Question

A road can be paved with either asphalt or concrete. Concrete costs $15,000/km and lasts 18 years. Assume the annual maintenance costs are $900 for concrete and $1300 for asphalt per kilometer per year. Use an interest rate of 4% per year and annual analysis to solve for the following: (a) What is the maximum cost/km that should be spent for asphalt if it lasts only 10 years? (b) Assume the asphalt road costs $7500 per kilometer. How long must it last to be the preferred alternative?

Answer 1

(a) What is the maximum cost/km that should be spent for asphalt if it lasts only 10 years?
Concrete Equivalent Annual Cost=15000*4%/(1-1/1.04^18)+900
Asphalt Equivalent Annual Cost=x*4%/(1-1/1.04^10)+1300
Hence, x=6366.241466
Maximum cost/km=6366.241466

(b) Assume the asphalt road costs $7500 per kilometer. How long must it last to be the preferred alternative?
7500*4%/(1-1/1.04^t)+1300<15000*4%/(1-1/1.04^18)+900
=>t>12.27957524
So, it should last for 13 years