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


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