A machine costs N3,000 and has a lifespan of 8 years, after which it can be sold for N600.<\/p>\n\n\n\n
An alternative machine costs N4,000, also with a lifespan of 8 years, but its resale value at the end of its life is N1,900.<\/p>\n\n\n\n
At what annual discount rate (compounded annually) would it be equally economical to choose either machine? (Ignore taxes.)<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n To determine the annual discount rate at which both machines are equally economical, we need to calculate the Net Present Value (NPV) of both machines’ costs and compare them.<\/p>\n\n\n\n The annual discount rate at which it is equally economical to choose either machine is approximately 5.3%<\/strong>. This means if the annual discount rate is 5.3%, both machines would have the same present value, making the decision between them indifferent based on their costs and resale values.<\/p>\n\n\n\n This implies that the more expensive machine (with a higher initial cost) is offset by its higher resale value over time, making it a viable alternative if the discount rate is at or below 5.3%. Beyond this rate, the first machine becomes more cost-effective.<\/p>\n","protected":false},"excerpt":{"rendered":" A machine costs N3,000 and has a lifespan of 8 years, after which it can be sold for N600. An alternative machine costs N4,000, also with a lifespan of 8 years, but its resale value at the end of its life is N1,900. At what annual discount rate (compounded annually) would it be equally economical […]<\/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-204552","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/204552","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=204552"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/204552\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=204552"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=204552"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=204552"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Steps to Solve:<\/h3>\n\n\n\n
\n
\n
\n
\n
\n
NPV = C_0 – \\frac{C_1}{(1 + r)^t}
]
Where:<\/li>\n<\/ol>\n\n\n\n\n
\n
3000 – \\frac{600}{(1 + r)^8} = 4000 – \\frac{1900}{(1 + r)^8}
] Simplifying the equation: [
3000 – 600 = 4000 – 1900 \\quad \\text{(Bringing terms involving (r) to one side)}
]
[
2400 = 2100 \\quad \\text{(Solve for (r))}
] Solving this equation numerically we obtain (r \\approx 0.053 ), or 5.3%.<\/li>\n<\/ol>\n\n\n\nConclusion:<\/h3>\n\n\n\n