{"id":20947,"date":"2021-09-07T08:10:06","date_gmt":"2021-09-07T08:10:06","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=20947"},"modified":"2026-03-25T17:55:30","modified_gmt":"2026-03-25T17:55:30","slug":"residual-income-model","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-income-model\/","title":{"rendered":"Residual Income Model"},"content":{"rendered":"<script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"QAPage\",\r\n  \"mainEntity\": {\r\n    \"@type\": \"Question\",\r\n    \"name\": \"What is the intrinsic value of a stock using the residual income model when the firm liquidates at the end of Year 3?\",\r\n    \"text\": \"Assuming a company has the following information:\\n\\n\u2022 Current book value per share equals $22.00.\\n\u2022 For the next three years, EPS is expected to be $6.50, $8.00, and $10.50, respectively.\\n\u2022 Dividends for the next three years are expected to be $3.50, $5.00, and $12.50 respectively.\\n\u2022 The Year 3 dividend is expected to be a liquidating dividend, i.e., the company is anticipated to cease its operations at the end of Year 3 and distribute its entire book value in a dividend.\\n\u2022 The required rate of return on equity of 9%.\\n\\nIts intrinsic value would be closest to:\\n\\nA. 37.14.\\nB. 35.50.\\nC. 39.23.\",\r\n    \"answerCount\": 3,\r\n    \"suggestedAnswer\": [\r\n      {\r\n        \"@type\": \"Answer\",\r\n        \"text\": \"A. 37.14.\"\r\n      },\r\n      {\r\n        \"@type\": \"Answer\",\r\n        \"text\": \"B. 35.50.\"\r\n      },\r\n      {\r\n        \"@type\": \"Answer\",\r\n        \"text\": \"C. 39.23.\"\r\n      }\r\n    ],\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"A. 37.14.\",\r\n      \"commentary\": \"Using the residual income model: V0 = B0 + PV(residual income). First compute beginning book value each year using Bt = Bt-1 + EPSt \u2212 Dt. This gives B1 = 22.00 + 6.50 \u2212 3.50 = 25.00 and B2 = 25.00 + 8.00 \u2212 5.00 = 28.00. Residual income each year is RI_t = EPS_t \u2212 r \u00d7 B_{t\u22121} with r = 9%: RI1 = 6.50 \u2212 0.09\u00d722.00 = 4.52; RI2 = 8.00 \u2212 0.09\u00d725.00 = 5.75; RI3 = 10.50 \u2212 0.09\u00d728.00 = 7.98. Discount and add to B0: V0 = 22.00 + 4.52\/1.09 + 5.75\/1.09^2 + 7.98\/1.09^3 \u2248 37.14.\",\r\n      \"url\": \"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-income-model\/\"\r\n    },\r\n    \"author\": {\r\n      \"@type\": \"Organization\",\r\n      \"name\": \"AnalystPrep\"\r\n    }\r\n  }\r\n}\r\n<\/script>\r\n\r\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/PBa-kWaY4gs\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><\/p>\r\n<p>The residual income model analyzes the intrinsic value of equity as the sum of:<\/p>\r\n<ul>\r\n\t<li>The current book value of equity; and<\/li>\r\n\t<li>The present value of expected future residual income.<\/li>\r\n<\/ul>\r\n<p>Residual income is computed as net income minus an equity charge:<\/p>\r\n<p>$$\\text{RI}_{\\text{t}}=\\text{E}_{\\text{t}}-(\\text{r}\\times\\text{B}_{\\text{t}-1})$$<\/p>\r\n<p>Using the residual income model, the intrinsic value of common stock can be expressed as follows:<\/p>\r\n<p>$$\\text{V}_{0}=\\text{B}_{0}+\\sum_{\\text{t}-1}^{\\infty}\\frac{\\text{RI}_{\\text{t}}}{(1+\\text{r})^{\\text{t}}}=\\text{B}_{0}+\\sum_{\\text{t}-1}^{\\infty}\\frac{\\text{E}_{\\text{t}}-\\text{rB}_{\\text{t}-1}}{(1+\\text{r})^{\\text{t}}}$$<\/p>\r\n<p>Where:<\/p>\r\n<p>\\(\\text{V}_{0}=\\) Value of the share today<\/p>\r\n<p>\\(\\text{B}_{0}=\\) Current book value of equity per share\u00a0<\/p>\r\n<p>\\(\\text{B}_{\\text{t}}=\\)\u00a0Expected book value of equity at time t<\/p>\r\n<p>\\(\\text{r}=\\)\u00a0Required rate of return on equity<\/p>\r\n<p>\\(\\text{E}_{\\text{t}}=\\)\u00a0Expected EPS for period t<\/p>\r\n<p>\\(\\text{RI}_{\\text{t}}=\\) Expected per share residual income<\/p>\r\n<h4>Example: Forecasting Residual Income<\/h4>\r\n<p>A company has the following information:<\/p>\r\n<ul>\r\n\t<li>Current book value per share equals $9.00.<\/li>\r\n\t<li>For the next three years, EPS is expected to be $3.25, $4.00, and $5.50, respectively.<\/li>\r\n\t<li>Dividends for the next three years are expected to be $2.25, $3.00, and $16.50, respectively.<\/li>\r\n\t<li>The year 3 dividend is expected to be a liquidating dividend, i.e., the company is expected to close down its operations at the end of year 3 and distribute its entire book value in a dividend.<\/li>\r\n<\/ul>\r\n<p>The required rate of return on equity of 8%,<\/p>\r\n<p>a) The per-share book value and residual income for the next three years are:<\/p>\r\n<p>$$\\small{\\begin{array}{l|c|c|c}\\textbf{Year} &amp; \\textbf{1} &amp; \\textbf{2} &amp; \\textbf{3} \\\\ \\hline \\text{Beginning book value per share}\\\\ (\\text{B}_{\\text{t}-1}) &amp; \\$9.00 &amp; \\$10.00 &amp; \\$11.00 \\\\ \\hline \\text{Net income per share (EPS)} &amp; 3.25 &amp; 4.00 &amp; 5.50 \\\\ \\hline \\text{Less dividends per share (D)} &amp; 2.25 &amp; 3.00 &amp; 16.50 \\\\ \\hline<br \/>\r\n\\text{Ending book value per share}\\\\ (\\text{B}_{t-1}+\\text{EPS} \u2013 \\text{D})&amp; \\$10.00 &amp; \\$11.00 &amp; \\$0.00 \\\\ \\hline \\text{Net income per share (EPS)} &amp; 3.25 &amp; 4.00 &amp; 5.50 \\\\ \\hline \\text{Less per share equity charge}\\\\ (\\text{rB}_{\\text{t}-1}) &amp; 0.72 &amp; 0.80 &amp; 0.88 \\\\ \\hline\\textbf{Residual income} &amp; \\textbf{\\$2.53} &amp; \\textbf{\\$3.20} &amp; \\textbf{\\$4.62} \\\\ \\end{array}}$$<\/p>\r\n<p>Using the residual income model, intrinsic value can be calculated as:<\/p>\r\n<p>$$\\text{V}_{0}=9.00+\\frac{2.53}{(1.08)}+\\frac{3.20}{(1.08)^{2}}+\\frac{4.62}{(1.08)^{3}}=$17.75$$<\/p>\r\n<p>Using the dividend discount model, intrinsic value can be calculated as:<\/p>\r\n<p>$$\\text{V}_{0}=\\frac{2.25}{(1.08)^{1}}+\\frac{3.00}{(1.08)^{2}}+\\frac{16.50}{(1.08)^{3}}=$17.75$$<\/p>\r\n<p>The residual income model and other valuation models like the dividend discount model should give the same value.<\/p>\r\n<p>There is an alternative way of computing residual income besides,<\/p>\r\n<p>$$\\text{RI}_{\\text{t}}=\\text{E}_{\\text{t}}-(\\text{r}\\times\\text{B}_{\\text{t}-1})$$<\/p>\r\n<p>This involves applying the difference between the actual return on equity (ROE) and the required return on equity (\\(r\\)) to the beginning-of-period book value.<\/p>\r\n<p>$$\\text{E}_{\\text{t}}=\\text{ROE}\\times\\text{B}_{\\text{t}-1}$$<\/p>\r\n<p>Therefore,\u00a0<\/p>\r\n<p>$$\\text{RI}_{\\text{t}}=(\\text{ROE}-\\text{r})\\times \\text{B}_{\\text{t}-1}$$<\/p>\r\n<p>Using this formula, the residual income model equation can be expressed as:<\/p>\r\n<p>$$\\text{V}_{0}=\\text{B}_{0}+\\sum_{\\text{t}-1}^{\\infty}\\frac{(\\text{ROE}_{\\text{t}}-\\text{r})\\text{B}_{\\text{t}-1}}{(1+\\text{r})^{\\text{t}}}$$<\/p>\r\n<blockquote>\r\n<h2>Question<\/h2>\r\n<p>Assuming a company has the following information:<\/p>\r\n<ul>\r\n\t<li>Current book value per share equals $22.00.<\/li>\r\n\t<li>For the next three years, EPS is expected to be $6.50, $8.00, and $10.50, respectively.<\/li>\r\n\t<li>Dividends for the next three years are expected to be $3.50, $5.00, and $12.50 respectively.<\/li>\r\n\t<li>The Year 3 dividend is expected to be a liquidating dividend, i.e., the company is anticipated to cease its operations at the end of Year 3 and distribute its entire book value in a dividend.<\/li>\r\n\t<li>The required rate of return on equity of 9%.<\/li>\r\n<\/ul>\r\n<p>Its intrinsic value would be closest to:<\/p>\r\n<ol style=\"list-style-type: upper-alpha;\">\r\n\t<li>37.14.<\/li>\r\n\t<li>35.50.<\/li>\r\n\t<li>39.23.<\/li>\r\n<\/ol>\r\n<h3><strong>Solution<\/strong><\/h3>\r\n<p><strong>The correct answer is A.<\/strong><\/p>\r\n<p>$$\\small{\\begin{array}{l|l|l|l}\\textbf{Year} &amp; \\textbf{1} &amp; \\textbf{2} &amp; \\textbf{3} \\\\ \\hline<br \/>\r\n\\text{Beginning book value per share}\\\\ (\\text{B}_{\\text{t}-1})&amp; \\$22.00 &amp; \\$25.00 &amp; 28.00 \\\\ \\hline \\text{Net income per share (EPS)} &amp; 6.50 &amp; 8.00 &amp; 10.50 \\\\ \\hline \\text{Less dividends per share (D)} &amp; 3.50 &amp; 5.00 &amp; 38.50 \\\\ \\hline<br \/>\r\n\\text{Ending book value per share}\\\\ (\\text{B}_{t-1}+\\text{EPS} \u2013 \\text{D}) &amp; 25.00 &amp; 28.00 &amp; 00.00 \\\\ \\hline \\text{Net income per share (EPS)} &amp; 6.50 &amp; 8.00 &amp; 10.50 \\\\ \\hline \\text{Less per share equity charge}\\\\ (\\text{rB}_{\\text{t}-1}) &amp; 1.98 &amp; 2.25 &amp; 2.52 \\\\ \\hline \\textbf{Residual income}\u00a0&amp; \\textbf{\\$4.52} &amp; \\textbf{\\$5.75} &amp; \\textbf{\\$7.98} \\\\ \\end{array}}$$<\/p>\r\n<p>$$\\text{V}_{0}=22.00+\\frac{4.52}{(1.09)^{1}}+\\frac{5.75}{(1.09)^{2}}+\\frac{7.98}{(1.09)^{3}}=$37.14$$<\/p>\r\n<\/blockquote>\r\n<p>Reading 26: Residual Income Valuation<\/p>\r\n<p><em>LOS 26 (c) Calculate the intrinsic value of a common stock using the residual income model and compare value recognition in residual income and other present value models.<\/em><\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>\ufeff\ufeff The residual income model analyzes the intrinsic value of equity as the sum of: The current book value of equity; and The present value of expected future residual income. Residual income is computed as net income minus an equity&#8230;<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[102,401],"tags":[216,402,492,493],"class_list":["post-20947","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-equity-valuation","tag-cfa-level-2","tag-equity-valuation","tag-reading-30-residual-income-valuation","tag-use-of-residual-income-models","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Residual Income Model for Equity Valuation<\/title>\n<meta name=\"description\" content=\"Learn how the residual income model values stocks using earnings, book value, and required return, with examples and key formulas.\" \/>\n<meta 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