{"id":17345,"date":"2021-07-09T20:09:42","date_gmt":"2021-07-09T20:09:42","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=17345"},"modified":"2026-03-23T09:57:56","modified_gmt":"2026-03-23T09:57:56","slug":"the-dividend-discount-model","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/the-dividend-discount-model\/","title":{"rendered":"The Dividend Discount Model"},"content":{"rendered":"<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/fiJA5WhgigU\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n<p><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\": \"Methods for valuing a share with indefinite dividends\",\r\n    \"text\": \"Which of the following is the least likely method of estimating the value of a share using an indefinite number of future dividends?\\n\\nA. The Gordon growth model.\\n\\nB. The two-stage model.\\n\\nC. The present value of future dividends and terminal price.\",\r\n    \"answerCount\": 1,\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"The correct answer is C.\\n\\nThe present value of future dividends and terminal price is used when valuing a share assuming a finite number of dividends followed by a terminal value.\\n\\nThe Gordon growth model and the two-stage model both assume an indefinite stream of future dividends and are therefore appropriate for valuing shares with perpetual dividend payments.\"\r\n    }\r\n  }\r\n}\r\n<\/script><\/p>\r\n\r\n<h2>Single Holding Period<\/h2>\r\n<p>The cash flows to an investor who holds shares are the dividends paid and the market price of the share when they sell the share. For example, suppose an investor expects to hold the share for one year. In that case, the value of the share today is the present value of the anticipated dividend plus the present value of the anticipated selling price in one year.<\/p>\r\n<p>$$V_0= \\frac{D_1}{(1+r)^1} + \\frac{P_1}{(1+r)^1} = \\frac{(D_1+ P_1)}{(1+r)^1}$$<\/p>\r\n<p>Where:<\/p>\r\n<p>\\(V_{0}=\\) The value of a share today, at \\(t = 0\\).<\/p>\r\n<p>\\(P_{1}=\\) The anticipated price per share at \\(t = 1\\).<\/p>\r\n<p>\\(D_{1}=\\) The expected dividends per share to be paid at the end of the year at \\(t = 1\\).<\/p>\r\n<p><em>\\(<\/em>r =<em>\\) <\/em>The discount rate of the stock.<\/p>\r\n<div style=\"text-align: center; margin: 25px 0;\"><a style=\"display: inline-flex; align-items: center; justify-content: center; padding: 10px 18px; border: 2px solid #1a73e8; border-radius: 999px; color: #1a73e8; text-decoration: none; font-weight: 500; background-color: #f5f9ff; white-space: nowrap;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener\"> Analyze equity valuation using the dividend discount model <\/a><\/div>\r\n<h4>Example: Single Period DDM<\/h4>\r\n<p>An investor expects a company to pay a dividend of $1.50 at the end of the year. The investor anticipates selling the share for $38.00 immediately after. With a required rate of return of 9%, the value of the stock is <em>closest to<\/em>:<\/p>\r\n<p>$$\\begin{align*}V_0&amp;=\\frac{(D_1+ P_1)}{(1+r)^1}\\\\ \\\\ &amp;= \\frac{(1.50+ 38.00)}{(1.09)}=36.24\\end{align*}$$<\/p>\r\n<h2>Multiple Period DDM<\/h2>\r\n<p>Suppose an investor plans to hold the share for two years. In that case, the value of the share is the sum of the present value of the expected dividends at the end of year 1, the present value of the expected dividends at the end of year 2, and the present value of the expected selling price at the end of year 2.<\/p>\r\n<p>$$\\begin{align*}V_0 &amp;= \\frac{D_1}{(1+r)^1} + \\frac{D_2}{(1+r)^2} +\\frac{P_2}{(1+r)^2} \\\\ \\\\ &amp;= \\frac{D_1}{(1+r)^1} + \\frac{(D_2+ P_2)}{(1+r)^2}\\end{align*}$$<\/p>\r\n<p>For <em>n<\/em> periods, the share value is the sum of the present value of the expected dividends for the <em>n<\/em> periods and the present value of the expected price at period <em>t<\/em> = <em>n.<\/em><\/p>\r\n<p>$$\\begin{align*}V_0&amp;= \\frac{D_1}{(1+r)^1} +\u22ef+ \\frac{D_n}{(1+r)^n} +\\frac{P_n}{(1+r)^n} \\\\ \\\\ &amp; = \u2211_{(t=1)}^n\\frac{D_t}{(1+r)^t} + \\frac{P_n}{(1+r)^n} \\end{align*}$$<\/p>\r\n<p>With a finite holding period, the DDM finds the value of a stock as the sum of:<\/p>\r\n<ol style=\"list-style-type: lower-roman;\">\r\n\t<li>The present value of the expected dividends throughout the holding period.<\/li>\r\n\t<li>The present value of the expected share price at the end of the holding period<\/li>\r\n<\/ol>\r\n<p>If the holding period reaches the indefinite future, the share\u2019s value is the present value of all expected future dividends.<\/p>\r\n<p>$$\\begin{align*} V_0&amp;= \\frac{D_1}{(1+r)^1} +\u22ef+ \\frac{D_n}{(1+r)^n} \\\\ \\\\&amp;= \u2211_{(t=1)}^\u221e\\frac{D_t}{(1+r)^t} \\end{align*}$$<\/p>\r\n<h4>Example: Multiple Period DDM<\/h4>\r\n<p>ABC Inc. expects dividends of $2 and $2.5 at the end of the next two years, respectively. The expected stock price at the end of year 2 is $48. If the required rate of return is 15%, then the value of ABC\u2019s share today is <em>closest<\/em> to:<\/p>\r\n<h4>Solution<\/h4>\r\n<p>$$\\begin{align*}V_0&amp;= \\frac{D_1}{(1+r)^1} +\u22ef+ \\frac{D_n}{(1+r)^n} +\\frac{P_n}{(1+r)^n}\\\\ \\\\&amp;=\\frac{\\$2}{1.15}+\\frac{(\\$2.5+\\$48)}{(1.15)^2} =\\$39.92\\end{align*}$$<\/p>\r\n<p>Forecasting dividends into the indefinite future is a challenge due to the uncertainty of the variables involved. There are two approaches used to solve this:<\/p>\r\n<p>i. The forecasted dividends can be assigned several growth patterns. These patterns are:<\/p>\r\n<ul>\r\n\t<li>Constant growth (the Gordon growth model).<\/li>\r\n\t<li>Two distinct stages of growth (the two-stage model and the H-model).<\/li>\r\n\t<li>Three definite stages of growth (the three-stage growth model).<\/li>\r\n<\/ul>\r\n<p>The DDM value of the share is calculated as the sum of the discounted values of future dividends.<\/p>\r\n<p>ii. Forecasting a finite number of dividends up to a terminal point. The forecasted period depends on the predictability of the company\u2019s earnings. After this period:<\/p>\r\n<ul>\r\n\t<li>The remaining dividends from the terminal point can be assigned a growth pattern.<\/li>\r\n\t<li>The analyst can forecast the share price at the terminal point.<\/li>\r\n<\/ul>\r\n<p>The DDM value of the share is calculated by discounting the dividends and the forecasted terminal share price, if any.<\/p>\r\n<blockquote>\r\n<h2>Question<\/h2>\r\n<p>Which of the following is the <em>least likely <\/em>method of estimating the value of a share using an indefinite number of future dividends?<\/p>\r\n<ol style=\"list-style-type: upper-alpha;\">\r\n\t<li>The Gordon growth model.<\/li>\r\n\t<li>The two-stage model.<\/li>\r\n\t<li>The present value of future dividends and terminal price.<\/li>\r\n<\/ol>\r\n<h4>Solution<\/h4>\r\n<p><strong>The correct answer is C.\u00a0<\/strong><\/p>\r\n<p>The present value of future dividends and terminal price is a method used to estimate the value of a share assuming a finite number of dividends.<\/p>\r\n<p><strong>A is incorrect. <\/strong>The Gordon growth model assumes a constant growth of indefinite dividends into the future to estimate the value of a share.<\/p>\r\n<p><strong>B is incorrect.\u00a0<\/strong>The two-stage model is an approach for estimating the value of a share that assumes an indefinite number of future dividends.<\/p>\r\n<\/blockquote>\r\n<p>Reading 23: Discounted Dividend Valuation<\/p>\r\n<p><em>LOS 23 (b) C<\/em><em>alculate and interpret the value of common stock using the dividend discount model (DDM) for single and multiple holding periods.<\/em><\/p>\r\n<div style=\"text-align: center; margin: 32px 0;\"><a style=\"display: inline-block; background-color: #1e63ff; color: #ffffff; padding: 12px 26px; border-radius: 12px; font-weight: 600; font-size: 16px; text-decoration: none;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"> Start Free Trial \u2192 <\/a>\r\n<div style=\"margin-top: 10px; font-size: 14px; color: #374151;\">Practice equity valuation questions using Gordon growth and multistage dividend discount models with CFA Level II style solutions.<\/div>\r\n<\/div>\r\n","protected":false},"excerpt":{"rendered":"<p>Single Holding Period The cash flows to an investor who holds shares are the dividends paid and the market price of the share when they sell the share. For example, suppose an investor expects to hold the share for one&#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":[216,402,440,442],"class_list":["post-17345","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-equity-valuation","tag-cfa-level-2","tag-equity-valuation","tag-reading-27-discounted-dividend-valuation","tag-the-dividend-discount-model","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>Dividend Discount Model (DDM) | CFA Level II Notes<\/title>\n<meta name=\"description\" content=\"Explains the dividend discount model, including the DDM formula, valuation logic, and how dividends and terminal value 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