{"id":219485,"date":"2025-05-26T08:29:01","date_gmt":"2025-05-26T08:29:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=219485"},"modified":"2025-05-26T08:29:03","modified_gmt":"2025-05-26T08:29:03","slug":"four-mutually-exclusive-alternatives-are-being-evaluated-and-their-costs-and-revenues-are-itemized-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/26\/four-mutually-exclusive-alternatives-are-being-evaluated-and-their-costs-and-revenues-are-itemized-below\/","title":{"rendered":"Four mutually exclusive alternatives are being evaluated, and their costs and revenues are itemized below."},"content":{"rendered":"\n<p>Four mutually exclusive alternatives are being evaluated, and their costs and revenues are itemized below.<\/p>\n\n\n\n<p>Mutually Exclusive Alternatives II III IV<br>Capital Investment 100,000 152,000 184,000 220,000<br>Annual revenues less expenses 15,200 31,900 35,900 41,500<br>Market Value 10,000 0 15,000 20,000<br>Useful life (years) 12 12 12 12<br>a. If the MARR is 15% per year and the analysis period is 12 years, use the PW method to determine which alternatives are economically acceptable and which one should be selected.<\/p>\n\n\n\n<p>b. If the total capital investment budget available is $200,000, which alternative should be selected?<\/p>\n\n\n\n<p>c. If the total capital investment budget available is $150,000, which alternative should be selected?<\/p>\n\n\n\n<p>d. If the total capital investment budget available is $200,000, which alternative should be selected (if the alternatives are independent)?<\/p>\n\n\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To analyze these four mutually exclusive alternatives using the <strong>Present Worth (PW)<\/strong> method at a <strong>Minimum Attractive Rate of Return (MARR) of 15%<\/strong> over a <strong>12-year<\/strong> period, we calculate the present worth of each alternative using the formula: PW=\u2212Capital&nbsp;Investment+(Annual&nbsp;Net&nbsp;Cash&nbsp;Flow\u00d7P\/A,15%,12)+Market&nbsp;Value\u00d7(P\/F,15%,12)PW = &#8211; \\text{Capital Investment} + (\\text{Annual Net Cash Flow} \\times P\/A, 15\\%, 12) + \\text{Market Value} \\times (P\/F, 15\\%, 12)<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P\/AP\/A is the present worth factor for an annuity<\/li>\n\n\n\n<li>P\/FP\/F is the present worth factor for a single future amount<\/li>\n\n\n\n<li>(P\/A,15%,12)=5.091(P\/A, 15\\%, 12) = 5.091<\/li>\n\n\n\n<li>(P\/F,15%,12)=0.1827(P\/F, 15\\%, 12) = 0.1827<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>a. PW Calculations (Mutually Exclusive Alternatives)<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Alt<\/th><th>Investment<\/th><th>Annual Net<\/th><th>Salvage<\/th><th>PW Calculation<\/th><th>PW Value ($)<\/th><\/tr><\/thead><tbody><tr><td>I<\/td><td>100,000<\/td><td>15,200<\/td><td>10,000<\/td><td>-100,000 + (15,200 \u00d7 5.091) + (10,000 \u00d7 0.1827)<\/td><td>-100,000 + 77,383.2 + 1,827 = <strong>-20,789.8<\/strong><\/td><\/tr><tr><td>II<\/td><td>152,000<\/td><td>31,900<\/td><td>0<\/td><td>-152,000 + (31,900 \u00d7 5.091)<\/td><td>-152,000 + 162,412.9 = <strong>10,412.9<\/strong><\/td><\/tr><tr><td>III<\/td><td>184,000<\/td><td>35,900<\/td><td>15,000<\/td><td>-184,000 + (35,900 \u00d7 5.091) + (15,000 \u00d7 0.1827)<\/td><td>-184,000 + 182,766.9 + 2,740.5 = <strong>1,507.4<\/strong><\/td><\/tr><tr><td>IV<\/td><td>220,000<\/td><td>41,500<\/td><td>20,000<\/td><td>-220,000 + (41,500 \u00d7 5.091) + (20,000 \u00d7 0.1827)<\/td><td>-220,000 + 211,276.5 + 3,654 = <strong>-5,069.5<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Answer for (a):<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Alternatives <strong>II<\/strong> and <strong>III<\/strong> have <strong>positive PW<\/strong>, so they are economically acceptable.<\/li>\n\n\n\n<li>Since <strong>Alternative II<\/strong> has the <strong>highest PW ($10,412.9)<\/strong>, it should be selected.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>b. Budget = $200,000 (Mutually Exclusive)<\/strong><\/h3>\n\n\n\n<p>Still choose the one with the highest PW under budget:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Select Alternative II<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>c. Budget = $150,000 (Mutually Exclusive)<\/strong><\/h3>\n\n\n\n<p>Only <strong>Alternative I<\/strong> is within budget, but PW = <strong>\u2013$20,789.8<\/strong> \u2192 <strong>not acceptable<\/strong>.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>None of the alternatives should be selected.<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>d. Budget = $200,000 (Independent Alternatives)<\/strong><\/h3>\n\n\n\n<p>Select combination of alternatives with <strong>maximum total PW<\/strong> under budget.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Alternative II: Investment = $152,000, PW = $10,412.9<\/li>\n\n\n\n<li>Remaining budget = $48,000 \u2192 can&#8217;t afford any other alternative.<\/li>\n\n\n\n<li>Alternative III: Investment = $184,000, PW = $1,507.4<\/li>\n\n\n\n<li>Remaining budget = $16,000 \u2192 still can&#8217;t afford any other.<\/li>\n<\/ul>\n\n\n\n<p><strong>Better to choose Alternative II alone.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation<\/strong><\/h3>\n\n\n\n<p>When evaluating investment alternatives, the Present Worth (PW) method is a reliable tool for comparing mutually exclusive and independent projects based on time value of money. In this case, four alternatives are analyzed over a 12-year period with a 15% Minimum Attractive Rate of Return (MARR).<\/p>\n\n\n\n<p>For mutually exclusive alternatives, only one can be selected. We calculate the PW for each alternative by discounting the annual net cash flows and salvage value, then subtracting the initial investment. Alternatives II and III yield positive PW values, while Alternatives I and IV result in negative PW. Among them, <strong>Alternative II has the highest PW of $10,412.90<\/strong> and is therefore the most economically desirable.<\/p>\n\n\n\n<p>Under a $200,000 budget for mutually exclusive alternatives (part b), <strong>Alternative II<\/strong> remains the optimal choice because it fits within budget and offers the highest economic return. However, under a tighter $150,000 budget (part c), only Alternative I fits the constraint\u2014but its negative PW means it\u2019s not economically viable, so <strong>no investment should be made<\/strong>.<\/p>\n\n\n\n<p>In part (d), assuming the alternatives are <strong>independent<\/strong> (i.e., more than one can be chosen if funds allow), the goal shifts to maximizing total PW within budget. Evaluating combinations under the $200,000 limit shows that <strong>Alternative II alone provides the best return<\/strong>, as combining it with any other would exceed the budget. Alternative III, while feasible, offers a significantly lower PW than Alternative II.<\/p>\n\n\n\n<p>Thus, the analysis concludes that <strong>Alternative II is the best choice under both mutually exclusive and independent investment scenarios<\/strong> with a $200,000 budget.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/05\/learnexams-banner10-9.jpeg\" alt=\"\" class=\"wp-image-219486\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Four mutually exclusive alternatives are being evaluated, and their costs and revenues are itemized below. Mutually Exclusive Alternatives II III IVCapital Investment 100,000 152,000 184,000 220,000Annual revenues less expenses 15,200 31,900 35,900 41,500Market Value 10,000 0 15,000 20,000Useful life (years) 12 12 12 12a. If the MARR is 15% per year and the analysis period [&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-219485","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/219485","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=219485"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/219485\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=219485"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=219485"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=219485"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}