Question

2) [Problem 9-50) Consider four mutually exclusive alternatives: A B C D Cost $65 $55 $25 $80 Uniform annual benefit 16.3 15.1 2 5. 2 1.3 AL Each alternative has a 6-yeatuseful life and no salvage value. The MARR is 9%. Which alternative should be selected, based on, ? a) The payback period b) Future worth analysis c) Benefit-cost ratio analysis

Answer 1

2.

A.

Payback period for alternative A = 65/16.3 = 3.99 years

Payback period for alternative B = 55/15.1 = 3.64 years

Payback period for alternative C = 25/5.2 = 4.81 years

Payback period for alternative D = 80/21.3 = 3.76 years

The alternative B will be selected, because it has smallest payback period that is 3.64 years.

B .

Future worth of alternative A = 16.3*(1.09^6 - 1)/.09 - 65*1.09^6 = $13.62

Future worth of alternative B = 15.1*(1.09^6 - 1)/.09 - 55*1.09^6 = $21.36

Future worth of alternative C = 5.2*(1.09^6 - 1)/.09 - 25*1.09^6 = -$2.81

Future worth of alternative D = 21.3*(1.09^6 - 1)/.09 - 80*1.09^6 = $26.08

Alternative D will be selected because, it has higher future worth that is $26.08.

C.

Benefit cost ratio of alternative A = (16.3*(1-1/1.09^6)/.09)/65 = 1.124

Benefit cost ratio of alternative B = (15.1*(1-1/1.09^6)/.09)/55 = 1.232

Benefit cost ratio of alternative C = (5.2*(1-1/1.09^6)/.09)/25 = .933

Benefit cost ratio of alternative D = (21.3*(1-1/1.09^6)/.09)/80 = 1.194

The alternative B will be selected, because it has highest benefit cost ratio of 1.232.