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: 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
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