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<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>80</svg>8182<a class="skip" href="#main">Aller au contenu</a>83<header class="topbar">84 <div class="topbar-inner">85 <a class="brand" href="/" aria-label="IMM1003 — 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">IMM1003</span><span class="brand-title">Éléments d’évaluation immobilière</span></span></a>86 <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 l’évaluation immobilière</div><a href="/seance/01/" data-ch="01"><span class="pastille" style="background:#2976bb">1</span><span>Introduction à l'évaluation immobilière</span></a><a href="/seance/02/" data-ch="02"><span class="pastille" style="background:#2976bb">2</span><span>Le cadre professionnel au Québec</span></a><a href="/seance/03/" data-ch="03"><span class="pastille" style="background:#2976bb">3</span><span>Les principes fondamentaux de l'évaluation</span></a><div class="dd-part"><i style="background:#0f8b8d"></i>Partie II — Valeur, marché et données</div><a href="/seance/04/" data-ch="04"><span class="pastille" style="background:#0f8b8d">4</span><span>La valeur : concepts et types</span></a><a href="/seance/05/" data-ch="05"><span class="pastille" style="background:#0f8b8d">5</span><span>Le marché immobilier québécois</span></a><a href="/seance/06/" data-ch="06"><span class="pastille" style="background:#0f8b8d">6</span><span>Collecte et analyse des données</span></a><a href="/seance/07/" data-ch="07"><span class="pastille" style="background:#0f8b8d">7</span><span>Examen mi-session : révision des blocs 1 et 2</span></a><div class="dd-part"><i style="background:#cca424"></i>Partie III — Les trois méthodes d’évaluation</div><a href="/seance/08/" data-ch="08"><span class="pastille" style="background:#cca424">8</span><span>La méthode de comparaison — Partie 1 : principes et sélection des comparables</span></a><a href="/seance/09/" data-ch="09"><span class="pastille" style="background:#cca424">9</span><span>La méthode de comparaison — Partie 2 : ajustements et réconciliation</span></a><a href="/seance/10/" data-ch="10"><span class="pastille" style="background:#cca424">10</span><span>La méthode du coût</span></a><a href="/seance/11/" data-ch="11"><span class="pastille" style="background:#cca424">11</span><span>La méthode du revenu — Partie 1 : du revenu brut au RNE</span></a><a href="/seance/12/" data-ch="12"><span class="pastille" style="background:#cca424">12</span><span>La méthode du revenu — Partie 2 : le taux et le DCF</span></a><div class="dd-part"><i style="background:#6b4fbb"></i>Partie IV — Synthèse et pratique professionnelle</div><a href="/seance/13/" data-ch="13"><span class="pastille" style="background:#6b4fbb">13</span><span>Le rapport d'évaluation</span></a><a href="/seance/14/" data-ch="14"><span class="pastille" style="background:#6b4fbb">14</span><span>Révision générale et cas intégrateur</span></a><div class="dd-part">Enregistrements</div><a href="/videos/"><span class="pastille" style="background:var(--rouge)">▶</span><span>Séances vidéo — enregistrements Zoom, transcription synchronisée</span></a><div class="dd-part">Annexes</div><a href="/aide-memoire/"><span class="pastille">A</span><span>Aide-mémoire des formules</span></a><a href="/glossaire/"><span class="pastille">B</span><span>Glossaire</span></a><a href="/rapport/"><span class="pastille" style="background:var(--teal)">R</span><span>Rapport — Le marché de l’habitation au Québec</span></a></div></div><a class="nav-video" href="/videos/"><svg class="" aria-hidden="true"><use href="#i-video"/></svg> Vidéos</a><div class="dd"><button type="button" aria-expanded="false" aria-haspopup="true">Réviser <span class="caret" aria-hidden="true">▾</span></button><div class="dd-menu "><a href="/aide-memoire/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span>Aide-mémoire<span class="dd-desc">Toutes les formules commentées</span></span></a><a href="/glossaire/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span>Glossaire<span class="dd-desc">Termes du métier, équivalents anglais</span></span></a><a href="/definitions/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-list"/></svg></span><span>Toutes les définitions<span class="dd-desc">Les formulations attendues aux examens</span></span></a><a href="/fiches/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-cards"/></svg></span><span>Fiches de révision<span class="dd-desc">Recto-verso, suivi d’acquisition</span></span></a><a href="/carte/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-network"/></svg></span><span>Carte du cours<span class="dd-desc">Les 14 séances et leurs objectifs en un coup d’œil</span></span></a><a href="/exercices/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span>Banque d’exercices<span class="dd-desc">Tous les exercices corrigés</span></span></a></div></div><div class="dd"><button type="button" aria-expanded="false" aria-haspopup="true">S’exercer <span class="caret" aria-hidden="true">▾</span></button><div class="dd-menu "><a href="/quiz/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-quiz"/></svg></span><span>Quiz et examens blancs<span class="dd-desc">QCM avec rétroaction, chronomètre</span></span></a><a href="/entrainement/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-dumbbell"/></svg></span><span>Entraînement<span class="dd-desc">Problèmes à données aléatoires, corrigés pas à pas</span></span></a><a href="/jeux/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-game"/></svg></span><span>Jeux de révision<span class="dd-desc">Association, vrai ou faux, remise en ordre</span></span></a><a href="/outils/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-calc"/></svg></span><span>Calculateurs<span class="dd-desc">Les formules en interactif</span></span></a><a href="/progression/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-progress"/></svg></span><span>Ma progression<span class="dd-desc">Lecture, quiz, objectifs, notes</span></span></a></div></div><div class="dd"><button type="button" aria-expanded="false" aria-haspopup="true">Ressources <span class="caret" aria-hidden="true">▾</span></button><div class="dd-menu "><a href="/diapositives/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-slides"/></svg></span><span>Diapositives<span class="dd-desc">Les 14 présentations en ligne</span></span></a><a href="/videos/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-video"/></svg></span><span>Séances vidéo<span class="dd-desc">Enregistrements Zoom : chapitres, transcription, sous-titres</span></span></a><a href="/ressources/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-download"/></svg></span><span>Téléchargements<span class="dd-desc">Manuel, plan, TP, gabarits Excel</span></span></a><a href="/rapport/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-report"/></svg></span><span>Rapport marché QC<span class="dd-desc">Indices de prix, macro, abordabilité — 26 sections, 67 figures</span></span></a><a href="/bibliographie/"><span class="dd-ico"><svg class="" 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class="readbar-fill"></div></div>94</header>9596<main id="main" class="chapter-page" data-chapter="11" data-title="Séance 11 — La méthode du revenu — Partie 1 : du revenu brut au RNE" data-words="8051">97 98<header class="ch-hero">99 <svg class="deco" viewBox="0 0 1200 300" preserveAspectRatio="xMaxYMin slice" aria-hidden="true"><circle cx="1090" cy="20" r="110"/><circle cx="1160" cy="110" r="160"/><circle class="gold" cx="990" cy="170" r="45"/></svg>100 <div class="watermark" aria-hidden="true">11</div>101 <div class="ch-hero-inner">102 <div class="eyebrow"><span class="part-chip">Partie III</span> Les trois méthodes d’évaluation · Séance 11 · IMM1003</div>103 <h1>La méthode du revenu — Partie 1 : du revenu brut au RNE</h1>104 <div class="ch-sub">Éléments d’évaluation immobilière · Automne 2026 · Simon-Pierre Boucher · UQO</div>105 <div class="ch-meta">106 <span class="chip"><svg class="" aria-hidden="true"><use href="#i-list"/></svg> 7 sections</span>107 <span class="chip"><svg class="" aria-hidden="true"><use href="#i-book"/></svg> 10 définitions</span>108 <span class="chip"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg> 4 formules</span>109 <span class="chip"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg> 4 exemples</span>110 <span class="chip"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg> 5 exercices</span>111 <span class="chip"><svg class="" aria-hidden="true"><use href="#i-eye"/></svg> ≈ 45 min de lecture</span>112 <span class="chip"><svg class="" aria-hidden="true"><use href="#i-chart"/></svg> 1 explorateur interactif</span>113 114 </div>115 <div class="ch-tools">116 117 <a class="btn btn-ghost" href="/files/slides/seance11.pdf" target="_blank" rel="noopener"><svg class="" aria-hidden="true"><use href="#i-slides"/></svg> Diapositives (PDF)</a>118 <button class="btn btn-ghost" type="button" data-action="revision" aria-pressed="false"><svg class="" aria-hidden="true"><use href="#i-eye"/></svg> Mode révision</button>119 <button class="btn btn-ghost" type="button" data-action="tts"><svg class="" aria-hidden="true"><use href="#i-audio"/></svg> Écouter</button>120 <a class="btn btn-ghost" href="#quiz"><svg class="" aria-hidden="true"><use href="#i-quiz"/></svg> Quiz de la séance</a>121 </div>122 </div>123</header>124<div class="stepper-wrap"><nav class="stepper" aria-label="Sections"><a href="#s-11-1"><span class="n">1</span>Le fondement : acheter un flux de revenus</a><a href="#s-11-2"><span class="n">2</span>Les revenus : du potentiel à l'effectif</a><a href="#s-11-3"><span class="n">3</span>Les dépenses d'exploitation</a><a href="#s-11-4"><span class="n">4</span>Le RNE : reconstruction, normalisation, stabilisation</a><a href="#s-11-5"><span class="n">5</span>Cas complet : un 6-plex à Gatineau</a><a href="#s-11-6"><span class="n">6</span>Le contexte locatif québécois : synthèse pour l'évaluateur</a><a href="#s-11-7"><span class="n">7</span>Exercices</a><span class="rem" id="read-remaining"></span></nav></div>125 <div class="ch-layout">126 127<aside class="ch-toc" aria-label="Sommaire de la séance">128 <div class="toc-progress"><div class="bar"><i></i></div><span>0 % lu</span></div>129 <h4>Dans cette séance</h4>130 <ol><li class="lvl2"><a href="#s-11-1"><span class="toc-num">11.1</span><span>Le fondement : acheter un flux de revenus</span></a></li><li class="lvl3"><a href="#s-11-1-1"><span class="toc-num">11.1.1</span><span>Le principe d'anticipation</span></a></li><li class="lvl3"><a href="#s-11-1-2"><span class="toc-num">11.1.2</span><span>L'équation fondamentale</span></a></li><li class="lvl3"><a href="#s-11-1-3"><span class="toc-num">11.1.3</span><span>Capitalisation directe ou DCF?</span></a></li><li class="lvl3"><a href="#s-11-1-4"><span class="toc-num">11.1.4</span><span>Quelle méthode pour quel immeuble?</span></a></li><li class="lvl2"><a href="#s-11-2"><span class="toc-num">11.2</span><span>Les revenus : du potentiel à l'effectif</span></a></li><li class="lvl3"><a href="#s-11-2-1"><span class="toc-num">11.2.1</span><span>Le revenu brut potentiel (RBP)</span></a></li><li class="lvl3"><a href="#s-11-2-2"><span class="toc-num">11.2.2</span><span>Loyers du marché contre loyers contractuels</span></a></li><li class="lvl3"><a href="#s-11-2-3"><span class="toc-num">11.2.3</span><span>Les baux au Québec : le cadre juridique</span></a></li><li class="lvl3"><a href="#s-11-2-4"><span class="toc-num">11.2.4</span><span>La fixation des loyers : le régime 2026 du TAL</span></a></li><li class="lvl3"><a href="#s-11-2-5"><span class="toc-num">11.2.5</span><span>L'inoccupation : les données SCHL</span></a></li><li class="lvl3"><a href="#s-11-2-6"><span class="toc-num">11.2.6</span><span>Les revenus accessoires</span></a></li><li class="lvl3"><a href="#s-11-2-7"><span class="toc-num">11.2.7</span><span>Le revenu brut effectif (RBE)</span></a></li><li class="lvl2"><a href="#s-11-3"><span class="toc-num">11.3</span><span>Les dépenses d'exploitation</span></a></li><li class="lvl3"><a href="#s-11-3-1"><span class="toc-num">11.3.1</span><span>Trois blocs : fixes, variables, réserve</span></a></li><li class="lvl3"><a href="#s-11-3-2"><span class="toc-num">11.3.2</span><span>Les exclusions absolues</span></a></li><li class="lvl3"><a href="#s-11-3-3"><span class="toc-num">11.3.3</span><span>Les ratios de contrôle</span></a></li><li class="lvl2"><a href="#s-11-4"><span class="toc-num">11.4</span><span>Le RNE : reconstruction, normalisation, stabilisation</span></a></li><li class="lvl3"><a href="#s-11-4-1"><span class="toc-num">11.4.1</span><span>La chaîne complète</span></a></li><li class="lvl3"><a href="#s-11-4-2"><span class="toc-num">11.4.2</span><span>Pourquoi « reconstruire » le RNE?</span></a></li><li class="lvl2"><a href="#s-11-5"><span class="toc-num">11.5</span><span>Cas complet : un 6-plex à Gatineau</span></a></li><li class="lvl3"><a href="#s-11-5-1"><span class="toc-num">11.5.1</span><span>L'immeuble et le mandat</span></a></li><li class="lvl3"><a href="#s-11-5-2"><span class="toc-num">11.5.2</span><span>Étape 1 — Le RBP aux loyers du marché</span></a></li><li class="lvl3"><a href="#s-11-5-3"><span class="toc-num">11.5.3</span><span>Étape 2 — Du RBP au RBE</span></a></li><li class="lvl3"><a href="#s-11-5-4"><span class="toc-num">11.5.4</span><span>Étape 3 — Les dépenses d'exploitation</span></a></li><li class="lvl3"><a href="#s-11-5-5"><span class="toc-num">11.5.5</span><span>Étape 4 — Le RNE et sa vérification</span></a></li><li class="lvl2"><a href="#s-11-6"><span class="toc-num">11.6</span><span>Le contexte locatif québécois : synthèse pour l'évaluateur</span></a></li><li class="lvl3"><a href="#s-11-6-1"><span class="toc-num">11.6.1</span><span>Le TAL en bref</span></a></li><li class="lvl3"><a href="#s-11-6-2"><span class="toc-num">11.6.2</span><span>Le marché locatif, tendances 2024–2026</span></a></li><li class="lvl3"><a href="#s-11-6-3"><span class="toc-num">11.6.3</span><span>La liste de vigilance de l'évaluateur québécois</span></a></li><li class="lvl2"><a href="#s-11-7"><span class="toc-num">11.7</span><span>Exercices</span></a></li></ol>131 <div class="toc-extra">132 <a href="#objectifs"><svg class="" aria-hidden="true"><use href="#i-target"/></svg> Objectifs d’apprentissage</a>133 <a href="#synthese"><svg class="" aria-hidden="true"><use href="#i-clipboard"/></svg> L’essentiel de la séance</a>134 <a href="#quiz"><svg class="" aria-hidden="true"><use href="#i-quiz"/></svg> Testez-vous</a>135 136 <a href="/fiches/?ch=11"><svg class="" aria-hidden="true"><use href="#i-cards"/></svg> Fiches de la séance</a>137 <a href="/entrainement/"><svg class="" aria-hidden="true"><use href="#i-dumbbell"/></svg> Entraînement</a>138 <a href="/aide-memoire/"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg> Aide-mémoire</a>139 </div>140 <h4 style="margin-top:14px">Raccourcis</h4>141 <div style="font-size:.76rem;color:var(--gris)"><kbd>←</kbd> <kbd>→</kbd> séance précédente / suivante · <kbd>⌘K</kbd> recherche · sélectionnez un passage pour le surligner</div>142</aside>143 <div class="ch-body">144 <div class="revision-banner"><svg class="" aria-hidden="true"><use href="#i-eye"/></svg><span><strong>Mode révision</strong> — seuls les définitions, formules, mises en garde, « À retenir », notes marginales et la fiche synthèse sont affichés.</span><button class="btn btn-sm btn-ghost" type="button" data-action="revision-off">Quitter</button></div>145 <div style="display:flex;justify-content:flex-end;margin-bottom:8px"><button class="btn btn-sm btn-ghost" type="button" data-action="toggle-solutions">Révéler toutes les solutions</button></div>146 <article class="prose" id="notes">147 <p id="p11-1">Troisième et dernière grande méthode : la <span class="motcle" data-term="méthode du revenu">méthode du revenu</span>. Elle change radicalement de point de vue. La comparaison regardait ce que paient les acheteurs; le coût regardait ce que coûterait un substitut; le revenu regarde ce que l'immeuble <em>rapporte</em>. Pour un investisseur, un immeuble locatif n'est pas d'abord un assemblage de briques : c'est une machine à produire des flux monétaires, et sa valeur est la valeur présente de ces flux. Cette première séance construit le numérateur de la méthode : le <span class="motcle" data-term="revenu net d'exploitation">revenu net d'exploitation</span> (RNE), obtenu en partant du revenu brut potentiel, en passant par le revenu brut effectif, puis en soustrayant les dépenses d'exploitation. Le tout est ancré dans le contexte locatif québécois — où le Tribunal administratif du logement (TAL) façonne les loyers d'une manière qu'aucun manuel américain ne décrit. La séance 12 s'occupera du dénominateur : le taux.</p>148<section class="box box-obj" id="objectifs"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-target"/></svg></span><span class="box-label">Objectifs d’apprentissage</span><span class="obj-progress" aria-live="polite"></span></div><div class="box-body"><ul><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-11-1" data-obj="obj-11-1"><span class="obj-text">Énoncer le fondement de la méthode du revenu et la formule de capitalisation directe <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mtext>RNE</mtext><mi mathvariant="normal">/</mi><mtext>TGA</mtext></mrow><annotation encoding="application/x-tex">V = \text{RNE}/\text{TGA}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord text"><span class="mord">RNE</span></span><span class="mord">/</span><span class="mord text"><span class="mord">TGA</span></span></span></span></span>;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-11-2" data-obj="obj-11-2"><span class="obj-text">Distinguer capitalisation directe et actualisation des flux (DCF), et savoir quand chacune s'impose;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-11-3" data-obj="obj-11-3"><span class="obj-text">Calculer le revenu brut potentiel (RBP) aux loyers du <em>marché</em> et justifier ce choix face aux loyers contractuels;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-11-4" data-obj="obj-11-4"><span class="obj-text">Construire le revenu brut effectif (RBE) : inoccupation, mauvaises créances, revenus accessoires;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-11-5" data-obj="obj-11-5"><span class="obj-text">Classer les dépenses d'exploitation (fixes, variables, réserve) et identifier les exclusions absolues (dette, amortissement, impôt);</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-11-6" data-obj="obj-11-6"><span class="obj-text">Reconstruire, normaliser et stabiliser un RNE à partir des états du propriétaire;</span></label></li><li class="obj"><label><input type="checkbox" class="obj-cb" id="obj-11-7" data-obj="obj-11-7"><span class="obj-text">Mener le calcul complet sur un 6-plex de Gatineau et situer chaque hypothèse dans le cadre québécois (TAL, SCHL, bail résidentiel).</span></label></li></ul></div></section>149<h2 id="s-11-1" class="h-section"><span class="h-num">11.1</span><span class="h-text">Le fondement : acheter un flux de revenus</span><a class="h-anchor" href="#s-11-1" aria-label="Lien vers cette section">#</a></h2>150<h3 id="s-11-1-1" class="h-subsection"><span class="h-num">11.1.1</span><span class="h-text">Le principe d'anticipation</span><a class="h-anchor" href="#s-11-1-1" aria-label="Lien vers cette section">#</a></h3>151<div class="box box-def" id="def-11-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 11.1</span><span class="box-title">— principe fondamental de la méthode du revenu</span><a class="box-anchor" href="#def-11-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-9">La valeur d'un immeuble à revenus correspond à la <strong>valeur présente des bénéfices futurs</strong> que cet immeuble peut générer pour son propriétaire. Un investisseur rationnel paie en fonction de la capacité de l'immeuble à produire des revenus nets.</p></div></div>152<p id="p11-10">La méthode repose sur le <span class="motcle" data-term="principe d'anticipation">principe d'anticipation</span> vu à la séance 3<label for="sn-11-1" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-11-1" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-repere">Séance 3 : la valeur naît de l'anticipation des bénéfices futurs.</span> : l'acheteur d'un immeuble locatif acquiert un <em>flux de revenus futurs</em>, pas seulement un bâtiment. C'est la méthode privilégiée pour tout ce qui se loue — plex, multilogements, immeubles de bureaux, commerces — parce qu'elle reproduit le raisonnement réel des acheteurs de ces immeubles.</p>153<h3 id="s-11-1-2" class="h-subsection"><span class="h-num">11.1.2</span><span class="h-text">L'équation fondamentale</span><a class="h-anchor" href="#s-11-1-2" aria-label="Lien vers cette section">#</a></h3>154<div class="box box-form" id="form-11-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 11.1</span><span class="box-title">— capitalisation directe</span><a class="box-anchor" href="#form-11-1" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-11-1"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable width="100%"><mtr><mtd width="50%"></mtd><mtd><mrow><mi>V</mi><mtext> </mtext><mo>=</mo><mtext> </mtext><mfrac><mtext>RNE</mtext><mtext>TGA</mtext></mfrac></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(11.1)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">V \;=\; \frac{\text{RNE}}{\text{TGA}}\tag{11.1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.0463em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3603em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">TGA</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">RNE</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="katex-tag"><span class="katex-strut" style="height:2.0463em;vertical-align:-0.686em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">11.1</span></span><span class="mord">)</span></span></span></span></span></span></div>155<p id="p11-11">où <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi></mrow><annotation encoding="application/x-tex">V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span></span></span></span> est la valeur de l'immeuble ($), RNE le revenu net d'exploitation ($/an) et TGA le taux global d'actualisation (aussi appelé taux de capitalisation).</p></div></div>156<div class="box box-ex" id="ex-11-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 11.1</span><span class="box-title">— première capitalisation</span><a class="box-anchor" href="#ex-11-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-12">Un immeuble génère un RNE de <span class="num">60 000 $</span> par année. Le TGA observé sur le marché pour ce type d'immeuble est de 5,5 %.</p>157<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>V</mi><mo>=</mo><mfrac><mrow><mn>60</mn><mtext> </mtext><mn>000</mn></mrow><mn>0,055</mn></mfrac><mo>=</mo><mn>1</mn><mtext> </mtext><mn>090</mn><mtext> </mtext><mn>909</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>≈</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">1</mn><mtext> </mtext><mn mathvariant="bold">091</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">V = \frac{60\,000}{0{,}055} = 1\,090\,909\,\$ \approx \uqotitle{1\,091\,000\,\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height: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">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">055</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">60</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em;"><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:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">090</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">909</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">1</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">091</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">000</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span></span></div>158<p id="p11-13">Une division — mais chacun des deux termes condense un travail d'analyse considérable. Ce chapitre construit le numérateur; le chapitre 12, le dénominateur.</p></div></div>159<p id="p11-14">Les étudiants qui ont suivi un cours de finance reconnaîtront la parenté : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mtext>RNE</mtext><mi mathvariant="normal">/</mi><mtext>TGA</mtext></mrow><annotation encoding="application/x-tex">V = \text{RNE}/\text{TGA}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord text"><span class="mord">RNE</span></span><span class="mord">/</span><span class="mord text"><span class="mord">TGA</span></span></span></span></span> est la formule de la <strong class="c-or">perpétuité</strong> — la valeur présente d'un flux constant qui se répète indéfiniment, égale au flux divisé par le taux d'actualisation. L'immobilier s'y prête mieux que la plupart des actifs : un immeuble bien entretenu produit des loyers sur des décennies, et la réserve pour remplacement (on y viendra) sert justement à rendre ce flux perpétuel en finançant le renouvellement des composantes. La même parenté éclaire le rôle du taux : comme le rendement exigé d'une action ou d'une obligation, le TGA prix le <em>risque</em> du flux — un RNE fragile (locataires précaires, immeuble vieillissant, marché en détente) se capitalise à un taux plus élevé, donc à une valeur moindre, qu'un RNE solide. La séance 12 fera de cette intuition un outil de calcul ; pour l'instant, elle suffit à comprendre pourquoi la qualité de l'analyse du RNE — l'objet de ce chapitre — conditionne tout le reste.</p>160<p id="p11-15">Les trois variables de l'équation forment un triangle : connaissant deux d'entre elles, on déduit toujours la troisième.</p>161<div class="center"><div class="tikz"><img src="/assets/fig/d939dd935cc84036.svg" alt="Figure" width="439" height="170" style="width:min(100%,637px)" loading="lazy" decoding="async"></div></div>162<p id="p11-16">L'évaluateur estime le RNE et le TGA pour en déduire la valeur; l'analyste de marché, à l'inverse, extrait le TGA des ventes où prix et RNE sont connus — c'est l'extraction directe de la séance 12.</p>163<h3 id="s-11-1-3" class="h-subsection"><span class="h-num">11.1.3</span><span class="h-text">Capitalisation directe ou DCF?</span><a class="h-anchor" href="#s-11-1-3" aria-label="Lien vers cette section">#</a></h3>164<p id="p11-17">Deux techniques mettent ce principe en œuvre.</p>165<div class="box box-def" id="def-11-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 11.2</span><span class="box-title">— capitalisation directe</span><a class="box-anchor" href="#def-11-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-18">Convertit le RNE <strong>stabilisé d'une seule année</strong> en valeur : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mtext>RNE</mtext><mi mathvariant="normal">/</mi><mtext>TGA</mtext></mrow><annotation encoding="application/x-tex">V = \text{RNE}/\text{TGA}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord text"><span class="mord">RNE</span></span><span class="mord">/</span><span class="mord text"><span class="mord">TGA</span></span></span></span></span>. Simple et rapide, elle suppose des revenus et des dépenses <strong>stables</strong> et s'appuie sur des <strong>comparables fiables</strong> (ventes d'immeubles à revenus dont on connaît le RNE).</p></div></div>166<div class="box box-def" id="def-11-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 11.3</span><span class="box-title">— actualisation des flux monétaires (DCF)</span><a class="box-anchor" href="#def-11-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-19">Actualise <strong>chaque flux futur</strong> sur une période de détention (5 à 10 ans), plus la valeur de revente :</p>167<div class="eq" id="eq-11-2"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable width="100%"><mtr><mtd width="50%"></mtd><mtd><mrow><mi>V</mi><mtext> </mtext><mo>=</mo><mtext> </mtext><munderover><mo>∑</mo><mrow><mi>t</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mfrac><mrow><mi>C</mi><msub><mi>F</mi><mi>t</mi></msub></mrow><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mi>r</mi><msup><mo stretchy="false">)</mo><mi>t</mi></msup></mrow></mfrac><mtext> </mtext><mo>+</mo><mtext> </mtext><mfrac><msub><mi>V</mi><mi>n</mi></msub><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mi>r</mi><msup><mo stretchy="false">)</mo><mi>n</mi></msup></mrow></mfrac></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(11.2)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">V \;=\; \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t} \;+\; \frac{V_n}{(1+r)^n}\tag{11.2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.9185em;vertical-align:-1.2671em;"></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:-1.8829em;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">t</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:1.2671em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3603em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">r</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7196em;"><span style="top:-2.989em;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">t</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.1389em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><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">t</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.2963em;vertical-align:-0.936em;"></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="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">r</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.5904em;"><span style="top:-2.989em;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">n</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="katex-tag"><span class="katex-strut" style="height:2.9185em;vertical-align:-1.2671em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">11.2</span></span><span class="mord">)</span></span></span></span></span></span></div>168<p id="p11-20">Plus complexe mais plus flexible, elle admet des revenus et des dépenses <strong>variables</strong> d'une année à l'autre.</p></div></div>169<p id="p11-21"><label for="sn-11-2" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-11-2" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-terme"><strong class="sn-term">Cap. directe</strong> Une année stabilisée, un taux. Marché actif requis.</span><label for="sn-11-3" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-11-3" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-terme"><strong class="sn-term">DCF</strong> Flux année par année <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> revente. Trajectoires atypiques.</span>En première approximation : immeuble stabilisé dans un marché actif <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> capitalisation directe; flux en transition (loyers sous le marché à rattraper, repositionnement, baux commerciaux échelonnés) <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> DCF. La séance 12 développe le DCF en détail.</p>170<p id="p11-22">Il faut comprendre que les deux techniques ne s'opposent pas : elles répondent à des questions différentes posées au même principe. La capitalisation directe demande au marché « combien payez-vous, aujourd'hui, pour un dollar de RNE stabilisé de ce type d'immeuble? » — et la réponse, le TGA, absorbe implicitement toutes les anticipations de croissance et de risque que les acheteurs partagent. Elle est donc redoutablement fiable quand l'immeuble sujet ressemble aux immeubles dont on extrait le taux, et muette dès qu'il s'en écarte. Le DCF, lui, rend ces anticipations <em>explicites</em> : croissance des loyers année par année, rattrapage des baux sous le marché, travaux prévus, revente en fin d'horizon. Cette transparence a un prix — chaque hypothèse explicite est une hypothèse contestable, et un DCF mal discipliné devient une machine à justifier n'importe quel prix. La sagesse professionnelle québécoise tient en une phrase : capitalisation directe comme méthode principale dès que le marché la permet, DCF comme méthode d'appoint lorsque la trajectoire des flux s'écarte du profil stabilisé.</p>171<h3 id="s-11-1-4" class="h-subsection"><span class="h-num">11.1.4</span><span class="h-text">Quelle méthode pour quel immeuble?</span><a class="h-anchor" href="#s-11-1-4" aria-label="Lien vers cette section">#</a></h3>172<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Type d'immeuble</th><th>Approche privilégiée</th><th>Justification</th></tr></thead><tbody><tr><td>Duplex / triplex</td><td>Comparaison <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> revenu</td><td>Marché actif, mais le revenu reste pertinent</td></tr><tr><td>Plex (4–5 logements)</td><td>Revenu <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> comparaison</td><td>Les acheteurs sont des investisseurs qui analysent les revenus</td></tr><tr><td>Multilogements (6+)</td><td>Revenu (primaire)</td><td>Prix négociés directement sur le RNE</td></tr><tr><td>Commercial / bureaux</td><td>Revenu (primaire)</td><td>Baux complexes, analyse des flux</td></tr><tr><td>Industriel</td><td>Revenu <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> coût</td><td>Selon le type d'occupant</td></tr><tr><td>Unifamiliale</td><td>Comparaison</td><td>Propriétaire-occupant, pas de revenu</td></tr></tbody></table></div></div>173<h2 id="s-11-2" class="h-section"><span class="h-num">11.2</span><span class="h-text">Les revenus : du potentiel à l'effectif</span><a class="h-anchor" href="#s-11-2" aria-label="Lien vers cette section">#</a></h2>174<h3 id="s-11-2-1" class="h-subsection"><span class="h-num">11.2.1</span><span class="h-text">Le revenu brut potentiel (RBP)</span><a class="h-anchor" href="#s-11-2-1" aria-label="Lien vers cette section">#</a></h3>175<div class="box box-def" id="def-11-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 11.4</span><span class="box-title">— revenu brut potentiel</span><a class="box-anchor" href="#def-11-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-23">Le <strong>revenu brut potentiel</strong> (RBP) est le revenu total que l'immeuble pourrait générer si <strong>tous les logements étaient loués à 100 %</strong> aux loyers du marché, sans aucune perte.</p></div></div>176<p id="p11-24">Trois précisions font toute la différence entre un RBP correct et un RBP d'examen raté<label for="sn-11-4" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-11-4" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-repere">RBP : loyers du <em>marché</em>, occupation pleine, revenus accessoires exclus (ils entrent au RBE).</span>. D'abord, le RBP se calcule aux <strong class="c-or">loyers du marché</strong>, et non aux loyers des baux en vigueur — distinction capitale au Québec, que la sous-section suivante développe. Ensuite, il suppose une occupation de 100 % : non pas que l'évaluateur croie à la pleine occupation perpétuelle, mais parce que la méthode isole d'abord le potentiel brut de l'immeuble avant d'en retrancher, à l'étape suivante et à un taux de <em>marché</em> documenté, la perte d'inoccupation normale. Séparer les deux estimations rend chacune vérifiable ; les fusionner (« je mets les loyers un peu plus bas pour tenir compte des logements vides ») rend le calcul incontrôlable. Enfin, les revenus accessoires — stationnement, buanderie, entreposage — ne figurent pas au RBP : ils s'ajoutent plus loin, dans le calcul du RBE, parce qu'ils obéissent à une dynamique propre et ne subissent pas l'inoccupation de la même manière que les loyers.</p>177<div class="widget" data-widget="cascade-revenus"></div>178<h3 id="s-11-2-2" class="h-subsection"><span class="h-num">11.2.2</span><span class="h-text">Loyers du marché contre loyers contractuels</span><a class="h-anchor" href="#s-11-2-2" aria-label="Lien vers cette section">#</a></h3>179<div class="box box-def" id="def-11-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 11.5</span><span class="box-title">— loyer du marché vs loyer contractuel</span><a class="box-anchor" href="#def-11-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-25">Le <strong>loyer du marché</strong> est celui qu'obtiendrait chaque logement s'il était mis en location aujourd'hui, établi à partir des comparables; il reflète l'offre et la demande actuelles. Le <strong>loyer contractuel</strong> est celui que paie réellement le locataire selon le bail en vigueur.</p></div></div>180<p id="p11-26">Dans un marché sans friction, les deux convergeraient au fil des renouvellements. Au Québec, ils divergent durablement.</p>181<div class="box box-qc" id="quebec-11-27"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-map"/></svg></span><span class="box-label">l'effet TAL sur les loyers contractuels</span><a class="box-anchor" href="#quebec-11-27" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-28">Le Tribunal administratif du logement encadre les hausses de loyer résidentiel : le locataire peut refuser une augmentation, et le TAL fixe alors le loyer selon ses critères. Résultat : les loyers de locataires de longue date peuvent être <strong>significativement inférieurs</strong> au marché — des écarts de 20 à 30 % ne sont pas rares après dix ans d'occupation continue. L'évaluateur québécois vit donc en permanence avec <em>deux</em> grilles de loyers : celle des baux et celle du marché.</p></div></div>182<div class="box box-ex" id="ex-11-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 11.2</span><span class="box-title">— l'écart contractuel–marché sur le 6-plex du chapitre</span><a class="box-anchor" href="#ex-11-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-29">Aperçu du cas complet de la section <a class="xref" href="#s-11-5">11.5</a> — un 6-plex de Gatineau :</p>183<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Logement</th><th class="al-r">Contractuel</th><th class="al-r">Marché</th><th class="al-r">Écart</th></tr></thead><tbody><tr><td>4½ (locataire depuis 8 ans)</td><td class="al-r">950 $/mois</td><td class="al-r">1 150 $/mois</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><mn>200</mn></mrow><annotation encoding="application/x-tex">-200</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">200</span></span></span></span> $</td></tr><tr><td>4½ (nouveau bail)</td><td class="al-r">1 100 $/mois</td><td class="al-r">1 150 $/mois</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><mn>50</mn></mrow><annotation encoding="application/x-tex">-50</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">50</span></span></span></span> $</td></tr><tr><td>4½ (locataire depuis 12 ans)</td><td class="al-r">800 $/mois</td><td class="al-r">1 150 $/mois</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><mn>350</mn></mrow><annotation encoding="application/x-tex">-350</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">350</span></span></span></span> $</td></tr><tr><td>3½ (locataire depuis 9 ans)</td><td class="al-r">750 $/mois</td><td class="al-r">950 $/mois</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><mn>200</mn></mrow><annotation encoding="application/x-tex">-200</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">200</span></span></span></span> $</td></tr><tr><td>3½ (locataire depuis 4 ans)</td><td class="al-r">900 $/mois</td><td class="al-r">950 $/mois</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><mn>50</mn></mrow><annotation encoding="application/x-tex">-50</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">50</span></span></span></span> $</td></tr><tr><td>3½ (nouveau bail)</td><td class="al-r">950 $/mois</td><td class="al-r">950 $/mois</td><td class="al-r">0 $</td></tr></tbody></table></div></div>184<p id="p11-30">Écart total : 850 $/mois, soit <span class="num">10 200 $</span> par année — la trace directe de l'encadrement des loyers. Notez la corrélation parfaite entre l'ancienneté du locataire et la profondeur de l'écart.</p></div></div>185<div class="box box-att" id="attention-11-31"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">pourquoi le marché, alors que les baux sont opposables?</span><a class="box-anchor" href="#attention-11-31" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-32">Utiliser les loyers du marché au RBP ne nie pas l'existence des baux : cela établit le <em>potentiel</em> de l'immeuble, que le roulement naturel des locataires permet de rattraper graduellement. Un acheteur paie pour ce potentiel — en l'escomptant selon la vitesse de rattrapage attendue. Dans une analyse fine (DCF, séance 12), l'écart contractuel–marché se modélise explicitement; en capitalisation directe, on capitalise le RNE au marché et l'on discute l'écart dans la réconciliation. Ce qui est fautif, c'est de mélanger : un RBP mi-contractuel mi-marché ne mesure plus rien.</p></div></div>186<h3 id="s-11-2-3" class="h-subsection"><span class="h-num">11.2.3</span><span class="h-text">Les baux au Québec : le cadre juridique</span><a class="h-anchor" href="#s-11-2-3" aria-label="Lien vers cette section">#</a></h3>187<p id="p11-33"><label for="sn-11-5" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-11-5" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-terme"><strong class="sn-term">Bail résidentiel</strong> C.c.Q., art. 1851–2000; reconduction automatique; TAL.</span>Le <span class="motcle" data-term="bail résidentiel">bail résidentiel</span> est régi par le Code civil du Québec (art. 1851–2000, « Du louage »), et ses traits distinctifs n'ont pas d'équivalent dans le reste de l'Amérique du Nord. Le premier est la <strong class="c-or">reconduction automatique</strong> : à l'échéance, le bail se renouvelle de plein droit, et le locataire peut refuser la hausse proposée <em>sans perdre son logement</em> — ce qui renverse le rapport de force qu'on observe ailleurs, où le refus d'une hausse équivaut à un préavis de départ. En cas de désaccord, c'est le <strong class="c-or">TAL qui fixe le loyer</strong> selon ses critères réglementaires : le locateur ne peut ni imposer sa hausse ni évincer le locataire récalcitrant. S'y ajoute la <strong class="c-or">clause G</strong> du bail obligatoire, qui contraint le locateur à divulguer le loyer le plus bas payé au cours des douze derniers mois — un mécanisme de transparence renforcé en 2024 (PL 31) qui freine les remises à niveau abruptes entre deux locataires. Enfin, la durée typique de douze mois avec échéance concentrée au 30 juin produit le folklore bien réel du « bail du 1<sup>er</sup> juillet » : un marché locatif dont tout le roulement se joue sur quelques semaines d'été, ce que l'évaluateur doit garder en tête lorsqu'il interprète des taux d'inoccupation saisonniers.</p>188<p id="p11-34">Le <span class="motcle" data-term="bail commercial">bail commercial</span>, lui, relève du même Code civil mais <strong>sans encadrement</strong> du TAL : liberté contractuelle complète. On y rencontre les types brut, net, net net et triple net — le locataire assumant de plus en plus de charges à mesure qu'on avance dans la liste —, des durées de trois à dix ans avec options de renouvellement, des clauses d'indexation (IPC, pourcentage des ventes) et aucune reconduction automatique. La nature du bail change donc complètement l'analyse des revenus <em>et</em> des dépenses : un triple net transfère presque toutes les dépenses au locataire, ce qui gonfle mécaniquement le ratio RNE/RBE.</p>189<h3 id="s-11-2-4" class="h-subsection"><span class="h-num">11.2.4</span><span class="h-text">La fixation des loyers : le régime 2026 du TAL</span><a class="h-anchor" href="#s-11-2-4" aria-label="Lien vers cette section">#</a></h3>190<div class="box box-qc" id="quebec-11-35"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-map"/></svg></span><span class="box-label">nouvelle méthode de fixation depuis le 1<sup>er</sup> janvier 2026</span><a class="box-anchor" href="#quebec-11-35" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-36">Le critère de base est désormais la <strong>moyenne de l'IPC des trois dernières années</strong>, appliquée au loyer : pour 2026, cet ajustement de base s'établit à <strong>3,1 %</strong> (baux débutant entre le 2 avril 2026 et le 1<sup>er</sup> avril 2027). À ce socle s'ajoutent les <strong>variations réelles</strong> des taxes municipales et scolaires et des assurances — répercutées au dollar près, à la hausse comme à la baisse —, ainsi que les <strong>travaux majeurs</strong> admissibles, transférés au loyer à raison de <strong>5 % par année</strong> des dépenses engagées. La partie du loyer liée aux services à la personne (résidences pour aînés) suit un régime distinct, indexée à 6,7 %. Le locataire conserve dans tous les cas le droit de refuser la hausse, le TAL tranchant alors selon ces critères. L'ancien régime — le calcul poste par poste des dépenses d'énergie, d'entretien et de services de la « Section G » — ne s'applique plus qu'aux avis donnés avant 2026.</p></div></div>191<p id="p11-37">Pour l'évaluateur, trois conséquences : la croissance des revenus résidentiels devient plus <em>prévisible</em>, ancrée sur l'IPC; les travaux majeurs se répercutent <em>graduellement</em> (5 %/an) plutôt qu'en bloc; et ces paramètres balisent directement les hypothèses de croissance du DCF (séance 12). Un rapport qui projette 6 % de croissance annuelle des loyers résidentiels au Québec devra expliquer comment il contourne le régime du TAL — roulement de locataires, logements neufs exemptés, ou optimisme injustifiable.</p>192<h3 id="s-11-2-5" class="h-subsection"><span class="h-num">11.2.5</span><span class="h-text">L'inoccupation : les données SCHL</span><a class="h-anchor" href="#s-11-2-5" aria-label="Lien vers cette section">#</a></h3>193<p id="p11-38">Chaque octobre, la SCHL publie son <em>Rapport sur le marché locatif</em>, la référence pour les taux d'inoccupation des immeubles de trois logements et plus. Repères d'octobre 2025<label for="sn-11-6" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-11-6" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-repere">SCHL, oct. 2025 : Montréal 2,1 %; Québec 0,9 %; Gatineau 3,8 %. Équilibre <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> 3 %.</span> :</p>194<div class="center"><div class="tikz"><img src="/assets/fig/fda784b47b2d71fc.svg" alt="Figure" width="422" height="174" style="width:min(100%,612px)" loading="lazy" decoding="async"></div></div>195<p id="p11-39">Le seuil d'environ 3 % marque l'<strong class="c-or">équilibre</strong> du marché locatif : en dessous, la pénurie pousse loyers et valeurs à la hausse; au-dessus, le marché se détend. Montréal (2,1 %) et surtout Québec (0,9 %) demeurent sous l'équilibre; <strong>Gatineau, à 3,8 %, est en détente</strong> — une donnée qui pèsera sur le choix du taux d'inoccupation du cas complet.</p>196<h3 id="s-11-2-6" class="h-subsection"><span class="h-num">11.2.6</span><span class="h-text">Les revenus accessoires</span><a class="h-anchor" href="#s-11-2-6" aria-label="Lien vers cette section">#</a></h3>197<p id="p11-40">Au-delà des loyers, l'immeuble génère des <span class="motcle" data-term="revenus accessoires">revenus accessoires</span> qu'il faut recenser exhaustivement : stationnement (typiquement 50 à 150 $/mois par place à Gatineau), buanderie payante, entreposage (casiers), baux d'antennes de télécommunications sur le toit, distributrices, panneaux publicitaires sur la façade. Sur un immeuble de taille moyenne, ils représentent souvent 3 à 6 % du revenu total — les oublier, c'est sous-évaluer d'autant.</p>198<p id="p11-41">Deux nuances de traitement méritent l'attention. D'une part, tous les revenus accessoires ne se valent pas en <em>qualité</em> : un bail d'antenne de télécommunications signé pour dix ans avec un opérateur national est un flux quasi obligataire, tandis que les recettes de distributrices fluctuent avec l'occupation. Dans une analyse fine, on peut capitaliser séparément un bail d'antenne à un taux plus bas que le reste de l'immeuble. D'autre part, il faut se garder de compter en revenu accessoire ce qui est déjà dans le loyer : si les baux incluent une place de stationnement, la « louer » une seconde fois dans le calcul gonfle fictivement le RBE. La règle est la même que partout ailleurs dans la méthode : chaque dollar de revenu doit avoir une source contractuelle ou de marché identifiable, et n'être compté qu'une fois.</p>199<h3 id="s-11-2-7" class="h-subsection"><span class="h-num">11.2.7</span><span class="h-text">Le revenu brut effectif (RBE)</span><a class="h-anchor" href="#s-11-2-7" aria-label="Lien vers cette section">#</a></h3>200<div class="box box-form" id="form-11-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 11.2</span><span class="box-title">— revenu brut effectif</span><a class="box-anchor" href="#form-11-2" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-11-3"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable width="100%"><mtr><mtd width="50%"></mtd><mtd><mrow><mtext>RBE</mtext><mtext> </mtext><mo>=</mo><mtext> </mtext><mtext>RBP</mtext><mtext> </mtext><mo>−</mo><mtext> </mtext><mtext>Inoccupation</mtext><mtext> </mtext><mo>−</mo><mtext> </mtext><mrow><mtext>Mauvaises cr</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>ances</mtext></mrow><mtext> </mtext><mo>+</mo><mtext> </mtext><mtext>Autres revenus</mtext></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(11.3)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">\text{RBE} \;=\; \text{RBP} \;-\; \text{Inoccupation}201\;-\; \text{Mauvaises créances} \;+\; \text{Autres revenus}\tag{11.3}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord text"><span class="mord">RBE</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 text"><span class="mord">RBP</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:0.8778em;vertical-align:-0.1944em;"></span><span class="mord text"><span class="mord">Inoccupation</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:0.7778em;vertical-align:-0.0833em;"></span><span class="mord text"><span class="mord">Mauvaises cr</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">ances</span></span><span 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:0.6833em;"></span><span class="mord text"><span class="mord">Autres revenus</span></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">11.3</span></span><span class="mord">)</span></span></span></span></span></span></div></div></div>202<p id="p11-42">Ordres de grandeur des pertes : inoccupation, 2 à 5 % du RBP selon la région et le segment; <span class="motcle" data-term="mauvaises créances">mauvaises créances</span> (loyers impayés, frais de recouvrement), 0,5 à 2 %; total des pertes, 3 à 7 % du RBP. Deux réflexes professionnels : le taux d'inoccupation retenu est un taux de <em>marché à long terme</em> (même si l'immeuble est plein aujourd'hui — la pleine occupation permanente n'existe pas), et il se <em>justifie par une source</em> (SCHL, enquêtes locales).</p>203<div class="box box-ex" id="ex-11-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 11.3</span><span class="box-title">— du RBP au RBE en cascade</span><a class="box-anchor" href="#ex-11-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-43">Immeuble dont le RBP est de <span class="num">72 000 $</span>; inoccupation de 3 %, mauvaises créances de 1 %, revenus accessoires de <span class="num">3600 $</span> :</p>204<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>RBE</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>72</mn><mtext> </mtext><mn>000</mn><mo>−</mo><munder><munder><mrow><mn>2</mn><mtext> </mtext><mn>160</mn></mrow><mo stretchy="true">⏟</mo></munder><mrow><mn>3</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow></munder><mo>−</mo><munder><munder><mn>720</mn><mo stretchy="true">⏟</mo></munder><mrow><mn>1</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow></munder><mo>+</mo><mn>3</mn><mtext> </mtext><mn>600</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">72</mn><mtext> </mtext><mn mathvariant="bold">720</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{RBE} &= 72\,000 - \underbrace{2\,160}_{3\,\%}205 - \underbrace{720}_{1\,\%} + 3\,600 = \uqotitle{72\,720\,\$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:2.2519em;vertical-align:-0.8759em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3759em;"><span style="top:-3.5359em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">RBE</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8759em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3759em;"><span style="top:-3.5359em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">72</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="minner munder"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6444em;"><span style="top:-1.627em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">3</span><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mtight">%</span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="minner munder"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6444em;"><span class="svg-align" style="top:-2.352em;"><span class="pstrut" style="height:3em;"></span><span class="katex-stretchy" style="height:0.548em;min-width:1.6em;"><span class="brace-left" style="height:0.548em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="0.548em" viewBox="0 0 400000 548" preserveAspectRatio="xMinYMin slice"><path d="M0 6l6-6h17c12.688 0 19.313.3 20 1 4 4 7.313 8.3 10 13206 35.313 51.3 80.813 93.8 136.5 127.5 55.688 33.7 117.188 55.8 184.5 66.5.688207 0 2 .3 4 1 18.688 2.7 76 4.3 172 5h399450v120H429l-6-1c-124.688-8-235-61.7208-331-161C60.687 138.7 32.312 99.3 7 54L0 41V6z"/></svg></span><span class="brace-center" style="height:0.548em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="0.548em" viewBox="0 0 400000 548" preserveAspectRatio="xMidYMin slice"><path d="M199572 214209c100.7 8.3 195.3 44 280 108 55.3 42 101.7 93 139 153l9 14c2.7-4 5.7-8.7 9-14210 53.3-86.7 123.7-153 211-199 66.7-36 137.3-56.3 212-62h199568v120H200432c-178.3211 11.7-311.7 78.3-403 201-6 8-9.7 12-11 12-.7.7-6.7 1-18 1s-17.3-.3-18-1c-1.3 0212-5-4-11-12-44.7-59.3-101.3-106.3-170-141s-145.3-54.3-229-60H0V214z"/></svg></span><span class="brace-right" style="height:0.548em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="0.548em" viewBox="0 0 400000 548" preserveAspectRatio="xMaxYMin slice"><path d="M399994 0l6 6v35l-6 11c-56 104-135.3 181.3-238 232-57.3213 28.7-117 45-179 50H-300V214h399897c43.3-7 81-15 113-26 100.7-33 179.7-91 237214-174 2.7-5 6-9 10-13 .7-1 7.3-1 20-1h17z"/></svg></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">160</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.648em;"><span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.4119em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="minner munder"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6444em;"><span style="top:-1.627em;"><span class="pstrut" style="height:3em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mtight">%</span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="minner munder"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6444em;"><span class="svg-align" style="top:-2.352em;"><span class="pstrut" style="height:3em;"></span><span class="katex-stretchy" style="height:0.548em;min-width:1.6em;"><span class="brace-left" style="height:0.548em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="0.548em" viewBox="0 0 400000 548" preserveAspectRatio="xMinYMin slice"><path d="M0 6l6-6h17c12.688 0 19.313.3 20 1 4 4 7.313 8.3 10 13215 35.313 51.3 80.813 93.8 136.5 127.5 55.688 33.7 117.188 55.8 184.5 66.5.688216 0 2 .3 4 1 18.688 2.7 76 4.3 172 5h399450v120H429l-6-1c-124.688-8-235-61.7217-331-161C60.687 138.7 32.312 99.3 7 54L0 41V6z"/></svg></span><span class="brace-center" style="height:0.548em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="0.548em" viewBox="0 0 400000 548" preserveAspectRatio="xMidYMin slice"><path d="M199572 214218c100.7 8.3 195.3 44 280 108 55.3 42 101.7 93 139 153l9 14c2.7-4 5.7-8.7 9-14219 53.3-86.7 123.7-153 211-199 66.7-36 137.3-56.3 212-62h199568v120H200432c-178.3220 11.7-311.7 78.3-403 201-6 8-9.7 12-11 12-.7.7-6.7 1-18 1s-17.3-.3-18-1c-1.3 0221-5-4-11-12-44.7-59.3-101.3-106.3-170-141s-145.3-54.3-229-60H0V214z"/></svg></span><span class="brace-right" style="height:0.548em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="0.548em" viewBox="0 0 400000 548" preserveAspectRatio="xMaxYMin slice"><path d="M399994 0l6 6v35l-6 11c-56 104-135.3 181.3-238 232-57.3222 28.7-117 45-179 50H-300V214h399897c43.3-7 81-15 113-26 100.7-33 179.7-91 237223-174 2.7-5 6-9 10-13 .7-1 7.3-1 20-1h17z"/></svg></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">720</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.648em;"><span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.4119em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">72</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">720</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8759em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>224<p id="p11-44">Les pertes se calculent sur le RBP (les loyers), jamais sur les revenus accessoires — une place de stationnement ne fait pas de mauvaise créance distincte de celle du logement.</p></div></div>225<h2 id="s-11-3" class="h-section"><span class="h-num">11.3</span><span class="h-text">Les dépenses d'exploitation</span><a class="h-anchor" href="#s-11-3" aria-label="Lien vers cette section">#</a></h2>226<p id="p11-45">Si les revenus se laissent lire dans les baux, les dépenses, elles, se cachent partout : dans les avis d'imposition, les polices d'assurance, les factures d'Hydro-Québec, les contrats de déneigement — et parfois nulle part, quand le propriétaire fait lui-même le travail sans se payer. La définition de référence est pourtant simple : les <span class="motcle" data-term="dépenses d'exploitation">dépenses d'exploitation</span> sont les débours <em>récurrents et nécessaires</em> pour maintenir les revenus de l'immeuble. Chaque mot compte. <em>Récurrents</em> : la dépense revient d'année en année, au moins en espérance — ce qui exclut le remplacement ponctuel d'une toiture, mais inclut la provision annuelle qui l'anticipe. <em>Nécessaires pour maintenir les revenus</em> : sans entretien, sans assurance, sans déneigement, les loyers finissent par s'effondrer — alors que l'immeuble produirait exactement les mêmes loyers sans hypothèque et sans l'impôt personnel du propriétaire, ce qui annonce déjà les exclusions absolues traitées plus loin dans cette section. La classification standard range ces dépenses en trois blocs, du plus prévisible au plus discrétionnaire.</p>227<h3 id="s-11-3-1" class="h-subsection"><span class="h-num">11.3.1</span><span class="h-text">Trois blocs : fixes, variables, réserve</span><a class="h-anchor" href="#s-11-3-1" aria-label="Lien vers cette section">#</a></h3>228<div class="box box-def" id="def-11-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 11.6</span><span class="box-title">— dépenses fixes</span><a class="box-anchor" href="#def-11-6" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-46">Dépenses qui ne varient pas (ou peu) avec le taux d'occupation : <strong>taxes foncières</strong> (municipales et scolaires) et <strong>assurances</strong> (immeuble et responsabilité civile).</p></div></div>229<div class="box box-def" id="def-11-7"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 11.7</span><span class="box-title">— dépenses variables</span><a class="box-anchor" href="#def-11-7" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-47">Dépenses qui fluctuent avec l'occupation ou l'utilisation : entretien et réparations, énergie des espaces communs, gestion immobilière, conciergerie, déneigement, entretien paysager, publicité et mise en location.</p></div></div>230<div class="box box-def" id="def-11-8"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 11.8</span><span class="box-title">— réserve pour remplacement</span><a class="box-anchor" href="#def-11-8" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-48">Provision annuelle pour le remplacement des composantes à <strong>durée de vie limitée</strong> (toiture, fenêtres, chauffe-eau, électroménagers). Typiquement 2 à 5 % du RBE. Aussi appelée « réserve structurale ».</p></div></div>231<h4 id="s-11-3-1-1" class="h-subsubsection"><span class="h-num">11.3.1.1</span><span class="h-text">Les dépenses fixes de plus près</span><a class="h-anchor" href="#s-11-3-1-1" aria-label="Lien vers cette section">#</a></h4>232<p id="p11-49">Les <strong>taxes foncières</strong> reposent sur la valeur inscrite au rôle d'évaluation (cycle triennal), multipliée par les taux de la municipalité — à Gatineau, la taxation se fait par unité de voisinage depuis 2024, avec un taux effectif variant selon la catégorie et le secteur (hypothèse illustrative du cas : environ 1,3 % de la valeur au rôle). Les <strong>assurances</strong> couvrent l'immeuble (incendie, dégâts d'eau, vandalisme) et la responsabilité civile; elles sont en forte hausse au Québec depuis 2020 et représentent typiquement 0,3 à 0,6 % de la valeur du bâtiment.</p>233<div class="box box-terrain" id="terrain-11-50"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-hardhat"/></svg></span><span class="box-label">valider plutôt qu'estimer</span><a class="box-anchor" href="#terrain-11-50" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-51">Pour les deux dépenses fixes, l'évaluateur ne devine pas : il demande les <strong>avis d'imposition</strong> et les <strong>polices d'assurance</strong>. Ce sont des documents objectifs, disponibles, vérifiables — les utiliser (et le mentionner au rapport) est une exigence élémentaire de diligence.</p></div></div>234<h4 id="s-11-3-1-2" class="h-subsubsection"><span class="h-num">11.3.1.2</span><span class="h-text">Les dépenses variables : ordres de grandeur québécois</span><a class="h-anchor" href="#s-11-3-1-2" aria-label="Lien vers cette section">#</a></h4>235<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Dépense</th><th>Estimation typique</th><th>Commentaire Québec</th></tr></thead><tbody><tr><td>Entretien / réparations</td><td>3–7 % du RBE</td><td>Plus élevé pour les immeubles anciens</td></tr><tr><td>Énergie (propriétaire)</td><td>800–1 500 $/log./an</td><td>Si le chauffage est inclus; Hydro-Québec</td></tr><tr><td>Gestion immobilière</td><td>5–8 % du RBE</td><td>Autogéré : imputer <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 % quand même</td></tr><tr><td>Conciergerie</td><td>3 000–8 000 $/an</td><td>Selon la taille de l'immeuble</td></tr><tr><td>Déneigement</td><td>2 000–5 000 $/an</td><td>Indispensable au Québec</td></tr><tr><td>Entretien paysager</td><td>1 000–3 000 $/an</td><td>Gazon, haies, été</td></tr><tr><td>Publicité / mise en location</td><td>0,5–1 % du RBE</td><td>Annonces, enquêtes de crédit</td></tr><tr><td>Divers / imprévus</td><td>1–2 % du RBE</td><td>Marge de prudence</td></tr></tbody></table></div></div>236<div class="box box-att" id="attention-11-52"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">la gestion « gratuite » n'existe pas</span><a class="box-anchor" href="#attention-11-52" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-53">Beaucoup de petits immeubles québécois sont autogérés par leur propriétaire, qui ne se verse aucun salaire. Le RNE économique doit quand même imputer des frais de gestion (<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 % du RBE) : le travail de gestion a une valeur de marché, et l'acheteur — qui devra gérer ou faire gérer — l'intégrera à son calcul. Omettre la gestion gonfle artificiellement le RNE, donc la valeur. C'est l'un des ajustements de normalisation les plus fréquents.</p></div></div>237<h4 id="s-11-3-1-3" class="h-subsubsection"><span class="h-num">11.3.1.3</span><span class="h-text">La réserve pour remplacement, composante par composante</span><a class="h-anchor" href="#s-11-3-1-3" aria-label="Lien vers cette section">#</a></h4>238<div class="box box-ex" id="ex-11-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-bulb"/></svg></span><span class="box-label">Exemple 11.4</span><span class="box-title">— réserve annuelle d'un 6-plex</span><a class="box-anchor" href="#ex-11-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-54">Estimation des composantes à durée de vie limitée d'un 6-plex :</p>239<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Composante</th><th class="al-r">Coût estimé</th><th class="al-r">Durée de vie</th></tr></thead><tbody><tr><td>Toiture</td><td class="al-r">25 000–40 000 $</td><td class="al-r">20–25 ans</td></tr><tr><td>Fenêtres</td><td class="al-r">20 000–35 000 $</td><td class="al-r">25–30 ans</td></tr><tr><td>Chauffe-eau (par logement)</td><td class="al-r">1 500–2 500 $</td><td class="al-r">10–12 ans</td></tr><tr><td>Électroménagers (par logement)</td><td class="al-r">3 000–5 000 $</td><td class="al-r">10–15 ans</td></tr><tr><td>Revêtement extérieur</td><td class="al-r">15 000–30 000 $</td><td class="al-r">25–35 ans</td></tr><tr><td>Système de chauffage</td><td class="al-r">10 000–20 000 $</td><td class="al-r">20–25 ans</td></tr><tr class="rule-above"><td><strong>Total estimé</strong></td><td class="al-r"><strong><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\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> 120 000 $</strong></td><td class="al-r">—</td></tr><tr><td><strong>Réserve annuelle</strong></td><td class="al-r"><strong><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\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> 5 000–6 000 $/an</strong></td><td class="al-r">—</td></tr></tbody></table></div></div>240<p id="p11-55">Le principe : diviser le coût de chaque composante par sa durée de vie, puis sommer. La réserve maintient le <em>potentiel de revenu</em> de l'immeuble — sans elle, le RNE d'aujourd'hui se paie en effondrement du RNE de demain.</p></div></div>241<p id="p11-56">La réserve est aussi le poste le plus débattu de l'état des dépenses, car peu de propriétaires la provisionnent réellement : elle n'existe souvent que dans le calcul de l'évaluateur. Certains praticiens l'omettent et compensent par un TGA plus élevé ; d'autres — c'est la position de ce cours — l'incluent systématiquement, parce qu'un RNE qui ignore l'usure programmée des composantes n'est pas un revenu <em>durable</em>, et que la cohérence avec les comparables l'exige : si le TGA a été extrait de ventes analysées <em>avec</em> réserve, il doit s'appliquer à un RNE calculé <em>avec</em> réserve. Mélanger les conventions — RNE sans réserve du sujet, TGA extrait de RNE avec réserve — produit une erreur silencieuse de 5 à 10 % de la valeur, indétectable dans le rapport final. Encore une fois : annoncez votre convention, et tenez-la d'un bout à l'autre du calcul.</p>242<h3 id="s-11-3-2" class="h-subsection"><span class="h-num">11.3.2</span><span class="h-text">Les exclusions absolues</span><a class="h-anchor" href="#s-11-3-2" aria-label="Lien vers cette section">#</a></h3>243<div class="box box-att" id="attention-11-57"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">à ne JAMAIS inclure dans les dépenses d'exploitation</span><a class="box-anchor" href="#attention-11-57" aria-label="Lien">#</a></div><div class="box-body"><ul><li>le <strong>service de la dette</strong> (paiements hypothécaires);</li><li>l'<strong>amortissement comptable</strong>;</li><li>l'<strong>impôt sur le revenu</strong> du propriétaire;</li><li>les <strong>dépenses en capital</strong> (améliorations majeures).</li></ul>244<p id="p11-62">C'est l'erreur la plus fréquente — et la plus coûteuse — des débutants.</p></div></div>245<p id="p11-63">Le raisonnement mérite d'être maîtrisé, pas seulement mémorisé. Le RNE mesure la performance <em>économique de l'immeuble</em>, indépendamment de la structure de financement et de la situation fiscale du propriétaire<label for="sn-11-7" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-11-7" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-repere">Le RNE appartient à l'immeuble; la dette et l'impôt appartiennent au propriétaire.</span>. La dette, d'abord, est un choix de l'<em>investisseur</em> et non une caractéristique de l'immeuble : le même 6-plex vaut la même chose qu'il soit acheté comptant ou financé à 80 %, et deux acheteurs aux montages financiers opposés doivent aboutir à la même valeur marchande. Inclure l'hypothèque dans les dépenses rendrait la « valeur » dépendante du financement particulier de chaque acheteur — un non-sens conceptuel, et la source de l'erreur chiffrée à l'exercice 11.5. L'impôt sur le revenu, de même, dépend du contribuable : particulier, société par actions, fonds de placement immobilier — chacun paie un taux différent sur le même flux, et l'amortissement fiscal est un avantage propre à chacun. L'immeuble, lui, génère le même RNE pour tout propriétaire, et c'est précisément cette invariance qui fait du RNE la bonne mesure de sa performance. Les dépenses en capital, enfin, ne sont pas des charges récurrentes d'exploitation : refaire une toiture n'appauvrit pas l'année du chantier de <span class="num">34 000 $</span> — c'est un investissement dont bénéficieront vingt années d'exploitation, et qui entre donc dans le calcul <em>lissé</em>, par la réserve pour remplacement.</p>246<h3 id="s-11-3-3" class="h-subsection"><span class="h-num">11.3.3</span><span class="h-text">Les ratios de contrôle</span><a class="h-anchor" href="#s-11-3-3" aria-label="Lien vers cette section">#</a></h3>247<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Type d'immeuble</th><th class="al-r">Dépenses/RBE</th><th class="al-r">RNE/RBE</th></tr></thead><tbody><tr><td>Plex (2–5 logements)</td><td class="al-r">30–40 %</td><td class="al-r">60–70 %</td></tr><tr><td>Multilogements (6–24 logements)</td><td class="al-r">35–45 %</td><td class="al-r">55–65 %</td></tr><tr><td>Multilogements (25+ logements)</td><td class="al-r">40–50 %</td><td class="al-r">50–60 %</td></tr><tr><td>Bureau (bail brut)</td><td class="al-r">40–50 %</td><td class="al-r">50–60 %</td></tr><tr><td>Commerce (triple net)</td><td class="al-r">5–15 %</td><td class="al-r">85–95 %</td></tr><tr><td>Industriel (net)</td><td class="al-r">10–25 %</td><td class="al-r">75–90 %</td></tr></tbody></table></div></div>248<p id="p11-64">Ces ratios sont des <em>guides de vraisemblance</em>, pas des normes : chaque immeuble s'analyse individuellement. Chauffage inclus ou conciergerie sur place tirent le ratio vers le haut; le climat québécois y ajoute structurellement le chauffage et le déneigement. Un état des dépenses qui sort de la fourchette de son segment appelle une explication — ou une correction.</p>249<p id="p11-65">L'écart spectaculaire du bail commercial <strong class="c-or">triple net</strong> (5 à 15 % de dépenses seulement) mérite un mot : il ne signifie pas que ces immeubles coûtent moins cher à exploiter, mais que le <em>locataire</em> assume directement taxes, assurances et entretien. Le RNE du propriétaire s'en trouve mécaniquement rapproché du revenu brut — et le risque, transféré : si le locataire fait défaut, le propriétaire récupère non seulement un local vide, mais toutes les charges qu'il avait externalisées. C'est pourquoi les immeubles triple net se capitalisent souvent à des taux qui reflètent davantage la solidité financière du locataire (son « covenant », dans le jargon) que la brique elle-même : évaluer un commerce loué vingt ans à une chaîne nationale, c'est presque évaluer une obligation de cette chaîne. Le réflexe à retenir : avant de comparer deux ratios de dépenses — ou deux TGA —, toujours vérifier que les baux mettent les mêmes charges du même côté.</p>250<h2 id="s-11-4" class="h-section"><span class="h-num">11.4</span><span class="h-text">Le RNE : reconstruction, normalisation, stabilisation</span><a class="h-anchor" href="#s-11-4" aria-label="Lien vers cette section">#</a></h2>251<h3 id="s-11-4-1" class="h-subsection"><span class="h-num">11.4.1</span><span class="h-text">La chaîne complète</span><a class="h-anchor" href="#s-11-4-1" aria-label="Lien vers cette section">#</a></h3>252<div class="box box-form" id="form-11-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 11.3</span><span class="box-title">— chaîne du RNE</span><a class="box-anchor" href="#form-11-3" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-11-4"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable width="100%"><mtr><mtd width="50%"></mtd><mtd><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>RBP</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mrow><mtext>somme des loyers du march</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext> (100</mtext><mtext> </mtext><mtext>% d’occupation)</mtext></mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>RBE</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mtext>RBP</mtext><mo>−</mo><mtext>Inoccupation</mtext><mo>−</mo><mrow><mtext>Mauvaises cr</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>ances</mtext></mrow><mo>+</mo><mtext>Autres revenus</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>RNE</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mtext>RBE</mtext><mo>−</mo><mrow><mtext>D</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>penses d’exploitation</mtext></mrow></mrow></mstyle></mtd></mtr></mtable></mtd><mtd width="50%"></mtd><mtd><mtext>(11.4)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{RBP} &= \text{somme des loyers du marché (100\,\% d'occupation)}253\\254\text{RBE} &= \text{RBP} - \text{Inoccupation} - \text{Mauvaises créances}255 + \text{Autres revenus} \\256\text{RNE} &= \text{RBE} - \text{Dépenses d'exploitation}\end{aligned}\tag{11.4}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:4.2em;vertical-align:-1.85em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35em;"><span style="top:-4.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">RBP</span></span></span></span><span style="top:-3.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">RBE</span></span></span></span><span style="top:-1.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">RNE</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.85em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35em;"><span style="top:-4.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord">somme des loyers du march</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord"> (100</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">% d’occupation)</span></span></span></span><span style="top:-3.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord">RBP</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord text"><span class="mord">Inoccupation</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord text"><span class="mord">Mauvaises cr</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">ances</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord text"><span class="mord">Autres revenus</span></span></span></span><span style="top:-1.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord">RBE</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord text"><span class="mord">D</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">penses d’exploitation</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.85em;"><span></span></span></span></span></span></span></span></span><span class="katex-tag"><span class="katex-strut" style="height:4.2em;vertical-align:-1.85em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">11.4</span></span><span class="mord">)</span></span></span></span></span></span></div></div></div>257<div class="center"><div class="tikz"><img src="/assets/fig/86c1c980b1618f3a.svg" alt="Figure" width="418" height="177" style="width:min(100%,607px)" loading="lazy" decoding="async"></div></div>258<p id="p11-66">Le RNE est le <em>numérateur</em> de la capitalisation directe : toute erreur s'y répercute directement sur la valeur, amplifiée par la division. À un TGA de 5,5 %, chaque dollar de RNE erroné déplace la valeur d'environ 18 $<label for="sn-11-8" class="sn-toggle" title="Note marginale"><span class="sn-mark" aria-hidden="true">◆</span></label><input type="checkbox" id="sn-11-8" class="sn-cb" aria-label="Afficher la note"><span class="sidenote sn-repere"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mi mathvariant="normal">/</mi><mn>0,055</mn><mo>≈</mo><mn>18,2</mn></mrow><annotation encoding="application/x-tex">1/0{,}055 \approx 18{,}2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1/0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">055</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">18</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">2</span></span></span></span> : le multiplicateur d'erreur du RNE.</span>.</p>259<h3 id="s-11-4-2" class="h-subsection"><span class="h-num">11.4.2</span><span class="h-text">Pourquoi « reconstruire » le RNE?</span><a class="h-anchor" href="#s-11-4-2" aria-label="Lien vers cette section">#</a></h3>260<p id="p11-67">Les états financiers du propriétaire ne reflètent pas nécessairement le RNE <em>économique</em> de l'immeuble : ils mélangent loyers contractuels et marché, incluent l'hypothèque et l'amortissement, omettent la gestion autogérée et la réserve, et charrient des dépenses ponctuelles. L'évaluateur <span class="motcle" data-term="reconstruit">reconstruit</span> donc le RNE en ajustant les données comptables des deux côtés de l'état des résultats. Côté revenus, il remplace les loyers contractuels par les loyers du <em>marché</em>, applique un taux d'inoccupation de marché même si l'immeuble affiche complet, estime les mauvaises créances au taux normal du segment et recense un à un les revenus accessoires que la comptabilité du propriétaire agrège ou oublie. Côté dépenses, il retire ce qui n'appartient pas à l'exploitation — la dette, l'impôt, l'amortissement —, ajoute ce que la comptabilité omet — les frais de gestion d'un immeuble autogéré, la réserve pour remplacement —, écarte les dépenses non récurrentes et ramène aux valeurs de marché les montants atypiques, qu'ils trahissent la négligence (entretien famélique d'un propriétaire qui laisse dépérir) ou la générosité comptable (salaire du conjoint passé en conciergerie). Le résultat n'est plus l'état des résultats du propriétaire : c'est l'état des résultats de l'<em>immeuble</em>.</p>261<div class="box box-def" id="def-11-9"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 11.9</span><span class="box-title">— normalisation et stabilisation</span><a class="box-anchor" href="#def-11-9" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-68"><strong>Normaliser</strong> : ajuster revenus et dépenses pour refléter ce qui est typique du marché et de l'immeuble (éliminer le non-récurrent, corriger le sous- ou surestimé, appliquer les taux de marché, recouper avec les ratios). <strong>Stabiliser</strong> : projeter un RNE représentatif d'une année <em>typique</em> — ni la meilleure ni la pire —, à taux d'occupation normal et à dépenses normales. C'est ce RNE stabilisé, et lui seul, que capitalise la méthode directe.</p></div></div>262<div class="box box-terrain" id="terrain-11-69"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-hardhat"/></svg></span><span class="box-label">trois à cinq ans d'états financiers</span><a class="box-anchor" href="#terrain-11-69" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-70">En pratique, l'évaluateur demande <strong>trois à cinq années</strong> d'états financiers. Une seule année peut être trompeuse : un toit refait gonfle les dépenses, un logement vacant six mois creuse les revenus. La série révèle les tendances et permet de distinguer le structurel du ponctuel. Elle révèle aussi, parfois, ce qu'on préférerait ne pas voir : un entretien qui décroît d'année en année pendant que l'immeuble vieillit est le signe classique du propriétaire qui « habille » son RNE avant la mise en vente — et la raison pour laquelle le réviseur expérimenté lit la <em>trajectoire</em> des postes autant que leur niveau.</p></div></div>263<h2 id="s-11-5" class="h-section"><span class="h-num">11.5</span><span class="h-text">Cas complet : un 6-plex à Gatineau</span><a class="h-anchor" href="#s-11-5" aria-label="Lien vers cette section">#</a></h2>264<p id="p11-71">Il est temps d'assembler la chaîne entière sur un immeuble unique — celui dont les loyers ont déjà servi d'illustration à la section <a class="xref" href="#s-11-2">11.2</a>. Le cas est construit pour concentrer les situations types du marché québécois : des baux d'ancienneté variable qui creusent l'écart contractuel–marché, une autogestion qui masque le coût réel de la gestion, une hypothèque bien visible qu'il faudra ignorer, et des documents officiels (avis d'imposition, police d'assurance) qui ancrent les dépenses fixes. Suivez chaque étape avec le réflexe du réviseur : d'où vient ce chiffre, et pourrais-je le défendre?</p>265<h3 id="s-11-5-1" class="h-subsection"><span class="h-num">11.5.1</span><span class="h-text">L'immeuble et le mandat</span><a class="h-anchor" href="#s-11-5-1" aria-label="Lien vers cette section">#</a></h3>266<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th colspan="4">6-plex — secteur Hull, Gatineau (évaluation : automne 2026)</th></tr></thead><tbody><tr><td>Type</td><td>6-plex résidentiel, 1985</td><td>Valeur au rôle</td><td>520 000 $</td></tr><tr><td>Composition</td><td>3 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\times</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">×</span></span></span></span> 4½ et 3 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\times</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">×</span></span></span></span> 3½</td><td>Taxes foncières</td><td>7 800 $/an (avis)</td></tr><tr><td>Stationnements</td><td>4 places extérieures</td><td>Assurances</td><td>3 200 $/an (police)</td></tr><tr><td>Buanderie</td><td>commune, payante</td><td>Gestion</td><td>autogéré</td></tr><tr><td>Chauffage</td><td>aux frais des locataires</td><td>Hypothèque</td><td>2 800 $/mois (<strong class="c-rouge">exclue du RNE!</strong>)</td></tr><tr><td>État</td><td>bon, partiellement rénové</td><td></td><td></td></tr></tbody></table></div></div>267<h3 id="s-11-5-2" class="h-subsection"><span class="h-num">11.5.2</span><span class="h-text">Étape 1 — Le RBP aux loyers du marché</span><a class="h-anchor" href="#s-11-5-2" aria-label="Lien vers cette section">#</a></h3>268<div class="center"><div class="table-wrap"><table class="tbl table-wide"><thead><tr><th>Logement</th><th>Type</th><th class="al-r">Contractuel</th><th class="al-r">Marché</th><th class="al-r">Annuel (marché)</th></tr></thead><tbody><tr><td>1</td><td>4½</td><td class="al-r">950 $/mois</td><td class="al-r">1 150 $/mois</td><td class="al-r">13 800 $</td></tr><tr><td>2</td><td>4½</td><td class="al-r">1 100 $/mois</td><td class="al-r">1 150 $/mois</td><td class="al-r">13 800 $</td></tr><tr><td>3</td><td>4½</td><td class="al-r">800 $/mois</td><td class="al-r">1 150 $/mois</td><td class="al-r">13 800 $</td></tr><tr><td>4</td><td>3½</td><td class="al-r">750 $/mois</td><td class="al-r">950 $/mois</td><td class="al-r">11 400 $</td></tr><tr><td>5</td><td>3½</td><td class="al-r">900 $/mois</td><td class="al-r">950 $/mois</td><td class="al-r">11 400 $</td></tr><tr><td>6</td><td>3½</td><td class="al-r">950 $/mois</td><td class="al-r">950 $/mois</td><td class="al-r">11 400 $</td></tr><tr class="rule-above"><td colspan="4"><strong>Total RBP (loyers du marché)</strong></td><td class="al-r"><strong>75 600 $</strong></td></tr></tbody></table></div></div>269<p id="p11-72">Les loyers contractuels totalisent <span class="num">65 400 $</span> par année, contre <span class="num">75 600 $</span> au marché : un écart de <span class="num">10 200 $</span> (13,5 %), conséquence directe de l'encadrement des loyers sur des baux anciens.</p>270<h3 id="s-11-5-3" class="h-subsection"><span class="h-num">11.5.3</span><span class="h-text">Étape 2 — Du RBP au RBE</span><a class="h-anchor" href="#s-11-5-3" aria-label="Lien vers cette section">#</a></h3>271<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Poste</th><th>Calcul</th><th class="al-r">Montant</th></tr></thead><tbody><tr><td>Revenu brut potentiel (RBP)</td><td></td><td class="al-r">75 600 $</td></tr><tr><td><em>Moins :</em> inoccupation (3,0 %)</td><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>75</mn><mtext> </mtext><mn>600</mn><mo>×</mo><mn>0,03</mn></mrow><annotation encoding="application/x-tex">75\,600 \times 0{,}03</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">75</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">03</span></span></span></span></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><mn>2</mn><mtext> </mtext><mn>268</mn></mrow><annotation encoding="application/x-tex">-2\,268</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">268</span></span></span></span> $</td></tr><tr><td><em>Moins :</em> mauvaises créances (1,0 %)</td><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>75</mn><mtext> </mtext><mn>600</mn><mo>×</mo><mn>0,01</mn></mrow><annotation encoding="application/x-tex">75\,600 \times 0{,}01</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">75</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">01</span></span></span></span></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><mn>756</mn></mrow><annotation encoding="application/x-tex">-756</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">756</span></span></span></span> $</td></tr><tr><td><em>Plus :</em> stationnement (4 places à 75 $/mois)</td><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4</mn><mo>×</mo><mn>75</mn><mo>×</mo><mn>12</mn></mrow><annotation encoding="application/x-tex">4 \times 75 \times 12</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">4</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">75</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">12</span></span></span></span></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><mn>3</mn><mtext> </mtext><mn>600</mn></mrow><annotation encoding="application/x-tex">+3\,600</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">+</span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span></span></span></span> $</td></tr><tr><td><em>Plus :</em> buanderie</td><td>estimé</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><mn>1</mn><mtext> </mtext><mn>200</mn></mrow><annotation encoding="application/x-tex">+1\,200</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">+</span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span></span></span></span> $</td></tr><tr class="rule-above"><td><strong>Revenu brut effectif (RBE)</strong></td><td></td><td class="al-r"><strong>77 376 $</strong></td></tr></tbody></table></div></div>272<div class="box box-rem" id="remarque-11-73"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pen"/></svg></span><span class="box-label">justification des taux — à imiter dans vos travaux</span><a class="box-anchor" href="#remarque-11-73" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-74">Inoccupation : la SCHL observe <strong>3,8 %</strong> à Gatineau (octobre 2025); l'hypothèse retenue est de <strong>3,0 %</strong> à long terme, le taux d'équilibre — le 3,8 % courant reflète une détente que rien n'indique comme permanente. Mauvaises créances : 1,0 %, pratique standard. Chaque taux est <em>sourcé et motivé</em> : c'est exactement le niveau de justification attendu à l'examen et dans un rapport.</p></div></div>273<h3 id="s-11-5-4" class="h-subsection"><span class="h-num">11.5.4</span><span class="h-text">Étape 3 — Les dépenses d'exploitation</span><a class="h-anchor" href="#s-11-5-4" aria-label="Lien vers cette section">#</a></h3>274<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Dépense</th><th class="al-r">Montant</th><th>Note</th></tr></thead><tbody><tr><td><em>Fixes :</em> taxes foncières</td><td class="al-r">7 800 $</td><td>avis d'imposition</td></tr><tr><td><em>Fixes :</em> assurances</td><td class="al-r">3 200 $</td><td>police en vigueur</td></tr><tr><td>Entretien et réparations</td><td class="al-r">3 500 $</td><td><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> 4,5 % du RBE</td></tr><tr><td>Énergie (espaces communs)</td><td class="al-r">1 800 $</td><td>électricité, éclairage</td></tr><tr><td>Gestion immobilière (5 %)</td><td class="al-r">3 869 $</td><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>77</mn><mtext> </mtext><mn>376</mn><mo>×</mo><mn>0,05</mn></mrow><annotation encoding="application/x-tex">77\,376 \times 0{,}05</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">77</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">376</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">05</span></span></span></span> — imputée malgré l'autogestion</td></tr><tr><td>Conciergerie</td><td class="al-r">2 400 $</td><td>entretien des communs</td></tr><tr><td>Déneigement</td><td class="al-r">2 500 $</td><td>contrat annuel</td></tr><tr><td>Entretien paysager</td><td class="al-r">1 000 $</td><td>été</td></tr><tr><td>Réserve pour remplacement</td><td class="al-r">4 500 $</td><td><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> 5,8 % du RBE</td></tr><tr class="rule-above"><td><strong>Total des dépenses</strong></td><td class="al-r"><strong>30 569 $</strong></td><td><strong>39,5 % du RBE</strong></td></tr></tbody></table></div></div>275<p id="p11-75">Remarquez ce qui <em>ne figure pas</em> au tableau : l'hypothèque de 2 800 $/mois (<span class="num">33 600 $</span> par année!). L'inclure aurait presque doublé les « dépenses » et détruit le calcul.</p>276<h3 id="s-11-5-5" class="h-subsection"><span class="h-num">11.5.5</span><span class="h-text">Étape 4 — Le RNE et sa vérification</span><a class="h-anchor" href="#s-11-5-5" aria-label="Lien vers cette section">#</a></h3>277<div class="box box-form" id="form-11-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule 11.4</span><span class="box-title">— RNE du cas</span><a class="box-anchor" href="#form-11-4" aria-label="Lien">#</a></div><div class="box-body"><div class="eq" id="eq-11-5"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable width="100%"><mtr><mtd width="50%"></mtd><mtd><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>RBP (loyers du march</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>)</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>75</mn><mtext> </mtext><mn>600</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mo>−</mo><mtext> </mtext><mrow><mtext>inoccupation (3,0</mtext><mtext> </mtext><mtext>%)</mtext></mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mo>−</mo><mn>2</mn><mtext> </mtext><mn>268</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mo>−</mo><mtext> </mtext><mrow><mtext>mauvaises cr</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>ances (1,0</mtext><mtext> </mtext><mtext>%)</mtext></mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mo>−</mo><mn>756</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mo>+</mo><mtext> autres revenus</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mo>+</mo><mn>4</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>RBE</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>77</mn><mtext> </mtext><mn>376</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mo>−</mo><mtext> </mtext><mrow><mtext>d</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>penses d’exploitation</mtext></mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mo>−</mo><mn>30</mn><mtext> </mtext><mn>569</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext mathvariant="bold">RNE</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">46</mn><mtext> </mtext><mn mathvariant="bold">807</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable></mtd><mtd width="50%"></mtd><mtd><mtext>(11.5)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{RBP (loyers du marché)} &= 75\,600\,\$ \\278-\ \text{inoccupation (3,0\,\%)} &= -2\,268\,\$ \\279-\ \text{mauvaises créances (1,0\,\%)} &= -756\,\$ \\280+\ \text{autres revenus} &= +4\,800\,\$ \\281\text{RBE} &= 77\,376\,\$ \\282-\ \text{dépenses d'exploitation} &= -30\,569\,\$ \\283\textbf{RNE} &= \uqotitle{46\,807\,\$}\end{aligned}\tag{11.5}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:10.2em;vertical-align:-4.85em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:5.35em;"><span style="top:-7.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">RBP (loyers du march</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">)</span></span></span></span><span style="top:-6.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">−</span><span class="mspace"> </span><span class="mord text"><span class="mord">inoccupation (3,0</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%)</span></span></span></span><span style="top:-4.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">−</span><span class="mspace"> </span><span class="mord text"><span class="mord">mauvaises cr</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">ances (1,0</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%)</span></span></span></span><span style="top:-3.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">+</span><span class="mspace"> </span><span class="mord text"><span class="mord">autres revenus</span></span></span></span><span style="top:-1.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">RBE</span></span></span></span><span style="top:-0.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">−</span><span class="mspace"> </span><span class="mord text"><span class="mord">d</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">penses d’exploitation</span></span></span></span><span style="top:1.49em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord textbf">RNE</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:4.85em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:5.35em;"><span style="top:-7.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">75</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-6.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">−</span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">268</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-4.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">−</span><span class="mord">756</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-3.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">+</span><span class="mord">4</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-1.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">77</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">376</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-0.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">−</span><span class="mord">30</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">569</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:1.49em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">46</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">807</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:4.85em;"><span></span></span></span></span></span></span></span></span><span class="katex-tag"><span class="katex-strut" style="height:10.2em;vertical-align:-4.85em;"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">11.5</span></span><span class="mord">)</span></span></span></span></span></span></div></div></div>284<p id="p11-76"><strong>Contrôle par les ratios</strong> : dépenses/RBE <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>30</mn><mtext> </mtext><mn>569</mn><mi mathvariant="normal">/</mi><mn>77</mn><mtext> </mtext><mn>376</mn><mo>=</mo><mn>39,5</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">= 30\,569/77\,376 =28539{,}5\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">569/77</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">376</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">39</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> et RNE/RBE <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>60,5</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">= 60{,}5\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">60</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span> — au cœur de la fourchette de marché d'un immeuble de cette taille (35–45 % de dépenses). Le calcul est vraisemblable.</p>286<p id="p11-77"><strong>Valeur indicative</strong> : si le TGA de marché est de 5,5 % (il sera extrait rigoureusement à la séance 12),</p>287<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>V</mi><mo>=</mo><mfrac><mrow><mn>46</mn><mtext> </mtext><mn>807</mn></mrow><mn>0,055</mn></mfrac><mo>=</mo><mn>851</mn><mtext> </mtext><mn>036</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>≈</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">851</mn><mtext> </mtext><mn mathvariant="bold">000</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">V = \frac{46\,807}{0{,}055} = 851\,036\,\$ \approx \uqotitle{851\,000\,\$}.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height: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">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">055</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">46</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">807</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:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">851</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">036</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">851</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">000</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span><span class="mord">.</span></span></span></span></span></div>288<p id="p11-78">Prenez un instant pour mesurer le chemin parcouru : partis d'une liasse de baux, d'un avis d'imposition, d'une police d'assurance et des états financiers d'un propriétaire autogéré, nous avons produit un RNE économique dont chaque ligne est sourcée, normalisée et défendable. C'est ce travail — et non la division finale — qui distingue l'évaluation professionnelle du calcul de coin de table. Notez aussi ce que la valeur indicative de <span class="num">851 000 $</span> dit du marché : rapportée au RBP de <span class="num">75 600 $</span>, elle représente un multiplicateur d'environ 11,3 fois le revenu brut — un ordre de grandeur que les courtiers en immeubles multirésidentiels de l'Outaouais manient quotidiennement, et qui servira de recoupement à la séance 12 quand les multiplicateurs bruts (MRB) seront formellement introduits.</p>289<h2 id="s-11-6" class="h-section"><span class="h-num">11.6</span><span class="h-text">Le contexte locatif québécois : synthèse pour l'évaluateur</span><a class="h-anchor" href="#s-11-6" aria-label="Lien vers cette section">#</a></h2>290<h3 id="s-11-6-1" class="h-subsection"><span class="h-num">11.6.1</span><span class="h-text">Le TAL en bref</span><a class="h-anchor" href="#s-11-6-1" aria-label="Lien vers cette section">#</a></h3>291<div class="box box-def" id="def-11-10"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span class="box-label">Définition 11.10</span><span class="box-title">— Tribunal administratif du logement</span><a class="box-anchor" href="#def-11-10" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-79">Le TAL (anciennement la Régie du logement, jusqu'en 2020) encadre les relations entre locateurs et locataires pour les logements résidentiels au Québec. Il fixe les augmentations de loyer en cas de désaccord, autorise ou refuse les reprises de logement, tranche les litiges, ordonne des réparations et autorise les résiliations de bail.</p></div></div>292<p id="p11-80">Son impact sur l'évaluation se déploie en cascade. Parce que le locataire peut refuser une hausse sans perdre son logement, les loyers contractuels des locataires de longue date glissent <em>sous le marché</em> — premier effet. Parce que l'ajustement de base est désormais arrimé à l'IPC de trois ans, la croissance des revenus résidentiels est <em>balisée</em> et prévisible — deuxième effet, qui discipline les projections. La combinaison des deux creuse un écart <em>durable</em> entre le RBP contractuel et le RBP au marché, écart qui pèse sur la valeur à court terme : l'acheteur paie pour des revenus qu'il ne touchera pas immédiatement. Mais cet écart n'est pas une perte sèche — il se résorbe <em>graduellement</em>, au rythme du roulement naturel des locataires, et c'est précisément cette trajectoire de rattrapage que le DCF de la séance 12 saura modéliser là où la capitalisation directe ne peut que la constater.</p>293<h3 id="s-11-6-2" class="h-subsection"><span class="h-num">11.6.2</span><span class="h-text">Le marché locatif, tendances 2024–2026</span><a class="h-anchor" href="#s-11-6-2" aria-label="Lien vers cette section">#</a></h3>294<p id="p11-81">Le marché québécois combine une croissance démographique soutenue, des coûts de construction élevés et une offre locative accrue qui produit une <strong class="c-or">détente graduelle</strong> depuis 2024–2025, après l'épisode de taux d'intérêt 2022–2024 qui avait comprimé la rentabilité. Repères SCHL (octobre 2025) : Montréal, inoccupation 2,1 % et loyer moyen deux chambres <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span></span></span></span> 1 175 $; Québec, 0,9 % et <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span></span></span></span> 1 160 $; Gatineau, 3,8 % et <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span></span></span></span> 1 420 $ — marché en détente, mais loyer moyen le plus élevé au Québec, effet de la proximité d'Ottawa.</p>295<p id="p11-82">Ce dernier chiffre surprend toujours les étudiants et mérite explication. Le marché locatif de Gatineau vit en symbiose avec celui d'Ottawa : une partie substantielle des locataires travaille de l'autre côté de la rivière, où les salaires fédéraux sont élevés et les loyers ontariens — non encadrés de la même manière — nettement supérieurs. Gatineau offre donc aux ménages de la capitale fédérale un arbitrage loyer–navettage qui soutient ses loyers au-dessus de la moyenne québécoise, tout en les maintenant sous les niveaux d'Ottawa. Pour l'évaluateur, cette situation frontalière a deux conséquences pratiques : les comparables de loyers doivent rester du côté québécois (le cadre juridique ontarien rend les loyers d'Ottawa non comparables), mais la conjoncture de l'emploi fédéral — embauches, télétravail, compressions — est une variable d'analyse de marché aussi importante à Gatineau que l'économie locale elle-même.</p>296<h3 id="s-11-6-3" class="h-subsection"><span class="h-num">11.6.3</span><span class="h-text">La liste de vigilance de l'évaluateur québécois</span><a class="h-anchor" href="#s-11-6-3" aria-label="Lien vers cette section">#</a></h3>297<div class="box box-ret" id="aretenir-11-83"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-star"/></svg></span><span class="box-label">six points de vigilance — immeubles locatifs au Québec</span><a class="box-anchor" href="#aretenir-11-83" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-84">Devant tout immeuble locatif québécois, six réflexes. <strong>Un</strong> : reconstituer le RBP aux loyers du marché et chiffrer l'écart contractuel–marché — il y en a presque toujours un. <strong>Deux</strong> : vérifier qui paie le chauffage, car la réponse déplace 800 à 1 500 $/logement/an d'un côté ou de l'autre de l'état des dépenses. <strong>Trois</strong> : se rappeler le « bail du 1<sup>er</sup> juillet » — échéances concentrées au 30 juin, roulement et remise en location saisonniers, taux d'inoccupation à interpréter en conséquence. <strong>Quatre</strong> : intégrer l'encadrement du TAL, dont l'ajustement de base (moyenne de l'IPC sur trois ans; 3,1 % pour 2026) balise toute projection de croissance des loyers. <strong>Cinq</strong> : tenir compte de la clause G — la divulgation du loyer le plus bas des douze derniers mois (PL 31, 2024) freine les remises à niveau espérées. <strong>Six</strong> : sourcer chaque hypothèse — loyers, inoccupation et dépenses se valident avec la SCHL et les associations de propriétaires, pas au jugé.</p></div></div>298<p id="p11-85">Le chapitre s'arrête volontairement au numérateur. Nous disposons d'un RNE stabilisé de <span class="num">46 807 $</span> pour le 6-plex de Hull, et d'une valeur indicative obtenue avec un taux posé en hypothèse. Tout l'enjeu de la séance 12 sera de remplacer cette hypothèse par une <em>mesure</em> : extraire le TGA de ventes réelles, le décomposer en bande d'investissement pour en comprendre les ressorts, puis, quand la trajectoire des flux l'exige, déployer l'actualisation complète. Les exercices qui suivent verrouillent d'abord la mécanique du RNE — car aucun raffinement de taux ne rattrape un numérateur mal construit.</p>299<h2 id="s-11-7" class="h-section"><span class="h-num">11.7</span><span class="h-text">Exercices</span><a class="h-anchor" href="#s-11-7" aria-label="Lien vers cette section">#</a></h2>300<div class="box box-exo" id="exo-11-1"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 11.1</span><span class="box-title">— triangle valeur–RNE–TGA</span><a class="box-anchor" href="#exo-11-1" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-86"><strong>a)</strong> Un immeuble affiche un RNE stabilisé de <span class="num">84 500 $</span> et le marché indique un TGA de 6,2 % : quelle est sa valeur? <strong>b)</strong> Un immeuble s'est vendu <span class="num">1 450 000 $</span> avec un RNE de <span class="num">78 300 $</span> : quel TGA cette vente exprime-t-elle? <strong>c)</strong> Un acheteur exige un TGA de 5,75 % et dispose de <span class="num">900 000 $</span> : quel RNE minimal doit-il trouver?</p></div></div>301<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p11-87"><strong>a)</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mn>84</mn><mtext> </mtext><mn>500</mn><mi mathvariant="normal">/</mi><mn>0,062</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>362</mn><mtext> </mtext><mn>903</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>≈</mo><mn>1</mn><mtext> </mtext><mn>363</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">V = 84\,500 / 0{,}062 = 1\,362\,903\,\$ \approx3021\,363\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">84</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500/0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">062</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">362</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">903</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">363</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>.<br> <strong>b)</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>TGA</mtext><mo>=</mo><mn>78</mn><mtext> </mtext><mn>300</mn><mi mathvariant="normal">/</mi><mn>1</mn><mtext> </mtext><mn>450</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>0,0540</mn><mo>=</mo><mn>5,40</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">\text{TGA} = 78\,300 / 1\,450\,000 = 0{,}0540 = 5{,}40\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord text"><span class="mord">TGA</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">78</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">300/1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">450</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0540</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">5</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">40</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>.<br> <strong>c)</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>RNE</mtext><mo>=</mo><mi>V</mi><mo>×</mo><mtext>TGA</mtext><mo>=</mo><mn>900</mn><mtext> </mtext><mn>000</mn><mo>×</mo><mn>0,0575</mn><mo>=</mo><mn>51</mn><mtext> </mtext><mn>750</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">\text{RNE} = V \times \text{TGA} = 900\,000 \times 0{,}0575 =30351\,750\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord text"><span class="mord">RNE</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord text"><span class="mord">TGA</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">900</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0575</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">51</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">750</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> par année.<br> Les trois questions sont les trois faces du même triangle : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mtext>RNE</mtext><mi mathvariant="normal">/</mi><mtext>TGA</mtext></mrow><annotation encoding="application/x-tex">V =304\text{RNE}/\text{TGA}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord text"><span class="mord">RNE</span></span><span class="mord">/</span><span class="mord text"><span class="mord">TGA</span></span></span></span></span>, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>TGA</mtext><mo>=</mo><mtext>RNE</mtext><mi mathvariant="normal">/</mi><mi>V</mi></mrow><annotation encoding="application/x-tex">\text{TGA} = \text{RNE}/V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord text"><span class="mord">TGA</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord text"><span class="mord">RNE</span></span><span class="mord">/</span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span></span></span></span> et <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>RNE</mtext><mo>=</mo><mi>V</mi><mo>×</mo><mtext>TGA</mtext></mrow><annotation encoding="application/x-tex">\text{RNE} = V \times305\text{TGA}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord text"><span class="mord">RNE</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord text"><span class="mord">TGA</span></span></span></span></span>.</p></div></details>306<div class="box box-exo" id="exo-11-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 11.2</span><span class="box-title">— RBP et RBE d'un 8-plex</span><a class="box-anchor" href="#exo-11-2" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-88">Un 8-plex de Gatineau compte 4 logements de 4½ (loyer du marché : 1 175 $/mois) et 4 logements de 3½ (marché : 975 $/mois). Les baux en vigueur totalisent 8 150 $/mois. L'immeuble offre 6 places de stationnement à 70 $/mois et une buanderie rapportant environ <span class="num">1400 $</span>/an. Hypothèses : inoccupation de 3,0 %, mauvaises créances de 1,0 %. <strong>a)</strong> Calculez le RBP. <strong>b)</strong> Calculez le RBE. <strong>c)</strong> Chiffrez l'écart annuel contractuel–marché et donnez-en la cause probable.</p></div></div>307<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p11-89"><strong>a) RBP aux loyers du marché :</strong></p>308<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mn>4</mn><mo>×</mo><mn>1</mn><mtext> </mtext><mn>175</mn><mo>×</mo><mn>12</mn></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>56</mn><mtext> </mtext><mn>400</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mn>4</mn><mo>×</mo><mn>975</mn><mo>×</mo><mn>12</mn></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>46</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>RBP</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>56</mn><mtext> </mtext><mn>400</mn><mo>+</mo><mn>46</mn><mtext> </mtext><mn>800</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">103</mn><mtext> </mtext><mn mathvariant="bold">200</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}4 \times 1\,175 \times 12 &= 56\,400\,\$\\3094 \times 975 \times 12 &= 46\,800\,\$\\310\text{RBP} &= 56\,400 + 46\,800 = \uqotitle{103\,200\,\$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:4.2em;vertical-align:-1.85em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35em;"><span style="top:-4.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">175</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">12</span></span></span><span style="top:-3.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">975</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">12</span></span></span><span style="top:-1.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">RBP</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.85em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35em;"><span style="top:-4.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">56</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-3.01em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">46</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-1.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">56</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">46</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">103</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">200</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.85em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>311<p id="p11-90"><strong>b) RBE :</strong></p>312<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Inoccupation (3</mtext><mtext> </mtext><mtext>%)</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>103</mn><mtext> </mtext><mn>200</mn><mo>×</mo><mn>0,03</mn><mo>=</mo><mn>3</mn><mtext> </mtext><mn>096</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Mauvaises cr</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>ances (1</mtext><mtext> </mtext><mtext>%)</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>103</mn><mtext> </mtext><mn>200</mn><mo>×</mo><mn>0,01</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>032</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Stationnement</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>6</mn><mo>×</mo><mn>70</mn><mo>×</mo><mn>12</mn><mo>=</mo><mn>5</mn><mtext> </mtext><mn>040</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>RBE</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>103</mn><mtext> </mtext><mn>200</mn><mo>−</mo><mn>3</mn><mtext> </mtext><mn>096</mn><mo>−</mo><mn>1</mn><mtext> </mtext><mn>032</mn><mo>+</mo><mn>5</mn><mtext> </mtext><mn>040</mn><mo>+</mo><mn>1</mn><mtext> </mtext><mn>400</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">105</mn><mtext> </mtext><mn mathvariant="bold">512</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Inoccupation (3\,\%)} &= 103\,200 \times 0{,}03 = 3\,096\,\$\\313\text{Mauvaises créances (1\,\%)} &= 103\,200 \times 0{,}01 = 1\,032\,\$\\314\text{Stationnement} &= 6 \times 70 \times 12 = 5\,040\,\$\\315\text{RBE} &= 103\,200 - 3\,096 - 1\,032 + 5\,040 + 1\,400316 = \uqotitle{105\,512\,\$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:5.7em;vertical-align:-2.6em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.1em;"><span style="top:-5.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Inoccupation (3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%)</span></span></span></span><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Mauvaises cr</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">ances (1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%)</span></span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Stationnement</span></span></span></span><span style="top:-0.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">RBE</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.6em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.1em;"><span style="top:-5.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">103</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">03</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">096</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">103</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">01</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">032</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">6</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">70</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">040</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-0.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">103</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">096</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">032</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">040</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">105</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">512</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.6em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>317<p id="p11-91"><strong>c)</strong> Loyers contractuels annuels : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>8</mn><mtext> </mtext><mn>150</mn><mo>×</mo><mn>12</mn><mo>=</mo><mn>97</mn><mtext> </mtext><mn>800</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">8\,150 \times 12 = 97\,800\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">8</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">150</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">97</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; écart : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>103</mn><mtext> </mtext><mn>200</mn><mo>−</mo><mn>97</mn><mtext> </mtext><mn>800</mn><mo>=</mo><mn>5400</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">103\,200 - 97\,800 = 5400\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">103</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">97</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">5400</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>/an (5,2 %). Cause probable : l'encadrement des loyers par le TAL, qui maintient sous le marché les loyers des locataires en place — l'écart se rattrapera au rythme du roulement.</p></div></details>318<div class="box box-exo" id="exo-11-3"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 11.3</span><span class="box-title">— tri des dépenses admissibles</span><a class="box-anchor" href="#exo-11-3" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-92">L'état des résultats fourni par le propriétaire d'un 12-logements contient les postes suivants. Pour chacun, indiquez s'il entre dans les dépenses d'exploitation du RNE (tel quel, ajusté, ou exclu) et pourquoi : taxes foncières <span class="num">16 500 $</span>; assurances <span class="num">6800 $</span>; intérêts hypothécaires <span class="num">38 200 $</span>; amortissement <span class="num">21 000 $</span>; déneigement <span class="num">3500 $</span>; remplacement complet de la toiture <span class="num">34 000 $</span> (fait cette année); aucune gestion (autogéré); électricité des communs <span class="num">3600 $</span>.</p></div></div>319<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p11-93">Les taxes foncières, les assurances, le déneigement et l'électricité des communs sont admissibles tels quels — total <span class="num">30 400 $</span> —, en validant taxes et assurances sur les documents officiels. Les intérêts hypothécaires (<span class="num">38 200 $</span>) sont <strong class="c-rouge">exclus</strong> : service de la dette, choix de financement du propriétaire. L'amortissement (<span class="num">21 000 $</span>) est <strong class="c-rouge">exclu</strong> : écriture comptable et fiscale, sans sortie de fonds d'exploitation. La toiture (<span class="num">34 000 $</span>) est <strong class="c-rouge">exclue comme dépense de l'année</strong> : dépense en capital non récurrente, elle entre <em>lissée</em> par la réserve pour remplacement (par exemple <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>34</mn><mtext> </mtext><mn>000</mn><mi mathvariant="normal">/</mi><mn>22</mn></mrow><annotation encoding="application/x-tex">34\,000 / 22</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">34</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000/22</span></span></span></span> ans <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span></span></span></span> 1 545 $/an dans la réserve globale). À l'inverse, la gestion est <strong class="c-vert">à ajouter</strong> même si l'immeuble est autogéré — environ 5 % du RBE, valeur de marché du travail de gestion — et il faudra <strong class="c-vert">ajouter</strong> une réserve pour remplacement complète si l'état n'en contient pas. L'exercice reproduit la reconstruction type : les états du propriétaire mélangent exploitation, financement, fiscalité et capital — le RNE économique ne garde que l'exploitation.</p></div></details>320<div class="box box-exo" id="exo-11-4"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 11.4</span><span class="box-title">— reconstruction complète d'un RNE</span><a class="box-anchor" href="#exo-11-4" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-94">Reconstituez le RNE économique d'un 10-logements de Hull : 6 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\times</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">×</span></span></span></span> 4½ au marché à 1 125 $/mois, 4 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\times</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">×</span></span></span></span> 3½ au marché à 925 $/mois; 8 stationnements à 65 $/mois; buanderie <span class="num">1500 $</span>/an; inoccupation 3,0 %; mauvaises créances 1,0 %; taxes <span class="num">13 200 $</span>; assurances <span class="num">5400 $</span>; entretien 4,5 % du RBE; énergie des communs <span class="num">2600 $</span>; gestion 5,0 % du RBE; conciergerie <span class="num">3600 $</span>; déneigement <span class="num">3000 $</span>; paysager <span class="num">1200 $</span>; réserve <span class="num">6500 $</span>. Calculez RBP, RBE, dépenses totales, RNE, puis les ratios dépenses/RBE et RNE/RBE, et commentez leur vraisemblance.</p></div></div>321<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p11-95"><strong>RBP :</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>6</mn><mo>×</mo><mn>1</mn><mtext> </mtext><mn>125</mn><mo>×</mo><mn>12</mn><mo>=</mo><mn>81</mn><mtext> </mtext><mn>000</mn></mrow><annotation encoding="application/x-tex">6 \times 1\,125 \times 12 = 81\,000</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">6</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">125</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">81</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span></span></span></span>; <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4</mn><mo>×</mo><mn>925</mn><mo>×</mo><mn>12</mn><mo>=</mo><mn>44</mn><mtext> </mtext><mn>400</mn></mrow><annotation encoding="application/x-tex">4 \times 925 \times 12322= 44\,400</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">4</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">925</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">44</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span></span></span></span>; RBP <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">125</mn><mtext> </mtext><mn mathvariant="bold">400</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">= \uqotitle{125\,400\,\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">125</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">400</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span>.<br> <strong>RBE :</strong></p>323<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Inoccupation</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>125</mn><mtext> </mtext><mn>400</mn><mo>×</mo><mn>0,03</mn><mo>=</mo><mn>3</mn><mtext> </mtext><mn>762</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>Mauvaises cr</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>ances</mtext></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>125</mn><mtext> </mtext><mn>400</mn><mo>×</mo><mn>0,01</mn><mo>=</mo><mn>1</mn><mtext> </mtext><mn>254</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Stationnement</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>8</mn><mo>×</mo><mn>65</mn><mo>×</mo><mn>12</mn><mo>=</mo><mn>6</mn><mtext> </mtext><mn>240</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>RBE</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>125</mn><mtext> </mtext><mn>400</mn><mo>−</mo><mn>3</mn><mtext> </mtext><mn>762</mn><mo>−</mo><mn>1</mn><mtext> </mtext><mn>254</mn><mo>+</mo><mn>6</mn><mtext> </mtext><mn>240</mn><mo>+</mo><mn>1</mn><mtext> </mtext><mn>500</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">128</mn><mtext> </mtext><mn mathvariant="bold">124</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Inoccupation} &= 125\,400 \times 0{,}03 = 3\,762\,\$\\324\text{Mauvaises créances} &= 125\,400 \times 0{,}01 = 1\,254\,\$\\325\text{Stationnement} &= 8 \times 65 \times 12 = 6\,240\,\$\\326\text{RBE} &= 125\,400 - 3\,762 - 1\,254 + 6\,240 + 1\,500327 = \uqotitle{128\,124\,\$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:5.7em;vertical-align:-2.6em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.1em;"><span style="top:-5.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Inoccupation</span></span></span></span><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Mauvaises cr</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">ances</span></span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Stationnement</span></span></span></span><span style="top:-0.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">RBE</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.6em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.1em;"><span style="top:-5.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">125</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">03</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">762</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">125</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">01</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">254</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">8</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">65</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">6</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">240</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span><span style="top:-0.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">125</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">762</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">254</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">6</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">240</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">128</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">124</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.6em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>328<p id="p11-96"><strong>Dépenses :</strong> entretien <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>128</mn><mtext> </mtext><mn>124</mn><mo>×</mo><mn>0,045</mn><mo>=</mo><mn>5</mn><mtext> </mtext><mn>766</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 128\,124 \times 0{,}045 = 5\,766\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">128</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">124</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">045</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">766</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; gestion <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>128</mn><mtext> </mtext><mn>124</mn><mo>×</mo><mn>0,05</mn><mo>=</mo><mn>6</mn><mtext> </mtext><mn>406</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">= 128\,124 \times 0{,}05 = 6\,406\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">128</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">124</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">05</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">6</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">406</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>;</p>329<div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mtext>Total</mtext></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>13</mn><mtext> </mtext><mn>200</mn><mo>+</mo><mn>5</mn><mtext> </mtext><mn>400</mn><mo>+</mo><mn>5</mn><mtext> </mtext><mn>766</mn><mo>+</mo><mn>2</mn><mtext> </mtext><mn>600</mn><mo>+</mo><mn>6</mn><mtext> </mtext><mn>406</mn><mo>+</mo><mn>3</mn><mtext> </mtext><mn>600</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mspace width="1em"/><mo>+</mo><mn>3</mn><mtext> </mtext><mn>000</mn><mo>+</mo><mn>1</mn><mtext> </mtext><mn>200</mn><mo>+</mo><mn>6</mn><mtext> </mtext><mn>500</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">47</mn><mtext> </mtext><mn mathvariant="bold">672</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{Total} &= 13\,200 + 5\,400 + 5\,766 + 2\,600 + 6\,406 + 3\,600\\330&\quad + 3\,000 + 1\,200 + 6\,500 = \uqotitle{47\,672\,\$}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:2.7em;vertical-align:-1.1em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6em;"><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Total</span></span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.1em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6em;"><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">13</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">766</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">6</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">406</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:1em;"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">200</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">6</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">47</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">672</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.1em;"><span></span></span></span></span></span></span></span></span></span></span></span></div>331<p id="p11-97"><strong>RNE :</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>128</mn><mtext> </mtext><mn>124</mn><mo>−</mo><mn>47</mn><mtext> </mtext><mn>672</mn><mo>=</mo><mstyle mathcolor="#003E7E"><mrow><mn mathvariant="bold">80</mn><mtext> </mtext><mn mathvariant="bold">452</mn><mtext> </mtext><mi mathvariant="bold">$</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">128\,124 - 47\,672 = \uqotitle{80\,452\,\$}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">128</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">124</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">47</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">672</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord" style="color:#003E7E;"><span class="mord mathbf" style="color:#003E7E;">80</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">452</span><span class="mspace" style="color:#003E7E;margin-right:0.1667em;"></span><span class="mord mathbf" style="color:#003E7E;">$</span></span></span></span></span>.<br> <strong>Ratios :</strong> dépenses/RBE <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>47</mn><mtext> </mtext><mn>672</mn><mi mathvariant="normal">/</mi><mn>128</mn><mtext> </mtext><mn>124</mn><mo>=</mo><mn>37,2</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">= 47\,672/128\,124 = 37{,}2\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">47</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">672/128</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">124</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">37</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>; RNE/RBE <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mn>62,8</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">=33262{,}8\,\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.3669em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">62</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">8</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>. Pour un multilogements de 10 unités, chauffage aux locataires, la fourchette de marché est de 35–45 % : le calcul est vraisemblable. À un TGA de 5,5 %, la valeur indicative serait <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>80</mn><mtext> </mtext><mn>452</mn><mi mathvariant="normal">/</mi><mn>0,055</mn><mo>≈</mo><mn>1</mn><mtext> </mtext><mn>463</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">80\,452/0{,}055 \approx3331\,463\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">80</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">452/0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">055</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">463</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>.</p></div></details>334<div class="box box-exo" id="exo-11-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span class="box-label">Exercice 11.5</span><span class="box-title">— l'erreur du service de la dette</span><a class="box-anchor" href="#exo-11-5" aria-label="Lien">#</a></div><div class="box-body"><p id="p11-98">Un étudiant évalue le 6-plex du chapitre en incluant l'hypothèque (2 800 $/mois) dans les dépenses d'exploitation. <strong>a)</strong> Recalculez son « RNE » et la « valeur » qu'il obtient à un TGA de 5,5 %. <strong>b)</strong> Chiffrez l'erreur de valeur. <strong>c)</strong> Expliquez en deux phrases pourquoi le raisonnement est fautif.</p></div></div>335<details class="box box-sol"><summary><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-check"/></svg></span><span class="box-label">Solution</span><span class="sol-hint">Cliquer pour révéler</span></summary><div class="box-body"><p id="p11-99"><strong>a)</strong> Dette annuelle : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mn>800</mn><mo>×</mo><mn>12</mn><mo>=</mo><mn>33</mn><mtext> </mtext><mn>600</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">2\,800 \times 12 = 33\,600\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">800</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">33</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>. « RNE » fautif : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>46</mn><mtext> </mtext><mn>807</mn><mo>−</mo><mn>33</mn><mtext> </mtext><mn>600</mn><mo>=</mo><mn>13</mn><mtext> </mtext><mn>207</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">46\,807 - 33\,600 = 13\,207\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">46</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">807</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">33</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">600</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">13</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">207</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>; « valeur » : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>13</mn><mtext> </mtext><mn>207</mn><mi mathvariant="normal">/</mi><mn>0,055</mn><mo>=</mo><mn>240</mn><mtext> </mtext><mn>127</mn><mtext> </mtext><mi mathvariant="normal">$</mi><mo>≈</mo><mn>240</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">13\,207 / 0{,}055 =336240\,127\,\$ \approx 240\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">13</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">207/0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">055</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">240</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">127</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">240</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span>.<br> <strong>b)</strong> Erreur : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>851</mn><mtext> </mtext><mn>000</mn><mo>−</mo><mn>240</mn><mtext> </mtext><mn>000</mn><mo>=</mo><mn>611</mn><mtext> </mtext><mn>000</mn><mtext> </mtext><mi mathvariant="normal">$</mi></mrow><annotation encoding="application/x-tex">851\,000 - 240\,000 = 611\,000\,\$</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">851</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">240</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">611</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">000</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">$</span></span></span></span> — la « valeur » fautive ne représente que 28 % de la vraie. La division par le taux transforme une erreur de dépense en catastrophe d'évaluation.<br> <strong>c)</strong> Le financement est un choix de l'investisseur, pas une caractéristique de l'immeuble : le même 6-plex génère le même RNE qu'il soit payé comptant ou financé à 80 %. Inclure la dette ferait dépendre la « valeur marchande » de la situation bancaire d'un propriétaire particulier, ce qui contredit la définition même de la valeur marchande.</p></div></details>337<section class="box box-synth" id="synthese"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-clipboard"/></svg></span><span class="box-label">L’essentiel de la séance</span></div><div class="box-body"><ul><li><strong>Fondement</strong> : principe d'anticipation — l'acheteur d'un immeuble locatif achète un flux de revenus. Capitalisation directe : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mtext>RNE</mtext><mi mathvariant="normal">/</mi><mtext>TGA</mtext></mrow><annotation encoding="application/x-tex">V = \text{RNE}/\text{TGA}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord text"><span class="mord">RNE</span></span><span class="mord">/</span><span class="mord text"><span class="mord">TGA</span></span></span></span></span>; DCF pour les flux variables (séance 12).</li><li><strong>Chaîne du revenu</strong> : RBP (loyers du <em>marché</em>, occupation pleine) <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">-</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> inoccupation <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> mauvaises créances <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> revenus accessoires <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> RBE <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">-</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> dépenses d'exploitation <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> RNE.</li><li><strong>Loyers du marché <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo mathvariant="normal">≠</mo></mrow><annotation encoding="application/x-tex">\neq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mrel"><span class="mrel"><span class="mord katex-vbox"><span class="katex-thinbox"><span class="rlap"><span class="katex-strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="katex-inner"><span class="mord"><span class="mrel"></span></span></span><span class="katex-fix"></span></span></span></span></span><span class="mspace nobreak"></span><span class="mrel">=</span></span></span></span></span> loyers contractuels</strong> : au Québec, le TAL creuse un écart durable (13,5 % sur le cas du chapitre); le RBP se reconstruit toujours au marché, l'écart se discute ensuite.</li><li><strong>Régime TAL 2026</strong> : ajustement 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">=</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> moyenne IPC 3 ans (3,1 % en 2026) <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> variations réelles taxes/assurances <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> travaux majeurs à 5 %/an — balises des projections de croissance.</li><li><strong>Inoccupation</strong> : taux de marché justifié par la SCHL (Gatineau 3,8 % en oct. 2025; équilibre <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> 3 %), même si l'immeuble est plein.</li><li><strong>Dépenses</strong> : fixes (taxes, assurances — valider sur documents) <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> variables (entretien, énergie, gestion, conciergerie, déneigement...) <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> réserve pour remplacement (2–5 % du RBE).</li><li><strong>Exclusions absolues</strong> : service de la dette, amortissement, impôt du propriétaire, dépenses en capital. Imputer la gestion même en autogestion (<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 % du RBE).</li><li><strong>Reconstruire–normaliser–stabiliser</strong> : partir de 3–5 ans d'états financiers, éliminer le non-récurrent, appliquer les taux de marché, viser l'année typique.</li><li><strong>Contrôle de vraisemblance</strong> : ratios dépenses/RBE par segment (plex 30–40 %; 6–24 logements 35–45 %; triple net 5–15 %).</li><li><strong>Cas du chapitre</strong> : RBP 75 600 $ <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> RBE 77 376 $ <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> dépenses 30 569 $ (39,5 %) <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> RNE 46 807 $ <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> à 5,5 % : <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> 851 000 $.</li></ul></div></section>338 </article>339 </div>340 </div>341 <section 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