Question

[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

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

Step-by-step solution

Calculate the Amount Owed

The amount owed can be calculated by adding the initial mortgage taken (which is the difference between the home price and the down payment) to the additional funds borrowed. We have: Initial Mortgage = \(400,000 - 100,000 = 300,000\$ \) Additional loans = \$50,000 The total amount owed = initial mortgage + additional loans = \$300,000 + \$50,000 = \$350,000.

Calculate Equity

Equity can be calculated by subtracting the amount owed from the current home price. In this case, current home price = \$500,000 (as stated in the problem). So, Equity = current home price - amount owed = \$500,000 - \$350,000 = \$150,000.

Calculate Leverage

Leverage is calculated as the ratio of the home's value to the equity. Therefore, Leverage = Home Value / Equity = \$500,000 / \$150,000 = approximately 3.33.

Calculate the Price Drop Percentage

The price drop percentage that would wipe out the equity is calculated as the ratio of the equity to the home's current price, expressed as a percentage. Price drop % = (Equity / Current Home Price) * 100 = (\$150,000 / \$500,000) * 100 = 30%.

Key concepts

Mortgage Finance

Understanding how to finance a home purchase with a mortgage is essential for prospective homeowners. A mortgage is essentially a loan from a bank or financial institution to buy a house or property. In the exercise, the initial purchase of a home involves a down payment of \(\$100,000\) against the total cost of \(\$400,000\), with the remaining \(\$300,000\) financed through a mortgage.

In simpler terms, when you buy a house, you usually pay a part of the total cost upfront—this is your down payment. Then, you borrow the rest of the money, which is the mortgage, from a lender and agree to pay it back over time, plus interest. If you don't follow through on your payments, the lender has the right to take your house through a process called foreclosure, since the house itself is the collateral for the mortgage loan.

Over time, as you pay down the mortgage, your equity in the home increases. Given that the house's value may fluctuate, the exact amount loaned versus the equity you have can change, similar to how the value rose to \(\$500,000\) in our exercise. Additionally, taking a home equity loan as in the exercise means borrowing further against your home's value, which can impact your overall financial commitment and equity.

Investment Leverage

Leverage in the context of investments like buying a house means using borrowed money to increase the potential return of an investment. In the original exercise, the homebuyer uses investment leverage by borrowing money to purchase a property that later appreciates in value.

In the real estate market, the initial down payment, paired with a mortgage or loan to cover the rest, allows an investor to control a large asset with a relatively small amount of their own money. This is a powerful tool but also introduces risks. If the value of the property increases, as it did in the exercise scenario (rising to \(\$500,000\)), the homeowner stands to make a larger profit on their initial investment when they sell the house. However, if the value of the property decreases, the homeowner can end up owing more than the property is worth—a situation sometimes referred to as being 'underwater' on a mortgage.

Equity Leverage Ratio

The equity leverage ratio is a measure used to determine how much of an asset is financed by the owner's funds versus borrowed funds. It can offer insights into the level of debt used to finance the asset, and in a homeowner's case, reflects their financial risk. The higher the ratio, the more the homeowner has borrowed relative to their equity.

In the exercise, the equity leverage ratio is calculated by dividing the home's current value (\$500,000) by the owner's equity in the home (\$150,000), giving a ratio of approximately 3.33. This means that for every dollar of equity, \(\$3.33\) of the home's value is financed through debt. A higher ratio implicates higher financial risk as it shows a greater reliance on borrowed money.

It's crucial to understand that the equity leverage ratio can change over time due to fluctuations in the property's value and as the owner pays down the debt. The homeowner's financial vulnerability is related to this ratio: if the property's value goes down significantly, the owner could owe more than the house is worth (negative equity). Conversely, if the value goes up, the owner's equity in the property increases, which could potentially allow them to borrow more against it or sell it for a greater profit.