Two 750 kVA transformers are compared over a 15-year study period at an interest rate of 8% per year. Unit A costs USD 60,000 installed, requires USD 4,500 per year for operation and maintenance, and has a salvage value of USD 8,000 at the end of year 15. Unit B costs USD 45,000 installed, requires USD 6,800 per year, and has no salvage value. The present worth advantage of Unit A over Unit B is most nearly:
- (A)USD 4,700
- (B)USD 7,200
- (C)USD 12,700
- (D)USD 19,700
Show worked solution
Answer: (B)
Unit A costs USD 15,000 more to install, but its lower annual cost and its salvage credit leave it about USD 7,200 ahead in present worth.
Costs arriving on different schedules become comparable only when the first cost, the annual series, and the end-of-life salvage are all referred to time zero over the same 15-year horizon.
Unit A carries the heavier purchase price but recovers part of it at retirement while committing to the smaller maintenance stream.
Unit B earns no salvage credit, so its cost stream is purchase price plus the discounted maintenance alone.
Fifteen years of the USD 2,300 per year maintenance penalty on Unit B swamp its USD 15,000 lower first cost, leaving Unit A ahead by about USD 7,200.
FE Reference Handbook — Engineering Economics: Uniform Series Present Worth Factor and Present Worth Analysis
Why the other choices appear
- (A)Omits the salvage credit on Unit A: 103,204 - (60,000 + 38,518) = 4,686.
- (C)Deducts the USD 8,000 salvage at face value instead of its present worth: 103,204 - (98,518 - 8,000) = 12,686.
- (D)Capitalizes only the USD 2,300 per year maintenance difference and ignores both the first-cost difference and salvage: 2,300(8.5595) = 19,687.