Question

A city is considering building a bridge with an initial cost of $85,000 and expected useful life of 30 years. Annual maintenance and benefits are $10,000 and $13,000, respectively. The benefit-cost ratio using a 4% interest rate is most nearly: a) 0.87, b)1.01, c)1.15 or d)1.30

Answer 1

Answer: a) 0.87

Explanation

Initial cost = $ 85000

Expected useful life = 30 years

Annual maintenance cost = $ 10000

Annual benifits = $ 13000

Interest rate = 4 %

Total present worth of cost = 85000 + 10000 ( P/A, 4 %,30)

= 85000 + 10000 (17.2920) = 85000 + 172920 = $ 257920

Total present worth of benifits = 13000 ( P/A , 4 % , 30) = 13000 * 17.2920 = $ 224796

Benifit - Cost ratio = Present worth of total benifits / Present worth to total cost

= $ 224796 / $ 257920 = 0.8715 or 0.87