{"id":24098,"date":"2024-07-19T10:57:25","date_gmt":"2024-07-19T14:57:25","guid":{"rendered":"https:\/\/www.sage.com\/en-us\/blog\/?p=24098"},"modified":"2024-07-19T10:57:27","modified_gmt":"2024-07-19T14:57:27","slug":"internal-rate-of-return-irr","status":"publish","type":"post","link":"https:\/\/www.sage.com\/en-us\/blog\/internal-rate-of-return-irr\/","title":{"rendered":"Internal rate of return (IRR): What is it and how is it calculated?"},"content":{"rendered":"<header class=\"entry-header has-dark-background-color entry-header--has-illustration entry-header--has-illustration--generic\">\n\t<div class=\"container\">\n\t\t<div class=\"entry-header__row row align-center\">\n\t\t\t<div class=\"col col-lg-7 col-xlg-6 entry-header__content\">\n\t\t\t\t\t\t\t<div class=\"component component-single-header\">\n\t\t\t\t\t\t\t\t\t\t<div class=\"entry-header__misc text--subtitle text--uppercase text--small\">\n\t\t\t\t\t\t\t<a href=\"https:\/\/www.sage.com\/en-us\/blog\/category\/money-matters\/\" class=\"entry-header__link\">Money Matters<\/a>\t\t\t\t\t\t<\/div>\n\t\t\t\t\n\t\t\t\t<div class=\"entry-title-wrapper\">\n\t\t\t\t\t<h1 class=\"entry-title\">\n\t\t\t\t\t\tInternal rate of return (IRR): What is it and how is it calculated?\t\t\t\t\t<\/h1>\n\t\t\t\t<\/div>\n\n\t\t\t\t\t\t\t\t\t<p class=\"entry-header__description\">\n\t\t\t\t\t\t\t\t\t\t\t<\/p>\n\t\t\t\t\n\t\t\t\t\n\t\t\t\t\n\t\t\t<\/div>\n\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t<\/div>\n\t<div class=\"single-post-details container\">\n\t\t<div class=\"col\">\n\t\t\t<span class=\"posted-on \"><time class=\"entry-date published\" datetime=\"2024-07-19T10:57:25-04:00\">July 19, 2024<\/time><\/span><span class=\"reading-time\"> min read<\/span>\n\t\t<button\n\t\t\ttype=\"button\"\n\t\t\tclass=\"social-share-button button button--icon button--secondary js-social-share-button\"\n\t\t\tdata-share-title=\"Internal rate of return (IRR): What is it and how is it calculated?\"\n\t\t\tdata-share-url=\"https:\/\/www.sage.com\/en-us\/blog\/internal-rate-of-return-irr\/\"\n\t\t\tdata-share-text=\"Please read this interesting article\"\n\t\t>\n\t\t\t<span class=\"social-share-button__share-label\">Share<\/span>\n\t\t\t<span class=\"social-share-button__copy-label\" hidden>Copy Link<\/span>\n\t\t\t<span class=\"social-share-button__copy-tooltip\" aria-hidden=\"true\" hidden>Copied<\/span>\n\t\t<\/button>\n\n\t\t\t\t<\/div>\n\t<\/div>\n<\/header>\n\n\n<div class=\"wp-block-post-author has-dark-background-color alignfull\">\n\t<div class=\"container\">\n\t\t<div class=\"col\">\n\t\t\t\t\t\t\t<div class=\"co-authors\">\n\t\t\t\t\t\n\t\t<div class=\"entry-author-wrapper\">\n\t\t\t<a class=\"entry-author\" href=\"https:\/\/www.sage.com\/en-us\/blog\/author\/yassirmalik\/\">\n\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"40\" height=\"40\" src=\"https:\/\/www.sage.com\/en-us\/blog\/wp-content\/uploads\/sites\/2\/2024\/03\/Yassir-Malik.jpg\" class=\"entry-author__image\" alt=\"yassir-malik-profile-picture\" \/>\t\t\t\t<span class=\"entry-author__name\">Yassir Malik<\/span>\n\t\t\t<\/a>\n\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t<\/div>\n<\/div>\n\n\n\n<p>Companies and investors need to be able to assess the various investment options available to them. To do so, it is crucial to know how to calculate the IRR.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>We\u2019ll explain what the internal rate of return is and why it\u2019s one of the most commonly used formulas for choosing from among several investment options.<\/li>\n\n\n\n<li>We\u2019ll show you the different ways of calculating the IRR.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h-here-s-what-we-ll-cover\">Here&#8217;s what we&#8217;ll cover<\/h4>\n\n\n<?xml encoding=\"utf-8\" ?><div class=\"wp-block-yoast-seo-table-of-contents yoast-table-of-contents\"><ul><li><a href=\"#h-what-is-the-internal-rate-of-return\" data-level=\"2\">What is the internal rate of return?<\/a><\/li><li><a href=\"#h-what-is-the-irr-formula\" data-level=\"2\">What is the IRR formula?<\/a><\/li><li><a href=\"#h-interpreting-the-irr\" data-level=\"2\">Interpreting the IRR<\/a><\/li><li><a href=\"#h-an-example-of-calculating-the-internal-rate-of-return\" data-level=\"2\">An example of calculating the Internal Rate of Return<\/a><\/li><\/ul><\/div>\n\n\n\n<p>When considering whether to invest in a project, there are two key points for investors: an executive summary that entices them and an <strong>internal rate of return <\/strong>that guarantees the <strong>project\u2019s profitability<\/strong>.<\/p>\n\n\n\n<p> Companies also use the IRR to <strong>decide which projects to invest in<\/strong>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-the-internal-rate-of-return\">What is the internal rate of return?<\/h2>\n\n\n\n<p>The IRR is an <strong>indicator of the profitability, or yield, of projects or investments<\/strong>, such that the higher the IRR, the higher the yield. By calculating the internal rate of return for different projects, it becomes easier to decide which to invest in.<\/p>\n\n\n\n<p>In the simplest terms, we can define the IRR as the percentage of revenues or losses that will occur as a result of an investment.<\/p>\n\n\n\n<p>This financial concept can be compared with the <strong>minimum acceptable rate for investing<\/strong>, which is the risk-free rate of return, or with the <strong>interest rate that will be applied to the financing<\/strong> of a project.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In the first case: if the <strong>IRR<\/strong> <strong>is higher than the risk-free rate of return or the opportunity cost<\/strong>, the investment is selected; if not, it is rejected.<\/li>\n\n\n\n<li>In the second case: the <strong>IRR has to be higher than the interest rate of the project\u2019s financing<\/strong>. Here, the internal rate of return would be the maximum interest rate for the financing at which the company or investor would not lose money in the investment.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-the-irr-formula\">What is the IRR formula?<\/h2>\n\n\n\n<p>The IRR is the <strong>discount rate at which the<\/strong> <strong>net present value (NPV) becomes zero<\/strong> or, putting it another way, the rate at which the sum of the present value of outlays becomes equal to the sum of the present value of the forecasted revenues.<\/p>\n\n\n\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69eb81db99d7d&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69eb81db99d7d\" class=\"wp-block-image size-full wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"882\" height=\"273\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/www.sage.com\/en-us\/blog\/wp-content\/uploads\/sites\/2\/2024\/07\/Irr-Image-1.jpg\" alt=\"\" class=\"wp-image-24100\" srcset=\"https:\/\/www.sage.com\/en-us\/blog\/wp-content\/uploads\/sites\/2\/2024\/07\/Irr-Image-1.jpg 882w, https:\/\/www.sage.com\/en-us\/blog\/wp-content\/uploads\/sites\/2\/2024\/07\/Irr-Image-1-768x238.jpg 768w\" sizes=\"auto, (max-width: 882px) 100vw, 882px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Enlarge\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-interpreting-the-irr\">Interpreting the IRR<\/h2>\n\n\n\n<p>If you\u2019re an investor with your own money to potentially invest in a project, the following cases are possible.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h-irr-0\">IRR > 0<\/h4>\n\n\n\n<p>The project is acceptable, given that its yield is higher than the minimum required yield or opportunity cost. <\/p>\n\n\n\n<p>This means that if you invest in this project you would make more money than if you had invested in Government Bonds.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h-irr-lt-0\">IRR &lt; 0<\/h4>\n\n\n\n<p>The project should be rejected. <\/p>\n\n\n\n<p>The reason is that the project\u2019s yield is lower than the minimum required yield. In this situation, it wouldn\u2019t make sense to proceed with the investment given that you\u2019d make more money investing in Government Bonds.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h-irr-0-0\">IRR = 0<\/h4>\n\n\n\n<p>In this case, it makes no difference whether you proceed or not, given that you wouldn\u2019t make or lose money. <\/p>\n\n\n\n<p>When the IRR is zero or close to zero, you have to take into consideration other types of advantages you\u2019d get by investing.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>If you need financing to invest in a project, you have to compare the IRR with the cost of money, which we can call k.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h-irr-k\">IRR &#8211; k<\/h4>\n\n\n\n<p>In this case, the net yield of the project is the difference between the IRR and the cost of the loan (IRR &#8211; k).<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>If IRR > k<\/strong>. The project can be accepted. The yield is higher than the cost of the capital lent to you.<\/li>\n\n\n\n<li><strong>If IRR &lt; k<\/strong>. The project should be rejected. The yield of the project would not cover the cost of the loan.<\/li>\n\n\n\n<li><strong>If IRR = k<\/strong>. Other factors would have to be considered, given that you would neither make nor lose money.<\/li>\n<\/ul>\n\n\n\n<p>If you\u2019re considering which one of two projects to select, in theory it is recommended to choose the one with the higher IRR; however you also need to consider each project\u2019s risk, duration and initial investment.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-an-example-of-calculating-the-internal-rate-of-return\">An example of calculating the Internal Rate of Return<\/h2>\n\n\n\n<p>To carry out a project, a company has to make an initial investment of $10,000, from which two cash inflows are expected: $4,000 in the first year and $9,000 in the second year. You can calculate the internal rate of return in one of two ways:<\/p>\n\n\n\n<p><strong>Using the internal rate of return formula<\/strong>, in which NPV is made equal to zero:<\/p>\n\n\n\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69eb81db9b052&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69eb81db9b052\" class=\"wp-block-image size-full wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"1274\" height=\"232\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/www.sage.com\/en-us\/blog\/wp-content\/uploads\/sites\/2\/2024\/07\/Irr-Image-2.jpg\" alt=\"\" class=\"wp-image-24101\" srcset=\"https:\/\/www.sage.com\/en-us\/blog\/wp-content\/uploads\/sites\/2\/2024\/07\/Irr-Image-2.jpg 1274w, https:\/\/www.sage.com\/en-us\/blog\/wp-content\/uploads\/sites\/2\/2024\/07\/Irr-Image-2-768x140.jpg 768w\" sizes=\"auto, (max-width: 1274px) 100vw, 1274px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Enlarge\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n\n\n\n<p>IRR is the unknown quantity. Solving the equation gives an internal rate of return of 0.17, so the investment\u2019s yield is 17%.<\/p>\n\n\n\n<p>Using a <strong>financial<\/strong> <strong>calculator or a spreadsheet such as Excel<\/strong>. <\/p>\n\n\n\n<p>In Excel, the calculation is straightforward: first you need a column or row containing the flow of profits generated by the investment, with the initial flow given a negative sign as it\u2019s the initial capital outlay; next, insert the IRR financial function in another cell \u2014 for the formula, select the range of capital flows for the project, including the initial one.<\/p>\n\n\n\n<p>If you need to assess various investment projects, you have to use the <strong>Internal Rate of Return to select the best option<\/strong> and avoid choosing a project that would lose you money.<\/p>\n\n\n<div class=\"single-cta\">\n\t<div class=\"single-cta__positioner\">\n\t\t<div class=\"single-cta__wrapper has-dark-background-color\">\n\t\t\t<div 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48em) 33vw, 100vw\" \/>\t\t\t<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>To know the future profitability of your projects when investing in them, it is necessary to know the internal rate of return (IRR).<\/p>\n","protected":false},"author":1774,"featured_media":24104,"menu_order":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_sage_video":false,"post_featured_image_hide":false,"footnotes":""},"categories":[43],"tags":[110],"business_type":[40],"lilypad":[],"context":[],"industry":[],"persona":[98,96,97],"imagine_tag":[233,230],"coauthors":[509],"class_list":["post-24098","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-money-matters","tag-accounting-101","business_type-small-business"],"sage_meta":{"region":"en-us","author_name":"Yassir Malik","featured_image":"https:\/\/www.sage.com\/en-us\/blog\/wp-content\/uploads\/sites\/2\/2024\/07\/GettyImages-1266123239-1440x810-1.jpg","imagine_tags":{"233":"Medium Businesses","230":"Small business"}},"distributor_meta":false,"distributor_terms":false,"distributor_media":false,"distributor_original_site_name":"Sage Advice US","distributor_original_site_url":"https:\/\/www.sage.com\/en-us\/blog","push-errors":false,"_links":{"self":[{"href":"https:\/\/www.sage.com\/en-us\/blog\/api\/wp\/v2\/posts\/24098","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sage.com\/en-us\/blog\/api\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sage.com\/en-us\/blog\/api\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sage.com\/en-us\/blog\/api\/wp\/v2\/users\/1774"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sage.com\/en-us\/blog\/api\/wp\/v2\/comments?post=24098"}],"version-history":[{"count":0,"href":"https:\/\/www.sage.com\/en-us\/blog\/api\/wp\/v2\/posts\/24098\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.sage.com\/en-us\/blog\/api\/wp\/v2\/media\/24104"}],"wp:attachment":[{"href":"https:\/\/www.sage.com\/en-us\/blog\/api\/wp\/v2\/media?parent=24098"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sage.com\/en-us\/blog\/api\/wp\/v2\/categories?post=24098"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sage.com\/en-us\/blog\/api\/wp\/v2\/tags?post=24098"},{"taxonomy":"business_type","embeddable":true,"href":"https:\/\/www.sage.com\/en-us\/blog\/api\/wp\/v2\/business_type?post=24098"},{"taxonomy":"lilypad","embeddable":true,"href":"https:\/\/www.sage.com\/en-us\/blog\/api\/wp\/v2\/lilypad?post=24098"},{"taxonomy":"context","embeddable":true,"href":"https:\/\/www.sage.com\/en-us\/blog\/api\/wp\/v2\/context?post=24098"},{"taxonomy":"industry","embeddable":true,"href":"https:\/\/www.sage.com\/en-us\/blog\/api\/wp\/v2\/industry?post=24098"},{"taxonomy":"persona","embeddable":true,"href":"https:\/\/www.sage.com\/en-us\/blog\/api\/wp\/v2\/persona?post=24098"},{"taxonomy":"imagine_tag","embeddable":true,"href":"https:\/\/www.sage.com\/en-us\/blog\/api\/wp\/v2\/imagine_tag?post=24098"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.sage.com\/en-us\/blog\/api\/wp\/v2\/coauthors?post=24098"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}