Practice Problems and Solutions - Topic 14 - Residential Own-Rent

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Jan 9, 2024

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Professor Todd Sinai Wharton Real Estate Investments 1 Real Estate Investments: Practice Problems Topic #14: Residential Own/Rent Analysis 1) True, False, or Uncertain (and why): The reason families with higher effective income tax rates have a lower cost of homeownership is because, holding the value of the house and all other factors fixed, their after-tax interest costs are the smallest. 2) Upon graduating from Wharton, you are considering purchasing for $850,000 a condominium in Washington, DC, where you will be employed. You will borrow 75 percent of the purchase price. You expect to stay in the condominium for at least 10 years. The condominium is located in the Dupont Circle area, a lively area with a young population and a hopping nightlife. You recall from your real estate finance class, however, that you should first assess the appropriateness of the cost of owning versus renting. Here’s what you know: Your combined federal and District of Columbia income tax rate will be 43 percent and you plan to itemize on your tax return. Currently, 10-year Treasuries are yielding 1.5 percent and 30-year mortgages cost 3.5 percent. Over the last 50 years, condominium prices in DC have grown at a nominal rate of 2.0 percent, though over the past 5 years the nominal growth of prices has been just above 8 percent. Your nominal pre-tax risk-adjusted required return on an equity investment in a condominium is 11 percent. You do not need to pay any maintenance directly, but annual condominium fees run $12,000. Property taxes are $7,400 per year. By way of comparison, a neighbor in the condominium complex is renting out her identical unit for $2,800 per month. a) Leaving aside any transaction costs of buying the condo, what is the user cost of this condominium? b) What could explain the difference between the user cost and the rent?

Professor Todd Sinai Wharton Real Estate Investments 2 Suggested solutions: 1) False. The income tax deduction for mortgage interest is just one reason high-tax rate families have lower user costs. The value of the property tax deduction also increases with the tax rate. And, most importantly, the opportunity cost of the equity investment in the house declines with the tax rate. These three factors combine to reduce the user cost of owner- occupied housing for higher-tax rate homeowners. (As a side note, in the U.S., high-tax rate families might not have any interest or property tax deductions at all if they don’t itemize on their tax returns, so the only way that high-tax rate families will always have a lower user cost than low-tax rate families (all else being equal) is through the opportunity cost of equity.) People often make the mistake of arguing that housing costs as a percent of income or wealth for high-tax rate families would be lower since high-tax families have high incomes. Although that is true, it has nothing to do with the user cost, which is housing costs as a percent of house value.

Professor Todd Sinai Wharton Real Estate Investments 3 2a) The user cost is 3.0 percent, or $25,260 per year. When you do these calculations, keep in mind that the expected capital gain that you should use, is the long run nominal trend, not the 8 percent growth of late. (Would you expect that to continue over your 10-year holding period?) 2b) There are a whole host of reasons why your monthly user cost of owning is below the market rent. Here are two I think are most likely:  The typical residents of Dupont Circle are young, which means they will have short expected durations in their residences. (While the problem does not explain this, many are interning on Capitol Hill.) That means their effective user cost of owning will be higher than yours due to the fixed costs of buying. An implication of this is that they would be willing to pay higher rent than you before owning was worthwhile, and landlords raise rents in response to that inflexibility.  You presumably have a higher tax rate (due to your higher income) than a typical Dupont Circle resident, so market rents reflect their user costs rather than yours. Assumptions: Purchase price: 850,000 Tax rate: 43.0% LTV: 75.0% Property taxes: 7,400 Mortgage rate: 3.5% Maintenance: 12,000 Treasury rate: 1.5% Nominal price growth: 2.0% Equivalent-risk leveraged equity yield: 11.0% Solution: Purchase price: 850,000 Down payment: 212,500 (1 - 0.75) x 850,000 First-year interest payment: 22,313 850,000 x 75.0% x 3.5% - Interest tax deduction: -9,594 0.43 x 22,313 = After-tax interest: 12,718 Opportunity cost of equity: 23,375 212,500 x 11.0% - Tax on equity yield: -10,051 = After-tax opportunity cost of equity: 13,324 Property taxes: 7,400 - Property tax deduction: -3,182 0.43 x 7,400 = After-tax property taxes: 4,218 Maintenance and depreciation: 12,000 Subtotal: 42,260 - Nominal capital gain: -17,000 850,000 x 2.0% Total user cost: Annual: 25,260 Monthly: 2,105 Percent: 3.0% 25,260 / 850,000

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