A government is considering paving a highway with a newly developed “wear-proof”
ID: 2427612 • Letter: A
Question
A government is considering paving a highway with a newly developed “wear-proof” material. Paving the highway would cost $4 billion today, but it would save $400 million in maintenance costs for each of the next 10 years. 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%? 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?
Explanation / Answer
Answer:
if Government borrows at interest rate of 4%:
Cash Outflow = $4,000
Present Value of saving for 10 years = Saving amount * PV value(4%, 10years)
= $400* 8.1109
= $3,244
Net Present value = PV of inflows or savings - PV of cash outflows
= $3244- $4000
= -$756
Since the net present value is negative, the goovernment should not accept the project.
If borrowing rate is 0%:
Cash Outflow = $4,000
Present Value of saving for 10 years = Saving amount * PV value(0%, 10years)
= $400* 10
= $4000
Net Present value = PV of inflows or savings - PV of cash outflows
= $4000- $4000
= 0
Since the net present value is zero, the goovernment can accept the project.
If borrowing rate is 8%:
Cash Outflow = $4,000
Present Value of saving for 10 years = Saving amount * PV value(8%, 10years)
= $400* 6.7100
= $2684
Net Present value = PV of inflows or savings - PV of cash outflows
= $2684- $4000
= -$1316
Since the net present value is negative, the goovernment should not accept the project.
As the above calculations of different scenerios shows that the project is worth undertaking at 0% or 4% interest rate, but it is not worth undertaking at 8%. Hence, the politicians's argument is incorrect because it ignores the fact of interest rate which government needs to pay on amount of loan borrowed to finance the project.