Question

A nonprofit government corporation is considering two alternatives for generating power. The useful life of both alternatives is years. Using an interest rate of ​%, determine which alternative​ (if either) should be selected according to the conventional​ B-C-ratio method.

Answer 1

Note The full question is attached as picture below

a. B-C ratio = Equivalent annual worth of Benefits / Equivalent annual worth of costs

Alternative A

B-C ratio = Equivalent annual worth of Benefits for alternative A / Equivalent annual worth of costs for alternative A

B-C ratio = (Power Sales + Annual benefits from new industry) / ((Capital cost * Annuity factor(5%,50 years)) + Operating and maintenance costs costs)

B-C ratio = ($1,000,000 + $500,000) / (($20,000,000*(0.05 / (1 - 1.05^(-50))) + $200,000)

B-C ratio = ($1,500,000 / ($1,095,534.71 + $200,000))

B-C ratio = $1,500,000 / $1,295,534.71

B-C ratio = 1.1578

B-C ratio = 1.16

Alternative B

B-C ratio = Equivalent annual worth of Benefits for alternative B / Equivalent annual worth of costs for alternative B

B-C ratio = (Power Sales + Sum of all Annual benefits) / ((Capital cost*Annuity factor (5%,50 years)) + Operating and maintenance costs costs)

B-C ratio = ($800,000 + $600,000 + $400,000 + $200,000 + $100,000) / ($30000000 *(0.05/(1-1.05^(-50))) + $100,000)

B-C ratio = $2,100,000 / ($1,643,302 + $100,000)

B-C ratio = 1.2046

B-C ratio = 1.20

Conclusion: Alternative B should be selected because it has higher B/C ratio.

b Incremental B-C ratio for final pair = (Equivalent Annual Benefits of B - Equivalent Annual Benefits of A) / (Equivalent annual costs of B - Equivalent annual costs of A)

Incremental B-C ratio for final pair = ($2,100,000 - $1,500,000) / ($1,743,302 - $1,295,534.71)

Incremental B-C ratio for final pair = $600,000 / $447,767.29

Incremental B-C ratio for final pair = 1.339982

Incremental B-C ratio for final pair = 1.34