Two alternatives are under consideration for maintenance of a bridge. Select the most cost-effective alternative using present worth analysis. Assume an interest rate of 10% per year and a design life of 50 years for each alternative. Alternative A consists of annual maintenance costs of $5,000 per year for the design life except for: Year 20, in which bridge deck repairs will cost $20,000 Year 30, in which a deck overlay and structural repairs will cost $105,000 Alternative B consists of annual maintenance costs of $3,000 per year for the design life except for: Year 20, in which bridge deck repairs will cost $35,000 Year 30, in which a deck overlay and structural repairs will cost $85,000

Question

What will be an ideal response?

Answer 1

NPWA = – {5000(P/A,10%,50) + 15000(P/F,10%,20) + 100000(P/F,10%,30)}
NPWA = – {5000(1/0.1009) + 15000(0.1486) + 100000(0.0573)} = – $57,513
NPWB = – {3000(P/A,10%,50) + 32000(P/F,10%,20) + 82000(P/F,10%,30)}
NPWB = – {3000(1/0.1009) + 32000(0. 1486) + 82000(0.0573)} = – $39,186
Alternative B is the most cost-effective (higher net present worth).