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?