{"id":38200,"date":"2025-06-26T08:37:51","date_gmt":"2025-06-26T08:37:51","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=38200"},"modified":"2025-06-26T08:37:53","modified_gmt":"2025-06-26T08:37:53","slug":"a-company-is-considering-buying-a-new-piece-of-machinery-that-costs-20000-and-has-a-salvage-value-of-8000-at-the-end-of-its-5-year-useful-life","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-company-is-considering-buying-a-new-piece-of-machinery-that-costs-20000-and-has-a-salvage-value-of-8000-at-the-end-of-its-5-year-useful-life\/","title":{"rendered":"A company is considering buying a new piece of machinery that costs $20,000 and has a salvage value of $8,000 at the end of its 5-year useful life"},"content":{"rendered":"\n<p>A company is considering buying a new piece of machinery that costs $20,000 and has a salvage value of $8,000 at the end of its 5-year useful life. The machinery nets $5,000 per year in annual revenues. MARR = 8%. The internal rate of return (IRR) on this investment is between A. 16% &#8211; 17% B. 2% &#8211; 3% C. 6% &#8211; 7% D. 4% &#8211; 5% E. 11% &#8211; 12%<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer: A. 16% &#8211; 17%<\/strong><\/p>\n\n\n\n<p>To determine the internal rate of return (IRR), we need to solve for the interest rate that makes the net present value (NPV) of the cash flows equal to zero.<\/p>\n\n\n\n<p><strong>Given:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Initial investment = $20,000 (cash outflow at time 0)<\/li>\n\n\n\n<li>Annual net revenue = $5,000 for 5 years (cash inflow)<\/li>\n\n\n\n<li>Salvage value = $8,000 at the end of year 5 (additional cash inflow)<\/li>\n\n\n\n<li>MARR = 8% (not used for IRR, but for comparison)<\/li>\n\n\n\n<li>IRR is the rate rr that satisfies: 0=\u221220,000+\u2211t=155,000(1+r)t+8,000(1+r)50 = -20,000 + \\sum_{t=1}^{5} \\frac{5,000}{(1 + r)^t} + \\frac{8,000}{(1 + r)^5}<\/li>\n<\/ul>\n\n\n\n<p>This is a trial-and-error or numerical method problem. We test several rates:<\/p>\n\n\n\n<p><strong>Try 16%:<\/strong> NPV=\u221220,000+[5,000\u00d7(P\/A,16%,5)]+8,000(1.16)5NPV = -20,000 + \\left[5,000 \\times (P\/A,16\\%,5)\\right] + \\frac{8,000}{(1.16)^5} (P\/A,16%,5)\u22483.2743;(P\/F,16%,5)\u22480.4761(P\/A,16\\%,5) \u2248 3.2743; \\quad (P\/F,16\\%,5) \u2248 0.4761 NPV\u2248\u221220,000+(5,000\u00d73.2743)+(8,000\u00d70.4761)=\u221220,000+16,371.5+3,808.8=+180.3NPV \u2248 -20,000 + (5,000 \u00d7 3.2743) + (8,000 \u00d7 0.4761) = -20,000 + 16,371.5 + 3,808.8 = +180.3<\/p>\n\n\n\n<p><strong>Try 17%:<\/strong> (P\/A,17%,5)\u22483.1993;(P\/F,17%,5)\u22480.4406(P\/A,17\\%,5) \u2248 3.1993; \\quad (P\/F,17\\%,5) \u2248 0.4406 NPV\u2248\u221220,000+(5,000\u00d73.1993)+(8,000\u00d70.4406)=\u221220,000+15,996.5+3,524.8=\u2212478.7NPV \u2248 -20,000 + (5,000 \u00d7 3.1993) + (8,000 \u00d7 0.4406) = -20,000 + 15,996.5 + 3,524.8 = -478.7<\/p>\n\n\n\n<p>At 16%, NPV is positive. At 17%, NPV is negative. Therefore, IRR lies between 16% and 17%.<\/p>\n\n\n\n<p>The internal rate of return helps a company determine the rate at which their investment breaks even in present value terms. Because the IRR is higher than the company\u2019s minimum attractive rate of return (MARR of 8%), this investment is financially viable. Choosing projects where IRR exceeds MARR maximizes value and profitability.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A company is considering buying a new piece of machinery that costs $20,000 and has a salvage value of $8,000 at the end of its 5-year useful life. The machinery nets $5,000 per year in annual revenues. MARR = 8%. The internal rate of return (IRR) on this investment is between A. 16% &#8211; 17% [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-38200","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38200","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=38200"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38200\/revisions"}],"predecessor-version":[{"id":38202,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38200\/revisions\/38202"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=38200"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=38200"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=38200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}