{"id":18366,"date":"2021-07-23T04:04:05","date_gmt":"2021-07-23T04:04:05","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=18366"},"modified":"2026-02-24T08:41:06","modified_gmt":"2026-02-24T08:41:06","slug":"free-cash-flow-variations","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/free-cash-flow-variations\/","title":{"rendered":"Single-Stage, Two-Stage, and Three-Stage FCFF and FCFE Models"},"content":{"rendered":"<script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"VideoObject\",\r\n  \"name\": \"Free Cash Flow Valuation (2025 Level II CFA\u00ae Exam \u2013 Equity \u2013 Learning Module 3)\",\r\n  \"description\": \"CFA Level II Equity lesson on Free Cash Flow Valuation covering FCFF vs FCFE approaches, required adjustments from net income, EBIT, EBITDA, and CFO, forecasting free cash flows, multi-stage valuation models, terminal value estimation, sensitivity analysis, 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Discount Model (Version 2)\",\r\n  \"width\": 768,\r\n  \"height\": 681,\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  \"isPartOf\": {\r\n    \"@type\": \"WebPage\",\r\n    \"@id\": \"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/free-cash-flow-variations\/\"\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 discount rate is applied to FCFF when computing the firm\u2019s value?\",\r\n    \"text\": \"Which of the following discount rates is applied to free cash flow to the firm (FCFF) when computing the firm\u2019s value?\",\r\n    \"answerCount\": 3,\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"The weighted average cost of capital (WACC). WACC reflects the firm\u2019s blended cost of capital across equity, debt, and other financing sources and is the appropriate discount rate for valuing FCFF.\",\r\n      \"confidence\": 0.63\r\n    },\r\n    \"suggestedAnswer\": [\r\n      {\r\n        \"@type\": \"Answer\",\r\n        \"text\": \"WACC\"\r\n      },\r\n      {\r\n        \"@type\": \"Answer\",\r\n        \"text\": \"r \u2212 g\"\r\n      },\r\n      {\r\n        \"@type\": \"Answer\",\r\n        \"text\": \"r\"\r\n      }\r\n    ]\r\n  }\r\n}\r\n<\/script>\r\n\r\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/A10ZXpSEZaM\" 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><\/iframe><\/p>\r\n\r\n<h2><span lang=\"EN-US\">Single-Stage (Constant-Growth) <\/span>Free Cash Flow Models<\/h2>\r\n<h3><span lang=\"EN-US\">FCFF Calculation<\/span><\/h3>\r\n<p>Assuming FCFF grows at a constant, \\(g\\)<em>, <\/em>the next period\u2019s FCFF will be:<\/p>\r\n<p>$$\\text{FCFF}_\\text{t}=\\text{FCFF}_{\\text{t}-1} (1+\\text{g})$$<\/p>\r\n<p>If FCFF grows at a constant rate, the value of the firm is calculated as:<\/p>\r\n<p>$$\\text{Firm value}=\\frac{\\text{FCFF}_{1}}{\\text{WACC}-\\text{g}}=\\frac{\\text{FCFF}_0 (1+\\text{g})}{\\text{WACC}-\\text{g}}$$<\/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    Analyze how growth and WACC assumptions affect firm value estimates\r\n  <\/a>\r\n<\/div>\r\n<h3><span lang=\"EN-US\">FCFE Calculation<\/span><\/h3>\r\n<p>Assuming FCFE grows at a constant rate, \\(g\\),<em>\u00a0<\/em>the next period\u2019s FCFE will be:<\/p>\r\n<p>$$\\text{FCFE}_\\text{t}=\\text{FCFE}_{\\text{t}-1} (1+\\text{g})$$<\/p>\r\n<p>The value of equity is calculated as:<\/p>\r\n<p>$$\\text{Equity value}=\\frac{\\text{FCFE}_1}{\\text{r}-\\text{g}}=\\frac{\\text{FCFE}_0 (1+\\text{g})}{\\text{r}-\\text{g}}$$<\/p>\r\n<p>Where:<\/p>\r\n<p>\\(\\text{r}=\\) Required rate of return on equity.<\/p>\r\n<p>\\(\\text{g}=\\) Constant growth rate.<\/p>\r\n<h2>Two-stage Free Cash Flow Models<\/h2>\r\n<p>In a two-stage free cash flow model, the growth rate in the second stage is a long-term sustainable growth rate. For a declining industry, the second stage growth rate could be slightly lower than the economic growth rate or slightly higher for an industry experiencing strong growth.<\/p>\r\n<p>There are two approaches to the two-stage FCFF and FCFE model differentiated by the growth rate in the first stage:<\/p>\r\n<ol style=\"list-style-type: lower-roman;\">\r\n\t<li>The growth rate is constant in stage 1 then abruptly drops to the long-term sustainable growth rate in stage 2.<br \/>\r\n<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\" \/><\/li>\r\n\t<li>The growth rate declines in stage 1 to reach the long-term sustainable rate at the beginning of stage 2. This is similar to the H-model in the dividend discounted model.<br \/>\r\n<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\" \/><\/li>\r\n<\/ol>\r\n<p>In free cash flow models, the growth rate may possibly refer to different variables, namely FCFF or FCFE, earnings (net income or operating income), or sales growth rates.<\/p>\r\n<h3><span lang=\"EN-US\">FCFF Calculation<\/span><\/h3>\r\n<p>The general two-stage FCFF valuation model is:<\/p>\r\n<p>$$\\text{Firm value}= \u2211_{\\text{t}=1}^\\text{n}\\frac{\\text{FCFF}_\\text{t}}{(1+\\text{WACC})^\\text{t}} +\\frac{\\text{FCFF}_{\\text{n}+1}}{(\\text{WACC}-\\text{g})}\\frac{1}{(1+\\text{WACC})^\\text{n}}$$<\/p>\r\n<p>The terminal value is estimated by using a constant growth FCFF model, \\(\\frac{\\text{FCFF}_{\\text{n}+1}}{(\\text{WACC}-\\text{g})}\\), which is discounted to the present by \\(\\frac{1}{(1+\\text{WACC})^\\text{n}}\\).<\/p>\r\n<p>Subtracting the value of outstanding debt from the firm value gives the value of equity. Finally, the value per share is estimated by dividing the total value of equity by the number of outstanding shares.<\/p>\r\n<h3><span lang=\"EN-US\">FCFF Calculation<\/span><\/h3>\r\n<p>The general two-stage FCFE valuation model is:<\/p>\r\n<p>$$\\text{Equity value}= \u2211_{\\text{t}=1}^\\text{n}\\frac{\\text{FCFE}_\\text{t}}{(1+\\text{r})^\\text{t}}+\\frac{\\text{FCFE}_{\\text{n}+1}}{\\text{r}-\\text{g}} \\frac{1}{(1+\\text{r})^\\text{n}}$$<\/p>\r\n<p>The terminal value is estimated by using the constant growth FCFE model, \\(\\frac{\\text{FCFE}_{\\text{n}+1}}{\\text{r}-\\text{g}}\\), which is discounted to the present by \\(\\frac{1}{(1+\\text{r})^\\text{n}}\\).<\/p>\r\n<p>The terminal value could also be estimated using the multiples approach. Here again, the value per share is calculated by dividing the total value of equity by the number of outstanding shares.<\/p>\r\n<p>If a company has significant non-operating assets, such as excess cash and marketable securities, the company\u2019s non-operating assets should be valued separately and then added to the value of the company\u2019s operating assets to find total firm value.<\/p>\r\n<p>$$\\text{Value of the firm}=\\text{Value of operating assets}+\\text{Value of non-operating assets}$$<\/p>\r\n<h2>Three-Stage Growth Models<\/h2>\r\n<p>There are two approaches to this:<\/p>\r\n<ol style=\"list-style-type: lower-roman;\">\r\n\t<li>Assume a constant but different growth rate for the three stages.<br \/>\r\n<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\" \/><\/li>\r\n\t<li>Assume a constant growth rate in stages 1 and 3 and a declining growth rate in stage 2.<br \/>\r\n<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\" \/><\/li>\r\n<\/ol>\r\n<blockquote>\r\n<h2>Question<\/h2>\r\n<p>Which of the following discount rates is applied to FCFF when computing the firm\u2019s value?<\/p>\r\n<ol style=\"list-style-type: upper-alpha;\">\r\n\t<li>WACC.<\/li>\r\n\t<li>r\u2212g.<\/li>\r\n\t<li>r.<\/li>\r\n<\/ol>\r\n<h4>Solution<\/h4>\r\n<p><strong>The correct answer is A. <\/strong><\/p>\r\n<p>The weighted average cost of capital (WACC) represents its blended cost of capital across all sources, including common shares, preferred shares, and debt. It is the rate that discounts the free cash flow to the firm (FCFF) to arrive at the value of the firm.<\/p>\r\n<p><strong>B is incorrect. <\/strong>r\u2212g is used to discount FCFE.<\/p>\r\n<p><strong>C is incorrect. <\/strong>r is <em><strong>not<\/strong> <\/em>used to discount FCFF.<\/p>\r\n<\/blockquote>\r\n<p>Reading 24: Free Cash Flow Valuation<\/p>\r\n<p><em>LOS 24 (i) Explain the single-stage (stable-growth), two-stage, and three-stage FCFF and FCFE models and select and justify the appropriate model given a company\u2019s characteristics.<\/em><\/p>\r\n<!-- Text editor end -->\r\n<div style=\"text-align:center; margin:40px 0 10px 0;\">\r\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\"\r\n     style=\"display:inline-block; padding:14px 34px; background:#1a73e8; color:#ffffff; border-radius:999px; font-weight:700; text-decoration:none;\">\r\n    Start Free Trial\r\n  <\/a>\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\ufeff Single-Stage (Constant-Growth) Free Cash Flow Models FCFF Calculation Assuming FCFF grows at a constant, \\(g\\), the next period\u2019s FCFF will be: $$\\text{FCFF}_\\text{t}=\\text{FCFF}_{\\text{t}-1} (1+\\text{g})$$ If FCFF grows at a constant rate, the value of the firm is calculated as: $$\\text{Firm&#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":[216,402,467,459],"class_list":["post-18366","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-equity-valuation","tag-cfa-level-2","tag-equity-valuation","tag-free-cash-flow-variations","tag-reading-28-free-cash-flow-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\/ 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