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Chapter 4: Problem 13

[Requires appendix.] Suppose, as in the 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 also borrow \(\$ 50,000\) in additional funds using the home as collateral (called a "home equity loan"). Assume that, at the end of the three years, you still owe the \(\$ 50,000\), as well as your original mortgage. a. What is your equity in the home at the end of the three years? b. How many times are you leveraged on your investment in the home at the end of the three years? c. By what percentage could your home's price fall (after it reaches \(\$ 500,000\) ) before your equity in the home is wiped out?

Short Answer

Expert verified
a. The equity in the home after three years is \$ 150,000. b. The investment in the home is 3.33 times leveraged. c. The home's price could fall by 30% before the equity in the home is wiped out.

Step by step solution

01

Calculate Equity in the Home

Equity in the home can be calculated by subtracting the total amount owed on the home (the mortgage and additional funds) from the total value of the home. The original mortgage is \(\$ 400,000 - \$ 100,000 = \$ 300,000\). The total amount owed is therefore \(\$ 300,000 + \$ 50,000 = \$ 350,000\). So, the equity is \(\$ 500,000 - \$ 350,000 = \$ 150,000\).
02

Compute Investment Leverage

Leverage is a measure of how much of the investment is funded by borrowed money. This can be calculated as the total value of the home divided by the equity. So, the leverage is \(\$ 500,000 / \$ 150,000 = 3.33\). Hence, the investment is 3.33 times leveraged.
03

Determine Equity Wipe-out Percentage

The percentage drop in the home's price that would wipe out the home's equity can be calculated by dividing the equity by the home's value and then multiplying by 100 to express the result as a percentage. So, the percentage drop to wipe out equity is \(\$ 150,000 / \$ 500,000 * 100% = 30%\). If the home's price were to fall by this percentage (30%), the resulting price equals to the total amount owed , thus deleting the home's equity.

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Most popular questions from this chapter

Every year, the housing market in Monotone, Arizona, has the same experience: The demand curve for housing shifts rightward by 500 homes, 500 new homes are built, and the price of the average home doesn't change. Using supply and demand diagrams, illustrate how each of the following new events, ceteris paribus, would affect the price of homes in Monotone over the current year, and state whether the price rises or falls. a. Because of special tax breaks offered to Monotone home builders, 800 new housing units are built during the current year. b. Because of events in the overall economy, interest ratcs fall. c. The Monotone city council passes a new zoning law that prevents any new home construction in Monotone during the year. d. Because of the new zoning law, and the resulting change in home prices, people begin to think that homes in Monotone are a better investment than they had thought before. c. Five hundred new homes are built in Monotonic during the year. But that same year, an earthquake destroys 2,000 preexisting homes. As a result of the earthquake, 3,000 homeowners decide they no longer want to live in or own homes in Monotone.

[Requires appendix.] A homeowner is said to be "under water" if he or she owes more on the mortgage than the home is worth. Suppose someone bought a home for \(\$ 300,000\) with a \(\$ 60,000\) down payment, and took out a mortgage loan for the rest. A few years later, the value of the home has fallen by \(15 \%,\) but the amount owed on the home has not changed. a. In this example, how much was borrowed to buy the home? b. What was the leverage ratio when the home was first purchased? c. After the home drops in value, is the homeowner under water? d. Answer the three questions above again, this time assuming that the down payment was only \(\$ 30,000\) e. Based on your answers above, when home prices are falling, what is the general relationship between the degree of leverage on a home and the likelihood that the owner will end up "under water" on the home?

In the chapter, you learned that one way the government enforces agricultural price floors is to buy up the excess supply itself. If the government wanted to follow a similar kind of policy to enforce a price ceiling (such as rent control), and thereby prevent black market-type activity, what would it have to do? Is this a sensible solution for enforcing rent control? Briefly, why or why not?

[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?

In a study session, one of your fellow students says, "I think our econ text book has a mistake: It shows the supply curve for housing as a vertical line, which implies that a rise in price causes no change in quantity supplied. But everyone knows that if home prices rise, construction firms will build more homes and supply them to the market. So the supply curve should be drawn with an upward slope: higher price, greater quantity supplied." Explain briefly the mistake this student is making.
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