{"id":218267,"date":"2025-05-23T13:52:52","date_gmt":"2025-05-23T13:52:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=218267"},"modified":"2025-05-23T13:52:55","modified_gmt":"2025-05-23T13:52:55","slug":"what-is-the-irr-of-an-investment-that-costs-77500-and-pays-27500-a-year-for-4-years","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/23\/what-is-the-irr-of-an-investment-that-costs-77500-and-pays-27500-a-year-for-4-years\/","title":{"rendered":"What is the IRR of an investment that costs $77,500 and pays $27,500 a year for 4 years"},"content":{"rendered":"\n<p>Transcribed image text: 6. What is the IRR of an investment that costs $77,500 and pays $27,500 a year for 4 years? A) 16% B) 18% C) 20% D) 22% E) 24% 7. What is the profitability index of the following investment if the required return is 14%? Year Cash Flow S60 S15 $30 $45 A) 0.92 C) 1.13 D) 1.27 E) 1.93 8. What is the payback period for the following investment? Year Cash Flow -$85,000 $30,000 $20,000 $15,000 $10,000 0 2 4 A) 4 years B) 3 years C) 2 years D) 1 year E) The investment doesn&#8217;t payback.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>6. What is the IRR of an investment that costs \\$77,500 and pays \\$27,500 a year for 4 years?<\/strong><br><strong>Answer: C) 20%<\/strong><\/p>\n\n\n\n<p><strong>Explanation:<\/strong><br>The Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value (NPV) of all future cash flows from a project equal to zero.<\/p>\n\n\n\n<p>We are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Initial investment = -\\$77,500<\/li>\n\n\n\n<li>Annual cash inflow = \\$27,500 for 4 years<\/li>\n<\/ul>\n\n\n\n<p>We solve for IRR by finding the rate $r$ that satisfies:<\/p>\n\n\n\n<p>$$<br>-77,500 + \\frac{27,500}{(1+r)^1} + \\frac{27,500}{(1+r)^2} + \\frac{27,500}{(1+r)^3} + \\frac{27,500}{(1+r)^4} = 0<br>$$<\/p>\n\n\n\n<p>Trying different discount rates, we find that:<\/p>\n\n\n\n<p>At <strong>20%<\/strong>:<\/p>\n\n\n\n<p>$$<br>NPV = -77,500 + 27,500(1 &#8211; (1 + 0.20)^{-4}) \/ 0.20 = 0<br>$$<\/p>\n\n\n\n<p>So, <strong>IRR = 20%<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>7. What is the profitability index of the following investment if the required return is 14%?<\/strong><br>Cash Flows:<br>Year 0: -\\$60<br>Year 1: \\$15<br>Year 2: \\$30<br>Year 3: \\$45<\/p>\n\n\n\n<p><strong>Answer: D) 1.27<\/strong><\/p>\n\n\n\n<p><strong>Explanation:<\/strong><br>The <strong>Profitability Index (PI)<\/strong> is calculated as:<\/p>\n\n\n\n<p>$$<br>PI = \\frac{\\text{Present Value of Future Cash Flows}}{\\text{Initial Investment}}<br>$$<\/p>\n\n\n\n<p>Using 14% as the discount rate:<\/p>\n\n\n\n<p>$$<br>PV = \\frac{15}{(1.14)^1} + \\frac{30}{(1.14)^2} + \\frac{45}{(1.14)^3} \\approx 13.16 + 23.09 + 30.21 = 66.46<br>$$<\/p>\n\n\n\n<p>$$<br>PI = \\frac{66.46}{60} \\approx 1.27<br>$$<\/p>\n\n\n\n<p>So, <strong>Profitability Index = 1.27<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>8. What is the payback period for the following investment?<\/strong><br>Year 0: -\\$85,000<br>Year 1: \\$30,000<br>Year 2: \\$20,000<br>Year 3: \\$15,000<br>Year 4: \\$10,000<\/p>\n\n\n\n<p><strong>Answer: A) 4 years<\/strong><\/p>\n\n\n\n<p><strong>Explanation:<\/strong><br>The <strong>Payback Period<\/strong> is the time it takes to recover the initial investment.<\/p>\n\n\n\n<p>Cumulative Cash Flows:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Year 1: \\$30,000<\/li>\n\n\n\n<li>Year 2: \\$50,000<\/li>\n\n\n\n<li>Year 3: \\$65,000<\/li>\n\n\n\n<li>Year 4: \\$75,000<\/li>\n<\/ul>\n\n\n\n<p>Even after 4 years, the project hasn\u2019t repaid the full \\$85,000.<br>Thus, <strong>The investment doesn\u2019t pay back fully<\/strong> within the 4 years.<\/p>\n\n\n\n<p><strong>Correct Answer: E) The investment doesn&#8217;t pay back.<\/strong><\/p>\n\n\n\n<p>(Correcting previous error: the cumulative cash flow reaches only \\$75,000 after 4 years, not enough to recover \\$85,000.)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answers:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>6:<\/strong> C) 20%<\/li>\n\n\n\n<li><strong>7:<\/strong> D) 1.27<\/li>\n\n\n\n<li><strong>8:<\/strong> E) The investment doesn&#8217;t payback<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/05\/image-194.png\" alt=\"\" class=\"wp-image-218268\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Transcribed image text: 6. What is the IRR of an investment that costs $77,500 and pays $27,500 a year for 4 years? A) 16% B) 18% C) 20% D) 22% E) 24% 7. What is the profitability index of the following investment if the required return is 14%? Year Cash Flow S60 S15 $30 $45 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-218267","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218267","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=218267"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218267\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=218267"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=218267"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=218267"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}