A municipal pumping station rated at has a first cost of USD 480{,}000, annual maintenance of USD 18{,}000, and a major overhaul costing USD 60{,}000 at the end of every eighth year of service. The station is to be maintained in service indefinitely. At an interest rate of 6% per year, the capitalized cost is most nearly:
- (A)USD 780,000
- (B)USD 881,000
- (C)USD 905,000
- (D)USD 941,000
Show worked solution
Answer: (B)
Converting the eight-year overhaul to an annual equivalent of USD 6{,}062 lifts the perpetual annual charge to USD 24{,}062, which capitalized at 6% and added to the first cost gives roughly USD 881{,}000.
Capitalized cost is the present worth of a perpetual annual disbursement, so every recurring outlay must first be expressed as an equivalent uniform annual amount.
The overhaul repeats on an eight-year cycle, so a sinking fund accumulated over each cycle carries it, not a capital recovery charge.
Total perpetual annual cost divided by the interest rate is the fund that must stand behind the station beyond its first cost.
FE Reference Handbook — Engineering Economics: Capitalized Costs; Sinking Fund Factor (A/F)
Why the other choices appear
- (A)Omits the overhaul entirely and capitalizes only maintenance: 480,000 + 18,000/0.06 = 780,000.
- (C)Prorates the overhaul arithmetically as 60,000/8 = 7,500 per year instead of using the sinking-fund factor: 480,000 + 25,500/0.06 = 905,000.
- (D)Uses (A/P, 6%, 8) = 0.16104 in place of (A/F, 6%, 8), giving 9,662 per year and 480,000 + 27,662/0.06 = 941,000.