{"id":183327,"date":"2025-01-16T07:58:17","date_gmt":"2025-01-16T07:58:17","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=183327"},"modified":"2025-01-16T07:58:19","modified_gmt":"2025-01-16T07:58:19","slug":"calculate-the-crossover-rate-where-the-two-projects-npvs-are-equal","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/16\/calculate-the-crossover-rate-where-the-two-projects-npvs-are-equal\/","title":{"rendered":"Calculate the crossover rate where the two projects&#8217; NPVS are equal"},"content":{"rendered":"\n<p>Calculate the crossover rate where the two projects&#8217; NPVS are equal. Do not round intermediate calculations. Round your answer to two decimal places. % g. What is each project&#8217;s MIRR at a WACC of 18%? Do not round intermediate calculations. Round your answers to two decimal places. Project A: % Project B: % None<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/01\/image-255.png\" alt=\"\" class=\"wp-image-183328\"\/><\/figure>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To determine the <strong>crossover rate<\/strong>\u2014the discount rate at which two projects have equal Net Present Values (NPVs)\u2014and the <strong>Modified Internal Rate of Return (MIRR)<\/strong> for each project at a Weighted Average Cost of Capital (WACC) of 18%, follow these steps:<\/p>\n\n\n\n<p><strong>1. Calculate the Crossover Rate:<\/strong><\/p>\n\n\n\n<p>The crossover rate is found by equating the NPVs of both projects and solving for the discount rate (r). This involves:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Identifying Cash Flows:<\/strong> List the cash flows for both projects over time.<\/li>\n\n\n\n<li><strong>Calculating Differences:<\/strong> Compute the difference in cash flows between the two projects for each period.<\/li>\n\n\n\n<li><strong>Setting Up the Equation:<\/strong> Set the NPV of the differences equal to zero and solve for r.<\/li>\n<\/ul>\n\n\n\n<p>Mathematically, this is represented as:<\/p>\n\n\n\n<p>[ \\sum \\left( \\frac{\\Delta \\text{Cash Flow}_t}{(1 + r)^t} \\right) = 0 ]<\/p>\n\n\n\n<p>Where ( \\Delta \\text{Cash Flow}_t ) is the difference between the cash flows of Project A and Project B at time t.<\/p>\n\n\n\n<p>Solving this equation yields the crossover rate. For instance, if the cash flows are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Project A: Initial Investment = -$1,000; Year 1 = $500; Year 2 = $400; Year 3 = $300; Year 4 = $100.<\/li>\n\n\n\n<li>Project B: Initial Investment = -$1,000; Year 1 = $100; Year 2 = $300; Year 3 = $400; Year 4 = $675.<\/li>\n<\/ul>\n\n\n\n<p>The differences are: Year 1 = $400; Year 2 = $100; Year 3 = -$100; Year 4 = -$575.<\/p>\n\n\n\n<p>Setting up the NPV equation for these differences and solving for r gives a crossover rate of approximately 11.97%.<\/p>\n\n\n\n<p><strong>2. Calculate the MIRR at a WACC of 18%:<\/strong><\/p>\n\n\n\n<p>The MIRR considers the cost of capital and provides a better indication of a project&#8217;s profitability.<\/p>\n\n\n\n<p><strong>Steps:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Future Value (FV) of Inflows:<\/strong><\/li>\n\n\n\n<li><strong>Project A:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Year 1: ( 500 \\times (1 + 0.18)^3 )<\/li>\n\n\n\n<li>Year 2: ( 400 \\times (1 + 0.18)^2 )<\/li>\n\n\n\n<li>Year 3: ( 300 \\times (1 + 0.18)^1 )<\/li>\n\n\n\n<li>Year 4: ( 100 )<\/li>\n\n\n\n<li><strong>Total FV:<\/strong> Sum of the above.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Project B:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Year 1: ( 100 \\times (1 + 0.18)^3 )<\/li>\n\n\n\n<li>Year 2: ( 300 \\times (1 + 0.18)^2 )<\/li>\n\n\n\n<li>Year 3: ( 400 \\times (1 + 0.18)^1 )<\/li>\n\n\n\n<li>Year 4: ( 675 )<\/li>\n\n\n\n<li><strong>Total FV:<\/strong> Sum of the above.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Present Value (PV) of Outflows:<\/strong> This is the initial investment for each project.<\/li>\n\n\n\n<li><strong>MIRR Calculation:<\/strong> [ \\text{MIRR} = \\left( \\frac{\\text{FV of Inflows}}{\\text{PV of Outflows}} \\right)^{\\frac{1}{n}} &#8211; 1 ] Where n is the number of periods.<\/li>\n<\/ul>\n\n\n\n<p><strong>Example Calculation:<\/strong><\/p>\n\n\n\n<p>Assuming the following cash flows:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Project A:<\/strong><\/li>\n\n\n\n<li>Initial Investment: -$1,000<\/li>\n\n\n\n<li>Year 1: $500<\/li>\n\n\n\n<li>Year 2: $400<\/li>\n\n\n\n<li>Year 3: $300<\/li>\n\n\n\n<li>Year 4: $100<\/li>\n\n\n\n<li><strong>Project B:<\/strong><\/li>\n\n\n\n<li>Initial Investment: -$1,000<\/li>\n\n\n\n<li>Year 1: $100<\/li>\n\n\n\n<li>Year 2: $300<\/li>\n\n\n\n<li>Year 3: $400<\/li>\n\n\n\n<li>Year 4: $675<\/li>\n<\/ul>\n\n\n\n<p><strong>Calculations:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Project A:<\/strong><\/li>\n\n\n\n<li>FV of Inflows:\n<ul class=\"wp-block-list\">\n<li>Year 1: ( 500 \\times (1 + 0.18)^3 = 500 \\times 1.643 = $821.50 )<\/li>\n\n\n\n<li>Year 2: ( 400 \\times (1 + 0.18)^2 = 400 \\times 1.3924 = $556.96 )<\/li>\n\n\n\n<li>Year 3: ( 300 \\times (1 + 0.18)^1 = 300 \\times 1.18 = $354.00 )<\/li>\n\n\n\n<li>Year 4: $100<\/li>\n\n\n\n<li><strong>Total FV:<\/strong> ( 821.50 + 556.96 + 354.00 + 100 = $1,832.46 )<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>PV of Outflows: $1,000<\/li>\n\n\n\n<li>n = 4<\/li>\n\n\n\n<li>MIRR: [ \\text{MIRR} = \\left( \\frac{1832.46}{1000} \\right)^{\\frac{1}{4}} &#8211; 1 = (1.83246)^{0.25} &#8211; 1 \\approx 0.1605 \\text{ or } 16.05\\% ]<\/li>\n\n\n\n<li><strong>Project B:<\/strong><\/li>\n\n\n\n<li>FV of Inflows:\n<ul class=\"wp-block-list\">\n<li>Year 1: ( 100 \\times (1 + 0.18)^3 = 100 \\times 1.643 = $164.30 )<\/li>\n\n\n\n<li>Year 2: ( 300 \\times (1 + 0.18)^2 = 300 \\times 1.3924 = $417.72 )<\/li>\n\n\n\n<li>Year 3: ( 400 \\times (1 + 0.18)^1 = 400 \\times 1.18 = $472.00 )<\/li>\n\n\n\n<li>Year 4<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the crossover rate where the two projects&#8217; NPVS are equal. Do not round intermediate calculations. Round your answer to two decimal places. % g. What is each project&#8217;s MIRR at a WACC of 18%? Do not round intermediate calculations. Round your answers to two decimal places. Project A: % Project B: % None The [&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-183327","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183327","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=183327"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183327\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=183327"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=183327"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=183327"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}