Question

16. Use the Benefit-cost ratio analysis to determine the best alternative. Each alternative has a 6-year useful life. Assume 15% MARR. Show all work.

                                                A                     B                     C

First cost                                 $560                $340                $120

Annual Benefit                       $140                $100                $40

Salvage                                    $40                  $0                    $0

• you should compare the alternatives at the end

Answer 1

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Answer

B-C ratio is calculated by dividng present value of all the benefits by the present value of all the costs .
PV of benefits can be calculated by using P/A factor for 6 year
The salvage value will be discounted for 6 years

Project A  
PV of costs = 560 $
PV of benefits = 140 * P/A(15%,6) + 40/(1.15)⁶
= 140*3.7845 + 40/2.3130
=529.83 + 17.29
=547.12 $

B/C ratio = 547.12 /560
= .977

Project B

PV of costs = 340 $
PV of benefits = 100 * P/A(15%,6)
= 100 * 3.7845
=378.45

B/C ratio = 378.45/340
= 1.113

Project C

PV of costs = 120$
PV of benefits = 40 * P/A(15%,6)
= 40* 3.7845
=151.38

B/C ratio = 151.38 /120
= 1.2615


Project C has the highest B/C ratio . Project C should be selected . Project B might be selected if the sufficient amount is left after Project C to be invested. Project A is inviable as the ratio is less than 1.