A flood control dam with 100-year life has an intital cost of $25 million. The g

Question

A flood control dam with 100-year life has an intital cost of $25 million. The gates in the dam must be replaced every ten years, at a cost of $7 million. If the interest rate is 6% per year, compounded annually, a) what is the capitalized equivalent of the annual cost of the dam? b) what is the total present worth of the dam? A flood control dam with 100-year life has an intital cost of $25 million. The gates in the dam must be replaced every ten years, at a cost of $7 million. If the interest rate is 6% per year, compounded annually, a) what is the capitalized equivalent of the annual cost of the dam? b) what is the total present worth of the dam?

Explanation / Answer

Effective interest rate per 10 years, i = (1.06^10) - 1 = 0.79085

n = 10

annual cost = 25*(A/P, 0.79085, 10) + 7 million dollars

= 25*0.7931 + 7 = $26.8275 millions

b) NPV = -25-7*(P/A, 0.79085, 10) = -25 - 7*1.2607 = - $33.825 millions

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