Question

[Requires appendix.] Suppose you buy a home for \(\$ 400,000\) with a \(\$ 100,000\) down payment and finance the rest with a home mortgage. a. Immediately after purchasing your home, before any change in price, what is the value of your equity in the home? b. Immediately after purchasing your home, before any change in price, what is your simple leverage ratio on your investment in the home? c. Now suppose that over the next three years, the price of your home has increased to \(\$ 500,000 .\) Assuming you have not borrowed any additional funds using the home as collateral, but you still owe the entire mortgage amount, what is the new value of your equity in the home? Your new simple leverage ratio? d. Evaluate the following statement: "An increase in the value of a home, with no additional borrowing, increases the degree of leverage on the investment in the home." True or false? Explain.

Short answer

a. Initially, the value of equity was \$100,000. b. Initial simple leverage ratio was 4. c. The new value of equity is \$200,000 and the new simple leverage ratio is 2.5 d. The statement is false, an increase in the value of the home, with no additional borrowing reduces the leverage ratio not increase it.

Step-by-step solution

Calculate Initial Equity

Initially, the equity in the home can be calculated by subtracting the mortgage amount from the home's purchase price. In this case it would be \(\$400,000 - \$300,000 = \$100,000\). So initial equity in the home would be \$100,000

Calculate Initial Simple Leverage Ratio

The simple leverage ratio is calculated by dividing the value of the asset (house) by the equity invested. It can be calculated as \(\$400,000 / \$100,000 = 4\). Thus, the simple leverage ratio initially was 4.

Calculate New Equity after Price Increase

Assuming the price of the home increased to \$500,000 and there were no additional borrowings but the entire mortgage amount still owed, the new equity in home can be calculated as \(\$500,000 - \$300,000 = \$200,000\). The new equity in home after the price increase would be \$200,000.

Calculate New Simple Leverage Ratio

The new simple leverage ratio can be calculated by dividing the new value of the house (\$500,000) by the new equity (\$200,000). Hence, the new simple leverage ratio would be \(\$500,000 / \$200,000 = 2.5\)

Evaluate the statement

The statement says that 'An increase in the value of a home, with no additional borrowing, increases the degree of leverage on the investment in the home.' This is false, as we can see from the calculated values. When the value of the house increased from \$400,000 to \$500,000; the simple leverage ratio decreased from 4 to 2.5. Thus an increase in home value without any additional borrowing reduces the leverage ratio not increase it.