{"id":30438,"date":"2021-09-15T13:13:31","date_gmt":"2021-09-15T13:13:31","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=30438"},"modified":"2026-03-09T20:55:20","modified_gmt":"2026-03-09T20:55:20","slug":"calculating-cost-of-debt-capital","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/corporate-issuers\/calculating-cost-of-debt-capital\/","title":{"rendered":"Calculating Cost of Debt Capital"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Which statement accurately defines yield-to-maturity (YTM)?\",\n    \"text\": \"Which of the following statements gives an accurate definition of yield-to-maturity?\\n\\nA. A bond\u2019s yield-to-maturity is the semi-annual return an investor earns on a bond if they purchase the bond today and hold it until maturity.\\nB. A bond\u2019s yield-to-maturity is the annual return an investor earns on a bond if they purchase the bond today and hold it until maturity.\\nC. A bond\u2019s yield-to-maturity is the return an investor earns on a bond if they purchase the bond and sell it one year prior to maturity.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is B. A bond\u2019s yield-to-maturity is the annual return an investor earns if the bond is purchased today and held until maturity, assuming all coupon payments are reinvested at the same rate. Option A is incorrect because YTM is quoted as an annual return rather than a semi-annual return. Option C is incorrect because YTM assumes the bond is held until maturity.\"\n    }\n  }\n}\n<\/script>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Cost of Capital \u2013 Fundamental Topics (2025 CFA\u00ae Level I \u2013 Corporate Issuers \u2013 Module 6)\",\n  \"description\": \"This video explores the cost of capital, linking sources and uses of capital through concepts like WACC, CAPM, and flotation costs. It explains debt, equity, and preferred stock costs, beta estimation, tax impacts, and decision-making for investments using real-world examples and formulas to reinforce key finance principles.\",\n  \"uploadDate\": \"2021-10-17T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/HkoJ_nedolg\/maxresdefault.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/HkoJ_nedolg\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/HkoJ_nedolg\",\n  \"duration\": \"PT40M28S\",\n  \"publisher\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\",\n    \"logo\": {\n      \"@type\": \"ImageObject\",\n      \"url\": \"https:\/\/analystprep.com\/logo.png\",\n      \"width\": 200,\n      \"height\": 50\n    }\n  }\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/HkoJ_nedolg?si=CC06SzB-vBG7-kFe\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n\n\n<p>The cost of debt is the cost of financing a debt whenever a company incurs a debt by either issuing a bond or taking a bank loan. Two methods for estimating the before-tax cost of debt are the yield-to-maturity approach and the debt-rating approach.<\/p>\n<h2><strong>Yield-to-maturity Approach<\/strong><\/h2>\n<p>A bond&#8217;s yield-to-maturity is the annual return an investor earns on a bond if they purchase it today and hold it until maturity. It is the yield that equates the present value of the bond\u2019s promised payments to its market price.<\/p>\n<p>Assuming that a bond pays semi-annual interest and any intermediate cash flows are invested at the rate of <em>r<sub>d<\/sub>\/2<\/em>, then:<\/p>\n<p>$$ { P }_{ 0 }=\\left( \\sum _{ t=1 }^{ n }{ \\frac { { PMT }_{ t } }{ { \\left( 1+\\frac { { r }_{ d } }{ 2 } \\right) }^{ t } } } \\right) +\\frac { FV }{ { \\left( 1+\\frac { { r }_{ d } }{ 2 } \\right) }^{ n } }<br \/>$$<\/p>\n<p>Where:<\/p>\n<p><em>P<sub>0<\/sub><\/em> = The current market price of the bond.<\/p>\n<p><em>PMT<sub>t<\/sub><\/em> = The interest payment in period t.<\/p>\n<p><em>r<sub>d<\/sub><\/em> = The yield to maturity.<\/p>\n<p><em>n<\/em> = The number of periods remaining to maturity.<\/p>\n<p><em>FV<\/em> = The maturity value of the bond.<\/p>\n<h3><strong>Example: Calculating the Before-tax Cost of Debt and the After-tax Cost of Debt<\/strong><\/h3>\n<p>Suppose company A issues a new debt by offering a 20-year $100,000 face value and 10% semi-annual coupon bond. Upon issuance, the bond sells at $105,000. What is company A\u2019s before-tax cost of debt and after-tax cost of debt if the marginal tax rate is 40%?<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>Given:<\/p>\n<p>PV = $105,000.<\/p>\n<p>FV = $100,000.<\/p>\n<p>PMT = (10% of $100,000)\/2 = $5,000.<\/p>\n<p>N = 20 \u00d7 2 = 40.<\/p>\n<p>$$ $105,000=\\left( \\sum _{ t=1 }^{ 40 }{ \\frac { $5,000 }{ { \\left( 1+\\frac { { r }_{ d } }{ 2 } \\right) }^{ t } } } \\right) +\\frac { $1,00,000 }{ { \\left( 1+\\frac { { r }_{ d } }{ 2 } \\right) }^{ 40 } }<br \/>$$<\/p>\n<p>Using a financial calculator to solve for <em>r<sub>d<\/sub>\/2<\/em>, the six-month yield, we get <em>r<sub>d<\/sub>\/2<\/em> = 4.72%.<\/p>\n<p><em>Note PV = -$105,000 when using the calculator instead of the formula.<\/em><\/p>\n<p>The before-tax cost of debt is therefore <em>r<sub>d\u00a0<\/sub><\/em>= 4.72% \u00d7 2 = 9.44%, and the after-tax cost of debt = <em>r<sub>d<\/sub><\/em>(1 \u2013 t) = 9.44% (1 &#8211; 0.40) = 5.66%.<\/p>\n<h2><strong>Debt-rating Approach<\/strong><\/h2>\n<p>The debt-rating approach is a method for estimating the before-tax cost of debt for a company. This approach is applied whenever reliable, current market price data for a company&#8217;s debt is unavailable. In this method, the before-tax cost of debt is estimated by using the yield on comparably rated bonds for maturities that are closely aligned to the maturities of the company&#8217;s existing debt.<\/p>\n<h2><strong>Example: Debt-rating Approach<\/strong><\/h2>\n<p>Assume that company B has a senior, unsecured debt with an average maturity of 5 years, and the company&#8217;s marginal tax rate is 35%. If the debt rating of the company is BBB- and the yield on similar senior, unsecured debt with the same debt rating and maturity is 9%, then the after-tax cost of debt of the company is:<\/p>\n<p>$$ (1 \u2013 t) = 9\\% (1 \u2013 0.35) = 5.85\\% $$<\/p>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>Which of the following statements gives an accurate definition of yield-to-maturity?<\/p>\n<ol style=\"list-style-type: upper-alpha;\">\n<li>A bond&#8217;s yield-to-maturity is the semi-annual return\u00a0 an investor earns on a bond if they purchase the bond today and hold it until maturity.<\/li>\n<li>A bond&#8217;s yield-to-maturity is the annual return\u00a0 an investor earns on a bond if they purchase the bond today and hold it until maturity.<\/li>\n<li>A bond&#8217;s yield-to-maturity is the return an investor earns on a bond if they purchase the bond and sell it one year prior to maturity.<\/li>\n<\/ol>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is <strong>B<\/strong>.<\/p>\n<p>A bond&#8217;s yield-to-maturity is the annual return that an investor earns on a bond if they purchase the bond today and hold it until maturity.<\/p>\n<p><strong>A is incorrect<\/strong>. The yield-to-maturity is an annual return and not a semi-annual return.<\/p>\n<p><strong>\u00a0C is incorrect<\/strong>. A bond&#8217;s yield-to-maturity assumes that the investor holds the bond until maturity.<\/p>\n<\/blockquote>\n<div class=\"notes_inv\"><hr \/><\/div>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The cost of debt is the cost of financing a debt whenever a company incurs a debt by either issuing a bond or taking a bank loan. Two methods for estimating the before-tax cost of debt are the yield-to-maturity approach&#8230;<\/p>\n","protected":false},"author":15,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[25],"tags":[],"class_list":["post-30438","post","type-post","status-publish","format-standard","hentry","category-corporate-issuers","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>Cost of Debt: Before-Tax Formula &amp; Calculations | CFA 1<\/title>\n<meta name=\"description\" content=\"Learn how to calculate the before-tax cost of debt, explore the pre-tax cost of debt formula, and understand its role in financial analysis for CFA Level 1\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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