Question
In: Economics
Consider 3 mutually exclusive alternatives, each with a 10-year useful life. If the Minimum Attractive Rate...
Consider 3 mutually exclusive alternatives, each with a 10-year useful life. If the Minimum Attractive Rate of Return (MARR) is 14.5%, which alternative should be selected? Solve the problem using benefit-cost ratio analysis.
Alternative
| Choice #1 | Choice #2 | Choice #3 | |
| Cost | 810 | 305 | 145 |
| Uniform Annual Benefit | 131 | 62 | 36 |
Solutions
Expert Solution
For incremental B/C analysis we have to arrange alternatives in increasing order of initial cost
Choice 3 < choice 2 < choice 1
incremental B/C analysis of (choice 3 - Do nothing)
incremental cost (choice 3 - Do nothing) = 145 - 0 = 145
incremental annual benefit (choice 3 - Do nothing) = 36 - 0 = 36
incremental B/C = 36 / 145 * (A/P,14.5%,10)
= 36 / [145 * 0.145 * ((1 + 0.145)^10)/((1 + 0.145)^10-1)]
= 36 / [145 * 0.145 * ((1.145)^10)/((1.145)^10-1)]
= 36 / 145 * 0.195469
= 1.27
As incremental B/C of (choice 3 - Do nothing) is more than 1, choice 3 is selected
incremental B/C analysis of (choice 2 - choice 3)
incremental cost (choice 2 - choice 3) = 305 - 145 = 160
incremental annual benefit (choice 2 - choice 3) = 62 - 36 = 26
incremental B/C = 26 / 160 * (A/P,14.5%,10)
= 26 / 160 * 0.195469
= 0.83
As incremental B/C of (choice 2 - choice 3) is less than 1, choice 3 is selected
incremental B/C analysis of (choice 1 - choice 3)
incremental cost (choice 1 - choice 3) = 810 - 145 = 665
incremental annual benefit (choice 1 - choice 3) = 131 - 36 = 95
incremental B/C = 95 / 665 * (A/P,14.5%,10)
= 95 / 665 * 0.195469
= 0.73
As incremental B/C of (choice 1 - choice 3) is less than 1, choice 3 is selected
Choice 3 should be selected as per incremental B/C analysis
Rahul Sunny answered 1 year agoRelated Solutions
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