{"id":93,"date":"2019-09-05T00:02:34","date_gmt":"2019-09-05T00:02:34","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=93"},"modified":"2026-02-26T09:11:43","modified_gmt":"2026-02-26T09:11:43","slug":"net-present-value-investment-project","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/net-present-value-investment-project\/","title":{"rendered":"Net Present Value of an Investment Project"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Discounted Cash Flow Applications (2019 Level I CFA\u00ae Exam \u2013 Reading 7)\",\n  \"description\": \"Dive into the essentials of discounted cash flow applications! This session covers capital budgeting, NPV and IRR calculations, holding period returns, money market securities, and bond equivalent yields. Learn practical tools and techniques for evaluating investments and financial decisions. Perfect for mastering quantitative finance concepts!\",\n  \"uploadDate\": \"2019-06-06T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/lYpi92G13U4\/default.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/lYpi92G13U4\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/lYpi92G13U4\",\n  \"duration\": \"PT27M31S\"\n}\n<\/script>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Calculate the NPV of the project using a discount rate of 20% per year.\",\n    \"text\": \"A project generates the following cash flows:\\n\\nBeginning of years:\\n1: -$100,000 (contractors\u2019 fees)\\n2: -$200,000 (contractors\u2019 fees)\\n3: -$200,000 (contractors\u2019 fees)\\n\\nEnd of Year 3: +$1,000,000 (sales)\\n\\nCalculate the NPV of the project using a risk discount rate of 20% per year.\\n\\nA. $500,000\\nB. $173,148\\nC. $166,667\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The NPV is approximately $173,148 (Choice B).\\n\\nCash flows occur at the beginning of years 1, 2, and 3, and at the end of year 3:\\n- t=0: -100,000\\n- t=1: -200,000 \/ (1.2)^1 = -166,666.67\\n- t=2: -200,000 \/ (1.2)^2 = -138,888.89\\n- t=3: +1,000,000 \/ (1.2)^3 = +578,703.70\\n\\nNPV = -100,000 - 166,666.67 - 138,888.89 + 578,703.70 = 173,148.14 (\u2248 $173,148).\"\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?rel=0&#038;modestbranding=1&#038;playsinline=1&#038;vq=hd1080\"\n  title=\"YouTube video player\"\n  frameborder=\"0\"\n  allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\"\n  allowfullscreen>\n<\/iframe>\n\n\n\n<p>The Net present value (NPV) of a project refers to the present value of all cash inflows minus the present value of all cash outflows, evaluated at a given discount rate. The difference between the two represents the income generated by a project. A project whose cash inflows outweigh its cash outflows is generally considered financially viable, as it generates a positive return. However, there are projects in which the present value of cash outflows exceeds the present value of cash inflows. Such a project is not financially viable. To help you understand the NPV concept, consider the following example:<\/p>\n\n\n\n<p>Suppose the local government in a given location decides to build a bridge that will connect two cities, A and B. At the start of this project, the government will have to spend a considerable amount of money to acquire necessary construction material and also pay the constructor. Assume a risk discount rate of 10% per annum. After construction, more, but smaller amounts of money, will cater for maintenance costs. All these expenses constitute the cash outflows of the project. The project is then expected to generate a continuous stream of income in the form of toll fees paid by the users of the bridge. To simplify matters, let\u2019s assume that the project will generate income for ten years. Fees paid will constitute the project\u2019s cash inflows. Therefore, the government should only proceed with the project if the NPV is positive.<\/p>\n\n\n\n<div style=\"margin:18px 0;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     rel=\"noopener noreferrer\"\n     style=\"\n        display:block;\n        text-align:center;\n        padding:14px 18px;\n        border:2px solid #2F5BFF;\n        border-radius:18px;\n        color:#2F5BFF;\n        font-weight:600;\n        font-size:16px;\n        text-decoration:none;\n        background-color:#f9faff;\n     \">\n     Practice CFA questions on net present value analysis.\n  <\/a>\n<\/div>\n\n\n<h2><strong>Net Present Value Formula<\/strong><\/h2>\n<p>$$ NPV=\\sum { C_{ t }(1+r)^{ t } } \\text { for all } t\\ge 0 $$<\/p>\n<p>Where: C<sub>t <\/sub>is the cash flow at time t<\/p>\n<p>And r is the risk discount rate<\/p>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>A project generates the following cash flows;<\/p>\n<p>Beginning of years:<\/p>\n<p>1 &#8211; ($100,000) (contractors\u2019 fees)<\/p>\n<p>2 &#8211; ($200,000) (contractors\u2019 fees)<\/p>\n<p>3 &#8211;\u00a0 ($200,000) (contractors\u2019 fees)<\/p>\n<p>End of Year 3 : $1,000,000 (sales)<\/p>\n<p>Calculate the NPV of the project using a risk discount rate of 20% per year.<\/p>\n<p>A. $500,000<\/p>\n<p>B. $173,148<\/p>\n<p>C. $166,667<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is B.<\/p>\n<p>r = 0.2<\/p>\n<p>$$ \\begin{align*}<br \/>\\text{NPV} &amp; = &#8211; 100,000 &#8211; 200,000(1 + 0.2)^{-1} &#8211; 200,000(1 + 0.2) ^{-2} + 1000,000(1 + 0.2)^{-3} \\\\<br \/>&amp; = &#8211; 100,000 &#8211; 166,667 &#8211; 138,889 + 578,704 \\\\<br \/>&amp; = $173,148 \\\\<br \/>\\end{align*} $$<\/p>\n<p>Note that we do not discount cash flows occurring at the beginning of a project. Hence, the discount should be zero at<em> t<\/em> = 0.<\/p>\n<\/blockquote>\n<h2><strong>Advantages of the NPV method<\/strong><\/h2>\n<p>&#8211; NPV tells us whether a project will increase the value of a company, and by how much in terms of dollars.<\/p>\n<p>&#8211; The method takes into account all the cash flows associated with a particular project.<\/p>\n<p>&#8211; It considers the <a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/time-value-money-explained-example\/\">time value of money<\/a>.<\/p>\n<p>&#8211; Net present value method offers a convenient tool during appraisal of any given project.<\/p>\n<p><em>Reading 7 LOS 7a:<\/em><\/p>\n<p><em>Calculate and interpret the net present value (NPV) and the internal rate of<\/em><\/p>\n<p>return (IRR) of an investment<\/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>\n\n\n<div style=\"text-align:center; margin:40px 0 20px;\">\n\n  <div style=\"text-align:center; margin:40px 0 10px 0;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener\"\n     style=\"display:inline-block; padding:14px 36px; background:#1a73e8; color:#ffffff; border-radius:999px; font-weight:700; font-size:16px; text-decoration:none;\">\n    Start Free Trial \u2192\n  <\/a>\n<\/div>\n\n  <p style=\"\n        margin-top:18px;\n        font-size:16px;\n        line-height:1.6;\n        max-width:700px;\n        margin-left:auto;\n        margin-right:auto;\n        color:#333333;\n     \">\n     Strengthen your CFA Level I Quantitative Methods preparation with exam-style questions, QBank drills, and full mock exams designed to help you evaluate investment projects using net present value and cash flow analysis under exam conditions.\n  <\/p>\n\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>The Net present value (NPV) of a project refers to the present value of all cash inflows minus the present value of all cash outflows, evaluated at a given discount rate. The difference between the two represents the income generated&#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-93","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>Net Present Value (NPV) Explained | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Learn how to calculate net present value (NPV) by discounting cash inflows and outflows using a risk-adjusted rate. 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