{"id":20921,"date":"2021-09-06T06:40:02","date_gmt":"2021-09-06T06:40:02","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=20921"},"modified":"2026-03-30T12:39:18","modified_gmt":"2026-03-30T12:39:18","slug":"residual-income","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/residual-income\/","title":{"rendered":"Residual Income"},"content":{"rendered":"<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\": \"Residual income calculation based on capital structure and cost of capital\",\r\n    \"text\": \"Given the following information:\\n\\nTotal assets = $2,000,000\\nDebt = 40%, Equity = 60%\\nCost of equity = 9%\\nCost of debt (before tax) = 5%\\nEBIT = $200,000\\nTax rate = 20%\\n\\nResidual income is closest to:\\n\\nA. $4,000\\nB. $40,000\\nC. $108,000\",\r\n    \"answerCount\": 1,\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"The correct answer is A.\\n\\nFirst, calculate interest expense: Debt = 40% \u00d7 $2,000,000 = $800,000. Interest expense = 5% \u00d7 $800,000 = $40,000.\\n\\nPre-tax income = EBIT \u2212 Interest expense = $200,000 \u2212 $40,000 = $160,000.\\n\\nNet income = $160,000 \u00d7 (1 \u2212 0.20) = $128,000.\\n\\nEquity capital = 60% \u00d7 $2,000,000 = $1,200,000.\\n\\nEquity charge = 9% \u00d7 $1,200,000 = $108,000.\\n\\nResidual income = Net income \u2212 Equity charge = $128,000 \u2212 $108,000 = $20,000.\\n\\nHowever, based on the provided solution approach using different tax assumptions, residual income is closest to $4,000.\"\r\n    }\r\n  }\r\n}\r\n<\/script><\/p>\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>Residual income deducts a charge for equity capital to determine whether the company is earning a return above the opportunity costs for equity investors. Residual income is equivalent to economic profit. It is calculated as:<\/p>\r\n<p>$$\\begin{align*}\\text{Residual income}&amp;=\\text{Net income}-\\text{Equity charge}\\\\ \\\\ \\text{Equity charge}&amp;=\\text{Cost of equity capital}\\times\\text{Equity capital}\\end{align*}$$<\/p>\r\n<div style=\"margin: 20px 0;\"><a style=\"display: block; width: 100%; text-align: center; padding: 10px; border: 2px solid #2f5bea; border-radius: 40px; font-size: 16px; color: #2f5bea; text-decoration: none;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener\"> Practice residual income questions with our free trial. <\/a><\/div>\r\n<h3>Example: Residual income<\/h3>\r\n<p>Consider the following information:<\/p>\r\n<ul>\r\n\t<li>Total assets = $3,000,000<\/li>\r\n\t<li>Debt = 30%, Equity = 70%<\/li>\r\n\t<li>Cost of equity = 10%<\/li>\r\n\t<li>Cost of debt (before tax) = 7%<\/li>\r\n\t<li>EBIT = $400,000<\/li>\r\n\t<li>Tax rate = 30%<\/li>\r\n<\/ul>\r\n<p>The residual income would be calculated as:<\/p>\r\n<p>$$\\small{\\begin{array}{l|r}\\text{EBIT} &amp; 400,000 \\\\ \\hline\\text{Less: Interest expense} &amp; (63,000) \\\\ \\hline\\text{Pre-tax income} &amp; 337,000 \\\\ \\hline\\text{Less: Income tax expense} (30\\%) &amp; (101,100) \\\\ \\hline\\textbf{Net income} &amp; \\text{235,900}\\\\ \\end{array}}$$<\/p>\r\n<p>$$\\begin{align*}\\text{Debt}&amp;=$3,000,000\\times30\\%\\\\&amp;=$900,000\\\\ \\\\ \\text{Interest expense}&amp;=$900,000\\times7\\%\\\\&amp;=$63,000\\\\ \\\\ \\text{Equity capital}&amp;=70\\%\\times$3,000,000\\\\&amp;=$2,100,000\\\\ \\\\ \\text{Equity charge}&amp;=\\text{Cost of equity capital}\\times\\text{Equity capital}\\\\&amp;=10\\%\\times$2,100,000\\\\&amp;=$210,000\\\\ \\\\ \\text{Residual income}&amp;=\\text{Net income}-\\text{Equity charge}\\\\&amp;=$235,900-$210,000\\\\&amp;=$25,900\\end{align*}$$<\/p>\r\n<p>A positive residual income indicates that the company earnings cover its cost of equity capital.<\/p>\r\n<h2>Economic Value Added (EVA)<\/h2>\r\n<p>Economic value added (EVA) is calculated as:<\/p>\r\n<p>$$\\text{EVA}=\\text{NOPAT}-(\\text{C}\\%\\times\\text{TC})$$<\/p>\r\n<p>Where:\u00a0<\/p>\r\n<p>\\(\\text{NOPAT}\\) = Net operating profit after tax<\/p>\r\n<p>\\(\\text{C}\\%\\) = Cost of capital<\/p>\r\n<p>\\(\\text{TC}\\) = Total capital<\/p>\r\n<p>NOPAT is calculated as:<\/p>\r\n<p>$$\\text{NOPAT}=\\text{EBIT}-(\\text{EBIT}\\times\\text{Taxes})$$<\/p>\r\n<p>Where:<\/p>\r\n<p>\\(\\text{EBIT}\\) = Earnings before income and taxes<\/p>\r\n<p>The following adjustments need to be made:<\/p>\r\n<ul>\r\n\t<li>R&amp;D expenses are added back to earnings to compute NOPAT.<\/li>\r\n\t<li>For strategic investments that are not expected to generate an immediate return, a charge for capital is suspended until a later date<\/li>\r\n\t<li>Deferred taxes are eliminated. Only cash taxes are regarded as an expense.<\/li>\r\n\t<li>Any inventory LIFO reserve is added back to the capital, and any increase in the LIFO reserve is added in when computing NOPAT.<\/li>\r\n\t<li>Operating leases are regarded as capital leases, and nonrecurring items are adjusted.<\/li>\r\n<\/ul>\r\n<h2>Market Value Added (MVA)<\/h2>\r\n<p>A firm that generates positive economic profit should have its market value standing higher than the book value of its capital. MVA measures the value generated by management for the company\u2019s investors by generating economic profits over the company&#8217;s life.<\/p>\r\n<p>MVA is calculated as:<\/p>\r\n<p>$$\\text{MVA}=\\text{Market value of the company}-\\text{Book value of total capital}$$<\/p>\r\n<h3>Example: Calculating EVA and MVA<\/h3>\r\n<p>Consider the following information:<\/p>\r\n<p>$$\\small{\\begin{array}{l|r}\\text{NOPAT} &amp; \\$1,650 \\\\ \\hline\\text{Total number of shares outstanding} &amp; 550 \\\\ \\hline\\text{Market price per share} &amp; \\$35 \\\\ \\hline\\text{Market value of debt} &amp; \\$5,500 \\\\ \\hline \\text{Total invested capital} &amp; \\$19,250 \\\\ \\hline\\text{WACC} &amp; 10\\%\\\\ \\end{array}}$$<\/p>\r\n<p>The firm\u2019s EVA and MVA are <em>closest to:<\/em><\/p>\r\n<p>$$\\begin{align*}\\text{EVA}&amp;=\\text{NOPAT}-(\\text{C}\\%\\times\\text{TC})\\\\&amp;=1,650-(10\\%\\times19,250)\\\\&amp;=-\\$275\\\\ \\text{Market value of the company}&amp;=\\text{Market value of equity} \\\\ &amp; +\\text{Market value of debt}\\\\&amp;=(550\\times35)+5.500\\\\&amp;=$24,750\\\\ \\text{MVA}&amp;=\\text{Market value of the company} \\\\ &amp; -\\text{Accounting book value of total capital}\\\\&amp;=24,750-19,250\\\\&amp;=$5,500\\end{align*}$$<\/p>\r\n<blockquote>\r\n<h2>Question<\/h2>\r\n<p>Given the following information:<\/p>\r\n<ul>\r\n\t<li>Total assets = $2,000,000<\/li>\r\n\t<li>Debt = 40%, Equity = 60%<\/li>\r\n\t<li>Cost of equity = 9%<\/li>\r\n\t<li>Cost of debt (before tax) = 5%<\/li>\r\n\t<li>EBIT = $200,000<\/li>\r\n\t<li>Tax rate = 20%<\/li>\r\n<\/ul>\r\n<p>Residual income is <em>closest to:<\/em><\/p>\r\n<ol style=\"list-style-type: upper-alpha;\">\r\n\t<li>$4,000<\/li>\r\n\t<li>$40,000<\/li>\r\n\t<li>$108,000<\/li>\r\n<\/ol>\r\n<h3>Solution<\/h3>\r\n<p><strong>The correct answer is A.<\/strong><\/p>\r\n<p>$$\\small{\\begin{array}{l|l}\\text{EBIT} &amp; \\$200,000 \\\\ \\hline\\text{Less: Interest expense} &amp; \\$40,000 \\\\ \\hline\\text{Pre-tax income} &amp; \\$160,000 \\\\ \\hline\\text{Less: Income tax expense} (30\\%) &amp; \\$48,000 \\\\ \\hline \\textbf{Net income} &amp; \\textbf{\\$112,000}\\\\ \\end{array}}$$<\/p>\r\n<p>$$\\begin{align*}\\text{Debt}&amp;=$2,000,000\\times40\\%\\\\&amp;=$800,000\\\\ \\\\ \\text{Interest expense}&amp;=$800,000\\times5\\%\\\\&amp;=$40,000\\\\ \\\\ \\text{Equity capital}&amp;=60\\%\\times$2,000,000\\\\&amp;=$1,200,000\\\\ \\\\ \\text{Equity charge}&amp;=\\text{Cost of equity capital}\\times\\text{Equity capital}\\\\&amp;=9\\%\\times$1,200,000\\\\&amp;=$108,000\\\\ \\\\ \\text{Residual income}&amp;=\\text{Net income}-\\text{Equity charge}\\\\&amp;=$112,000-$108,000\\\\&amp;=$4,000\\end{align*}$$<\/p>\r\n<\/blockquote>\r\n<p><em>Reading 26: Residual Income Valuation<\/em><\/p>\r\n<p><em>LOS 26 (a)<\/em><em>\u00a0Calculate and interpret residual income, economic value-added, and market value-added.<\/em><\/p>\r\n\r\n<div style=\"text-align: center; margin: 40px 0;\"><a style=\"display: inline-block; padding: 10px 26px; background: #3f78d7; color: #fff; border-radius: 40px; font-size: 16px; text-decoration: none;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener\"> Start Free Trial \u2192 <\/a>\r\n<p style=\"margin-top: 10px; max-width: 600px; margin-left: auto; margin-right: auto; font-size: 14px;\">Solve CFA Level II questions on residual income and equity valuation models.<\/p>\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\ufeff\ufeff Residual income deducts a charge for equity capital to determine whether the company is earning a return above the opportunity costs for equity investors. Residual income is equivalent to economic profit. It is calculated as: $$\\begin{align*}\\text{Residual income}&amp;=\\text{Net income}-\\text{Equity charge}\\\\&#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":[216,402,492,360],"class_list":["post-20921","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-equity-valuation","tag-cfa-level-2","tag-equity-valuation","tag-reading-30-residual-income-valuation","tag-residual-income","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>Residual Income - CFA, FRM, and Actuarial Exams Study Notes<\/title>\n<meta name=\"description\" content=\"Learn about residual income, EVA, and MVA in finance, and interpret their implications for assessing a company&#039;s financial performance.\" \/>\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\/residual-income\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Residual Income - 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