Question

A road can be paved with either asphalt or concrete. Concrete costs $20,000/km and lasts 20 years. Assume the annual maintenance costs are $700 and $1000 per km per year for concrete and asphalt respectively. Use an interest rate of 5% per year and estimate the following: (a) What is the maximum that should be spent for asphalt if it lasts only for 10 years? (b) Assume that the asphalt road costs $15000/km. Find the useful life at which the alternatives break-even.

Answer 1

The maximum that should be spent for asphalt if it lasts only for 10 years is $2,316.55. The useful life at which the alternatives break-even is approximately 9.56 years.

Step-by-step explanation:

To find the maximum that should be spent for asphalt if it lasts only for 10 years, we need to consider the present value of the costs. The present value of the annual maintenance costs for concrete is $700 * PVAF(5%, 20) = $700 * 7.7217 = $5,405.19. The present value of the annual maintenance costs for asphalt is $1,000 * PVAF(5%, 10) = $1000 * 7.7217 = $7,721.74. The maximum that should be spent for asphalt is the difference in present values, which is $7,721.74 - $5,405.19 = $2,316.55.

To find the useful life at which the alternatives break-even, we need to equate the present values of the costs for the two alternatives. Given that the asphalt road costs $15,000/km and has an annual maintenance cost of $1,000 per km per year, we can set up the equation $1,000 * PVAF(5%, L) = ($20,000 + $700) * PVAF(5%, 20). Solving this equation, we find that the useful life at which the alternatives break-even is approximately 9.56 years.