{"id":21058,"date":"2021-09-07T17:57:17","date_gmt":"2021-09-07T17:57:17","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=21058"},"modified":"2025-12-26T11:51:38","modified_gmt":"2025-12-26T11:51:38","slug":"residual-income-valuation-vs-justified-p-b-ratio","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-income-valuation-vs-justified-p-b-ratio\/","title":{"rendered":"Residual Income Valuation vs. Justified P\/B Ratio"},"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 a share\u2019s intrinsic value when return on equity equals the required return on equity?\",\r\n    \"text\": \"If the return on equity equals the required rate of return on equity, a share\u2019s intrinsic value would most likely be equal to which of the following?\\n\\nA. Book value.\\nB. Present value of the expected residual income.\\nC. Earnings per share.\",\r\n    \"answerCount\": 3,\r\n    \"suggestedAnswer\": [\r\n      {\r\n        \"@type\": \"Answer\",\r\n        \"text\": \"A. Book value.\"\r\n      },\r\n      {\r\n        \"@type\": \"Answer\",\r\n        \"text\": \"B. Present value of the expected residual income.\"\r\n      },\r\n      {\r\n        \"@type\": \"Answer\",\r\n        \"text\": \"C. Earnings per share.\"\r\n      }\r\n    ],\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"A. Book value.\",\r\n      \"commentary\": \"When return on equity equals the required return on equity, residual income is zero. Under the residual income valuation model, this implies that intrinsic value equals the current book value. If ROE exceeds the required return, intrinsic value is greater than book value; if ROE is lower, intrinsic value is less than book value.\",\r\n      \"url\": \"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-income-valuation-vs-justified-p-b-ratio\/\"\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>Residual income models can be used to estimate justified price multiples. From the justified P\/B ratio based on fundamentals:<\/p>\r\n<p>$$\\frac{\\text{P}_{0}}{\\text{B}_{0}}=\\frac{\\text{ROE}-\\text{g}}{\\text{r}-\\text{g}}$$<\/p>\r\n<p>Which is mathematically equivalent to:<\/p>\r\n<p>$$\\frac{\\text{P}_{0}}{\\text{B}_{0}}=1+\\frac{\\text{ROE}-\\text{r}}{\\text{r}-\\text{g}}$$<\/p>\r\n<p>The approximated value of a share is the book value per share plus the present value of the expected stream of residual income.<\/p>\r\n<p>A stock\u2019s justified P\/B ratio is related to expected future residual income. A closely related concept is Tobin\u2019s <em>q<\/em>, the ratio of the market value of debt and equity to the replacement cost of total assets.<\/p>\r\n<p>$$\\text{Tobin\u2019s q}= \\frac{\\text{Market value of debt and equity}}{\\text{Replacement cost of total assets}}$$<\/p>\r\n<p>The denominator uses total assets and is valued at replacement costs. Replacement costs consider the effects of inflation. Tobin\u2019s <em>q <\/em>is expected to be higher the greater the productivity of a company\u2019s assets. A difficulty in computing Tobin\u2019s <em>q <\/em>is the lack of information on the replacement cost of assets.<\/p>\r\n<p>If the return on equity (ROE) is higher than the required return on equity (\\(r\\)), the stock&#8217;s intrinsic value will be greater than the book value. The justified P\/B ratio will be higher than one.<\/p>\r\n<p>If the return on equity (ROE) is less than the required return on equity (\\(r\\)), the stock&#8217;s intrinsic value will be less than book value. The justified P\/B ratio will be below one.<\/p>\r\n<blockquote>\r\n<h2>Question<\/h2>\r\n<p>If the return on equity equals the required rate of return on equity, a share\u2019s intrinsic value would most likely be equal to?<\/p>\r\n<ol style=\"list-style-type: upper-alpha;\">\r\n\t<li>Book value.<\/li>\r\n\t<li>Present value of the expected residual income.<\/li>\r\n\t<li>Earnings per share.<\/li>\r\n<\/ol>\r\n<h3>Solution<\/h3>\r\n<p><strong>The correct answer is A.\u00a0<\/strong><\/p>\r\n<p>If the return on equity equals the required return on equity, the share&#8217;s intrinsic value will be equal to the book value. If the return on equity is greater than the required return on equity, the stock&#8217;s intrinsic value will be higher than the book value. If the return on equity is less than the required return on equity, the stock&#8217;s intrinsic value will be less than the book value.<\/p>\r\n<p><strong>B is incorrect.\u00a0<\/strong>If the return on equity equals the required rate of return on equity, the residual income would be equal to zero.<\/p>\r\n<p><strong>C is incorrect.\u00a0<\/strong>If the return on equity equals the required rate of return on equity, the share price would not be equal to its earnings per share.<\/p>\r\n<\/blockquote>\r\n<p>Reading 26: Residual Income Valuation<\/p>\r\n<p><em>LOS 26 (e) Explain the relation between residual income valuation and the justified price-to-book ratio based on forecasted fundamentals.<\/em><\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>\ufeff\ufeff Residual income models can be used to estimate justified price multiples. From the justified P\/B ratio based on fundamentals: $$\\frac{\\text{P}_{0}}{\\text{B}_{0}}=\\frac{\\text{ROE}-\\text{g}}{\\text{r}-\\text{g}}$$ Which is mathematically equivalent to: $$\\frac{\\text{P}_{0}}{\\text{B}_{0}}=1+\\frac{\\text{ROE}-\\text{r}}{\\text{r}-\\text{g}}$$ The approximated value of a share is the book value per share plus&#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":[216,402,492,496],"class_list":["post-21058","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-residual-income-valuation-vs-justified-p-b-ratio","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Residual Income Valuation vs. Justified P\/B Ratio - CFA, FRM, and Actuarial Exams Study Notes<\/title>\n<meta name=\"description\" content=\"If the return on equity is higher than the required return on equity (r), the stock&#039;s intrinsic value will be greater than the book value.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-income-valuation-vs-justified-p-b-ratio\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Residual Income Valuation vs. Justified P\/B Ratio - CFA, FRM, and Actuarial Exams Study Notes\" \/>\n<meta property=\"og:description\" content=\"If the return on equity is higher than the required return on equity (r), the stock&#039;s intrinsic value will be greater than the book value.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-income-valuation-vs-justified-p-b-ratio\/\" \/>\n<meta property=\"og:site_name\" content=\"CFA, FRM, and Actuarial Exams Study Notes\" \/>\n<meta property=\"article:published_time\" content=\"2021-09-07T17:57:17+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-12-26T11:51:38+00:00\" \/>\n<meta name=\"author\" content=\"Irene R\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Irene R\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-income-valuation-vs-justified-p-b-ratio\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-income-valuation-vs-justified-p-b-ratio\/\"},\"author\":{\"name\":\"Irene R\",\"@id\":\"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/7002f30d8f174958802c1c30b167eaf5\"},\"headline\":\"Residual Income Valuation vs. Justified P\/B Ratio\",\"datePublished\":\"2021-09-07T17:57:17+00:00\",\"dateModified\":\"2025-12-26T11:51:38+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-income-valuation-vs-justified-p-b-ratio\/\"},\"wordCount\":460,\"keywords\":[\"CFA-level-2\",\"Equity Valuation\",\"Reading 30: Residual Income Valuation\",\"Residual Income Valuation Vs. 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