A government is considering paving a highway with a newly developed “wear-proof” mate- rial. Paving the highway with the new material would cost an additional $3 billion today, but it would save $400 million in maintenance costs every year for the next 10 years (starting from next year).
(a) Suppose the interest rate is 4%. What is the present discounted value of the savings in maintenance costs over 10 years if the “wear-proof” material is used in building the highway now? Based on your calculation, is the project with the new material worth undertaking?
(b) Answer the same question as in (a) if the interest rate is 8%.
(c) 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 all the rest is money in the bank.” What’s wrong with this argument, and why does the interest rate matter?
You can use a calculator or excel spreadsheet to compute, but write down the equation you use to compute.