A small business received a five-year $1,000,000 loan at a subsidized rate of 3 percent per year. The firm will pay 3 percent annual interest payment each year and the principal at the end of five years. If market interest rates on similar loans are 6 percent per year, what is the NPV of the loan? (Ignore taxes.)
A)+$126,371
B)+$348,369
C)−$501,595
D)−$137,391

Question

Quizplus · Accepted Answer

The NPV of the loan can be calculated by comparing the present value (PV) of the loan payments at the subsidized rate to the PV of the loan payments at the market rate. The annual interest payment at 3% is $30,000 ($1,000,000 * 0.03). The principal payment at the end of five years is $1,000,000. Using a discount rate of 6% (the market rate), the PV of these payments can be calculated.PV of interest payments = $30,000 * [1 - (1 + 0.06)^-5] / 0.06 = $30,000 * 4.21236 = $126,370.8 (approximately)PV of principal payment = $1,000,000 / (1 + 0.06)^5 = $747,258.48Total PV of payments at market rate = $126,370.8 + $747,258.48 = $873,629.28Since the loan amount is $1,000,000, the NPV of the loan is the difference between the loan amount and the total PV of payments at the market rate:NPV = $873,629.28 - $1,000,000 = -$126,370.72 (approximately)However, this calculation seems to have an error in interpretation. The correct approach to find the NPV of the loan's subsidy involves calculating the difference in interest payments between the market rate and the subsidized rate, then discounting these savings back to the present value at the market rate.Correct calculation:Interest savings per year = ($1,000,000 * 0.06) - ($1,000,000 * 0.03) = $60,000 - $30,000 = $30,000PV of interest savings = $30,000 * [1 - (1 + 0.06)^-5] / 0.06 = $30,000 * 4.21236 = $126,371.8 (approximately)Since the principal is repaid at its face value in both scenarios, the NPV of the loan subsidy is simply the present value of the interest savings, which is approximately +$126,371, making the correct answer A.

A Small Business Received a Five-Year $1,000,000 Loan at a Subsidized