{"id":21102,"date":"2021-09-08T05:00:16","date_gmt":"2021-09-08T05:00:16","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=21102"},"modified":"2026-06-24T19:55:11","modified_gmt":"2026-06-24T19:55:11","slug":"implied-growth-rate-in-residual-income","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/","title":{"rendered":"Implied Growth Rate in Residual Income"},"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\": \"Implied Growth Rate from Residual Income Model\",\r\n    \"text\": \"Assuming a company has the following information:\\n\\nCurrent book value per share = $12\\nExpected long-term ROE = 14%\\nRequired rate of return on equity = 9%\\nCurrent market price = $42\\n\\nThe implied growth rate is closest to?\\n\\nA. 6%\\nB. 7%\\nC. 8%\",\r\n    \"answerCount\": 1,\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"The correct answer is B (7%).\\n\\nUsing the implied growth rate formula:\\n\\ng = r \u2212 [(ROE \u2212 r) \u00d7 B\u2080 \/ (V\u2080 \u2212 B\u2080)]\\n\\ng = 9% \u2212 [(14% \u2212 9%) \u00d7 12 \/ (42 \u2212 12)]\\n\\ng = 9% \u2212 [0.05 \u00d7 0.4]\\n\\ng \u2248 7%\"\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\r\n<p>The single-stage residual income equation can be rearranged to calculate the growth implied by the current market price. The current market price would be assumed to equal the stock\u2019s intrinsic value. The intrinsic value is assumed to be the market price.<\/p>\r\n<p>$$\\text{g}=\\text{r}-\\bigg[\\frac{(\\text{ROE}-\\text{r})\\times\\text{B}_{0}}{\\text{V}_{0}-\\text{B}_{0}}\\bigg]$$<\/p>\r\n\r\n<div style=\"margin: 18px 0;\"><a style=\"display: block; text-align: center; padding: 14px 18px; border: 2px solid #2F5BFF; border-radius: 18px; color: #ffffff ; font-weight: 600; font-size: 16px; text-decoration: none; background-color: #1a73e8 ;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\">Practice implied growth rate concepts with our CFA Free Trial.<\/a><\/div>\r\n\r\n<h3>Example<\/h3>\r\n<p>Assuming a company has the following information:<\/p>\r\n<ul>\r\n\t<li>Current book value per share = $8<\/li>\r\n\t<li>Expected long-term ROE = 15%<\/li>\r\n\t<li>Required rate of return on equity = 8%<\/li>\r\n<\/ul>\r\n<p>If the current market price is $32, the implied growth rate can be calculated as:<\/p>\r\n<p>$$\\begin{align*}\\text{g}&amp;=\\text{r}-\\bigg[\\frac{(\\text{ROE}-\\text{r})\\times\\text{B}_{0}}{\\text{V}_{0}-\\text{B}_{0}}\\bigg]\\\\&amp;=0.08-\\bigg[\\frac{(0.15-0.08)\\times8}{32-8}\\bigg]\\\\&amp;=5.7\\%\\end{align*}$$<\/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 = $12<\/li>\r\n\t<li>Expected long-term ROE = 14%<\/li>\r\n\t<li>Required rate of return on equity = 9%<\/li>\r\n\t<li>Current market price = $42<\/li>\r\n<\/ul>\r\n<p>The implied growth rate is <em>closest to<\/em>?<\/p>\r\n<ol style=\"list-style-type: upper-alpha;\">\r\n\t<li>6%<\/li>\r\n\t<li>7%<\/li>\r\n\t<li>8%<\/li>\r\n<\/ol>\r\n<h4>Solution<\/h4>\r\n<p><strong>The correct answer is B.<\/strong><\/p>\r\n<p>$$\\begin{align*}\\text{g}&amp;=\\text{r}-\\bigg[\\frac{(\\text{ROE}-\\text{r})\\times\\text{B}_{0}}{\\text{V}_{0}-\\text{B}_{0}}\\bigg]\\\\&amp;=9\\%-\\bigg[\\frac{(14\\%-9\\%)\\times12}{42-12}\\bigg]\\\\&amp;=7\\%\\end{align*}$$<\/p>\r\n<\/blockquote>\r\n<p>Reading 26: Residual Income Valuation<\/p>\r\n<p><em>LOS 26 (g) Calculate the implied growth rate in residual income, given the market price-to-book ratio and an estimate of the required rate of return on equity.<\/em><\/p>\r\n<div style=\"text-align: center; margin: 30px 0;\"><a style=\"display: inline-flex; align-items: center; justify-content: center; padding: 12px 26px; border-radius: 9999px; background: #1e5bd8; color: #ffffff; font-weight: bold; text-decoration: none;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"> Start Free Trial \u2192 <\/a> <p style=\"margin-top: 12px; font-size: 16px; line-height: 1.5;\">Review implied growth rate in residual income with CFA Level 2 study notes, practice questions, mock exams, and video lessons designed to strengthen your exam preparation.<\/p>\r\n <\/div>\r\n\r\n","protected":false},"excerpt":{"rendered":"<p>\ufeff\ufeff The single-stage residual income equation can be rearranged to calculate the growth implied by the current market price. The current market price would be assumed to equal the stock\u2019s intrinsic value. The intrinsic value is assumed to be the&#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":[216,402,498,492],"class_list":["post-21102","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-equity-valuation","tag-cfa-level-2","tag-equity-valuation","tag-implied-growth-rate-in-residual-income","tag-reading-30-residual-income-valuation","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Implied Growth Rate in Residual Income | CFA Level II<\/title>\n<meta name=\"description\" content=\"Explains how to calculate the implied growth rate using the residual income formula by rearranging the single-stage residual income 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