A road is being proposed to facilitate a housing development on a scenic lake. T
ID: 2452725 • Letter: A
Question
A road is being proposed to facilitate a housing development on a scenic lake. Two alternatives have been suggested. One of the roadway alignments is to go around the lake and slightly impact a wetland. The second alternative will also go around the lake and will significantly impact two wetlands. The following table shows the anticipated costs for each alternative. Assuming that the annual interest rate is 7 %, determine which alternative is preferred using present worth of the investment. Present worth of salvage value A_i= S_i/(1 + r)^NExplanation / Answer
Alternative 1:
Annual cost = Maintenance + Wetland + Lighting
= 3,000 + 7,500 + 1,500
= $12,000
Present worth = First cost + Present worth of annual cost – Present worth of salvage
= 75,000 + 12,000 × Accumulated 7% rate till 15th year – 45,000 × 7% rate on 15th year
= 75,000 + 12,000 × 9.1079 – 45,000 × 0.3624
= 75,000 + 109,294.8 – 16,308
= $167,986.8
Alternative 2:
Annual cost = Maintenance + Wetland + Lighting
= 2,000 + 2,500 + 2,500
= $7,000
Present worth = First cost + Present worth of annual cost – Present worth of salvage
= 125,000 + 7,000 × Accumulated 7% rate till 15th year – 25,000 × 7% rate on 15th year
= 125,000 + 7,000 × 9.1079 – 25,000 × 0.3624
= 125,000 + 63,755.3 – 9,060
= $179,695.3
Answer: Alternative 1 is preferred, since it has lower present worth of the investment.
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