Question

[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?

Short answer

a. The home was purchased for \$240,000. b. The initial leverage ratio was 80%. c. The homeowner is not under water. d. With a \$30,000 down payment, the home was purchased for \$270,000 with an initial leverage ratio of 90%. In this case, the homeowner ends up under water. e. The degree of leverage is directly related to likelihood of ending up 'under water'; a greater leverage extent leads to a higher risk when home prices decrease.

Step-by-step solution

Mortgage Amount Calculation

For part a, subtract the down payment from the total cost of the home. So the amount borrowed to buy the home is \( \$300,000 - \$60,000 = \$240,000\)

Leverage Ratio Calculation

For part b, divide the mortgage loan by the total cost of the home. The leverage ratio when the home was first purchased is \( \$240,000 / \$300,000 = 0.8\) or 80%.

Calculate new value of the home and check underwater status

For part c, find out the fallen value of the home by subtracting 15% from the original home value and compare it with the loan amount. The new value is \( \$300,000 - 0.15*\$300,000 = \$255,000\). Since the owed amount \( \$240,000\) is less than the new value \( \$255,000\), the homeowner is not under water.

Deal with changed circumstances

For part d, do the same calculations as in part a, b, and c but with a down payment of \$30,000. The borrowed amount will be \$300,000 - \$30,000 = \$270,000. The leverage ratio will be \$270,000 / \$300,000 = 0.9 or 90%. The new home value will still be \$255,000. Now, since the owed amount (\$270,000) is more than the new value (\$255,000), the homeowner is under water.

Analyse the impact of leverage

For part e, the results from steps 1-4 clearly demonstrate that a higher degree of leverage (90% vs 80%) increased the likelihood of the homeowner ending up 'under water'. A greater leverage extent can lead to higher risk when home prices are on the decline.