{"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":"2026-01-10T07:00:42","modified_gmt":"2026-01-10T07:00:42","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<div style=\"margin: 0 0 20px 0;\">\r\n  <a\r\n    href=\"https:\/\/analystprep.com\/free-trial\/\"\r\n    target=\"_blank\"\r\n    rel=\"noopener noreferrer\"\r\n    style=\"\r\n      display: inline-block;\r\n      border: 2px solid #1e63ff;\r\n      color: #1e63ff;\r\n      background: #ffffff;\r\n      padding: 10px 14px;\r\n      border-radius: 10px;\r\n      font-weight: 500;\r\n      line-height: 1.35;\r\n      text-decoration: none;\r\n    \"\r\n  >\r\n    Want to practice finding implied growth rates in residual income valuation for CFA Level II? Try AnalystPrep\u2019s free trial now.\r\n  <\/a>\r\n<\/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: 32px 0;\">\r\n  <a\r\n    href=\"https:\/\/analystprep.com\/free-trial\/\"\r\n    target=\"_blank\"\r\n    rel=\"noopener noreferrer\"\r\n    style=\"\r\n      display: inline-block;\r\n      background-color: #1e63ff;\r\n      color: #ffffff;\r\n      padding: 12px 26px;\r\n      border-radius: 12px;\r\n      font-weight: 600;\r\n      font-size: 16px;\r\n      text-decoration: none;\r\n    \"\r\n  >\r\n    Start Free Trial \u2192\r\n  <\/a>\r\n\r\n  <div style=\"margin-top: 10px; font-size: 14px; color: #374151;\">\r\n    Practice residual income and equity valuation questions on implied growth, price to book links, and return on equity drivers with CFA Level II style solutions.\r\n  <\/div>\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 v26.9 - 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 equation.\" \/>\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\/implied-growth-rate-in-residual-income\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Implied Growth Rate in Residual Income | CFA Level II\" \/>\n<meta property=\"og:description\" content=\"Explains how to calculate the implied growth rate using the residual income formula by rearranging the single-stage residual income equation.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/\" \/>\n<meta property=\"og:site_name\" content=\"CFA, FRM, and Actuarial Exams Study Notes\" \/>\n<meta property=\"article:published_time\" content=\"2021-09-08T05:00:16+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-01-10T07:00:42+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=\"1 minute\" \/>\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\/implied-growth-rate-in-residual-income\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/\"},\"author\":{\"name\":\"Irene R\",\"@id\":\"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/7002f30d8f174958802c1c30b167eaf5\"},\"headline\":\"Implied Growth Rate in Residual Income\",\"datePublished\":\"2021-09-08T05:00:16+00:00\",\"dateModified\":\"2026-01-10T07:00:42+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/\"},\"wordCount\":292,\"keywords\":[\"CFA-level-2\",\"Equity Valuation\",\"Implied Growth Rate in Residual Income\",\"Reading 30: Residual Income Valuation\"],\"articleSection\":[\"CFA Level II Study Notes\",\"Equity Valuation\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/\",\"url\":\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/\",\"name\":\"Implied Growth Rate in Residual Income | CFA Level II\",\"isPartOf\":{\"@id\":\"https:\/\/analystprep.com\/study-notes\/#website\"},\"datePublished\":\"2021-09-08T05:00:16+00:00\",\"dateModified\":\"2026-01-10T07:00:42+00:00\",\"author\":{\"@id\":\"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/7002f30d8f174958802c1c30b167eaf5\"},\"description\":\"Explains how to calculate the implied growth rate using the residual income formula by rearranging the single-stage residual income equation.\",\"breadcrumb\":{\"@id\":\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/analystprep.com\/study-notes\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Implied Growth Rate in Residual Income\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/analystprep.com\/study-notes\/#website\",\"url\":\"https:\/\/analystprep.com\/study-notes\/\",\"name\":\"CFA, FRM, and Actuarial Exams Study Notes\",\"description\":\"Question Bank and Study Notes for the CFA, FRM, and Actuarial exams\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/analystprep.com\/study-notes\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/7002f30d8f174958802c1c30b167eaf5\",\"name\":\"Irene R\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/33caf1e1bcb63ee970b36351f165c7bc714b19614993ab9c2c8bf36273b7df48?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/33caf1e1bcb63ee970b36351f165c7bc714b19614993ab9c2c8bf36273b7df48?s=96&d=mm&r=g\",\"caption\":\"Irene R\"},\"url\":\"https:\/\/analystprep.com\/study-notes\/author\/irene\/\"}]}<\/script>\n<meta property=\"og:video\" content=\"https:\/\/www.youtube.com\/embed\/PBa-kWaY4gs\" \/>\n<meta property=\"og:video:type\" content=\"text\/html\" \/>\n<meta property=\"og:video:duration\" content=\"2803\" \/>\n<meta property=\"og:video:width\" content=\"480\" \/>\n<meta property=\"og:video:height\" content=\"270\" \/>\n<meta property=\"ya:ovs:adult\" content=\"false\" \/>\n<meta property=\"ya:ovs:upload_date\" content=\"2021-09-08T05:00:16+00:00\" \/>\n<meta property=\"ya:ovs:allow_embed\" content=\"true\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Implied Growth Rate in Residual Income | CFA Level II","description":"Explains how to calculate the implied growth rate using the residual income formula by rearranging the single-stage residual income equation.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/","og_locale":"en_US","og_type":"article","og_title":"Implied Growth Rate in Residual Income | CFA Level II","og_description":"Explains how to calculate the implied growth rate using the residual income formula by rearranging the single-stage residual income equation.","og_url":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/","og_site_name":"CFA, FRM, and Actuarial Exams Study Notes","article_published_time":"2021-09-08T05:00:16+00:00","article_modified_time":"2026-01-10T07:00:42+00:00","author":"Irene R","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Irene R","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/#article","isPartOf":{"@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/"},"author":{"name":"Irene R","@id":"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/7002f30d8f174958802c1c30b167eaf5"},"headline":"Implied Growth Rate in Residual Income","datePublished":"2021-09-08T05:00:16+00:00","dateModified":"2026-01-10T07:00:42+00:00","mainEntityOfPage":{"@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/"},"wordCount":292,"keywords":["CFA-level-2","Equity Valuation","Implied Growth Rate in Residual Income","Reading 30: Residual Income Valuation"],"articleSection":["CFA Level II Study Notes","Equity Valuation"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/","url":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/","name":"Implied Growth Rate in Residual Income | CFA Level II","isPartOf":{"@id":"https:\/\/analystprep.com\/study-notes\/#website"},"datePublished":"2021-09-08T05:00:16+00:00","dateModified":"2026-01-10T07:00:42+00:00","author":{"@id":"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/7002f30d8f174958802c1c30b167eaf5"},"description":"Explains how to calculate the implied growth rate using the residual income formula by rearranging the single-stage residual income equation.","breadcrumb":{"@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/implied-growth-rate-in-residual-income\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/analystprep.com\/study-notes\/"},{"@type":"ListItem","position":2,"name":"Implied Growth Rate in Residual Income"}]},{"@type":"WebSite","@id":"https:\/\/analystprep.com\/study-notes\/#website","url":"https:\/\/analystprep.com\/study-notes\/","name":"CFA, FRM, and Actuarial Exams Study Notes","description":"Question Bank and Study Notes for the CFA, FRM, and Actuarial exams","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/analystprep.com\/study-notes\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/7002f30d8f174958802c1c30b167eaf5","name":"Irene R","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/33caf1e1bcb63ee970b36351f165c7bc714b19614993ab9c2c8bf36273b7df48?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/33caf1e1bcb63ee970b36351f165c7bc714b19614993ab9c2c8bf36273b7df48?s=96&d=mm&r=g","caption":"Irene R"},"url":"https:\/\/analystprep.com\/study-notes\/author\/irene\/"}]},"og_video":"https:\/\/www.youtube.com\/embed\/PBa-kWaY4gs","og_video_type":"text\/html","og_video_duration":"2803","og_video_width":"480","og_video_height":"270","ya_ovs_adult":"false","ya_ovs_upload_date":"2021-09-08T05:00:16+00:00","ya_ovs_allow_embed":"true"},"_links":{"self":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts\/21102","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/comments?post=21102"}],"version-history":[{"count":13,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts\/21102\/revisions"}],"predecessor-version":[{"id":41829,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts\/21102\/revisions\/41829"}],"wp:attachment":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/media?parent=21102"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/categories?post=21102"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/tags?post=21102"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}