The city engineer has prepared two plans for roads in the city park. Both plans meet anticipated requirements for the next 40 years. The city uses 7% as the minimum attractive rate of return (MARR). Plan A is a three-stage development program: $300,000 is to be spent now, followed by $250,000 at the end of 15 years, and $300,000 at the end of 30 years. Annual maintenance will be $75,000 for the first 15 years, $125,000 for the next 15 years, , and $250,000 for the final 10 years. Plan B is a two-stage program: $450,000 is required now, followed by $50,000 at the end of 15 years. Annual maintenance will be $100,000 for the first 15 years, and $120,000 for the subsequent years. At the end of 40 years, this plan will have a salvage value of $150,000. Use a conventional benefit-cost ratio analysis to determine which plan should be chosen.

Plan B is the preferred

Explanation:

Plan A Plan B n = 15 n = 15. n = 10 $75,000 $125,000 $ 250,000 $300,000 $250,000$ 300,000

Differences between Alternatives A and examination of the differences between the alternatives will allow us to quickly know which plan we are to chose. Cash Flow Present Worth Year ABB- AAt 7%At 5%0-$300-$450-$150-$150-$1501- 15-$75-$100-$25-$228-$25915-$250-$50+$200+$72+$9616- 30-$125-$125$0$0$030-$300$0+$300+$39+$6931- 40-$250-$125+$125+$115+$22340$0+$150+$150+$10+$21Sum+$1,375*-$142$0* This is sum of -$150 – 15 ($25) + $200 …. (a)When the Present Worth of the B- A cash flow is computed at 7%, the NPW =-142. The increment is not desirable at i = 7%. n = 15n = 25$150,000$100,000$125,000$450,000$50,000n = 15n = 15n = 10$25,000$200,000$125,000$150,000$150,000$300,000

Choose Plan A. (b)For Plan B to be chosen, the increment B- A must be desirable. The last column in the table above shows that the B- A increment has a 5% rate of return. In other words, at all interest rates at or below 5%, the increment is desirable and hence Plan B is the one that is chosen.