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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"><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 current"><button type="button" aria-expanded="false" aria-haspopup="true">Réviser <span class="caret" aria-hidden="true">▾</span></button><div class="dd-menu "><a href="/aide-memoire/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span>Aide-mémoire<span class="dd-desc">Toutes les formules commentées</span></span></a><a href="/glossaire/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-book"/></svg></span><span>Glossaire<span class="dd-desc">Termes du métier, équivalents anglais</span></span></a><a href="/definitions/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-list"/></svg></span><span>Toutes les définitions<span class="dd-desc">Les formulations attendues aux examens</span></span></a><a href="/fiches/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-cards"/></svg></span><span>Fiches de révision<span class="dd-desc">Recto-verso, suivi d’acquisition</span></span></a><a href="/carte/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-network"/></svg></span><span>Carte du cours<span class="dd-desc">Les 14 séances et leurs objectifs en un coup d’œil</span></span></a><a href="/exercices/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-pencil"/></svg></span><span>Banque d’exercices<span class="dd-desc">Tous les exercices corrigés</span></span></a></div></div><div class="dd"><button type="button" aria-expanded="false" aria-haspopup="true">S’exercer <span class="caret" aria-hidden="true">▾</span></button><div class="dd-menu "><a href="/quiz/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-quiz"/></svg></span><span>Quiz et examens blancs<span class="dd-desc">QCM avec rétroaction, chronomètre</span></span></a><a href="/entrainement/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-dumbbell"/></svg></span><span>Entraînement<span class="dd-desc">Problèmes à données aléatoires, corrigés pas à pas</span></span></a><a href="/jeux/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-game"/></svg></span><span>Jeux de révision<span class="dd-desc">Association, vrai ou faux, remise en ordre</span></span></a><a href="/outils/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-calc"/></svg></span><span>Calculateurs<span class="dd-desc">Les formules en interactif</span></span></a><a href="/progression/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-progress"/></svg></span><span>Ma progression<span class="dd-desc">Lecture, quiz, objectifs, notes</span></span></a></div></div><div class="dd"><button type="button" aria-expanded="false" aria-haspopup="true">Ressources <span class="caret" aria-hidden="true">▾</span></button><div class="dd-menu "><a href="/diapositives/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-slides"/></svg></span><span>Diapositives<span class="dd-desc">Les 14 présentations en ligne</span></span></a><a href="/videos/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-video"/></svg></span><span>Séances vidéo<span class="dd-desc">Enregistrements Zoom : chapitres, transcription, sous-titres</span></span></a><a href="/ressources/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-download"/></svg></span><span>Téléchargements<span class="dd-desc">Manuel, plan, TP, gabarits Excel</span></span></a><a href="/rapport/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-report"/></svg></span><span>Rapport marché QC<span class="dd-desc">Indices de prix, macro, abordabilité — 26 sections, 67 figures</span></span></a><a href="/bibliographie/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-bib"/></svg></span><span>Bibliographie<span class="dd-desc">Références citées</span></span></a><a href="/recherche/"><span class="dd-ico"><svg class="" aria-hidden="true"><use href="#i-search"/></svg></span><span>Recherche<span class="dd-desc">Tout le manuel indexé</span></span></a></div></div></nav>87    <div class="topbar-actions">88      <button class="icon-btn search-btn" type="button" data-action="search" aria-label="Rechercher"><svg class="" aria-hidden="true"><use href="#i-search"/></svg><span>Rechercher</span><kbd>⌘K</kbd></button>89      <button class="icon-btn" type="button" data-action="theme" aria-label="Thème clair ou sombre" title="Thème"><svg class="" aria-hidden="true"><use href="#i-sun"/></svg></button>90      <button class="icon-btn menu-btn" type="button" aria-label="Menu" aria-expanded="false"><svg class="" aria-hidden="true"><use href="#i-menu"/></svg></button>91    </div>92  </div>93  94</header>9596<main id="main" class="page">97  <div class="page-head"><div class="eyebrow">Annexe A</div><h1>Aide-mémoire des formules</h1><p class="lead">Toutes les formules du cours, classées par thème, avec la définition de chaque variable et les repères chiffrés utiles.</p></div>98  <div class="two-col">99    <article class="prose"><p id="pA-1">Cette annexe regroupe toutes les formules du cours, classées par thème, avec la définition de chaque variable et les repères chiffrés utiles. C'est l'outil de révision par excellence : chaque formule doit pouvoir être écrite <em>et expliquée</em> de mémoire à l'examen final.</p>100<h2 id="s-A-1" class="h-section"><span class="h-num">A.1</span><span class="h-text">Méthode de comparaison</span><a class="h-anchor" href="#s-A-1" aria-label="Lien vers cette section">#</a></h2>101<div class="box box-form" id="form-A-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 A.1</span><span class="box-title">— valeur par comparaison</span><a class="box-anchor" href="#form-A-1" aria-label="Lien">#</a></div><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>V</mi><mtext>sujet</mtext></msub><mtext>  </mtext><mo>≈</mo><mtext>  </mtext><mtext>Prix du comparable</mtext><mtext>  </mtext><mo>±</mo><mtext>  </mtext><mtext>Ajustements</mtext></mrow><annotation encoding="application/x-tex">V_{\text{sujet}} \;\approx\; \text{Prix du comparable} \;\pm\; \text{Ajustements}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">sujet</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord text"><span class="mord">Prix du comparable</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">Ajustements</span></span></span></span></span></span></div>102<div class="center"><div class="table-wrap"><table class="tbl"><tbody><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mtext>sujet</mtext></msub></mrow><annotation encoding="application/x-tex">V_{\text{sujet}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">sujet</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span></td><td>Indication de valeur du bien évalué</td></tr><tr><td>Prix du comparable</td><td>Prix de vente réel et vérifié du bien comparable</td></tr><tr><td>Ajustements</td><td>Corrections (en $ ou en %) pour chaque différence pertinente</td></tr></tbody></table></div></div></div></div>103<div class="box box-form" id="form-A-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 A.2</span><span class="box-title">— ajustement en pourcentage</span><a class="box-anchor" href="#form-A-2" aria-label="Lien">#</a></div><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mtext>Ajustement (%)</mtext><mtext>  </mtext><mo>=</mo><mtext>  </mtext><mfrac><mrow><mtext>Diff</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>rence attribuable au facteur</mtext></mrow><mtext>Prix du comparable</mtext></mfrac><mo>×</mo><mn>100</mn></mrow><annotation encoding="application/x-tex">\text{Ajustement (\%)} \;=\; \frac{\text{Différence attribuable au facteur}}104{\text{Prix du comparable}} \times 100</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 text"><span class="mord">Ajustement (%)</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.2519em;vertical-align:-0.8804em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Prix du comparable</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">Diff</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">rence attribuable au facteur</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span 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">100</span></span></span></span></span></div></div></div>105<div class="box box-form" id="form-A-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 A.3</span><span class="box-title">— ajustement temporel (conditions de marché)</span><a class="box-anchor" href="#form-A-3" aria-label="Lien">#</a></div><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mtext>Ajustement temporel</mtext><mtext>  </mtext><mo>=</mo><mtext>  </mtext><mtext>Prix du comparable</mtext><mo>×</mo><msub><mi>g</mi><mtext>mensuel</mtext></msub><mo>×</mo><msub><mi>n</mi><mtext>mois</mtext></msub></mrow><annotation encoding="application/x-tex">\text{Ajustement temporel} \;=\; \text{Prix du comparable} \times g_{\text{mensuel}}106\times n_{\text{mois}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord text"><span class="mord">Ajustement temporel</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord text"><span class="mord">Prix du comparable</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7778em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0359em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">mensuel</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">mois</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></div>107<div class="center"><div class="table-wrap"><table class="tbl"><tbody><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>g</mi><mtext>mensuel</mtext></msub></mrow><annotation encoding="application/x-tex">g_{\text{mensuel}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0359em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">mensuel</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td><td>Taux de variation mensuel du marché (p. ex. 0,5 %/mois)</td></tr><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>n</mi><mtext>mois</mtext></msub></mrow><annotation encoding="application/x-tex">n_{\text{mois}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">mois</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td><td>Nombre de mois entre la vente et la date d'évaluation</td></tr></tbody></table></div></div></div></div>108<div class="box box-rem" id="remarque-A-2"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pen"/></svg></span><span class="box-label">règles de pratique — comparaison</span><a class="box-anchor" href="#remarque-A-2" aria-label="Lien">#</a></div><div class="box-body"><p id="pA-3">Les ajustements se font toujours <strong>du comparable vers le sujet</strong> : comparable supérieur <span class="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> ajustement <strong>négatif</strong> ; comparable inférieur <span class="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> ajustement <strong>positif</strong>. Seuils usuels : ajustement <strong>net <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≤</mo></mrow><annotation encoding="application/x-tex">\leq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mrel">≤</span></span></span></span> 15 %</strong> et <strong>brut <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≤</mo></mrow><annotation encoding="application/x-tex">\leq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mrel">≤</span></span></span></span> 25 %</strong> du prix de vente ; au-delà, le comparable perd sa fiabilité.</p></div></div>109<h2 id="s-A-2" class="h-section"><span class="h-num">A.2</span><span class="h-text">Méthode du coût</span><a class="h-anchor" href="#s-A-2" aria-label="Lien vers cette section">#</a></h2>110<div class="box box-form" id="form-A-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 A.4</span><span class="box-title">— valeur par la méthode du coût</span><a class="box-anchor" href="#form-A-4" aria-label="Lien">#</a></div><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><menclose notation="box"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>  </mtext><mi>V</mi><mtext>  </mtext><mo>=</mo><mtext>  </mtext><msub><mi>C</mi><mtext>neuf</mtext></msub><mtext>  </mtext><mo>−</mo><mtext>  </mtext><msub><mi>D</mi><mtext>totale</mtext></msub><mtext>  </mtext><mo>+</mo><mtext>  </mtext><msub><mi>V</mi><mtext>terrain</mtext></msub><mtext>  </mtext></mrow></mstyle></mstyle></mstyle></menclose></mrow><annotation encoding="application/x-tex">\boxed{\;V \;=\; C_{\text{neuf}} \;-\; D_{\text{totale}} \;+\; V_{\text{terrain}}\;}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.5133em;vertical-align:-0.49em;"></span><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0233em;"><span style="top:-3.5133em;"><span class="pstrut" style="height:3.5133em;"></span><span class="boxpad"><span class="mord"><span class="mord"><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">neuf</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">terrain</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span></span></span></span></span><span style="top:-3.0233em;"><span class="pstrut" style="height:3.5133em;"></span><span class="katex-stretchy fbox" style="height:1.5133em;border-style:solid;border-width:0.04em;"></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.49em;"><span></span></span></span></span></span></span></span></span></span></div>111<div class="center"><div class="table-wrap"><table class="tbl"><tbody><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mtext>neuf</mtext></msub></mrow><annotation encoding="application/x-tex">C_{\text{neuf}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">neuf</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td><td>Coût de remplacement (ou de reproduction) à neuf</td></tr><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>totale</mtext></msub></mrow><annotation encoding="application/x-tex">D_{\text{totale}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td><td>Dépréciation totale (physique + fonctionnelle + économique)</td></tr><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mtext>terrain</mtext></msub></mrow><annotation encoding="application/x-tex">V_{\text{terrain}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">terrain</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td><td>Valeur du terrain comme s'il était vacant</td></tr></tbody></table></div></div></div></div>112<div class="box box-form" id="form-A-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule A.5</span><span class="box-title">— coût de remplacement à neuf</span><a class="box-anchor" href="#form-A-5" aria-label="Lien">#</a></div><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>C</mi><mtext>neuf</mtext></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><mrow><mtext>Co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>ts directs</mtext></mrow><mtext>  </mtext><mo>+</mo><mtext>  </mtext><mrow><mtext>Co</mtext><mover accent="true"><mtext>u</mtext><mo>ˆ</mo></mover><mtext>ts indirects</mtext></mrow><mtext>  </mtext><mo>+</mo><mtext>  </mtext><mtext>Profit de l’entrepreneur</mtext></mrow><annotation encoding="application/x-tex">C_{\text{neuf}} \;=\; \text{Coûts directs} \;+\; \text{Coûts indirects}113\;+\; \text{Profit de l&#x27;entrepreneur}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">neuf</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7778em;vertical-align:-0.0833em;"></span><span class="mord text"><span class="mord">Co</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">u</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˆ</span></span></span></span></span></span></span><span class="mord">ts directs</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">Co</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">u</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˆ</span></span></span></span></span></span></span><span class="mord">ts indirects</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord text"><span class="mord">Profit de l’entrepreneur</span></span></span></span></span></span></div>114<div class="center"><div class="table-wrap"><table class="tbl"><tbody><tr><td>Coûts directs</td><td>Matériaux, main-d'œuvre, équipements (taux unitaires <span class="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> superficies)</td></tr><tr><td>Coûts indirects</td><td>Honoraires professionnels, permis, financement de chantier, assurances (souvent 10–15 % des coûts directs)</td></tr><tr><td>Profit</td><td>Profit de l'entrepreneur (souvent 8–10 % des coûts directs)</td></tr></tbody></table></div></div></div></div>115<div class="box box-form" id="form-A-6"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule A.6</span><span class="box-title">— dépréciation physique — méthode âge/vie</span><a class="box-anchor" href="#form-A-6" aria-label="Lien">#</a></div><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>D</mi><mtext>physique</mtext></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><mfrac><mrow><mover accent="true"><mtext>A</mtext><mo>ˆ</mo></mover><mtext>ge effectif</mtext></mrow><mrow><mtext>Vie utile </mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>conomique</mtext></mrow></mfrac><mo>×</mo><msub><mi>C</mi><mtext>neuf</mtext></msub></mrow><annotation encoding="application/x-tex">D_{\text{physique}} \;=\; \frac{\text{Âge effectif}}{\text{Vie utile économique}}116\times C_{\text{neuf}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">physique</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.5042em;vertical-align:-0.8804em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6238em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Vie utile </span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">conomique</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9468em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">A</span></span><span style="top:-3.2523em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˆ</span></span></span></span></span></span></span><span class="mord">ge effectif</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">neuf</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></div>117<div class="center"><div class="table-wrap"><table class="tbl"><tbody><tr><td>Âge effectif</td><td>Âge apparent compte tenu de l'entretien et des rénovations (peut différer de l'âge chronologique)</td></tr><tr><td>Vie utile économique</td><td>Durée totale pendant laquelle le bâtiment contribue à la valeur</td></tr></tbody></table></div></div></div></div>118<div class="box box-form" id="form-A-7"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule A.7</span><span class="box-title">— dépréciation totale ventilée</span><a class="box-anchor" href="#form-A-7" aria-label="Lien">#</a></div><div class="box-body"><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><msub><mi>D</mi><mtext>totale</mtext></msub><mo>=</mo><mrow></mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><msub><mi>D</mi><mtext>phys. curable</mtext></msub><mo>+</mo><msub><mi>D</mi><mtext>phys. incurable</mtext></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>+</mo><msub><mi>D</mi><mtext>fonct. curable</mtext></msub><mo>+</mo><msub><mi>D</mi><mtext>fonct. incurable</mtext></msub><mo>+</mo><msub><mi>D</mi><mrow><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>conomique</mtext></mrow></msub></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}D_{\text{totale}} = {} &amp; D_{\text{phys.\ curable}} + D_{\text{phys.\ incurable}} \\119&amp; + D_{\text{fonct.\ curable}} + D_{\text{fonct.\ incurable}} + D_{\text{économique}}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:2.7em;vertical-align:-1.1em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6em;"><span style="top:-3.76em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">totale</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"></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="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">phys. curable</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">phys. incurable</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">fonct. curable</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">fonct. incurable</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord katex-accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight">e</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight">ˊ</span></span></span></span></span></span></span><span class="mord mtight">conomique</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></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>120<p id="pA-4">Lorsque des éléments curables sont chiffrés d'abord, la dépréciation physique incurable se calcule sur la <strong>base résiduelle</strong> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mtext>phys. incurable</mtext></msub><mo>=</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mover accent="true"><mtext>A</mtext><mo>ˆ</mo></mover><mtext>ge effectif</mtext></mrow><mtext>Vie utile</mtext></mfrac></mstyle><mo>×</mo><mrow><mo fence="true">(</mo><msub><mi>C</mi><mtext>neuf</mtext></msub><mo>−</mo><msub><mi>D</mi><mtext>phys. curable</mtext></msub><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">D_{\text{phys.\ incurable}} = \dfrac{\text{Âge effectif}}{\text{Vie utile}}121\times \left(C_{\text{neuf}} - D_{\text{phys.\ curable}}\right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">phys. incurable</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.3098em;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:1.6238em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Vie utile</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9468em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">A</span></span><span style="top:-3.2523em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˆ</span></span></span></span></span></span></span><span class="mord">ge effectif</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0715em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">neuf</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0278em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">phys. curable</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span>.</p></div></div>122<div class="box box-rem" id="remarque-A-5"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-pen"/></svg></span><span class="box-label">remplacement ou reproduction</span><a class="box-anchor" href="#remarque-A-5" aria-label="Lien">#</a></div><div class="box-body"><p id="pA-6"><strong>Coût de remplacement</strong> : bâtiment d'<em>utilité équivalente</em>, matériaux et normes modernes — la base usuelle. <strong>Coût de reproduction</strong> : <em>réplique exacte</em>, mêmes matériaux et mêmes défauts — réservé aux bâtiments patrimoniaux ou à certains litiges.</p></div></div>123<h2 id="s-A-3" class="h-section"><span class="h-num">A.3</span><span class="h-text">Méthode du revenu</span><a class="h-anchor" href="#s-A-3" aria-label="Lien vers cette section">#</a></h2>124<div class="box box-form" id="form-A-8"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule A.8</span><span class="box-title">— cascade des revenus</span><a class="box-anchor" href="#form-A-8" aria-label="Lien">#</a></div><div class="box-body"><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>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> </mtext><mover accent="true"><mtext>a</mtext><mo>ˋ</mo></mover><mtext> 100 % 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><annotation encoding="application/x-tex">\begin{aligned}\text{RBP} &amp;= \text{Somme des loyers du marché à 100~\% d&#x27;occupation} \\125\text{RBE} &amp;= \text{RBP} - \text{Inoccupation} - \text{Mauvaises créances}126+ \text{Autres revenus} \\127\text{RNE} &amp;= \text{RBE} - \text{Dépenses d&#x27;exploitation}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:4.2em;vertical-align:-1.85em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35em;"><span style="top:-4.51em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">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"> </span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">a</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˋ</span></span></span></span></span></span></span><span class="mord"> 100</span><span class="mord nobreak"> </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></span></span></div>128<div class="center"><div class="table-wrap"><table class="tbl"><tbody><tr><td>RBP</td><td>Revenu brut potentiel</td></tr><tr><td>RBE</td><td>Revenu brut effectif</td></tr><tr><td>RNE</td><td>Revenu net d'exploitation (avant service de la dette et impôts)</td></tr></tbody></table></div></div></div></div>129<div class="box box-form" id="form-A-9"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule A.9</span><span class="box-title">— capitalisation directe</span><a class="box-anchor" href="#form-A-9" aria-label="Lien">#</a></div><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><menclose notation="box"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>  </mtext><mi>V</mi><mtext>  </mtext><mo>=</mo><mtext>  </mtext><mfrac><mtext>RNE</mtext><mtext>TGA</mtext></mfrac><mtext>  </mtext></mrow></mstyle></mstyle></mstyle></menclose><mspace width="2em"/><mrow><mtext>et, par sym</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>trie,</mtext></mrow><mspace width="2em"/><mtext>TGA</mtext><mo>=</mo><mfrac><mtext>RNE</mtext><mi>V</mi></mfrac></mrow><annotation encoding="application/x-tex">\boxed{\;V \;=\; \frac{\text{RNE}}{\text{TGA}}\;}130\qquad\text{et, par symétrie,}\qquad131\text{TGA} = \frac{\text{RNE}}{V}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:2.7263em;vertical-align:-1.026em;"></span><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.7003em;"><span style="top:-4.7263em;"><span class="pstrut" style="height:4.7263em;"></span><span class="boxpad"><span class="mord"><span class="mord"><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"><span class="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 class="mspace" style="margin-right:0.2778em;"></span></span></span></span></span><span style="top:-3.7003em;"><span class="pstrut" style="height:4.7263em;"></span><span class="katex-stretchy fbox" style="height:2.7263em;border-style:solid;border-width:0.04em;"></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.026em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:2em;"></span><span class="mord text"><span class="mord">et, par sym</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">trie,</span></span><span class="mspace" style="margin-right:2em;"></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: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 mathnormal" style="margin-right:0.2222em;">V</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></span></span></div></div></div>132<div class="box box-form" id="form-A-10"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule A.10</span><span class="box-title">— extraction du TGA sur ventes comparables</span><a class="box-anchor" href="#form-A-10" aria-label="Lien">#</a></div><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mtext>TGA</mtext><mtext>extrait</mtext></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><mfrac><mtext>RNE du comparable</mtext><mtext>Prix de vente du comparable</mtext></mfrac></mrow><annotation encoding="application/x-tex">\text{TGA}_{\text{extrait}} \;=\; \frac{\text{RNE du comparable}}133{\text{Prix de vente du comparable}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord text"><span class="mord">TGA</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">extrait</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.2519em;vertical-align:-0.8804em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Prix de vente du comparable</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 du comparable</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div>134<p id="pA-7">Retenir un taux <em>jugé</em> à partir des extractions — pondérer les comparables les plus semblables, ne pas faire une moyenne aveugle.</p></div></div>135<div class="box box-form" id="form-A-11"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule A.11</span><span class="box-title">— TGA par bande d'investissement (hypothèque–équité)</span><a class="box-anchor" href="#form-A-11" aria-label="Lien">#</a></div><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><menclose notation="box"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>  </mtext><mtext>TGA</mtext><mtext>  </mtext><mo>=</mo><mtext>  </mtext><mi>M</mi><mo>×</mo><msub><mi>R</mi><mi>m</mi></msub><mtext>  </mtext><mo>+</mo><mtext>  </mtext><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>M</mi><mo stretchy="false">)</mo><mo>×</mo><msub><mi>R</mi><mi>e</mi></msub><mtext>  </mtext></mrow></mstyle></mstyle></mstyle></menclose><mspace width="2em"/><msub><mi>R</mi><mi>m</mi></msub><mo>=</mo><mn>12</mn><mo>×</mo><mfrac><mrow><mi>i</mi><mi mathvariant="normal">/</mi><mn>12</mn></mrow><mrow><mn>1</mn><mo>−</mo><msup><mrow><mo fence="true">(</mo><mn>1</mn><mo>+</mo><mi>i</mi><mi mathvariant="normal">/</mi><mn>12</mn><mo fence="true">)</mo></mrow><mrow><mo>−</mo><mi>n</mi></mrow></msup></mrow></mfrac></mrow><annotation encoding="application/x-tex">\boxed{\;\text{TGA} \;=\; M \times R_m \;+\; (1 - M) \times R_e\;}136\qquad137R_m = 12 \times \frac{i/12}{1 - \left(1 + i/12\right)^{-n}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.68em;vertical-align:-0.59em;"></span><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.09em;"><span style="top:-3.68em;"><span class="pstrut" style="height:3.68em;"></span><span class="boxpad"><span class="mord"><span class="mord"><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord">TGA</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal" style="margin-right:0.109em;">M</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0077em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><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:0.109em;">M</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0077em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">e</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span></span></span></span></span><span style="top:-3.09em;"><span class="pstrut" style="height:3.68em;"></span><span class="katex-stretchy fbox" style="height:1.68em;border-style:solid;border-width:0.04em;"></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.59em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:2em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0077em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">12</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.4782em;vertical-align:-1.0512em;"></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:1.427em;"><span style="top:-2.1988em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><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="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</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">i</span><span class="mord">/12</span><span class="mclose delimcenter" style="top:0em;">)</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9112em;"><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">n</span></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">i</span><span class="mord">/12</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.0512em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div>138<div class="center"><div class="table-wrap"><table class="tbl"><tbody><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi></mrow><annotation encoding="application/x-tex">M</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:0.109em;">M</span></span></span></span></td><td>Ratio prêt/valeur (part hypothécaire du financement)</td></tr><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">R_m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0077em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</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></td><td>Constante hypothécaire annuelle (service de la dette <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>÷</mo></mrow><annotation encoding="application/x-tex">\div</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">÷</span></span></span></span> montant du prêt)</td></tr><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mi>e</mi></msub></mrow><annotation encoding="application/x-tex">R_e</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0077em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">e</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></td><td>Taux de rendement exigé sur l'équité</td></tr><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6595em;"></span><span class="mord mathnormal">i</span></span></span></span></td><td>Taux d'intérêt nominal annuel ; <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span> : nombre de mensualités</td></tr></tbody></table></div></div></div></div>139<div class="box box-form" id="form-A-12"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule A.12</span><span class="box-title">— construction du TGA par sommation</span><a class="box-anchor" href="#form-A-12" aria-label="Lien">#</a></div><div class="box-body"><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>TGA</mtext><mo>=</mo><mrow></mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mtext>Taux sans risque</mtext><mo>+</mo><mtext>Prime de risque immobilier</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>+</mo><mrow><mtext>Prime de non-liquidit</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover></mrow><mo>+</mo><mtext>Prime de gestion</mtext><mo>−</mo><mrow><mtext>Croissance anticip</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>e des revenus</mtext></mrow></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}\text{TGA} ={} &amp; \text{Taux sans risque} + \text{Prime de risque immobilier} \\140&amp; + \text{Prime de non-liquidité} + \text{Prime de gestion}141- \text{Croissance anticipée des revenus}\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">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 class="mord"></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="mord text"><span class="mord">Taux sans risque</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">Prime de risque immobilier</span></span></span></span><span style="top:-2.26em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="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">Prime de non-liquidit</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord text"><span class="mord">Prime de gestion</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">Croissance anticip</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">e des revenus</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></div></div>142<div class="box box-form" id="form-A-13"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule A.13</span><span class="box-title">— multiplicateurs de revenu</span><a class="box-anchor" href="#form-A-13" aria-label="Lien">#</a></div><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mtext>MRB</mtext><mo>=</mo><mfrac><mtext>Prix de vente</mtext><mtext>RBE</mtext></mfrac><mspace width="1em"/><mo>⇔</mo><mspace width="1em"/><mi>V</mi><mo>=</mo><mtext>RBE</mtext><mo>×</mo><mtext>MRB</mtext><mspace width="2em"/><mspace width="2em"/><mtext>MRN</mtext><mo>=</mo><mfrac><mtext>Prix de vente</mtext><mtext>RNE</mtext></mfrac><mo>=</mo><mfrac><mn>1</mn><mtext>TGA</mtext></mfrac></mrow><annotation encoding="application/x-tex">\text{MRB} = \frac{\text{Prix de vente}}{\text{RBE}}143\quad\Leftrightarrow\quad144V = \text{RBE} \times \text{MRB}145\qquad\qquad146\text{MRN} = \frac{\text{Prix de vente}}{\text{RNE}} = \frac{1}{\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">MRB</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:2.0574em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">RBE</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">Prix de vente</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:1em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⇔</span><span class="mspace" style="margin-right:1em;"></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7667em;vertical-align:-0.0833em;"></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><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord text"><span class="mord">MRB</span></span><span class="mspace" style="margin-right:2em;"></span><span class="mspace" style="margin-right:2em;"></span><span class="mord text"><span class="mord">MRN</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:2.0574em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">RNE</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">Prix de vente</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord 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">1</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></span></span></div>147<div class="center"><div class="table-wrap"><table class="tbl"><tbody><tr><td>MRB</td><td>Multiplicateur de revenu brut (sur le RBE)</td></tr><tr><td>MRN</td><td>Multiplicateur de revenu net — l'inverse du TGA</td></tr></tbody></table></div></div></div></div>148<h2 id="s-A-4" class="h-section"><span class="h-num">A.4</span><span class="h-text">Mathématiques financières et DCF</span><a class="h-anchor" href="#s-A-4" aria-label="Lien vers cette section">#</a></h2>149<div class="box box-form" id="form-A-14"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule A.14</span><span class="box-title">— valeur future et valeur présente</span><a class="box-anchor" href="#form-A-14" aria-label="Lien">#</a></div><div class="box-body"><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>F</mi><mi>V</mi><mo>=</mo><mi>P</mi><mi>V</mi><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mi>r</mi><msup><mo stretchy="false">)</mo><mi>n</mi></msup><mspace width="2em"/><mspace width="2em"/><mi>P</mi><mi>V</mi><mo>=</mo><mfrac><mrow><mi>F</mi><mi>V</mi></mrow><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><annotation encoding="application/x-tex">FV = PV \times (1+r)^n150\qquad\qquad151PV = \frac{FV}{(1+r)^n}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.1389em;">F</span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.1389em;">P</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:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord 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:0.7144em;"><span style="top:-3.113em;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 class="mspace" style="margin-right:2em;"></span><span class="mspace" style="margin-right:2em;"></span><span class="mord mathnormal" style="margin-right:0.1389em;">P</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:2.2963em;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 mathnormal" style="margin-right:0.1389em;">F</span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div>152<div class="center"><div class="table-wrap"><table class="tbl"><tbody><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mi>V</mi></mrow><annotation encoding="application/x-tex">PV</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.1389em;">P</span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span></span></span></span>, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mi>V</mi></mrow><annotation encoding="application/x-tex">FV</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.1389em;">F</span><span class="mord mathnormal" style="margin-right:0.2222em;">V</span></span></span></span></td><td>Valeur présente ; valeur future</td></tr><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi></mrow><annotation encoding="application/x-tex">r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">r</span></span></span></span></td><td>Taux d'intérêt ou d'actualisation par période</td></tr><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span></td><td>Nombre de périodes</td></tr></tbody></table></div></div></div></div>153<div class="box box-form" id="form-A-15"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule A.15</span><span class="box-title">— actualisation des flux monétaires (DCF)</span><a class="box-anchor" href="#form-A-15" aria-label="Lien">#</a></div><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><menclose notation="box"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>  </mtext><msub><mi>V</mi><mn>0</mn></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><munderover><mo>∑</mo><mrow><mi>t</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mfrac><msub><mtext>RNE</mtext><mi>t</mi></msub><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><mtext>  </mtext></mrow></mstyle></mstyle></mstyle></menclose><mspace width="2em"/><msub><mi>V</mi><mi>n</mi></msub><mo>=</mo><mfrac><msub><mtext>RNE</mtext><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><msub><mtext>TGA</mtext><mtext>sortie</mtext></msub></mfrac><mo>−</mo><mtext>frais de vente</mtext></mrow><annotation encoding="application/x-tex">\boxed{\;V_0 \;=\; \sum_{t=1}^{n} \frac{\text{RNE}_t}{(1+r)^t}154\;+\; \frac{V_n}{(1+r)^n}\;}155\qquad156V_n = \frac{\text{RNE}_{n+1}}{\text{TGA}_{\text{sortie}}} - \text{frais de vente}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:3.5985em;vertical-align:-1.6071em;"></span><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.9914em;"><span style="top:-5.5985em;"><span class="pstrut" style="height:5.5985em;"></span><span class="boxpad"><span class="mord"><span class="mord"><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="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"><span class="mord text"><span class="mord">RNE</span></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-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 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 class="mspace" style="margin-right:0.2778em;"></span></span></span></span></span><span style="top:-3.9914em;"><span class="pstrut" style="height:5.5985em;"></span><span class="katex-stretchy fbox" style="height:3.5985em;border-style:solid;border-width:0.04em;"></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.6071em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:2em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">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 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:2.1963em;vertical-align:-0.836em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3603em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord text"><span class="mord">TGA</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">sortie</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord text"><span class="mord">RNE</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2083em;"><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:0.836em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6944em;"></span><span class="mord text"><span class="mord">frais de vente</span></span></span></span></span></span></div>157<div class="center"><div class="table-wrap"><table class="tbl"><tbody><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">V_0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td><td>Valeur actuelle de l'immeuble</td></tr><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mtext>RNE</mtext><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">\text{RNE}_t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord text"><span class="mord">RNE</span></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-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></td><td>Revenu net d'exploitation de l'année <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi></mrow><annotation encoding="application/x-tex">t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6151em;"></span><span class="mord mathnormal">t</span></span></span></span></td></tr><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi></mrow><annotation encoding="application/x-tex">r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">r</span></span></span></span></td><td>Taux d'actualisation (rendement exigé par l'investisseur)</td></tr><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span></td><td>Période de détention (typiquement 5–10 ans)</td></tr><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">V_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">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></td><td>Valeur de réversion (revente) à la fin de l'année <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span></td></tr><tr><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mtext>TGA</mtext><mtext>sortie</mtext></msub></mrow><annotation encoding="application/x-tex">\text{TGA}_{\text{sortie}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord text"><span class="mord">TGA</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">sortie</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td><td>Taux de capitalisation à la revente (souvent <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>&gt;</mo></mrow><annotation encoding="application/x-tex">&gt;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">&gt;</span></span></span></span> TGA d'entrée)</td></tr></tbody></table></div></div></div></div>158<div class="box box-form" id="form-A-16"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule A.16</span><span class="box-title">— lien entre taux d'actualisation et TGA</span><a class="box-anchor" href="#form-A-16" aria-label="Lien">#</a></div><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><menclose notation="box"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>  </mtext><mi>r</mi><mtext>  </mtext><mo>≈</mo><mtext>  </mtext><mtext>TGA</mtext><mo>+</mo><mi>g</mi><mspace width="1em"/><mo>⇔</mo><mspace width="1em"/><mtext>TGA</mtext><mtext>  </mtext><mo>≈</mo><mtext>  </mtext><mi>r</mi><mo>−</mo><mi>g</mi><mtext>  </mtext></mrow></mstyle></mstyle></mstyle></menclose></mrow><annotation encoding="application/x-tex">\boxed{\;r \;\approx\; \text{TGA} + g159\quad\Leftrightarrow\quad160\text{TGA} \;\approx\; r - g\;}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:1.5578em;vertical-align:-0.5344em;"></span><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0233em;"><span style="top:-3.5578em;"><span class="pstrut" style="height:3.5578em;"></span><span class="boxpad"><span class="mord"><span class="mord"><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">r</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord">TGA</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 mathnormal" style="margin-right:0.0359em;">g</span><span class="mspace" style="margin-right:1em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⇔</span><span class="mspace" style="margin-right:1em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord text"><span class="mord">TGA</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">r</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:0.0359em;">g</span><span class="mspace" style="margin-right:0.2778em;"></span></span></span></span></span><span style="top:-3.0233em;"><span class="pstrut" style="height:3.5578em;"></span><span class="katex-stretchy fbox" style="height:1.5578em;border-style:solid;border-width:0.04em;"></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.5344em;"><span></span></span></span></span></span></span></span></span></span></div>161<p id="pA-8">où <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>g</mi></mrow><annotation encoding="application/x-tex">g</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.0359em;">g</span></span></span></span> est le taux de croissance anticipé des revenus. Un TGA <em>contient</em> implicitement les attentes de croissance ; un taux d'actualisation les isole.</p></div></div>162<div class="box box-form" id="form-A-17"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule A.17</span><span class="box-title">— réconciliation pondérée</span><a class="box-anchor" href="#form-A-17" aria-label="Lien">#</a></div><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>V</mi><mtext>conclue</mtext></msub><mtext>  </mtext><mo>=</mo><mtext>  </mtext><munder><mo>∑</mo><mi>i</mi></munder><msub><mi>w</mi><mi>i</mi></msub><mo>×</mo><msub><mi>V</mi><mi>i</mi></msub><mspace width="2em"/><mtext>avec </mtext><munder><mo>∑</mo><mi>i</mi></munder><msub><mi>w</mi><mi>i</mi></msub><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">V_{\text{conclue}} \;=\; \sum_{i} w_i \times V_i163\qquad \text{avec } \sum_i w_i = 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">conclue</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.3277em;vertical-align:-1.2777em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.05em;"><span style="top:-1.8723em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span></span></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><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.2777em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0269em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.3277em;vertical-align:-1.2777em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><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">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:2em;"></span><span class="mord text"><span class="mord">avec </span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.05em;"><span style="top:-1.8723em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</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><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.2777em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0269em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="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">1</span></span></span></span></span></div>164<p id="pA-9">où <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">V_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.2222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.2222em;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">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> est l'indication de la méthode <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6595em;"></span><span class="mord mathnormal">i</span></span></span></span> et <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>w</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">w_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0269em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="katex-sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> son poids, justifié par la pertinence de la méthode, la qualité des données et le comportement des acheteurs types.</p></div></div>165<h2 id="s-A-5" class="h-section"><span class="h-num">A.5</span><span class="h-text">Ratios de marché et de financement</span><a class="h-anchor" href="#s-A-5" aria-label="Lien vers cette section">#</a></h2>166<div class="box box-form" id="form-A-18"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule A.18</span><span class="box-title">— ratio prêt/valeur (RPV)</span><a class="box-anchor" href="#form-A-18" aria-label="Lien">#</a></div><div class="box-body"><div class="eq"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mtext>RPV</mtext><mtext>  </mtext><mo>=</mo><mtext>  </mtext><mfrac><mrow><mtext>Montant du pr</mtext><mover accent="true"><mtext>e</mtext><mo>ˆ</mo></mover><mtext>t</mtext></mrow><mtext>Valeur</mtext></mfrac><mo>×</mo><mn>100</mn></mrow><annotation encoding="application/x-tex">\text{RPV} \;=\; \frac{\text{Montant du prêt}}{\text{Valeur}} \times 100</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">RPV</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.0574em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">Valeur</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">Montant du pr</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˆ</span></span></span></span></span></span></span><span class="mord">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></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">100</span></span></span></span></span></div>167<p id="pA-10">Prêt <strong>conventionnel</strong> si RPV <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≤</mo></mrow><annotation encoding="application/x-tex">\leq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mrel">≤</span></span></span></span> 80 % ; au-delà, assurance prêt obligatoire (SCHL, Sagen, Canada Guaranty).</p></div></div>168<div class="box box-form" id="form-A-19"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule A.19</span><span class="box-title">— ratio de dépenses d'exploitation</span><a class="box-anchor" href="#form-A-19" aria-label="Lien">#</a></div><div class="box-body"><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><mrow><mtext>Ratio de d</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>penses</mtext></mrow><mtext>  </mtext><mo>=</mo><mtext>  </mtext><mfrac><mrow><mtext>D</mtext><mover accent="true"><mtext>e</mtext><mo>ˊ</mo></mover><mtext>penses d’exploitation</mtext></mrow><mtext>RBE</mtext></mfrac><mo>×</mo><mn>100</mn></mrow><annotation encoding="application/x-tex">\text{Ratio de dépenses} \;=\; \frac{\text{Dépenses d&#x27;exploitation}}{\text{RBE}}169\times 100</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord text"><span class="mord">Ratio de d</span><span class="mord katex-accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord">e</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˊ</span></span></span></span></span></span></span><span class="mord">penses</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:2.0574em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">RBE</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">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:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">100</span></span></span></span></span></div>170<p id="pA-11">Fourchette usuelle des multilogements québécois : <strong>35–45 %</strong> du RBE (chauffage à la charge du propriétaire, immeubles mixtes ou énergivores : davantage — documenter tout écart).</p></div></div>171<div class="box box-form" id="form-A-20"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-formula"/></svg></span><span class="box-label">Formule A.20</span><span class="box-title">— droits de mutation immobilière (Québec, 2026)</span><a class="box-anchor" href="#form-A-20" aria-label="Lien">#</a></div><div class="box-body"><p id="pA-12">Barème général par tranches du plus élevé du prix payé ou de la valeur marchande :</p>172<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Tranche de la base d'imposition</th><th class="al-r">Taux</th></tr></thead><tbody><tr><td>Jusqu'à <span class="num">62 900 $</span></td><td class="al-r">0,5 %</td></tr><tr><td>De <span class="num">62 900 $</span> à <span class="num">315 000 $</span></td><td class="al-r">1,0 %</td></tr><tr><td>Au-delà de <span class="num">315 000 $</span></td><td class="al-r">1,5 %</td></tr></tbody></table></div></div>173<p id="pA-13">Tranches indexées annuellement ; Montréal applique son propre barème (jusqu'à 4 % pour les tranches supérieures) <span class="citation">(<a class="cite" href="/bibliographie/#quebecMutations" data-cite="quebecMutations">Gouvernement du Québec, 2026</a>; <a class="cite" href="/bibliographie/#ldmi" data-cite="ldmi">Québec, 1976</a>)</span>.</p></div></div>174<h2 id="s-A-6" class="h-section"><span class="h-num">A.6</span><span class="h-text">Tableaux de repères</span><a class="h-anchor" href="#s-A-6" aria-label="Lien vers cette section">#</a></h2>175<h3 id="s-A-6-1" class="h-subsection"><span class="h-num">A.6.1</span><span class="h-text">Fourchettes indicatives</span><a class="h-anchor" href="#s-A-6-1" aria-label="Lien vers cette section">#</a></h3>176<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Paramètre</th><th>Repère indicatif (cours)</th></tr></thead><tbody><tr><td>TGA — multilogements Gatineau (2026)</td><td>environ 5,0–6,0 % selon l'âge, l'état et le secteur</td></tr><tr><td>MRB — immeubles à revenus</td><td>environ 9–11 <span class="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> le RBE</td></tr><tr><td>Inoccupation et mauvaises créances</td><td>3–5 % du RBP (selon SCHL et le secteur)</td></tr><tr><td>Ratio de dépenses</td><td>35–45 % du RBE</td></tr><tr><td>Coûts indirects de construction</td><td>10–15 % des coûts directs</td></tr><tr><td>Profit de l'entrepreneur</td><td>8–10 % des coûts directs</td></tr><tr><td>Gestion immobilière</td><td>environ 5 % du RBE</td></tr><tr><td>Frais de vente à la réversion (DCF)</td><td>environ 3 % de la valeur brute</td></tr><tr><td>Période de détention (DCF)</td><td>5–10 ans</td></tr></tbody></table></div></div>177<div class="box box-att" id="attention-A-14"><div class="box-head"><span class="box-icon"><svg class="" aria-hidden="true"><use href="#i-warning"/></svg></span><span class="box-label">Attention</span><a class="box-anchor" href="#attention-A-14" aria-label="Lien">#</a></div><div class="box-body"><p id="pA-15">Ces fourchettes sont des <strong>repères pédagogiques</strong> tirés des cas du cours, pas des normes : à l'examen, utilisez toujours les données de l'énoncé ; en pratique, extrayez toujours les taux du marché du bien évalué.</p></div></div>178<h3 id="s-A-6-2" class="h-subsection"><span class="h-num">A.6.2</span><span class="h-text">Seuils et règles à mémoriser</span><a class="h-anchor" href="#s-A-6-2" aria-label="Lien vers cette section">#</a></h3>179<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Règle</th><th>Valeur</th></tr></thead><tbody><tr><td>Ajustement net maximal (comparaison)</td><td>15 % du prix du comparable</td></tr><tr><td>Ajustement brut maximal (comparaison)</td><td>25 % du prix du comparable</td></tr><tr><td>RPV maximal d'un prêt conventionnel</td><td>80 %</td></tr><tr><td>Conservation des dossiers (OEAQ)</td><td>au moins 5 ans</td></tr><tr><td>Critères de l'utilisation optimale</td><td>légal, physique, financier, maximalement productif</td></tr><tr><td>Éléments de la certification</td><td>8 déclarations obligatoires</td></tr><tr><td>Note de passage du cours</td><td>60 %</td></tr></tbody></table></div></div>180<h3 id="s-A-6-3" class="h-subsection"><span class="h-num">A.6.3</span><span class="h-text">Conversions utiles</span><a class="h-anchor" href="#s-A-6-3" aria-label="Lien vers cette section">#</a></h3>181<div class="center"><div class="table-wrap"><table class="tbl"><thead><tr><th>Conversion</th><th>Facteur</th></tr></thead><tbody><tr><td>1 m<sup>2</sup></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> 10,764 pi<sup>2</sup></td></tr><tr><td>1 pi<sup>2</sup></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> 0,0929 m<sup>2</sup></td></tr><tr><td>1 mètre</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> 3,281 pieds</td></tr><tr><td>1 acre</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> <span class="num">43 560</span> pi<sup>2</sup> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4831em;"></span><span class="mrel">≈</span></span></span></span> <span class="num">4047</span> m<sup>2</sup></td></tr><tr><td>1 hectare</td><td>= <span class="num">10 000</span> m<sup>2</sup> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\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> 2,471 acres</td></tr></tbody></table></div></div><hr class="sep"><h2 class="h-section" id="index-formules"><span class="h-text">Toutes les formules numérotées du cours</span></h2><p>Les 27 formules encadrées dans les séances, dans leur contexte.</p><ul class="form-index"><li><span class="fi-ch">1.1</span><a href="/seance/01/#form-1-1">ratio prêt/valeur</a></li><li><span class="fi-ch">8.1</span><a href="/seance/08/#form-8-1">ajustement temporel au prorata</a></li><li><span class="fi-ch">8.2</span><a href="/seance/08/#form-8-2">ajustements net et brut</a></li><li><span class="fi-ch">9.1</span><a href="/seance/09/#form-9-1">composition des ajustements transactionnels</a></li><li><span class="fi-ch">9.2</span><a href="/seance/09/#form-9-2">capitalisation d'une différence de loyer</a></li><li><span class="fi-ch">10.1</span><a href="/seance/10/#form-10-1">méthode du coût</a></li><li><span class="fi-ch">10.2</span><a href="/seance/10/#form-10-2">décomposition de la dépréciation</a></li><li><span class="fi-ch">10.3</span><a href="/seance/10/#form-10-3">méthode âge/vie modifiée</a></li><li><span class="fi-ch">10.4</span><a href="/seance/10/#form-10-4">dépréciation totale, forme développée</a></li><li><span class="fi-ch">10.5</span><a href="/seance/10/#form-10-5">méthode d'extraction du terrain</a></li><li><span class="fi-ch">10.6</span><a href="/seance/10/#form-10-6">méthode de répartition</a></li><li><span class="fi-ch">10.7</span><a href="/seance/10/#form-10-7">conclusion du cas</a></li><li><span class="fi-ch">11.1</span><a href="/seance/11/#form-11-1">capitalisation directe</a></li><li><span class="fi-ch">11.2</span><a href="/seance/11/#form-11-2">revenu brut effectif</a></li><li><span class="fi-ch">11.3</span><a href="/seance/11/#form-11-3">chaîne du RNE</a></li><li><span class="fi-ch">11.4</span><a href="/seance/11/#form-11-4">RNE du cas</a></li><li><span class="fi-ch">12.1</span><a href="/seance/12/#form-12-1">bande d'investissement</a></li><li><span class="fi-ch">12.2</span><a href="/seance/12/#form-12-2">constante hypothécaire</a></li><li><span class="fi-ch">12.3</span><a href="/seance/12/#form-12-3">taux construit</a></li><li><span class="fi-ch">12.4</span><a href="/seance/12/#form-12-4">DCF immobilier</a></li><li><span class="fi-ch">12.5</span><a href="/seance/12/#form-12-5">valeur de réversion</a></li><li><span class="fi-ch">12.6</span><a href="/seance/12/#form-12-6">relation entre <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi></mrow><annotation encoding="application/x-tex">r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.0278em;">r</span></span></span></span>, TGA et croissance</a></li><li><span class="fi-ch">12.7</span><a href="/seance/12/#form-12-7">valeur par DCF</a></li><li><span class="fi-ch">12.8</span><a href="/seance/12/#form-12-8">multiplicateur du revenu brut</a></li><li><span class="fi-ch">12.9</span><a href="/seance/12/#form-12-9">multiplicateur du revenu net</a></li><li><span class="fi-ch">14.1</span><a href="/seance/14/#form-14-1">méthode du coût</a></li><li><span class="fi-ch">14.2</span><a href="/seance/14/#form-14-2">les quatre formules cardinales du cours</a></li></ul></article>182    <aside class="side"><h4>Aide-mémoire</h4><ol><li class="lvl2"><a href="#s-A-1">A.1 Méthode de comparaison</a></li><li class="lvl2"><a href="#s-A-2">A.2 Méthode du coût</a></li><li class="lvl2"><a href="#s-A-3">A.3 Méthode du revenu</a></li><li class="lvl2"><a href="#s-A-4">A.4 Mathématiques financières et DCF</a></li><li class="lvl2"><a href="#s-A-5">A.5 Ratios de marché et de financement</a></li><li class="lvl2"><a href="#s-A-6">A.6 Tableaux de repères</a></li><li class="lvl3"><a href="#s-A-6-1">A.6.1 Fourchettes indicatives</a></li><li class="lvl3"><a href="#s-A-6-2">A.6.2 Seuils et règles à mémoriser</a></li><li class="lvl3"><a href="#s-A-6-3">A.6.3 Conversions utiles</a></li></ol><h4>Voir aussi</h4><div class="toc-extra"><a href="#index-formules">Index des formules des séances</a><a href="/outils/">Calculateurs</a><a href="/entrainement/">Entraînement</a><a href="/fiches/">Fiches « formules »</a></div></aside>183  </div>184</main>185<footer class="site-footer">186  <div class="footer-inner">187    <div class="footer-brand">188      <img src="/assets/brand/uqo-logo-white.png" alt="UQO" width="140" height="59" style="width:140px;height:auto;margin-bottom:10px">189      <div class="brand-code">IMM1003</div>190      <div>Éléments d’évaluation immobilière</div>191      <div style="opacity:.7;margin-top:6px;font-size:.85rem">Automne 2026 · 3 crédits · premier cycle · 14 séances</div>192      <div style="margin-top:14px;font-size:.85rem">Simon-Pierre Boucher, professeur<br>Département des sciences administratives<br>Université du Québec en Outaouais<br><a href="mailto:simon-pierre.boucher@uqo.ca" style="display:inline;padding:0">simon-pierre.boucher@uqo.ca</a></div>193    </div>194    <div><h4>Étudier</h4><a href="/seance/01/">Séances</a><a href="/videos/">Séances vidéo</a><a href="/aide-memoire/">Aide-mémoire</a><a href="/glossaire/">Glossaire</a><a href="/definitions/">Toutes les définitions</a><a href="/carte/">Carte du 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Document destiné aux étudiantes et étudiants inscrits au cours IMM1003 ; toute reproduction ou diffusion sans autorisation écrite de l’auteur est interdite.</span><span>Généré depuis les sources LaTeX · KaTeX · TikZ</span></div></div>199</footer>200<div id="search-modal" class="search-modal" role="dialog" aria-modal="true" aria-label="Recherche dans les notes">201  <div class="search-box">202    <input type="search" placeholder="Rechercher une notion, une formule, un exemple…" autocomplete="off" spellcheck="false">203    <div class="search-results"></div>204    <div class="search-foot"><span><kbd>↑</kbd><kbd>↓</kbd> naviguer</span><span><kbd>↵</kbd> ouvrir</span><span><kbd>Échap</kbd> fermer</span><span style="margin-left:auto"><a href="/recherche/">Page de recherche complète</a></span></div>205  </div>206</div>207208<script src="/assets/js/app.js" defer></script>209</body>210</html>211