{"id":17793,"date":"2021-07-15T14:31:00","date_gmt":"2021-07-15T14:31:00","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=17793"},"modified":"2026-03-31T11:28:55","modified_gmt":"2026-03-31T11:28:55","slug":"multiperiod-models","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/multiperiod-models\/","title":{"rendered":"Multiperiod Models"},"content":{"rendered":"<script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"VideoObject\",\r\n  \"name\": \"Discounted Dividend Valuation (2025 Level II CFA\u00ae Exam \u2013 Equity \u2013 Learning Module 2)\",\r\n  \"description\": \"CFA Level II Equity lesson on Discounted Dividend Valuation covering dividend discount models (single-stage, multi-stage, Gordon growth, H-model), present value of growth opportunities (PVGO), justified P\/E ratios, terminal value estimation, sustainable growth rate, DuPont analysis, and evaluating whether a stock is overvalued or undervalued.\",\r\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/fiJA5WhgigU\/maxresdefault.jpg\",\r\n  \"uploadDate\": \"2021-07-13\",\r\n  \"duration\": \"PT1H9M15S\",\r\n  \"contentUrl\": \"https:\/\/www.youtube.com\/watch?v=fiJA5WhgigU\",\r\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/fiJA5WhgigU\"\r\n}\r\n<\/script>\r\n<script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"ImageObject\",\r\n  \"url\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Two-Stage-DDM.jpg\",\r\n  \"contentUrl\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Two-Stage-DDM.jpg\",\r\n  \"caption\": \"Two-Stage Dividend Discount Model (DDM)\",\r\n  \"width\": 1590,\r\n  \"height\": 1414,\r\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\r\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\r\n  \"creditText\": \"AnalystPrep Design Team\",\r\n  \"creator\": {\r\n    \"@type\": \"Organization\",\r\n    \"name\": \"AnalystPrep\"\r\n  }\r\n}\r\n<\/script>\r\n\r\n<script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"ImageObject\",\r\n  \"url\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/H-Model.jpg\",\r\n  \"contentUrl\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/H-Model.jpg\",\r\n  \"caption\": \"H-Model Dividend Discount Model\",\r\n  \"width\": 1590,\r\n  \"height\": 1405,\r\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\r\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\r\n  \"creditText\": \"AnalystPrep Design Team\",\r\n  \"creator\": {\r\n    \"@type\": \"Organization\",\r\n    \"name\": \"AnalystPrep\"\r\n  }\r\n}\r\n<\/script>\r\n\r\n<script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"ImageObject\",\r\n  \"url\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM.jpg\",\r\n  \"contentUrl\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM.jpg\",\r\n  \"caption\": \"Three-Stage Dividend Discount Model (DDM)\",\r\n  \"width\": 1590,\r\n  \"height\": 1369,\r\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\r\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\r\n  \"creditText\": \"AnalystPrep Design Team\",\r\n  \"creator\": {\r\n    \"@type\": \"Organization\",\r\n    \"name\": \"AnalystPrep\"\r\n  }\r\n}\r\n<\/script>\r\n\r\n<script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"ImageObject\",\r\n  \"url\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM-2nd-Version.jpg\",\r\n  \"contentUrl\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM-2nd-Version.jpg\",\r\n  \"caption\": \"Three-Stage Dividend Discount Model (Second Version)\",\r\n  \"width\": 1590,\r\n  \"height\": 1410,\r\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\r\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\r\n  \"creditText\": \"AnalystPrep Design Team\",\r\n  \"creator\": {\r\n    \"@type\": \"Organization\",\r\n    \"name\": \"AnalystPrep\"\r\n  }\r\n}\r\n<\/script>\r\n<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\": \"Which of the following is least likely an assumption of the H-model?\",\r\n    \"text\": \"Which of the following is least likely an assumption of the H-model?\\n\\nA. There are two stages in the H-model.\\n\\nB. A supernormal growth rate characterizes the final stage of the H-model.\\n\\nC. A sustainable long-term growth rate characterizes the final stage of the H-model.\",\r\n    \"answerCount\": 1,\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"The correct answer is B.\\n\\nIn the H-model, supernormal growth occurs in the initial stage and gradually declines over time. The final stage is characterized by a sustainable long-term growth rate that continues into perpetuity.\\n\\nOption A is incorrect because the H-model assumes two stages. Option C is incorrect because the final stage of the H-model is defined by a sustainable long-term growth rate.\"\r\n    }\r\n  }\r\n}\r\n<\/script>\r\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/fiJA5WhgigU\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n\r\n<h2>Two-Stage DDM<\/h2>\r\n<p>There are several assumptions of the first version of the two-stage DDM:<\/p>\r\n<ul>\r\n\t<li>The first stage represents a period of abnormal growth.<\/li>\r\n\t<li>The second stage represents a period of sustainable growth.<\/li>\r\n\t<li>There is a sudden transition from abnormal growth to mature growth.<\/li>\r\n<\/ul>\r\n<h4><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-26471\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Two-Stage-DDM.jpg\" alt=\"Two-Stage DDM\" width=\"1590\" height=\"1414\" srcset=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Two-Stage-DDM.jpg 1590w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Two-Stage-DDM-300x267.jpg 300w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Two-Stage-DDM-1024x911.jpg 1024w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Two-Stage-DDM-768x683.jpg 768w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Two-Stage-DDM-1536x1366.jpg 1536w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Two-Stage-DDM-400x356.jpg 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/>Formula:<\/h4>\r\n<p>$$\\text{V}_0= \u2211_{(\\text{t}=1)}^{\\text{n}}\\frac{\\text{D}_0(1+\\text{g}_{\\text{S}})^\\text{t}}{(1+\\text{r})^\\text{t}} +\\frac{\\text{D}_0 (1+\\text{g}_{\\text{S}})^\\text{n}(1+\\text{g}_{\\text{L}})}{(1+\\text{r})^\\text{n}(\\text{r}-\\text{g}_{\\text{L}})}$$<\/p>\r\n<p>Where:<\/p>\r\n<p>\\(\\text{g}_{\\text{S}}=\\) Supernormal growth rate at the first stage.<\/p>\r\n<p>\\(\\text{g}_{\\text{l}}=\\) Mature growth rate at the second stage.<\/p>\r\n<p>\\(\\text{r}=\\) Required rate of return.<\/p>\r\n<p>\\(\\text{n}=\\) Length of the extraordinary growth rate.<\/p>\r\n<div style=\"text-align:center; margin:22px 0;\">\r\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\"\r\n     style=\"display:inline-flex; align-items:center; justify-content:center; padding:12px 26px; border:2px solid #1a73e8; border-radius:999px; color:#1a73e8; font-weight:600; text-decoration:none;\">\r\n     Practice multiperiod valuation models with our free trial\r\n  <\/a>\r\n<\/div>\r\n<h2>The H-Model<\/h2>\r\n<p>The assumptions of the H-Model include:<\/p>\r\n<ul>\r\n\t<li>There are two stages similar to the general two-stage model.<\/li>\r\n\t<li>An initial high growth rate <em><strong>declines linearly<\/strong><\/em> over a particular duration until it reaches a sustainable long-term rate that exists in perpetuity.<\/li>\r\n\t<li>The transition from supernormal growth to the sustainable growth rate is relatively smooth.<\/li>\r\n<\/ul>\r\n<h4 style=\"text-align: left;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-26472\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/H-Model.jpg\" alt=\"H-Model\" width=\"1590\" height=\"1405\" srcset=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/H-Model.jpg 1590w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/H-Model-300x265.jpg 300w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/H-Model-1024x905.jpg 1024w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/H-Model-768x679.jpg 768w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/H-Model-1536x1357.jpg 1536w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/H-Model-400x353.jpg 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/>Formula:<\/h4>\r\n<p>$$\\text{V}_0= \\frac{\\text{D}_0 (1+\\text{g}_\\text{L})+\\text{D}_0\\text{H}(\\text{g}_{\\text{S}}-\\text{g}_{\\text{L}})}{\\text{r}-\\text{g}_{\\text{L}}}$$<\/p>\r\n<p>Where:<\/p>\r\n<p>\\(\\text{H}=\\) Half-life (years) of the high growth period.<\/p>\r\n<p>\\(\\text{g}_{\\text{S}}=\\)\u00a0 Initial short term high dividend growth rate.<\/p>\r\n<p>\\(\\text{g}_{\\text{l}}=\\) Sustainable long-term dividend growth rate.<\/p>\r\n<p>\\(\\text{r}=\\) Required rate of return.<\/p>\r\n<h2>Three-Stage DDM<\/h2>\r\n<p>This model is more suitable for companies that are expected to have three separate stages of earnings growth. It is a more complex refinement of the two-stage model.<\/p>\r\n<ul>\r\n\t<li>The initial stage of growth.<\/li>\r\n\t<li>The second stage of growth.<\/li>\r\n\t<li>The stable phase of growth.<\/li>\r\n<\/ul>\r\n<h3>The First Version of the Three-Stage DDM<\/h3>\r\n<ul>\r\n\t<li>The firm is assumed to have three phases.<\/li>\r\n\t<li>The growth rate during each phase is different but constant.<\/li>\r\n<\/ul>\r\n<p style=\"text-align: left;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-26473\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM.jpg\" alt=\"Three-Stage DDM\" width=\"1590\" height=\"1369\" srcset=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM.jpg 1590w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM-300x258.jpg 300w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM-1024x882.jpg 1024w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM-768x661.jpg 768w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM-1536x1323.jpg 1536w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM-400x344.jpg 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/>Calculation steps under this model are:<\/p>\r\n<ol style=\"list-style-type: lower-roman;\">\r\n\t<li>Estimate the dividends over the first two stages of growth.<\/li>\r\n\t<li>Discount estimated dividends to the present.<\/li>\r\n\t<li>Estimate the dividends for the first year of the 3<sup>rd<\/sup> stage.<\/li>\r\n\t<li>Calculate the terminal value at the beginning of the 3<sup>rd<\/sup> stage.<\/li>\r\n\t<li>Calculate the present value of the terminal value.<\/li>\r\n<\/ol>\r\n<h4>The Second Version of the Three-Stage Model<\/h4>\r\n<ul>\r\n\t<li>The second stage is similar to the first stage of the H-model.<\/li>\r\n<\/ul>\r\n<p>The steps under this model are:<\/p>\r\n<ol style=\"list-style-type: lower-roman;\">\r\n\t<li>Calculate the yearly dividends and the present values in stage 1.<\/li>\r\n\t<li>Apply the H-model to the 2<sup>nd<\/sup> and 3<sup>rd<\/sup> stages to determine the value of the share at the beginning of<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-26474\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM-2nd-Version.jpg\" alt=\"Three-Stage DDM (2nd Version)\" width=\"1590\" height=\"1410\" srcset=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM-2nd-Version.jpg 1590w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM-2nd-Version-300x266.jpg 300w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM-2nd-Version-1024x908.jpg 1024w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM-2nd-Version-768x681.jpg 768w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM-2nd-Version-1536x1362.jpg 1536w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/07\/Three-Stage-DDM-2nd-Version-400x355.jpg 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/> stage 2 (H-model value).<\/li>\r\n\t<li>Determine the present value of the H-model value.<\/li>\r\n\t<li>Sum the present value from stage 1 and the present value of the H-model value.<\/li>\r\n<\/ol>\r\n<h2>Spreadsheet Modeling<\/h2>\r\n<p>Spreadsheet modeling is used to build complicated models that would require different patterns of dividend growth. Built-in spreadsheet functions also make the calculation simpler. In addition, they allow several analysts to share their spreadsheet models, thus exchanging information.<\/p>\r\n<p>Spreadsheet models also reduce the probability of computational inaccuracies.<\/p>\r\n<blockquote>\r\n<h2>Question<\/h2>\r\n<p>Which of the following is the <em>least likely<\/em> an assumption of the H-model?<\/p>\r\n<ol style=\"list-style-type: upper-alpha;\">\r\n\t<li>There are two stages in the H-model.<\/li>\r\n\t<li>A supernormal growth rate characterizes the final stage of the H-model.<\/li>\r\n\t<li>A sustainable long term growth rate characterizes the final stage of the H-model.<\/li>\r\n<\/ol>\r\n<h4>Solution<\/h4>\r\n<p><strong>The correct answer is B.\u00a0<\/strong><\/p>\r\n<p>A supernormal growth rate does not characterize the final stage. It is during the first stage of the H-model that the growth rate is expected to be high.<strong>\u00a0<\/strong><\/p>\r\n<p><strong>A is incorrect. <\/strong>The H-model assumes there are two stages.<strong>\u00a0<\/strong><\/p>\r\n<p><strong>C is incorrect. <\/strong>The final stage of the H-model is characterized by a sustainable long-term growth rate that is expected to continue into perpetuity.<\/p>\r\n<\/blockquote>\r\n<p>Reading 23: Discounted Dividend Valuation<\/p>\r\n<p><em>LOS 23 (j) Explain the assumptions and justify the selection of the two-stage DDM, the H-model, the three-stage DDM, or spreadsheet modeling to value a company\u2019s common shares.<\/em><\/p>\r\n\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;\">Practice multiperiod models, valuation frameworks, and forecasting techniques with CFA Level II exam-style questions.<\/p> <\/div>","protected":false},"excerpt":{"rendered":"<p>Two-Stage DDM There are several assumptions of the first version of the two-stage DDM: The first stage represents a period of abnormal growth. The second stage represents a period of sustainable growth. There is a sudden transition from abnormal growth&#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":[216,402,449,440],"class_list":["post-17793","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-equity-valuation","tag-cfa-level-2","tag-equity-valuation","tag-multiperiod-models","tag-reading-27-discounted-dividend-valuation","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>Multiperiod Models &amp; H-Model | CFA II<\/title>\n<meta name=\"description\" content=\"Learn how multiperiod dividend discount models work, including the H-Model formula and long-term growth assumptions.\" \/>\n<meta name=\"robots\" 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