Question

Suppose you buy a home for 200,000 dollar with a 20,000 dollar down payment and finance the rest with a home mortgage. a. Suppose that if you default on your mortgage loan, you lose the home, but nothing else. By what percentage would housing prices have to fall to create an economic incentive for you to default on the loan? Explain briefly. b. Suppose that if you default on your mortgage loan, you not only lose the home, but also 10,000 dollar in moving and relocating expenses. By what percentage would housing prices have to fall now to create an economic incentive for default?

Short answer

a. Housing prices would have to fall by 10% to create an economic incentive for defaulting on the loan. b. If there was additional moving and relocating expenses to consider, housing prices would have to fall by 5% to create an economic incentive for default.

Step-by-step solution

Calculate the Mortgage Loan

First, let's find out the amount of the mortgage loan. The total price of the home is 200,000 dollar and the buyer made a down payment of 20,000 dollar, so we subtract this from the total price. The resulting loan is \(200,000 - 20,000 = 180,000\) dollar.

Calculate Housing Price Drop for Economic Incentive (Part a)

In part a, the buyer would only lose the house if he defaulted. Therefore, he'd have an incentive to default if the price of the house falls below the mortgage remaining. This would happen if the house price falls by \(100 * \frac{180,000}{200,000} = 90\%\). Hence, housing prices would have to fall by \(100 - 90 = 10\%\) to create an economic incentive for default.

Adjust Calculation for Additional Expenses (Part b)

In part b, there are additional moving and relocating expenses of 10,000 dollar if the borrower defaults. Therefore, the borrower would lose this amount in addition to the house. So to create an economic incentive for default, the housing prices would have to fall below the mortgage loan plus these additional expenses. This would occur if the house price falls to \(180,000 + 10,000 = 190,000\) dollar. That is equivalent to \(100 * \frac{190,000}{200,000} = 95\%\). Thus, housing prices would need to fall by \(100 - 95 = 5\%\) to create an economic incentive for default.

Key concepts

Mortgage Loan Calculation

Understanding mortgage loan calculation is essential when purchasing a home. It determines how much you will need to borrow from a lender after you've made a down payment. In the exercise, the home price is \(200,000 and the buyer has a \)20,000 down payment.

The amount borrowed is thus calculated as the total home price minus the down payment, yielding a mortgage loan of \(200,000 - 20,000 = 180,000\) dollars. This initial loan calculation is crucial as it sets the stage for understanding the financial implications of changing property values and potential default.

Housing Price Drop

A drop in housing prices can profoundly affect homeowners, particularly those with outstanding mortgage loans. In the exercise scenario, we explore the impact of a price decline on the economic incentive to default.

If the home's value decreases, at some point, it can fall below what the homeowner owes on the mortgage. To achieve an economic incentive for default, in part a, the reduction in value would need to be such that the house becomes worth less than the remaining mortgage, calculated as \(100 - \frac{180,000}{200,000} \times 100 = 10\%\) decrease.

Homeowners need to be aware of market trends and assess their financial situation to mitigate the risks associated with a potential decline in property value.

Default Risk Analysis

Default risk analysis is a process of evaluating the likelihood that a borrower will fail to repay their loan. It goes beyond the mere mortgage calculation to factor in additional costs and consequences of defaulting on the loan.

In the context of our exercise, the homeowner needs to consider not only the value of their home and the outstanding mortgage but also the added costs of moving and relocating, which amount to $10,000. The economic incentive for default exists when the drop in housing prices outweighs the total loss the homeowner would incur—the remaining mortgage plus these expenses.

Thus, for part b, the necessary decrease in the house's value is when it is worth less than the mortgage plus moving expenses, resulting in a \(100 - \frac{190,000}{200,000} \times 100 = 5\%\) decrease in market value required for an incentive to default. This analysis serves as a reminder of the broader financial impact that defaulting on a mortgage can have, and the importance of a complete risk assessment.