{"id":98,"date":"2019-10-01T13:28:00","date_gmt":"2019-10-01T13:28:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=98"},"modified":"2026-01-13T11:10:04","modified_gmt":"2026-01-13T11:10:04","slug":"internal-rate-return-example-question","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/internal-rate-return-example-question\/","title":{"rendered":"The Internal Rate of Return"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Probability Concepts (2021 Level I CFA\u00ae Exam \u2013 Reading 8)\",\n  \"description\": \"This lecture on probability concepts for CFA Level 1 covers definitions, types of probabilities, odds, conditional and unconditional probabilities, rules like multiplication and total probability, Bayes' theorem, portfolio analysis, covariance, and counting methods such as permutations and combinations. It emphasizes practical applications for finance and investment decision-making.\",\n  \"uploadDate\": \"2021-11-01T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/hu47ZbsskEw\/default.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/hu47ZbsskEw\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/hu47ZbsskEw\",\n  \"duration\": \"PT48M33S\"\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"What is the internal rate of return (IRR) for the project?\",\n    \"text\": \"Suppose we have a project with the following cash flows: Outgo: $150,000 at t = 0, $250,000 at t = 1, and $250,000 at t = 2. Income: $1 million at t = 3. Find the IRR of the project.\",\n    \"answerCount\": 3,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is A. We need to find the rate r such that: -150,000 - 250,000(1 + r) ^ -1 - 250,000(1 + r) ^ -2 + 1,000,000(1 + r) ^ -3 = 0. The IRR is 25.2%.\"\n    }\n  }\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\"\n  width=\"611\"\n  height=\"344\"\n  src=\"https:\/\/www.youtube.com\/embed\/lYpi92G13U4\"\n  title=\"YouTube video player\"\n  frameborder=\"0\"\n  allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\"\n  referrerpolicy=\"strict-origin-when-cross-origin\"\n  allowfullscreen>\n<\/iframe>\n\n\n\n<p>The internal rate of return is the discount rate that sets the <a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/time-value-money-explained-example\/\">present value<\/a> of all cash inflows of a project equal to the present value of all cash outflows of the same project. In other words, it is the effective rate of return that makes a project have a net present value of zero.<!--more--> Thus:<\/p>\n<p>NPV = 0 if r = IRR, for any given project.<\/p>\n<p>Or<\/p>\n<p>PV outgo = PV income when r = IRR<\/p>\n<p>The internal rate of return method of project appraisal assumes that all proceeds from the project can be re-invested immediately, and in projects offering returns equal to the IRR, until maturity. A higher IRR indicates a more \u201cprofitable\u201d project.<\/p>\n<h2><strong>Interpreting the Internal rate of Return<br \/><\/strong><\/h2>\n<p>You should note that the IRR need not be positive \u2013 It can be zero or even negative. A positive return indicates that the project makes money for the investor. A zero return indicates that the investor is neither profitable nor loss-making. Lastly, if the IRR is negative, the investor loses money. However, if the IRR is less than -1, it means the yield or rather the return is undefined.<\/p>\n<p>The internal rate of return is usually compared to the cost of capital, usually the weighted average cost of capital, WACC. A project whose IRR is above its WACC increases the shareholders\u2019 wealth. Otherwise, it would be unwise to borrow cash at an interest rate, say, 10% and then invest the money in a project with a rate of return less than 10%. The borrower would be unable to service the loan.<\/p>\n<p>Usually, candidates cannot solve questions involving IRR directly and you may need to carry out linear extrapolation. Working with a spreadsheet or calculator is also a better, easier approach. However, you should aim to understand the manual approach first. It will then be easier to use a calculator.<\/p>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>Suppose we have a project with the following cash flows;<\/p>\n<p>Outgo: $150,000 at t = 0, $250,000 at t = 1, and some more $250,000 at t = 2<\/p>\n<p>Income: $1 million at t = 3<\/p>\n<p>Find the IRR of the project.<\/p>\n<p>A. 25.2%<\/p>\n<p>B. 0%<\/p>\n<p>C. 23%<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is A.<\/p>\n<p>We need to find the rate r such that:<\/p>\n<p>$$<br \/>-150,000 \u2013 250,000(1 + r)^{-1} \u2013 250,000(1 + r)^{-2} + 1000,000( 1 + r )^{-3} = 0 $$<\/p>\n<p>$$<br \/>\\text{At } 20\\%, -150,000 \u2013 250,000 * 1.2^{-1} \u2013 250,000 * 1.2^{-2} + 1000,000 * 1.2^{-3} = 46,800 $$<\/p>\n<p>$$<br \/>\\text{At } 25\\%, -150,000 \u2013 250,000 * 1.2^{-1} \u2013 250,000 * 1.2^{-2} + 1000,000 * 1.2^{-3} = 2,000 $$<\/p>\n<p>We can approximate r by linear extrapolation using the two values:<\/p>\n<p>$$<br \/>r = 20\\% + \\cfrac {(0 &#8211; 46,800)}{(2 &#8211; 46,800)} * (25\\% &#8211; 20\\%) = 25.2\\%$$<\/p>\n<p>Suppose the WACC is 20% in the example above. What would be your advice to investors? Since WACC (20%) is less than IRR (25.2%), the project is economically viable and would increase the investors\u2019 wealth.<\/p>\n<p><strong>Conclusion<\/strong>: A capital project should be accepted if its IRR is greater than the cost of capital.<\/p>\n<\/blockquote>\n<p><em>Reading 7 LOS 7a (Part 2)<\/em><\/p>\n<p><em>Calculate and interpret the net present value (NPV) and the internal rate of return (IRR) of an investment.<\/em><\/p>\n<div class=\"notes_inv\"><hr \/>\n<p><a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/learning-sessions-curriculum\/\"><em>Quantitative Methods \u2013 Learning Sessions<\/em><\/a><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>The internal rate of return is the discount rate that sets the present value of all cash inflows of a project equal to the present value of all cash outflows of the same project. In other words, it is the&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-98","post","type-post","status-publish","format-standard","hentry","category-quantitative-methods","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>Internal Rate of Return (IRR) Example | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Understand the internal rate of return (IRR) concept and learn through examples how IRR sets the net present value (NPV) of a project to zero.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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