Answer to Question #65141 in Macroeconomics for KiefG

Question

A government is considering paving a highway with a newly developed “wear‐proof” material. Paving the highway could cost $4 billion today but would save $400 million in maintenance costs for each of the next ten years.
a. Use the concept of present value to determine whether the project is worth undertaking if the government can borrow at an interest rate of 4%. Is it worth it if the interest rate is 0%? 8%?
b. A politician says to you, “I don’t care what the interest rate is. The project is clearly a good investment: it more than pays for itself in only 8 years, and the all the rest is money in the bank.” What is wrong with this argument, and why does the interest rate matter?

Answer 1

a) Using the concept of present value we have that C=PV*(1+i)n, where C is the future amount of money that must be discounted, n is the number of compounding periods between the present date and the date where the sum is worth C, i is the interest rate for one compounding period. So, if the interest rate is 4% and 8%, the project is worth undertaking. But if the interest rate is 0%, the project is unprofitable.
b) Politician isn`t right, because the project pays for itself in only 8 years if interest rate will be 2,85%=(4 billion/( 400million*8))^1/8, but if the interest rate will less than 2,85% or may be o%, then the project doesn`t pay for itself.