A company is considering replacing its air conditioner. Management has narrowed the choices to alternatives that offer comparable performance and considerable savings over their present system. The effective annual interest rate is 8%. What is the benefit-cost ratio of the better alternative?

The benefit cost ratio of alternative 2 is 1.34

Explanation:

Initial cost $7000 $9000

Annual savings $1500 $1900

Salvage value $500 - $1250

Life 15 years 15 years

First, we calculate the present worth of Alternative 1 and 2, taking salvage value as a decrease in cost

.

For alternative 1

B1 = Benefits = ($1500) (P/A, 8%, 15) = ($1500) (8.5595) = $12,839

C1 = Cost = $7,000 - ($500) (P/F, 8%,15) = $7,000 - ($500) (0.3152) = $6842

Ratio of Benefit to Cost = Benefit/Cost = $12,839/$6842 = 1.88

For alternative 2

B2 = Benefits = ($1900) (P/A, 8%,15) = ($1900) (8.5595) = $16,263

C2 = Cost = $9000 + ($1250) (P/F, 8%,15) = $9000 + ($1250) (0.3152) = $9394

Ratio of Benefit to Cost = Benefit/Cost = $16,263/$9394 = 1.73

Both alternatives can't be compared directly unless we perform incremental analysis on both.

Incremental Analysis =. (B2 - B1) / (C2 - C1) = ($16,263 - $12,839) / ($9394 - $6842) = 1.34

Incremental Analysis is greater than 1, so alternative 2 is better than alternative 1