Question

[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?

Short answer

a. You borrow an additional $100,000 over three years. b. Your simple leverage ratio at the end of the three years is 4. c. The price of your home could fall by 20% from $500,000 before your equity is wiped out.

Step-by-step solution

- Calculate Available Equity after Home Value Increase

The equity of a home is the current market value minus any money owed on it. Initially, the home was purchased for $400,000, with a down payment of $100,000. So the initial mortgage is $400,000 - $100,000 = $300,000. If the price of the home rises to $500,000, then the new equity is $500,000 - $300,000 = $200,000. However, the initial equity was $100,000 (the down payment), so $100,000 additional equity is available to borrow against.

- Calculate Simple Leverage Ratio at the End of Three Years

The simple leverage ratio is calculated as total debt divided by equity. After borrowing $100,000 more (calculated in the previous step), the total debt is now $300,000 (original mortgage) + $100,000 (additional borrowing) = $400,000. The equity, after borrowing the maximum amount without changing the home equity, remains the original equity of $100,000 (down payment). So the simple leverage ratio is $400,000 / $100,000 = 4.

- Calculate the Price Fall Percentage before the Equity is Wiped Out

At this point, the homeowner will have no equity in the home if its value falls to the same as the total owed, which is $400,000 (total debt from step 2). The value of the home could fall from $500,000 to $400,000 before the equity is wiped out. This percentage decrease is 100 * (($500,000 - $400,000) / $500,000) = 20%.

Key concepts

Home Equity Calculation

When it comes to understanding the financial health of your property investment, the calculation of home equity is crucial. Home equity represents the portion of your property that you truly 'own.' Simply put, your home equity is the current market value of your property minus any liabilities, such as a mortgage, that are secured against it.

For example, let's say you buy a house for \(\$400,000\) and make a down payment of \(\$100,000\). This means you've taken out a mortgage of \(\$300,000\) for the remaining amount. If the market value of the home grows to \(\$500,000\), your equity increases because the liability (your mortgage) stays the same while the value of your asset (the home) rises. The equity in the home would then be the new market value (\(\$500,000\)) minus the mortgage (\(\$300,000\)), totaling \(\$200,000\).

Understanding home equity is important if you want to leverage your property's value to borrow funds or to evaluate how much of your mortgage you have paid off in terms of property value. It's also vital if you're considering selling your property or refinancing your mortgage.

Leverage Ratio in Real Estate

The leverage ratio in real estate is a measure of financial risk. In essence, it's the amount of debt you have on a property compared to your equity in that property. A higher leverage ratio means you've borrowed more against your property, which can amplify both gains and losses depending on market conditions.

Let's take the example from the exercise where your total debt after borrowing against the increased equity is \(\$400,000\), while your equity remains \(\$100,000\). By dividing the total debt by the equity, we get the leverage ratio of 4. This indicates that for every dollar of equity, there are four dollars of debt.

What does this mean in layman's terms?

Essentially, a high leverage ratio like this increases your potential for higher returns if the property value goes up since you're benefiting from the growth on the entire value of your property, not just your equity. However, it also means you have more to lose if the property value declines, outlining a double-edged sword scenario. Therefore, it's critical for homeowners and real estate investors to be aware of their leverage position and how it could affect their finances in changing market conditions.

Housing Market Price Fluctuation

Price fluctuation in the housing market is a constant force, capable of affecting homeowners' equity without a single change to their actual mortgage payments. These fluctuations are driven by an array of factors including economic trends, interest rates, supply and demand, and even regulatory changes.

As seen in our exercise scenario, if the market value of a home falls even 20% from \(\$500,000\) to \(\$400,000\), you could completely lose your equity, which underscores the risk of market volatility. When the price falls to equal the amount owed on the mortgage, this is known as being 'underwater' on your mortgage. In the exercise, a price reduction of 20% would be enough to wipe out the homeowner's equity, leaving the property worth precisely what is owed.

Understanding how price fluctuations can impact home equity and debt levels is vital for any homeowner. Being aware of market conditions and trends can help homeowners make informed decisions about whether to sell, refinance, or reassess their financial situation relative to their real estate holdings.