Question

[Requires appendix] Could any combination of home price, mortgage, or further borrowing on a home result in a simple leverage ratio of \(1 / 2 ?\) If yes, provide an example. If no, briefly explain why.

Short answer

Yes, a simple leverage ratio of \(1/2\) is possible. For instance, if a house is worth $200,000, a mortgage or further borrowing of $100,000 would result in a leverage ratio of \(1/2\) as long as the total debt doesn't exceed the half of the home's value.

Step-by-step solution

Understanding Leverage Ratio

Leasing or borrowing against the capital value is referred to as leverage. The leverage ratio is determined by dividing the total amount of debt (the mortgage + any other borrowing on the house) by the total value of the house. The formula to calculate the leverage ratio is: \( Leverage \ Ratio = \frac{Total \ Debt}{Home \ Price} \)

Investigating the problem

To obtain a leverage ratio of \(1/2\), the total debt should be half of the home's value, according to the formula. Therefore, if a house is worth $200,000, a mortgage or a combination of a mortgage and additional borrowing that totals $100,000 would result in a leverage ratio of \(1/2\) because \( \frac{100,000}{200,000} = 0.5 \ or \ 1/2 \).

Verify the result

Making sure that the debt does not exceed half the property's value is essential. Moreover, when paying the debt, the leverage ratio would decrease over time assuming the home value remains constant. This is because the numerator of our leverage ratio calculation (the total debt) is getting smaller while the denominator (the home value) stays the same.