td class="al-r"><span class="num">5200</span></td><td class="al-r">1,75 $</td><td class="al-r">9 100 $</td></tr><tr><td>Plancher de bois franc</td><td>pi<sup>2</sup></td><td class="al-r">850</td><td class="al-r">8,50 $</td><td class="al-r">7 225 $</td></tr><tr><td>Céramique (SdB, cuisine)</td><td>pi<sup>2</sup></td><td class="al-r">280</td><td class="al-r">12,00 $</td><td class="al-r">3 360 $</td></tr><tr><td>Armoires de cuisine</td><td>pi lin.</td><td class="al-r">22</td><td class="al-r">350,00 $</td><td class="al-r">7 700 $</td></tr><tr><td>Portes intérieures</td><td>unité</td><td class="al-r">12</td><td class="al-r">385,00 $</td><td class="al-r">4 620 $</td></tr><tr><td>Escalier</td><td>unité</td><td class="al-r">1</td><td class="al-r">3 500,00 $</td><td class="al-r">3 500 $</td></tr><tr><td>Comptoirs</td><td>pi lin.</td><td class="al-r">18</td><td class="al-r">175,00 $</td><td class="al-r">3 150 $</td></tr><tr class="rule-above"><td class="al-r" colspan="4"><em>Sous-total finitions</em></td><td class="al-r"><em>53 475 $</em></td></tr></tbody></table></div></div>195<h3 id="s-6-3-3" class="h-subsection"><span class="h-num">6.3.3</span><span class="h-text">Récapitulatif et structure des coûts</span><a class="h-anchor" href="#s-6-3-3" aria-label="Lien vers cette section">#</a></h3>196<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Section</th><th class="al-r">Montant</th><th class="al-r">Part</th></tr></thead><tbody><tr><td>Fondations et excavation</td><td class="al-r">20 810 $</td><td class="al-r">14,3 %</td></tr><tr><td>Structure (charpente)</td><td class="al-r">14 383 $</td><td class="al-r">9,9 %</td></tr><tr><td>Enveloppe</td><td class="al-r">24 940 $</td><td class="al-r">17,1 %</td></tr><tr><td>Mécanique et électricité</td><td class="al-r">32 225 $</td><td class="al-r">22,1 %</td></tr><tr><td>Finitions intérieures</td><td class="al-r">53 475 $</td><td class="al-r">36,7 %</td></tr><tr class="rule-above"><td><strong>Coûts directs</strong></td><td class="al-r"><strong>145 833 $</strong></td><td class="al-r">100 %</td></tr><tr><td>Frais généraux de chantier (18 %)</td><td class="al-r">26 250 $</td><td class="al-r"></td></tr><tr><td>Profit de l'entrepreneur (12 %)</td><td class="al-r">20 650 $</td><td class="al-r"></td></tr><tr class="rule-above"><td><strong>Coût de construction (entrepreneur)</strong></td><td class="al-r"><strong>192 733 $</strong></td><td class="al-r">(132,92 $/pi<sup>2</sup>)</td></tr></tbody></table></div></div>197<p id="p6-40">Retenir la hiérarchie des postes : les <strong class="c-bleu">finitions</strong> sont le premier poste (36,7 %), suivies de la mécanique/électricité (22,1 %) — la structure brute ne pèse que 10 %. C'est pourquoi la <em>qualité</em> des finitions fait basculer les classes de coûts.</p>198<p id="p6-41">Cette hiérarchie surprend systématiquement les étudiants, qui imaginent la charpente et les fondations comme le « gros » de la maison. En réalité, le squelette d'un bâtiment résidentiel est bon marché : c'est du bois d'œuvre posé rapidement par une équipe rodée. Ce qui coûte cher, c'est tout ce qui se voit et tout ce qui se branche — armoires, planchers, céramique, appareils, filage, plomberie. Cette réalité a deux conséquences pratiques pour l'évaluateur. D'une part, l'écart de coût entre deux maisons de même superficie s'explique presque entièrement par les finitions et la mécanique, d'où le poids du facteur de qualité. D'autre part, lors du calcul de la dépréciation au bloc 4, les composantes qui s'usent vite (finitions, mécanique) sont précisément les plus coûteuses — ce qui explique qu'un bâtiment de 25 ans puisse avoir consommé bien plus que 25/60<sup>e</sup> de son coût neuf.</p>199<h3 id="s-6-3-4" class="h-subsection"><span class="h-num">6.3.4</span><span class="h-text">La leçon de la portée des coûts</span><a class="h-anchor" href="#s-6-3-4" aria-label="Lien vers cette section">#</a></h3>200<div class="box box-att" id="attention-6-42"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">pourquoi 132,92 contre 194,36 $/pi<sup>2</sup>?</span><a class="box-anchor" href="#attention-6-42" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-43">Le <em>Quantity Survey</em> ci-dessus donne 132,92 $/pi<sup>2</sup>; la méthode comparative donnait 194,36 $/pi<sup>2</sup> pour le même type de maison. <strong class="c-rouge">Aucune des deux n'est fausse</strong> : elles n'ont pas la même portée. Le bordereau s'arrête au <strong>coût de construction de l'entrepreneur</strong>; les comparables reflètent le <strong>coût complet du projet</strong>, qui ajoute les coûts indirects du promoteur (honoraires professionnels, permis, financement intérimaire, assurances, mise en marché, marge) — environ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>40 %. Vérification : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>132,92</mn><mo>×</mo><mn>1,40</mn><mo>≈</mo><mn>186</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">132{,}92 \times 1{,}40 \approx201186~\$/\text{pi}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">132</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">92</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">40</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1219em;vertical-align:-0.25em;"></span><span class="mord">186</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>, à environ 4 % de la comparative — cohérent.</p></div></div>202<div class="box box-ret" id="aretenir-6-44"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-star"/></svg></span><span class="box-label">la leçon clé de la séance</span><a class="box-anchor" href="#aretenir-6-44" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-45">Toujours comparer des coûts de <strong>même portée</strong> : coûts directs, coût de construction (directs <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> frais de chantier <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> profit de l'entrepreneur) ou coût complet du projet (tout, y compris les indirects du promoteur). Un écart apparent de 45 % entre deux estimations révèle le plus souvent une différence de <em>définition</em>, pas une erreur de calcul.</p></div></div>203<p id="p6-46">Cette leçon dépasse largement le cadre de l'examen. Dans la pratique, c'est la première question à poser devant n'importe quel chiffre de coût, d'où qu'il vienne : le « 180 $ du pied carré » lancé par un entrepreneur au téléphone, le coût affiché dans un article de journal sur un projet public, la fourchette d'un guide commercial, le montant déclaré au permis. Chacun de ces chiffres est vrai <em>dans sa portée</em> et faux dans toutes les autres. L'évaluateur qui documente systématiquement, pour chaque donnée de coût recueillie, ce qu'elle inclut et ce qu'elle exclut, se met à l'abri de la principale source d'erreurs grossières de la méthode du coût — et se donne en prime un argument redoutable lorsque son estimation est contestée.</p>204<div class="box box-rem" id="remarque-6-47"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pen"/></svg></span><span class="box-label">avantages et limites du Quantity Survey</span><a class="box-anchor" href="#remarque-6-47" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-48"><strong>Pour</strong> : la plus précise, transparente et vérifiable poste par poste, adaptée aux bâtiments spécialisés. <strong>Contre</strong> : très longue (20–40 h) et coûteuse, exige une expertise en construction et des plans détaillés, risque d'omission de postes. Usage typique : estimateurs en construction, litiges et expertises judiciaires.</p></div></div>205<h2 id="s-6-4" class="h-section"><span class="h-num">6.4</span><span class="h-text">La méthode par composantes (Unit-in-Place)</span><a class="h-anchor" href="#s-6-4" aria-label="Lien vers cette section">#</a></h2>206<div class="box box-def" id="def-6-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 6.3</span><span class="box-title">— méthode par composantes</span><a class="box-anchor" href="#def-6-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-49">Décomposer le bâtiment en grandes composantes (fondations, structure, toiture, plomberie, etc.) et appliquer à chacune un <strong>coût installé</strong> — matériaux, main-d'œuvre et frais généraux de chantier compris :</p>207<div class="eq" id="eq-6-4"><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>C</mi><mtext>neuf</mtext></msub><mtext> </mtext><mo>=</mo><mtext> </mtext><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></munderover><msub><mi>S</mi><mi>j</mi></msub><mo>×</mo><msub><mi>C</mi><mi>j</mi></msub></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(6.4)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">C_{\text{neuf}} \;=\; \sum_{j=1}^{m} S_j \times C_j\tag{6.4}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">neuf</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span 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:3.0652em;vertical-align:-1.4138em;"></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" style="margin-right:0.0572em;">j</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">m</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.4138em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0576em;">S</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-left:-0.0576em;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:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.0572em;">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 class="katex-tag"><span class="katex-strut" style="height:3.0652em;vertical-align:-1.4138em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">6.4</span></span><span class="mord">)</span></span></span></span></span></span></div>208<p id="p6-50">où <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>S</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">S_j</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:0.0576em;">S</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-left:-0.0576em;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> est la quantité de la 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> et <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">C_j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.0572em;">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> son coût installé unitaire. Aussi appelée <em>Segregated Cost Method</em> ou <em>Unit-in-Place</em>; c'est la base de la méthode Marshall & Swift.</p></div></div>209<p id="p6-51">Le compromis est clair<label for="sn-6-3" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-6-3" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-repere">Composantes <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> 10 à 20 lignes. Quantity Survey <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> des centaines.</span> : au lieu de centaines de postes, une quinzaine de composantes à coûts installés. La précision reste bonne, l'effort raisonnable (4–8 h), et surtout la dépréciation pourra ensuite être analysée <strong class="c-bleu">composante par composante</strong> — un avantage décisif pour le bloc 4.</p>210<p id="p6-52">Ce dernier point mérite qu'on s'y arrête, car il explique pourquoi la méthode par composantes est celle de l'<em>évaluateur</em> plus encore que celle de l'estimateur. Quand viendra le temps de mesurer la dépréciation physique, il faudra distinguer les composantes à <em>courte durée de vie</em> (toiture, revêtements de sol, appareils mécaniques, dont l'usure se mesure sur 15 à 25 ans) des composantes à <em>longue durée de vie</em> (fondations, structure, qui vivent aussi longtemps que le bâtiment). Cette distinction n'est possible que si le coût neuf de chaque composante est connu séparément : on ne peut déprécier à 60 % une toiture dont on ignore le coût. La méthode par composantes prépare donc exactement le terrain dont le bloc 4 aura besoin — c'est un investissement, pas une dépense.</p>211<h3 id="s-6-4-1" class="h-subsection"><span class="h-num">6.4.1</span><span class="h-text">Coûts installés types</span><a class="h-anchor" href="#s-6-4-1" aria-label="Lien vers cette section">#</a></h3>212<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Composante</th><th>Unité</th><th>Coût installé</th><th>Inclut</th></tr></thead><tbody><tr><td>Fondations</td><td>pi<sup>2</sup> de dalle</td><td>22–35 $</td><td>Excavation, béton, armature</td></tr><tr><td>Structure de plancher</td><td>pi<sup>2</sup></td><td>8–15 $</td><td>Solives, contreplaqué</td></tr><tr><td>Murs extérieurs</td><td>pi<sup>2</sup> de mur</td><td>18–32 $</td><td>Montants, isolation, revêtement</td></tr><tr><td>Toiture</td><td>pi<sup>2</sup> projeté</td><td>12–22 $</td><td>Fermes, support, bardeaux</td></tr><tr><td>Fenêtration</td><td>pi<sup>2</sup> vitré</td><td>45–85 $</td><td>Fenêtres installées</td></tr><tr><td>Plomberie</td><td>appareil</td><td>2 800–4 500 $</td><td>Tuyauterie <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> appareils</td></tr><tr><td>Électricité</td><td>pi<sup>2</sup> bâtiment</td><td>10–18 $</td><td>Panneau, filage, prises</td></tr><tr><td>Chauffage/CVAC</td><td>pi<sup>2</sup> bâtiment</td><td>8–25 $</td><td>Système complet</td></tr><tr><td>Finitions intérieures</td><td>pi<sup>2</sup> bâtiment</td><td>25–55 $</td><td>Gypse, peinture, planchers</td></tr></tbody></table></div></div>213<p id="p6-53">Les fourchettes reflètent la qualité (standard à supérieure); coûts indicatifs 2025–2026, à valider sur les guides et les soumissions.</p>214<p id="p6-54">La subtilité des coûts installés tient à leurs <em>unités hétérogènes</em>, et c'est la première chose à maîtriser pour éviter les erreurs grossières. Les fondations se chiffrent au pied carré <em>de dalle</em>, pas de plancher total; les murs extérieurs, au pied carré <em>de mur</em> (périmètre <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> hauteur, ouvertures généralement incluses au prix du mur); la toiture, au pied carré <em>projeté</em> au sol, pas à la surface réelle des versants; la plomberie, à l'<em>appareil</em> (chaque évier, toilette, douche); l'électricité et le chauffage, au pied carré de bâtiment. Confondre la surface de mur et la surface de plancher — l'erreur la plus fréquente — peut fausser la composante murs de 30 à 50 %. Le bon réflexe : pour chaque ligne du bordereau, écrire l'unité en toutes lettres et vérifier que la quantité qui la multiplie est bien mesurée dans cette unité.</p>215<h3 id="s-6-4-2" class="h-subsection"><span class="h-num">6.4.2</span><span class="h-text">Exemple complet</span><a class="h-anchor" href="#s-6-4-2" aria-label="Lien vers cette section">#</a></h3>216<div class="box box-ex" id="ex-6-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 6.4</span><span class="box-title">— la même maison de <span class="num">1450</span> pi<sup>2</sup>, par composantes</span><a class="box-anchor" href="#ex-6-4" aria-label="Lien">#</a></div><div class="box-body"><div class="center"><div class="table-wrap"><table class="tbl table-wide"><thead><tr><th>Composante</th><th>Unité</th><th class="al-r">Qté</th><th class="al-r">Coût/u</th><th class="al-r">Total</th></tr></thead><tbody><tr><td>Fondations</td><td>pi<sup>2</sup> dalle</td><td class="al-r">725</td><td class="al-r">28,50 $</td><td class="al-r">20 663 $</td></tr><tr><td>Structure de plancher</td><td>pi<sup>2</sup></td><td class="al-r"><span class="num">1450</span></td><td class="al-r">11,50 $</td><td class="al-r">16 675 $</td></tr><tr><td>Murs extérieurs</td><td>pi<sup>2</sup> mur</td><td class="al-r"><span class="num">1920</span></td><td class="al-r">24,00 $</td><td class="al-r">46 080 $</td></tr><tr><td>Toiture</td><td>pi<sup>2</sup> proj.</td><td class="al-r">780</td><td class="al-r">16,50 $</td><td class="al-r">12 870 $</td></tr><tr><td>Plomberie</td><td>appareil</td><td class="al-r">8</td><td class="al-r">3 200 $</td><td class="al-r">25 600 $</td></tr><tr><td>Électricité</td><td>pi<sup>2</sup> bât.</td><td class="al-r"><span class="num">1450</span></td><td class="al-r">13,50 $</td><td class="al-r">19 575 $</td></tr><tr><td>Chauffage</td><td>pi<sup>2</sup> bât.</td><td class="al-r"><span class="num">1450</span></td><td class="al-r">6,50 $</td><td class="al-r">9 425 $</td></tr><tr><td>Finitions intérieures</td><td>pi<sup>2</sup> bât.</td><td class="al-r"><span class="num">1450</span></td><td class="al-r">35,00 $</td><td class="al-r">50 750 $</td></tr><tr class="rule-above"><td class="al-r" colspan="4"><strong>Coûts directs (installés)</strong></td><td class="al-r"><strong>201 638 $</strong></td></tr><tr><td class="al-r" colspan="4"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</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 indirects (15 %)</td><td class="al-r">30 246 $</td></tr><tr><td class="al-r" colspan="4"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> Profit entrepreneurial (10 %)</td><td class="al-r">23 188 $</td></tr><tr class="rule-above"><td class="al-r" colspan="4"><strong>Coût total de remplacement</strong></td><td class="al-r"><strong>255 072 $</strong></td></tr><tr><td class="al-r" colspan="4">Coût par pi<sup>2</sup></td><td class="al-r"><strong>175,91 $/pi<sup>2</sup></strong></td></tr></tbody></table></div></div>217<p id="p6-55">Le résultat (175,91 $/pi<sup>2</sup>) se situe entre le Quantity Survey (132,92 $, portée entrepreneur) et la comparative (194,36 $, coût complet) : les coûts installés intègrent les frais de chantier, mais pas tous les coûts du promoteur. Encore la portée!</p></div></div>218<div class="box box-rem" id="remarque-6-56"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pen"/></svg></span><span class="box-label">avantages et limites</span><a class="box-anchor" href="#remarque-6-56" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-57"><strong>Pour</strong> : bon équilibre précision/effort; dépréciation analysable par composante; données disponibles (M&S, RSMeans); bien adaptée aux évaluateurs. <strong>Contre</strong> : moins précise que le Quantity Survey; coûts installés <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> moyennes; difficile pour les composantes non standards; exige de bonnes mesures.</p></div></div>219<h2 id="s-6-5" class="h-section"><span class="h-num">6.5</span><span class="h-text">La méthode du coût indexé (Trended Cost)</span><a class="h-anchor" href="#s-6-5" aria-label="Lien vers cette section">#</a></h2>220<div class="box box-form" id="form-6-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 6.2</span><span class="box-title">— coût indexé</span><a class="box-anchor" href="#form-6-2" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-6-5"><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>C</mi><mtext>actuel</mtext></msub><mtext> </mtext><mo>=</mo><mtext> </mtext><msub><mi>C</mi><mtext>original</mtext></msub><mo>×</mo><mfrac><msub><mi>I</mi><mtext>actuel</mtext></msub><msub><mi>I</mi><mtext>original</mtext></msub></mfrac></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(6.5)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">C_{\text{actuel}} \;=\; C_{\text{original}} \times221\frac{I_{\text{actuel}}}{I_{\text{original}}}\tag{6.5}</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:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">actuel</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:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">original</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.3324em;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:1.3603em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0785em;">I</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:-0.0785em;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">original</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><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 mathnormal" style="margin-right:0.0785em;">I</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:-0.0785em;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">actuel</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9721em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="katex-tag"><span class="katex-strut" style="height:2.3324em;vertical-align:-0.9721em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">6.5</span></span><span class="mord">)</span></span></span></span></span></span></div>222<p id="p6-58">où <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mtext>original</mtext></msub></mrow><annotation encoding="application/x-tex">C_{\text{original}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">original</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span> est le coût de construction documenté (contrat, factures, permis, évaluation antérieure) et <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi></mrow><annotation encoding="application/x-tex">I</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.0785em;">I</span></span></span></span> l'indice de coûts.</p></div></div>223<p id="p6-59">C'est la méthode la plus rapide lorsque le coût original est <strong class="c-bleu">fiable</strong>. Les indices disponibles : l'IPCB de Statistique Canada (tableau 18-10-0289-01, base 2023 <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> 100, trimestriel, 15 RMR dont Montréal, Québec et Ottawa–Gatineau), les indices Altus (annuel), Marshall & Swift (mensuel), ENR et RSMeans. Toujours choisir un indice cohérent avec le type de bâtiment et la région.</p>224<p id="p6-60">Tout repose donc sur la qualité du coût de départ, et c'est là que l'évaluateur doit exercer son scepticisme. Un contrat d'entrepreneur général signé et payé constitue un excellent point d'ancrage; un coût déclaré au permis de construction, déjà moins — les demandeurs sous-déclarent parfois pour réduire les droits. Le coût d'une <strong class="c-bleu">autoconstruction</strong> est pratiquement inutilisable : le propriétaire n'a payé ni sa propre main-d'œuvre ni le profit d'un entrepreneur, et son « coût » peut représenter 60 % du coût de marché. De même, un immeuble construit par un promoteur pour son propre portefeuille peut porter un coût interne sans marge. Avant d'indexer, il faut donc qualifier la provenance du montant : qui l'a payé, à qui, et ce qu'il incluait. Un coût original douteux indexé avec trois décimales reste un coût douteux.</p>225<div class="box box-ex" id="ex-6-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 6.5</span><span class="box-title">— indexation d'un coût de 2015</span><a class="box-anchor" href="#ex-6-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-61">Maison construite en 2015 au coût de <span class="num">225 000 $</span>; IPCB résidentiel Québec (illustratif) : 2015 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> 62,6; 2025 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> 105,5.</p>226<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>C</mi><mn>2025</mn></msub><mo>=</mo><mn>225</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mfrac><mn>105,5</mn><mn>62,6</mn></mfrac><mo>=</mo><mn>225</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>1,6853</mn><mo>≈</mo><mrow><mtext>379</mtext><mtext> </mtext><mtext>193</mtext><mtext> </mtext><mtext>$</mtext></mrow><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">C_{2025} = 225\,000 \times \frac{105{,}5}{62{,}6} = 225\,000 \times 1{,}6853227\approx \text{379\,193\,\$}.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2025</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">225</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.2019em;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:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">62</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">6</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">105</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">225</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">6853</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord text"><span class="mord">379</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">193</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span><span class="mord">.</span></span></span></span></span></div>228<p id="p6-62">Hausse de 68,5 % en dix ans (taux composé <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span></span></span></span> 5,4 %/an), dont l'essentiel en 2021–2022. Sur une aussi longue période, valider avec une autre méthode.</p></div></div>229<div class="box box-ex" id="ex-6-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 6.6</span><span class="box-title">— bâtiment rénové : indexer chaque strate</span><a class="box-anchor" href="#ex-6-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-63">Bâtiment construit en 2010 (<span class="num">185 000 $</span>, indice 55,3), cuisine rénovée en 2020 (<span class="num">35 000 $</span>) et salle de bain en 2020 (<span class="num">18 000 $</span>), indice 2020 <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> 72,4; indice 2025 <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> 105,5.</p>230<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Élément</th><th class="al-r">Coût original</th><th class="al-c">Facteur</th><th class="al-r">Coût 2025</th></tr></thead><tbody><tr><td>Construction 2010</td><td class="al-r">185 000 $</td><td class="al-c">1,9078</td><td class="al-r">352 943 $</td></tr><tr><td>Cuisine 2020</td><td class="al-r">35 000 $</td><td class="al-c">1,4572</td><td class="al-r">51 002 $</td></tr><tr><td>Salle de bain 2020</td><td class="al-r">18 000 $</td><td class="al-c">1,4572</td><td class="al-r">26 230 $</td></tr><tr class="rule-above"><td class="al-r" colspan="3"><strong>Coût total indexé 2025</strong></td><td class="al-r"><strong>430 175 $</strong></td></tr></tbody></table></div></div>231<p id="p6-64">Chaque élément s'indexe <strong class="c-bleu">à partir de sa propre date</strong> de réalisation — indexer le tout depuis 2010 surestimerait les rénovations, déjà payées en dollars de 2020.</p></div></div>232<div class="box box-rem" id="remarque-6-65"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pen"/></svg></span><span class="box-label">avantages et limites</span><a class="box-anchor" href="#remarque-6-65" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-66"><strong>Pour</strong> : la plus rapide; coût original objectif; utile en évaluation de masse; indices accessibles. <strong>Contre</strong> : coût original parfois inconnu ou atypique (autoconstruction, prix d'ami); indices <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> moyennes régionales; fiabilité décroissante sur longues périodes; ignore les rénovations non documentées.</p></div></div>233<h2 id="s-6-6" class="h-section"><span class="h-num">6.6</span><span class="h-text">Choisir et réconcilier : les quatre méthodes face à face</span><a class="h-anchor" href="#s-6-6" aria-label="Lien vers cette section">#</a></h2>234<div class="center"><div class="table-wrap"><table class="tbl table-wide"><thead><tr><th>Critère</th><th>Comparative</th><th>Quantity S.</th><th>Composantes</th><th>Indexée</th></tr></thead><tbody><tr><td>Précision</td><td>Moyenne</td><td>Très élevée</td><td>Élevée</td><td>Faible–moy.</td></tr><tr><td>Complexité</td><td>Faible</td><td>Très élevée</td><td>Moyenne</td><td>Faible</td></tr><tr><td>Temps requis</td><td>1–2 h</td><td>20–40 h</td><td>4–8 h</td><td>0,5–1 h</td></tr><tr><td>Expertise</td><td>Évaluateur</td><td>Estimateur</td><td>Évaluateur</td><td>Évaluateur</td></tr><tr><td>Données requises</td><td>Comparables</td><td>Plans détaillés</td><td>Mesures</td><td>Coût original</td></tr><tr><td>Usage typique</td><td>Courant</td><td>Litiges, spécial</td><td>Courant</td><td>Masse, municipal</td></tr></tbody></table></div></div>235<p id="p6-67">En clair : bâtiments <strong>standards</strong> avec comparables <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> comparative; bâtiments <strong>spéciaux</strong> ou litiges <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> Quantity Survey; bâtiments <strong>atypiques</strong> sans comparables, ou analyse fine de la dépréciation <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>→</mo></mrow><annotation encoding="application/x-tex">\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> composantes; évaluation <strong>de masse</strong> ou vérification croisée avec coût original fiable <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> indexée.</p>236<div class="box box-terrain" id="terrain-6-68"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-hardhat"/></svg></span><span class="box-label">deux méthodes valent mieux qu'une</span><a class="box-anchor" href="#terrain-6-68" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-69">Dans un rapport professionnel, l'estimation du coût neuf gagne énormément en crédibilité lorsqu'elle s'appuie sur deux méthodes indépendantes dont les résultats convergent. La combinaison la plus fréquente : composantes (ou comparative) comme méthode principale, coût indexé comme contre-vérification lorsque le coût original est documenté. Si les deux résultats s'écartent de plus de 10 à 15 %, ne pas moyenner aveuglément : chercher la cause — presque toujours une différence de portée, une strate de rénovation oubliée ou un coût original suspect — et la résoudre avant de conclure.</p></div></div>237<h3 id="s-6-6-1" class="h-subsection"><span class="h-num">6.6.1</span><span class="h-text">Exercice intégrateur — un duplex, trois méthodes</span><a class="h-anchor" href="#s-6-6-1" aria-label="Lien vers cette section">#</a></h3>238<div class="box box-ex" id="ex-6-7"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 6.7</span><span class="box-title">— duplex de Gatineau, trois estimations</span><a class="box-anchor" href="#ex-6-7" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-70">Sujet : duplex de <span class="num">2400</span> pi<sup>2</sup> (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> <span class="num">1200</span>), qualité standard, construit en 2018 au coût documenté de <span class="num">310 000 $</span>.</p>239<p id="p6-71"><strong>1. Comparative.</strong> Trois duplex récents (coûts complets) : 178,00, 168,00 et 174,00 $/pi<sup>2</sup>, qui deviennent après ajustements (taille, date, qualité) 179,78, 166,32 et 180,96 $/pi<sup>2</sup>; moyenne 175,69 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mn>400</mn><mo>×</mo><mn>175,69</mn><mo>=</mo><mrow><mtext>421</mtext><mtext> </mtext><mtext>656</mtext><mtext> </mtext><mtext>$</mtext></mrow></mrow><annotation encoding="application/x-tex">2\,400 \times 175{,}69 =240\text{421\,656\,\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.2222em;"></span><span 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">175</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">69</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord text"><span class="mord">421</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">656</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span></span>.</p>241<p id="p6-72"><strong>2. Composantes.</strong> Fondations (<span class="num">1200</span> pi<sup>2</sup> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo></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> 30,00 $), planchers (<span class="num">2400</span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\times</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">×</span></span></span></span> 12,00), murs (<span class="num">2560</span> pi<sup>2</sup> de mur <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> 24,50), toiture (<span class="num">1200</span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\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> 17,00), plomberie (14 appareils <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> 3 100), électricité (<span class="num">2400</span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\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> 14,00), chauffage (<span class="num">2400</span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\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> 7,00), finitions (<span class="num">2400</span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\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> 38,00) : coûts directs 332 920 $; <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> 1,265 (indirects 15 % et profit 10 %) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span> <strong><span class="num">421 144 $</span></strong>.</p>242<p id="p6-73"><strong>3. Indexée.</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>310</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>105,5</mn><mi mathvariant="normal">/</mi><mn>68,1</mn><mo>=</mo><mn>310</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>1,5492</mn><mo>=</mo><mrow><mtext>480</mtext><mtext> </mtext><mtext>252</mtext><mtext> </mtext><mtext>$</mtext></mrow></mrow><annotation encoding="application/x-tex">310\,000 \times 105{,}5/68{,}1 = 310\,000 \times2431{,}5492 = \text{480\,252\,\$}</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">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><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">105</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5/68</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">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><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5492</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord text"><span class="mord">480</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">252</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span></span> (le coût original de 2018 incluait déjà indirects et profit).</p>244<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Méthode</th><th class="al-r">Coût estimé</th><th class="al-r">$/pi<sup>2</sup></th></tr></thead><tbody><tr><td>Comparative</td><td class="al-r">421 656 $</td><td class="al-r">175,69</td></tr><tr><td>Par composantes</td><td class="al-r">421 144 $</td><td class="al-r">175,48</td></tr><tr><td>Coût indexé</td><td class="al-r">480 252 $</td><td class="al-r">200,11</td></tr><tr class="rule-above"><td><strong>Moyenne pondérée (40/35/25)</strong></td><td class="al-r"><strong>436 100 $</strong></td><td class="al-r"><strong>181,71</strong></td></tr></tbody></table></div></div>245<p id="p6-74">L'indexée ressort 14 % plus haut : elle répercute intégralement le choc de coûts 2021–2022 sur un coût de 2018, alors que les deux autres méthodes lisent le marché de 2025 directement. La pondération retenue (composantes 40 %, comparative 35 %, indexée 25 %) reflète la fiabilité relative — et l'écart maximal de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>±</mo></mrow><annotation encoding="application/x-tex">\pm</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">±</span></span></span></span>10 % autour de la conclusion reste acceptable.</p></div></div>246<p id="p6-75">Cet exercice intégrateur enseigne une dernière chose sur la nature des trois résultats. La comparative et la méthode par composantes sont des mesures <em>contemporaines</em> : elles photographient le marché de la construction à la date d'évaluation, chacune par un chemin différent, et leur convergence à 0,1 % près n'a donc rien d'un hasard — elles observent la même réalité. L'indexée, elle, est une mesure <em>historique projetée</em> : elle suppose que le bâtiment de 2018 était payé à son juste coût et que l'indice régional décrit bien sa trajectoire — deux hypothèses raisonnables mais invérifiées. Quand une mesure historique diverge de deux mesures contemporaines concordantes, ce sont les mesures contemporaines qui l'emportent; l'indexée conserve néanmoins sa place dans la pondération, car elle est la seule des trois à s'ancrer dans un fait documenté plutôt que dans des moyennes. Savoir <em>pourquoi</em> chaque méthode dit ce qu'elle dit — et non seulement combien — est précisément ce qui distingue la réconciliation du simple calcul de moyenne.</p>247<h2 id="s-6-7" class="h-section"><span class="h-num">6.7</span><span class="h-text">Les facteurs d'ajustement transversaux</span><a class="h-anchor" href="#s-6-7" aria-label="Lien vers cette section">#</a></h2>248<p id="p6-76">Quatre facteurs s'appliquent, peu importe la méthode retenue.</p>249<h3 id="s-6-7-1" class="h-subsection"><span class="h-num">6.7.1</span><span class="h-text">Économies d'échelle</span><a class="h-anchor" href="#s-6-7-1" aria-label="Lien vers cette section">#</a></h3>250<p id="p6-77">Le coût unitaire décroît avec la taille : les coûts fixes (mobilisation, équipements mécaniques de base, cuisine) se répartissent sur plus de pieds carrés. Le phénomène a une explication comptable limpide : qu'une maison fasse 800 ou <span class="num">3000</span> pi<sup>2</sup>, il lui faut <em>une</em> cuisine, <em>un</em> panneau électrique, <em>une</em> entrée d'eau, <em>un</em> système de chauffage central et <em>une</em> mobilisation de chantier. Ces postes forfaitaires, qui représentent une part importante du budget d'une petite maison, se diluent à mesure que la superficie croît — tandis que les postes proportionnels (gypse, peinture, planchers) suivent la surface. La courbe du coût unitaire est donc décroissante mais s'aplatit : l'essentiel de l'économie d'échelle se réalise entre 800 et <span class="num">2000</span> pi<sup>2</sup>, et il en reste peu au-delà de <span class="num">3000</span>.</p>251<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th class="al-c">Superficie (pi<sup>2</sup>)</th><th class="al-c">Coût/pi<sup>2</sup></th><th class="al-c">Facteur</th></tr></thead><tbody><tr><td class="al-c">800</td><td class="al-c">215 $</td><td class="al-c">1,10</td></tr><tr><td class="al-c"><span class="num">1200</span></td><td class="al-c">200 $</td><td class="al-c">1,03</td></tr><tr><td class="al-c"><span class="num">1500</span> (base)</td><td class="al-c">195 $</td><td class="al-c">1,00</td></tr><tr><td class="al-c"><span class="num">2000</span></td><td class="al-c">185 $</td><td class="al-c">0,95</td></tr><tr><td class="al-c"><span class="num">3000</span></td><td class="al-c">172 $</td><td class="al-c">0,88</td></tr><tr><td class="al-c"><span class="num">5000</span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span></td><td class="al-c">158 $</td><td class="al-c">0,81</td></tr></tbody></table></div></div>252<h3 id="s-6-7-2" class="h-subsection"><span class="h-num">6.7.2</span><span class="h-text">Forme et périmètre</span><a class="h-anchor" href="#s-6-7-2" aria-label="Lien vers cette section">#</a></h3>253<div class="box box-form" id="form-6-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 6.3</span><span class="box-title">— ratio de périmètre</span><a class="box-anchor" href="#form-6-3" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-6-6"><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>R</mi><mi>p</mi></msub><mtext> </mtext><mo>=</mo><mtext> </mtext><mfrac><msub><mi>P</mi><mtext>sujet</mtext></msub><msub><mi>P</mi><mrow><mtext>carr</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext> </mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>quivalent</mtext></mrow></msub></mfrac><mspace width="2em"/><mrow><mtext>o</mtext><mover accent="true"><mtext>u</mtext><mo>ˋ</mo></mover></mrow><mspace width="2em"/><msub><mi>P</mi><mrow><mtext>carr</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover></mrow></msub><mo>=</mo><mn>4</mn><msqrt><mi>S</mi></msqrt><mi mathvariant="normal">.</mi></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(6.6)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">R_p \;=\; \frac{P_{\text{sujet}}}{P_{\text{carré équivalent}}}254\qquad\text{où}\qquad255P_{\text{carré}} = 4\sqrt{S}.\tag{6.6}</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:0.0077em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="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:2.3324em;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:1.3603em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.1389em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">carr</span><span class="mord katex-accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight">e</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˊ</span></span></span></span></span></span></span><span class="mord mtight"> </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">quivalent</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><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 mathnormal" style="margin-right:0.1389em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">sujet</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9721em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:2em;"></span><span class="mord text"><span class="mord">o</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">ˋ</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:2em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.1389em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">carr</span><span class="mord katex-accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight">e</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˊ</span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.04em;vertical-align:-0.0645em;"></span><span class="mord">4</span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9755em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord mathnormal" style="margin-right:0.0576em;">S</span></span></span><span style="top:-2.9355em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702256c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14257c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54258c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10259s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429260c69,-144,104.5,-217.7,106.5,-221261l0 -0262c5.3,-9.3,12,-14,20,-14263H400000v40H845.2724264s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7265c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z266M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.0645em;"><span></span></span></span></span></span><span class="mord">.</span></span><span class="katex-tag"><span class="katex-strut" style="height:2.3324em;vertical-align:-0.9721em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">6.6</span></span><span class="mord">)</span></span></span></span></span></span></div>267<p id="p6-78">Un bâtiment irrégulier a plus de murs extérieurs par pied carré de plancher qu'un carré de même superficie : son coût unitaire est majoré.</p></div></div>268<div class="box box-ex" id="ex-6-8"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 6.8</span><span class="box-title">— bâtiment en « L »</span><a class="box-anchor" href="#ex-6-8" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-79"><span class="num">1500</span> pi<sup>2</sup>, périmètre de 180 pi. Carré équivalent : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo>=</mo><mn>4</mn><msqrt><mrow><mn>1</mn><mtext> </mtext><mn>500</mn></mrow></msqrt><mo>=</mo><mn>4</mn><mo>×</mo><mn>38,73</mn><mo>=</mo><mn>154,92</mn></mrow><annotation encoding="application/x-tex">P = 4\sqrt{1\,500} = 4 \times 38{,}73 = 154{,}92</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:0.1389em;">P</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.04em;vertical-align:-0.1328em;"></span><span class="mord">4</span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9072em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span></span></span><span style="top:-2.8672em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702269c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14270c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54271c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10272s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429273c69,-144,104.5,-217.7,106.5,-221274l0 -0275c5.3,-9.3,12,-14,20,-14276H400000v40H845.2724277s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7278c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z279M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1328em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">4</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">38</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">73</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">154</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">92</span></span></span></span> pi. Ratio : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>180</mn><mi mathvariant="normal">/</mi><mn>154,92</mn><mo>=</mo><mn>1,162</mn></mrow><annotation encoding="application/x-tex">180/154{,}92 = 1{,}162</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">180/154</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">92</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">162</span></span></span></span>, d'où un ajustement de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>3 à <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>5 % du coût unitaire.</p></div></div>280<h3 id="s-6-7-3" class="h-subsection"><span class="h-num">6.7.3</span><span class="h-text">Hauteur</span><a class="h-anchor" href="#s-6-7-3" aria-label="Lien vers cette section">#</a></h3>281<p id="p6-80">Chaque étage supplémentaire renchérit le coût unitaire : structure plus robuste, fondations plus profondes, mécanique plus complexe, escaliers et ascenseurs, sécurité incendie, logistique de chantier. Facteurs types (inspirés de Marshall & Swift) : 1 étage <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> 1,00; 2 étages <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> 1,03–1,08; 3 étages <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> 1,06–1,15; 4–6 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> 1,10–1,25; 7–12 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> 1,20–1,40; 13 et plus <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo></mrow><annotation encoding="application/x-tex">=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span></span></span></span> 1,35–1,60<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>.</p>282<p id="p6-81">Deux seuils techniques expliquent les sauts de la progression. Le premier se situe vers quatre étages : le Code de construction impose alors généralement l'ascenseur et des exigences accrues de séparation coupe-feu, et l'ossature de bois conventionnelle atteint ses limites structurales (la construction de bois massif repousse aujourd'hui cette frontière, mais à un coût unitaire différent). Le second seuil apparaît au-delà d'une douzaine d'étages, où la tour exige béton armé ou acier de charpente, pompage du béton, grue à tour et gestion de chantier verticale — autant de coûts qui n'existent tout simplement pas dans un walk-up de trois étages. C'est pourquoi un facteur de hauteur ne s'interpole jamais linéairement entre deux classes : il faut se demander de quel <em>régime constructif</em> relève le bâtiment.</p>283<h3 id="s-6-7-4" class="h-subsection"><span class="h-num">6.7.4</span><span class="h-text">Qualité</span><a class="h-anchor" href="#s-6-7-4" aria-label="Lien vers cette section">#</a></h3>284<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th class="al-c">Classe</th><th>Désignation</th><th>Caractéristiques</th><th class="al-c">Facteur</th></tr></thead><tbody><tr><td class="al-c">1</td><td>Économique</td><td>Matériaux de base, finitions minimales</td><td class="al-c">0,70</td></tr><tr><td class="al-c">2</td><td>Bas de gamme</td><td>Qualité inférieure, construction simple</td><td class="al-c">0,85</td></tr><tr><td class="al-c">3</td><td>Standard</td><td>Construction typique conforme aux normes</td><td class="al-c">1,00</td></tr><tr><td class="al-c">4</td><td>Bon</td><td>Matériaux de meilleure qualité</td><td class="al-c">1,20</td></tr><tr><td class="al-c">5</td><td>Supérieur</td><td>Finitions haut de gamme</td><td class="al-c">1,45</td></tr><tr><td class="al-c">6</td><td>Luxe</td><td>Matériaux prestige, conception architecturale</td><td class="al-c">1,80<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></td></tr></tbody></table></div></div>285<div class="box box-terrain" id="terrain-6-82"><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-6-82" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-83">La classe de qualité se juge à l'<strong class="c-bleu">inspection</strong>, pas sur papier : revêtements extérieurs, fenêtration, armoires et comptoirs, systèmes mécaniques, isolation, finitions. Deux maisons de même superficie et de même plan peuvent différer de 80 % en coût selon la classe — c'est le facteur le plus puissant du tableau.</p></div></div>286<h2 id="s-6-8" class="h-section"><span class="h-num">6.8</span><span class="h-text">Les erreurs classiques de l'estimation des coûts</span><a class="h-anchor" href="#s-6-8" aria-label="Lien vers cette section">#</a></h2>287<p id="p6-84">Avant de passer aux exercices, il vaut la peine de récapituler, en un seul endroit, les fautes qui reviennent le plus souvent — dans les copies d'examen comme dans les rapports de débutants.</p>288<p id="p6-85">La première famille d'erreurs touche la <strong class="c-bleu">portée</strong>, déjà longuement discutée : mélanger dans une même analyse des coûts directs, des coûts de construction et des coûts complets. Elle est de loin la plus coûteuse, parce qu'elle produit des écarts de 25 à 45 % qui semblent inexplicables et minent la confiance du lecteur dans tout le rapport.</p>289<p id="p6-86">La deuxième famille touche les <strong class="c-bleu">quantités et les unités</strong> : superficie intérieure contre extérieure, surface de mur contre surface de plancher, toiture réelle contre toiture projetée, sous-sol aménagé compté en pleine valeur. Ces erreurs-là sont sournoises parce qu'elles sont plausibles — un bordereau faux de 12 % a exactement la même allure qu'un bordereau juste.</p>290<p id="p6-87">La troisième famille concerne la <strong class="c-bleu">main-d'œuvre</strong> : utiliser les taux de base de la CCQ sans les charges (sous-estimation d'un tiers), oublier que les taux changent chaque année de convention, ou appliquer des productivités de guide américain à un chantier québécois hivernal.</p>291<p id="p6-88">La quatrième famille relève du <strong class="c-bleu">double comptage</strong> : ajouter des coûts indirects à un coût installé qui incluait déjà les frais de chantier, calculer le profit sur les directs seuls quand la convention locale le calcule sur directs plus indirects, ou indexer un bâtiment rénové depuis sa date de construction d'origine en oubliant que les rénovations ont déjà été payées en dollars récents.</p>292<p id="p6-89">La parade est la même pour les quatre familles : documenter chaque chiffre — sa source, sa portée, son unité, sa date — et confronter le résultat final aux fourchettes de vraisemblance du chapitre <a class="xref" href="/seance/05/">5</a>. L'estimation de coûts n'exige pas de génie; elle exige une hygiène documentaire constante.</p>293<h2 id="s-6-9" class="h-section"><span class="h-num">6.9</span><span class="h-text">Exercices</span><a class="h-anchor" href="#s-6-9" aria-label="Lien vers cette section">#</a></h2>294<div class="box box-exo" id="exo-6-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 6.1</span><span class="box-title">— méthode comparative</span><a class="box-anchor" href="#exo-6-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-90">Un sujet de <span class="num">1700</span> pi<sup>2</sup> (standard, Gatineau, 2025) doit être estimé à partir de deux comparables à coût complet connu : comp. A, <span class="num">1500</span> pi<sup>2</sup>, 198 $/pi<sup>2</sup>, construit en 2024 (ajustements : taille <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>2 %, date <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>3 %); comp. B, <span class="num">1900</span> pi<sup>2</sup>, 182 $/pi<sup>2</sup>, construit en 2025, qualité légèrement inférieure (taille <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>2 %, qualité <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>4 %). Calculez le coût neuf du sujet.</p></div></div>295<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p6-91">Comp. A : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>198</mn><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mn>0,02</mn><mo>+</mo><mn>0,03</mn><mo stretchy="false">)</mo><mo>=</mo><mn>198</mn><mo>×</mo><mn>1,01</mn><mo>=</mo><mn>199,98</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">198 \times (1 - 0{,}02 + 0{,}03) = 198 \times 1{,}01 =296199{,}98~\$/\text{pi}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">198</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">02</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">03</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">198</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">01</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1219em;vertical-align:-0.25em;"></span><span class="mord">199</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">98</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>. Comp. B : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>182</mn><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mn>0,02</mn><mo>+</mo><mn>0,04</mn><mo stretchy="false">)</mo><mo>=</mo><mn>182</mn><mo>×</mo><mn>1,06</mn><mo>=</mo><mn>192,92</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">182 \times (1 + 0{,}02 + 0{,}04) = 182 \times 1{,}06 =297192{,}92~\$/\text{pi}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">182</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">02</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">04</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">182</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">06</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1219em;vertical-align:-0.25em;"></span><span class="mord">192</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">92</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>. Moyenne <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>196,45</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">\approx 196{,}45~\$/\text{pi}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1219em;vertical-align:-0.25em;"></span><span class="mord">196</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">45</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mtext> </mtext><mn>700</mn><mo>×</mo><mn>196,45</mn><mo>≈</mo><mn>333</mn><mtext> </mtext><mn>965</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">1\,700 \times 196{,}45 \approx 333\,965~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">700</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">196</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">45</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">333</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">965</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>, arrondi à <strong><span class="num">334 000 $</span></strong>. (Application des ajustements en somme algébrique des pourcentages, comme dans l'exemple du chapitre; en toute rigueur on peut aussi les composer multiplicativement — l'écart est négligeable à ces ordres de grandeur.)</p></div></details>298<div class="box box-exo" id="exo-6-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 6.2</span><span class="box-title">— coût chargé de la main-d'œuvre</span><a class="box-anchor" href="#exo-6-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-92">Un estimateur prévoit 260 heures d'électricien (taux de base 50,67 $/h) et 340 heures de charpentier-menuisier (47,77 $/h), secteur IC. En utilisant une charge de 52 %, calculez le coût total de main-d'œuvre, et l'erreur qu'aurait commise un estimé fondé sur les seuls taux de base.</p></div></div>299<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p6-93">Coûts chargés : électricien <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50,67</mn><mo>×</mo><mn>1,52</mn><mo>=</mo><mn>77,02</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><mi>h</mi></mrow><annotation encoding="application/x-tex">50{,}67 \times 1{,}52 = 77{,}02~\$/h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">50</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">67</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">52</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">77</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">02</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord mathnormal">h</span></span></span></span>; charpentier <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>47,77</mn><mo>×</mo><mn>1,52</mn><mo>=</mo><mn>72,61</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><mi>h</mi></mrow><annotation encoding="application/x-tex">47{,}77 \times 1{,}52 = 72{,}61~\$/h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">47</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">77</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">52</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">72</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">61</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord mathnormal">h</span></span></span></span>. Total chargé : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>260</mn><mo>×</mo><mn>77,02</mn><mo>+</mo><mn>340</mn><mo>×</mo><mn>72,61</mn><mo>=</mo><mn>20</mn><mtext> </mtext><mn>025</mn><mo>+</mo><mn>24</mn><mtext> </mtext><mn>687</mn><mo>=</mo><mn>44</mn><mtext> </mtext><mn>712</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">260 \times 77{,}02 + 340 \times 72{,}61 =30020\,025 + 24\,687 = 44\,712~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">260</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">77</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">02</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">340</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">72</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">61</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">025</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">687</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">44</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">712</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>. Aux taux de base : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>260</mn><mo>×</mo><mn>50,67</mn><mo>+</mo><mn>340</mn><mo>×</mo><mn>47,77</mn><mo>=</mo><mn>13</mn><mtext> </mtext><mn>174</mn><mo>+</mo><mn>16</mn><mtext> </mtext><mn>242</mn><mo>=</mo><mn>29</mn><mtext> </mtext><mn>416</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">260 \times 50{,}67 + 340 \times 47{,}77 =30113\,174 + 16\,242 = 29\,416~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">260</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">50</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">67</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">340</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">47</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">77</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">13</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">174</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">242</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">29</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">416</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>. L'estimé « taux de base » manquerait <span class="num">15 296 $</span>, soit une sous-estimation de 34 % de la main-d'œuvre — exactement le genre d'erreur que la règle du coût chargé prévient.</p></div></details>302<div class="box box-exo" id="exo-6-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 6.3</span><span class="box-title">— portée des coûts</span><a class="box-anchor" href="#exo-6-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-94">Trois sources donnent, pour le même modèle de maison : (i) un bordereau d'estimateur à 138 $/pi<sup>2</sup>; (ii) un contrat d'entrepreneur général à 172 $/pi<sup>2</sup>; (iii) des projets récents complets à 196 $/pi<sup>2</sup>. Expliquez la cohérence de ces trois chiffres et dites lequel utiliser pour la méthode du coût.</p></div></div>303<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p6-95">(i) est un coût <em>direct</em> (matériaux <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> main-d'œuvre); (ii) est le coût de <em>construction</em> — directs <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> frais généraux de chantier <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> profit de l'entrepreneur (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>138</mn><mo>×</mo><mo>≈</mo><mn>1,25</mn><mo>≈</mo><mn>172</mn></mrow><annotation encoding="application/x-tex">138 \times \approx 1{,}25 \approx 172</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">138</span><span class="mord">×</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">25</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">172</span></span></span></span>); (iii) est le coût <em>complet du projet</em>, ajoutant les indirects du promoteur (honoraires, permis, financement, marge : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>172</mn><mo>×</mo><mo>≈</mo><mn>1,14</mn></mrow><annotation encoding="application/x-tex">172 \times \approx 1{,}14</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">172</span><span class="mord">×</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">14</span></span></span></span>, ou <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>138</mn><mo>×</mo><mo>≈</mo><mn>1,42</mn></mrow><annotation encoding="application/x-tex">138 \times \approx 1{,}42</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">138</span><span class="mord">×</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">42</span></span></span></span>). Les trois sont cohérents entre eux. Pour la méthode du coût en évaluation, on recherche le <strong>coût complet</strong> (iii) : c'est lui qui correspond à ce qu'un acheteur devrait débourser pour se procurer un bâtiment neuf équivalent, terrain exclu.</p></div></details>304<div class="box box-exo" id="exo-6-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 6.4</span><span class="box-title">— méthode par composantes</span><a class="box-anchor" href="#exo-6-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-96">Estimez le coût de remplacement d'un bungalow de <span class="num">1300</span> pi<sup>2</sup> avec les coûts installés suivants : fondations 30 $/pi<sup>2</sup> de dalle (<span class="num">1300</span> pi<sup>2</sup>); murs extérieurs 26 $/pi<sup>2</sup> de mur (<span class="num">1500</span> pi<sup>2</sup>); toiture 18 $/pi<sup>2</sup> projeté (<span class="num">1400</span>); plomberie 7 appareils à 3 300 $; électricité 14 $/pi<sup>2</sup>; chauffage 9 $/pi<sup>2</sup>; finitions 36 $/pi<sup>2</sup>; structure de plancher 10 $/pi<sup>2</sup>. Indirects 14 %, profit 11 %.</p></div></div>305<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p6-97">Directs : fondations <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>39</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">39\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">39</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>; murs <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>39</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">39\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">39</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>; toiture <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>25</mn><mtext> </mtext><mn>200</mn></mrow><annotation encoding="application/x-tex">25\,200</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">25</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span></span></span></span>; plomberie <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>23</mn><mtext> </mtext><mn>100</mn></mrow><annotation encoding="application/x-tex">23\,100</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">23</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">100</span></span></span></span>; électricité <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>18</mn><mtext> </mtext><mn>200</mn></mrow><annotation encoding="application/x-tex">18\,200</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">18</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span></span></span></span>; chauffage <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>11</mn><mtext> </mtext><mn>700</mn></mrow><annotation encoding="application/x-tex">11\,700</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">11</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">700</span></span></span></span>; finitions <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>46</mn><mtext> </mtext><mn>800</mn></mrow><annotation encoding="application/x-tex">46\,800</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">46</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span></span></span></span>; planchers <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>13</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">13\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">13</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>; total <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>216</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 216\,000~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">216</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>. Indirects : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>216</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,14</mn><mo>=</mo><mn>30</mn><mtext> </mtext><mn>240</mn></mrow><annotation encoding="application/x-tex">216\,000 \times 0{,}14 = 30\,240</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">216</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">14</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">240</span></span></span></span>; sous-total <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>246</mn><mtext> </mtext><mn>240</mn></mrow><annotation encoding="application/x-tex">246\,240</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">246</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">240</span></span></span></span>; profit : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo><mn>0,11</mn><mo>=</mo><mn>27</mn><mtext> </mtext><mn>086</mn></mrow><annotation encoding="application/x-tex">\times 0{,}11 = 27\,086</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">×</span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">11</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">27</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">086</span></span></span></span>. <strong>Coût de remplacement</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>273</mn><mtext> </mtext><mn>326</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\approx 273\,326~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">273</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">326</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>, arrondi à <strong><span class="num">273 000 $</span></strong> (210 $/pi<sup>2</sup>) — une valeur plausible pour un bungalow standard, à valider par la comparative.</p></div></details>306<div class="box box-exo" id="exo-6-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 6.5</span><span class="box-title">— coût indexé avec rénovations</span><a class="box-anchor" href="#exo-6-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-98">Un triplex construit en 2012 (<span class="num">420 000 $</span>, indice 57,8) a reçu une toiture neuve en 2022 (<span class="num">38 000 $</span>, indice 97,1) et des balcons en 2024 (<span class="num">22 000 $</span>, indice 102,4). Indice 2025 : 105,5. Calculez le coût indexé 2025 et identifiez la principale fragilité de cette estimation.</p></div></div>307<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p6-99">Construction : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>420</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>105,5</mn><mi mathvariant="normal">/</mi><mn>57,8</mn><mo>=</mo><mn>420</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>1,8253</mn><mo>=</mo><mn>766</mn><mtext> </mtext><mn>609</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">420\,000 \times 105{,}5/57{,}8 = 420\,000 \times 1{,}8253 =308766\,609~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">105</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5/57</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">8</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">420</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">8253</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">766</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">609</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>. Toiture : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>38</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>105,5</mn><mi mathvariant="normal">/</mi><mn>97,1</mn><mo>=</mo><mn>38</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>1,0865</mn><mo>=</mo><mn>41</mn><mtext> </mtext><mn>287</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">38\,000 \times 105{,}5/97{,}1 = 38\,000 \times 1{,}0865 =30941\,287~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">38</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">105</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5/97</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">38</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0865</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">41</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">287</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>. Balcons : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>22</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>105,5</mn><mi mathvariant="normal">/</mi><mn>102,4</mn><mo>=</mo><mn>22</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>1,0303</mn><mo>=</mo><mn>22</mn><mtext> </mtext><mn>666</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">22\,000 \times 105{,}5/102{,}4 = 22\,000 \times 1{,}0303 =31022\,666~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">105</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5/102</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">4</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0303</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">22</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">666</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>. <strong>Total indexé</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo><mn>830</mn><mtext> </mtext><mn>562</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\approx 830\,562~\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">830</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">562</span><span class="mspace nobreak"> </span><span class="mord">$</span></span></span></span>, arrondi à <strong><span class="num">830 000 $</span></strong>. Fragilité principale : 13 ans séparent le coût de construction de la date d'évaluation, et l'essentiel du total repose sur cette strate — l'indice est une moyenne régionale qui peut mal représenter ce bâtiment précis (qualité atypique, autoconstruction, marché local). Il y a aussi un risque de <em>double comptage</em> : la toiture de 2022 remplace une composante déjà incluse dans le coût de 2012. La bonne pratique : valider par la comparative ou les composantes.</p></div></details>311<div class="box box-exo" id="exo-6-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 6.6</span><span class="box-title">— facteurs de forme et de hauteur</span><a class="box-anchor" href="#exo-6-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p6-100">(a) Un bâtiment de <span class="num">2000</span> pi<sup>2</sup> a un périmètre de 200 pi : calculez le ratio de périmètre et l'ajustement suggéré. (b) Un coût de base de 210 $/pi<sup>2</sup> (1 étage) doit servir pour un immeuble de 3 étages (facteur 1,10) de qualité « bon » (facteur 1,20) : calculez le coût unitaire ajusté.</p></div></div>312<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p6-101">(a) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mtext>carr</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover></mrow></msub><mo>=</mo><mn>4</mn><msqrt><mrow><mn>2</mn><mtext> </mtext><mn>000</mn></mrow></msqrt><mo>=</mo><mn>4</mn><mo>×</mo><mn>44,72</mn><mo>=</mo><mn>178,89</mn></mrow><annotation encoding="application/x-tex">P_{\text{carré}} = 4\sqrt{2\,000} = 4 \times 44{,}72 = 178{,}89</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.1389em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">carr</span><span class="mord katex-accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight">e</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˊ</span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.04em;vertical-align:-0.1328em;"></span><span class="mord">4</span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9072em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span><span style="top:-2.8672em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702313c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14314c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54315c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10316s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429317c69,-144,104.5,-217.7,106.5,-221318l0 -0319c5.3,-9.3,12,-14,20,-14320H400000v40H845.2724321s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7322c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z323M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1328em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">4</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">44</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">72</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">178</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">89</span></span></span></span> pi; <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mi>p</mi></msub><mo>=</mo><mn>200</mn><mi mathvariant="normal">/</mi><mn>178,89</mn><mo>=</mo><mn>1,118</mn></mrow><annotation encoding="application/x-tex">R_p = 200/178{,}89 = 1{,}118</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0077em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">200/178</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">89</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">118</span></span></span></span> — environ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>12 % de périmètre excédentaire, d'où un ajustement d'environ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>3 à <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>4 % du coût unitaire (l'enveloppe ne représente qu'une partie du coût total). (b) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>210</mn><mo>×</mo><mn>1,10</mn><mo>×</mo><mn>1,20</mn><mo>=</mo><mn>277,20</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mi mathvariant="normal">/</mi><msup><mtext>pi</mtext><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">210 \times 1{,}10 \times 1{,}20 = 277{,}20~\$/\text{pi}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">210</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">10</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">20</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.1219em;vertical-align:-0.25em;"></span><span class="mord">277</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">20</span><span class="mspace nobreak"> </span><span class="mord">$/</span><span class="mord"><span class="mord text"><span class="mord">pi</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>. Les facteurs se composent multiplicativement — comme dans la formule calculator de Marshall & Swift.</p></div></details>324<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>Quatre méthodes : <strong>comparative</strong> (rapide, coût au pi<sup>2</sup> ajusté), <strong>Quantity Survey</strong> (la plus précise, poste par poste), <strong>composantes / Unit-in-Place</strong> (équilibre, coûts installés — base de Marshall & Swift), <strong>coût indexé</strong> (coût original <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> ratio d'indices).</li><li>Comparative : comparables récents (<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:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel"><</span></span></span></span> 3 ans), même type et région, taille <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>±</mo></mrow><annotation encoding="application/x-tex">\pm</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">±</span></span></span></span>20 %; six ajustements (taille, qualité, date, localisation, hauteur, forme).</li><li>Quantity Survey : main-d'œuvre au coût <strong>chargé</strong> (taux CCQ <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> 45–60 % de charges); structure type des coûts directs résidentiels : finitions <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> 37 %, mécanique/électricité <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> 22 %, enveloppe <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> 17 %, fondations <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> 14 %, charpente <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> 10 %.</li><li><strong>La portée avant tout</strong> : coûts directs <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo><</mo></mrow><annotation encoding="application/x-tex"><</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel"><</span></span></span></span> coût de construction de l'entrepreneur (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> frais de chantier <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> profit) <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:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel"><</span></span></span></span> coût complet du projet (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> indirects du promoteur, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span></span></span></span> <span class="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>40 % sur les directs). Ne jamais comparer des portées différentes.</li><li>Composantes : 10–20 lignes à coûts installés; permet ensuite la dépréciation <em>par composante</em> (bloc 4).</li><li>Indexée : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mo>=</mo><msub><mi>C</mi><mn>0</mn></msub><mo>×</mo><mi>I</mi><mi mathvariant="normal">/</mi><msub><mi>I</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">C = C_0 \times I/I_0</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:0.0715em;">C</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.0785em;">I</span><span class="mord">/</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0785em;">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">0</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>; indexer chaque rénovation depuis <em>sa</em> date; fiabilité décroissante au-delà de <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span></span></span></span> 10 ans.</li><li>Choix : standard <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> comparative; litige/spécial <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> Quantity Survey; atypique ou analyse de dépréciation <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>→</mo></mrow><annotation encoding="application/x-tex">\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> composantes; masse/vérification <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> indexée. Réconcilier en pondérant selon la fiabilité.</li><li>Facteurs transversaux : échelle (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>2 à <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span>5 % par <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span>20 % de superficie), périmètre (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mtext>carr</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover></mrow></msub><mo>=</mo><mn>4</mn><msqrt><mi>S</mi></msqrt></mrow><annotation encoding="application/x-tex">P_{\text{carré}} = 4\sqrt{S}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.1389em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">carr</span><span class="mord katex-accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight">e</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˊ</span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.04em;vertical-align:-0.1133em;"></span><span class="mord">4</span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9267em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord mathnormal" style="margin-right:0.0576em;">S</span></span></span><span style="top:-2.8867em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702325c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14326c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54327c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10328s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429329c69,-144,104.5,-217.7,106.5,-221330l0 -0331c5.3,-9.3,12,-14,20,-14332H400000v40H845.2724333s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7334c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z335M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1133em;"><span></span></span></span></span></span></span></span></span>), hauteur (1,03–1,60 selon les étages), qualité (0,70 à 1,80<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> — le plus puissant).</li><li>Toujours documenter sources et ajustements, et vérifier la cohérence du résultat avec le marché local.</li></ul></div></section>336 </article>337 </div>338 </div>339 <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>340 341<nav class="ch-pager" aria-label="Navigation entre les séances">342 <a class="prev" href="/seance/05/"><small>← Séance 5</small><b>Coût de reproduction et coût de remplacement</b></a>343 <a class="next" href="/seance/07/"><small>Séance 7 →</small><b>Coûts directs de construction</b></a>344</nav>345 346<div class="read-tools" role="toolbar" aria-label="Outils de lecture">347 <button type="button" data-action="notes" data-tip="Mes notes et surlignages" 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