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Chapter 4: Problem 8

Suppose you buy a home for \(200,000,\) using your own funds. The annual interest rate you could earn by investing your funds elsewhere is \(5 \% .\) (Ignore any sales commissions or fees associated with buying or selling a home.) a. If the price at which you could sell the home remains at \(200,000,\) what is your annual interest cost of home ownership? b. Suppose that, after a few years of owning, home prices rise dramatically, and you can now sell your home for \(300,000 .\) If you continue to own, what is your annual interest cost now? c. Suppose once again that, after a few years of owning, you can now sell your home for \(300,000.\) But the interest rate you could earn by investing your funds elsewhere has risen to \(7 \%\). If you continue to own, what is your annual interest cost now?

Short Answer

Expert verified
a. The annual interest cost of home ownership when the house's selling price remains at \$200,000 is \$10,000. b. The annual interest cost increases to \$15,000 when the selling price of the home becomes \$300,000. c. When the interest rate for other investments increases to \(7%\), the annual interest cost will be \$21,000.

Step by step solution

01

Calculate Annual Interest Cost (Scenario A)

The annual interest cost is the amount of money one could have had if the amount spent to purchase the house was invested elsewhere. In this part of the exercise, the purchase price of the house remains the same as the selling price and the annual interest from alternative investment is given as \(5%\). Hence, the annual interest cost for this scenario would be \(200,000 \times 0.05 = \$10,000\).
02

Calculate Annual Interest Cost (Scenario B)

In this scenario, the selling price of the house increases to \$300,000 but the interest rate remains the same. We calculate the opportunity cost based on the value of the house since the cost of opportunity depends on the selling price (current value) and not the buying price. Hence, the annual interest cost would now be \(300,000 \times 0.05 = \$15,000\).
03

Calculate Annual Interest Cost (Scenario C)

In the final scenario, both the selling price of the home and the interest rate for other investments increase. Hence, we calculate the annual interest cost the same way as earlier, using the new values: \(300,000 \times 0.07 = \$21,000\).

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Most popular questions from this chapter

State whether each of the following is a stock variable or a flow variable, and explain your answer briefly. a. Total farm acreage in the U.S. b. Total spending on food in China c. The total value of U.S. imports from Europe d. Worldwide iPhone sales e. The total number of parking spaces in Los Angeles f. The total value of human capital in India g. Investment in new human capital in India

[Requires appendix.] Suppose, as in a previous problem, you buy a home for \(\$ 400,000\) with a down payment of \(\$ 100,000\) and take out a mortgage for the remainder. Over the next three years, the price of the home rises to \(\$ 500,000\). However, during those three years, you borrow the maximum amount you can borrow without changing the value of your home equity. Assume that, at the end of the three years, you still owe all that you have borrowed, including your original mortgage. a. How much do you borrow (beyond the mortgage) over the three years? b. What is your simple leverage ratio at the end of the three years? c. By what percentage could your home's price fall (from \(\$ 500,000\) ) before your equity in the home is wiped out?

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