If the cost of building a new road is $2,500,000 per linear-mile, and the expect

Question

If the cost of building a new road is $2,500,000 per linear-mile, and the expected annual maintenance cost is $350,000 per linear-mile for 20 years of service-life. At the end of its service-life, the road will be demolish at a cost of $750,000 per linear-mile; and the salvage value is expected to be $50,000 per linear-mile. Assuming a discount rate of 4.00 percent, determine the present value of the life-cycle cost of a proposed five-mile long roadway. Clearly show all calculations to receive credit.

Explanation / Answer

PV factor at 4% Present value Cost of building new five mile long road $12,500,000 1 $ 12,500,000 Expected annual maintenance cost $ 1,750,000 13.5903 $ 23,783,025 Demolition cost $ 3,750,000 0.4564 $ 1,711,500 Salvage value $ 250,000 0.4564 $ (114,100) Present value of life-cycle cost $ 37,880,425

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