Question

You have decided to purchase an industrial warehouse. The purchase price is $1 million and you expect to hold the property for five years. You have narrowed your choice of debt financing packages to the following two alternatives: $700,000 loan, 6 percent interest rate, 30-year term, annual, interest-only payments (the annual payment will not include any amortization of principal), and $50,000 in up-front financing costs.$750,000 loan, 6 percent interest rate, 30-year term, annual, interest-only payments. No up-front financing costs. Required:What is the difference in the present value of these two loan alternatives

Answer 1

To find the difference in present value between the two financing alternatives, calculate the annual interest payments and present value of those payments for the duration of the expected holding period of five years for both loans, then include the additional upfront financing costs for the first loan in its present value calculation.

Step-by-step explanation:

The question concerns the comparison of two debt financing packages for purchasing an industrial warehouse. I will calculate the present value (PV) of the two loan options to determine which is more financially advantageous. We will ignore the long-term balance as it is not part of the question, focusing on the upfront and interest costs over five years. The key factors for calculating the present value are the loan amount, interest rate, term of the loan, and any upfront costs.

The first loan requires a $50,000 upfront fee, so its PV of costs will be the sum of this fee and the present value of the interest payments:

1. Calculate the annual interest for the $700,000 loan: 0.06 * $700,000 = $42,000 per year.
2. Calculate the PV of five years of interest payments using a financial calculator or a present value formula, assuming a discount rate equal to the interest rate (as the problem does not provide an alternative rate).
3. Add the $50,000 upfront fee directly to the sum of PV of interest payments.

The second loan has no upfront costs, so its PV of costs is simply the PV of the interest payments:

1. Calculate the annual interest for the $750,000 loan: 0.06 * $750,000 = $45,000 per year.
2. Calculate the PV of five years of interest payments as in the earlier step, with the adjusted annual interest amount.

After calculating the respective present values, the difference between the two options will be the PV of the first loan minus the PV of the second loan.