Houses: Buying Versus Renting

Margaret Smith
Professor of Economics, Pomona College

Gary Smith
Professor of Economics, Pomona College

Part of the American Dream is to own your own home, whether it be a log cabin in Oregon, a farmhouse in Iowa, or a penthouse in Manhattan. The financial reality is that a home is the largest investment most people ever make. For many, it becomes their most profitable investment; for some, it becomes a financial and emotional disaster.

How can we tell whether a house is likely to be a profitable or unprofitable investment? Residential real estate is usually valued by looking at “comps,” the prices for recent transactions of comparable homes. The comps may be analyzed informally by realtors or systematically by multiple regression models and other statistical techniques (for example, Isakson 1998; Detweiler and Radigan 1996, 1999; Nguen and Cripps 2001).

Comps can help us judge whether the price of a particular house is high or low relative to the prices of other houses, but they tell us nothing about whether housing prices are high or low in any absolute sense. First-time homebuyers invariably ask, “Is now a good time to buy?” Clients who already own homes often ask if trading up is a good investment or if downsizing is a smart financial move. We have also had clients ask if we are in a housing bubble and if they should sell their house and rent until sanity returns.

One appealing way to address these questions is to determine the present value of the anticipated cash flow. This is a robust and well-established procedure that is widely used to value bonds, stocks, business projects, and commercial and industrial real estate. It is can also be used to value owner-occupied houses, although the details are different than with other assets. For example, the cash flow from commercial apartment buildings includes items such as depreciation, vacancies, bad debts, professional management fees, and advertising that would not be included in an analysis of owner-occupied housing and excludes rental savings, which is central to an analysis of owner-occupied housing. In addition, income-based appraisals of commercial and industrial property generally ignore the debt that will be used to finance the purchase, no doubt because the amount of debt and the tax consequences vary from buyer to buyer. With residential real estate, the mortgage is a crucial factor is deciding whether to buy or rent, and also complicates the present value analysis. We will show how a relatively simple spreadsheet can be used to do these present value calculations.

The Rent Alternative

The primary cash flow from owner-occupied housing is the rental payments the owner would otherwise have to pay. Some authors recognize that renting is a an alternative to buying a house, but simply list the pluses and minus of buying and renting (Goodman 2001, Miller 2002, Orman 2001). A more substantive approach is to compare the monthly mortgage payments with the monthly rent for a similar property. For example, in its 2002 housing report, the Joint Center for Housing Studies of Harvard University estimated that in 2001 the average renter paid $481/month while the average purchaser of the median single-family home paid $821 in after-tax mortgage payments. This comparison is obviously flawed. The median single-family home isn’t necessarily equivalent to the average rental property. Even if it were, the monthly mortgage payments depend on the size of the downpayment and the length of the mortgage. Suppose, for an extreme example, someone paid cash for a house and had no mortgage payments. Is buying therefore better than renting? Also, the Harvard calculations don’t consider that rents usually increase over time, while mortgage payments are constant and end when the loan is repaid.

UCLA economist Edward Leamer recommends calculating the percentage change in a house’s P/E: the ratio of the house’s market value to its annual rental value. An article describing this approach says that “it’s the change in P/E that matters—not the number” (Feldman 2003). An accompanying table looks for evidence of a housing bubble by showing that housing prices increased more than rents between 1993 and 2002 and identifies those cities in which the P/E increased the most. In reality, if we are deciding whether to buy or rent, what matters is the levels of housing prices and rents today, not the changes from some earlier period.

Just as with stocks, there are valid reasons for P/Es to go up and down and for different assets to have different P/Es. If interest rates fall, as they did between 1993 and 2002, the P/Es for stocks, houses, and other assets should rise. Companies with rapidly growing earnings and housing markets with rapidly growing rents should have higher P/Es than slow-growth stocks and slow-growth housing markets. In fact, the article’s table shows that the housing markets with the strongest P/Es are those in which rents were increasing the most rapidly.

Quinn (1997) shows a table that compares the costs of buying and renting taking into account rent increases, but this table ignores property taxes, utilities, maintenance and other expenses and assumes a 7-year holding period. Personal finance textbooks are not much better. For example, Keown (1998) uses a worksheet with a 7-year horizon that neglects present value and rent increases. Ramaglia and MacDonald (1999) does the same, but additionally ignores the equity component of mortgage payments, the appreciation in a house’s value, and selling costs.

Our clients deserve a more thoughtful analysis. This article will discuss the relevant financial principles and show how to construct a simple spreadsheet to do the appropriate financial calculations for comparing buying and renting.

Intrinsic Value

The best way to answer the question of whether a house is a good investment is to think of houses the same way we think of stocks and apply the same intrinsic-value principles. When we consider buying stock, the proper question is not whether it is a good company, but whether the stock is cheap or expensive. Is it worth what it costs? When we consider buying a house, we should ask the same question—not whether it is a good house, but whether the house is cheap or expensive. Is it worth what it costs?

The intrinsic value of a stock depends on its cash flow. The same is true of a house, with the wrinkle that one of the financial benefits of owning a home is not having to pay rent to someone else. The intrinsic-value calculations for a house are a bit messy and are best done with a spreadsheet. But first, let’s develop some insight through a simplified analysis.

Paying Cash

Consider first the unlikely case where you pay cash for a house, the same way that you might pay cash for a stock. Just like a stock, your rate of return consists of the income and the capital gain or loss:

The income from a stock is the dividends. If you pay $100 for a stock that currently pays an annual dividend of $2, the income is 2%; if the stock’s price increases by 7%, your total rate of return is 9%.

For a house, the income is the rent you would otherwise have to pay to live in this house minus the expenses associated with home ownership. If you would otherwise pay $2,500 a month ($30,000 a year) to rent this house, home ownership implicitly gives you $30,000 that you otherwise would pay to someone else. On the other hand, as a homeowner, you will have to pay property taxes, insurance, maintenance, and some utilities that you would not have to pay if you were a renter. If these expenses are $18,000 a year, then your implicit net annual income is $30,000 - $18,000 = $12,000. If the price of this house is $400,000, the $12,000 net income provides a 3% return: 100($12,000/$400,000) = 3%.

To this we add the capital gain. A simple procedure would be to predict the rate of increase in the consumer price index (CPI) and assume that housing prices will rise by a comparable amount. If, for example, the CPI is predicted to increase by 5 percent a year, you might assume that housing prices will increase by 5 percent a year, too. Adding a 5% capital gain to the 3% income gives a total return of 8%.

Although this analysis is for a single year, it works year after year if housing income and prices rise by comparable amounts, keeping the income/price ratio constant. Here, if income and price rise by 5% annually, the income/price ratio stays at 3% and the annual percentage return continues to be 8%.

If housing income and prices do not increase at the same rate, then the income/price ratio (and its inverse, the price/income ratio) will change over time. Suppose, for example, that price/income ratio for a group of houses is $400,000/$12,000 = 33.33 and that housing income increases by 5% a year. If housing prices also increase by 5% a year, the price/income ratio will stay at 33.33. If, instead, housing prices increase by 10% a year, the price/income ratio will increase by about 5% a year and will be 53 after 10 years and 85 after 20 years. If, on the other hand, housing income increases by 5% a year and housing prices are constant, the price/income ratio will fall by about 5% a year and will be 20 after 10 years and 13 after 20 years. These sorts of calculations can provide a reality check if we are tempted to assume that prices will increase at a substantially faster or slower rate than income over an extended period of time.

Leverage

A client bought her first house in 1971 for $28,000. She put $4,000 down and borrowed $24,000. Seven years later, she sold the house for $56,000, twice what she paid for it. This works out to an impressive, but not extraordinary, return of 10.4 percent a year.

But wait! She only invested $4,000 of her own money in this house. Let’s see how much her equity increased. The monthly payments on a 30-year mortgage don’t reduce the principal much for the first several years and, indeed, she still owed the bank almost $22,200 when she sold this house. After repaying the mortgage, her $4,000 investment in 1971 turned into $56,000 - $22,200 = $33,800 of equity in 1978. A 100 percent increase in the value of the house increased her equity by 745 percent, from $4,000 to $33,800! Her annualized return was 35.6 percent. All she did was buy a rather ordinary house that appreciated by 10.4 percent a year, and she made 35.6 percent a year—better than Warren Buffett.

The point of this story is not that this client is a better investor than Warren Buffett—she’s not—but that the leveraged purchase of a house can be an astonishingly profitable investment. In this example, $4,000 in equity was used to reap the returns on a $28,000 house, which created 7-to-1 leverage: $28,000/$4,000 = 7.

You may have noticed that we left out some details, like the rental savings and the mortgage payments. We will soon see how to take these into account. The general principle for leverage is that your financial success depends on whether your investment return from the house (the net income plus capital gain) is greater than the mortgage rate. If it is, the extraordinary leverage involved in most home purchases can make a house the most profitable investment you will ever make. If it isn’t, it can be a money pit.

A More Complete Analysis

We’ve now discussed two issues that are crucial to understanding the financial implications of home ownership:

• The return on a house is the net rental savings plus the capital gains.
  
• Leverage works in your favor if the house’s rate of return is greater than the mortgage rate.

A full analysis is complicated by several factors: (a) unlike other expenses, mortgage payments don’t grow each year; (b) a mortgage has a finite life; (c) mortgage payments build up equity; and (d) the part of the annual mortgage payment that is tax-deductible interest declines over time. We can use a spreadsheet to handle this complexity. We record each cash payment or receipt as it occurs so that we can take into account the time value of money. If we are sticklers for timing, we can use the exact dates on which mortgage payments are made, property taxes are paid, and so on. Because the cash flows are guesstimates, it is generally sufficient to work with monthly or annual approximations.

The guiding principle is to determine the after-tax cash flow each year. Don’t be sidetracked by accounting labels. All we really care about are the dollars coming in and dollars going out. Cash is King! In general, the equation for the net present value (NPV) looks like this:

where the cash flows are discounted by the homebuyer’s required rate of return R. The initial net cash flow is equal to the downpayment and other closing costs. The net cash flows Xt until the sale of the house consist of each period’s rental savings net of the mortgage payments and other expenses associated with home ownership. The final cash flow is the sale price net of the brokerage commission and other expenses and the mortgage balance including any prepayment penalties.

One issue is whether to calculate the NPV for a specified required return R or to calculate the internal rate of return (IRR) that makes the NPV equal to zero. The IRR has the virtue of identifying a breakeven required return for which the investor is indifferent about the investment, but it also has potential pitfalls, including the possibility of (a) an inverted NPV curve (with positive NPV for R > IRR and negative NPV for R < IRR) if the cash flow is positive in the early years and negative in later years; or (b) multiple IRRs if there is more than one sign change in the cash flow.

It is safest to calculate the NPV for a variety of required rates of return; however, the IRR can often be used when comparing buying and renting because the cash flow is typically negative initially and positive in later years, with just one sign change. A situation that might make the IRR misleading is major remodeling expenses that give negative cash flows in the future and more than one sign change.

A free program for calculating the NPV and IRR for the buy-rent comparison is available at this web site. Table 1 shows a summary spreadsheet for HW, a single 34-year-old college professor who lives in a Los Angeles suburb. She wants to compare buying versus renting for a 3-bedroom, 2-bath house with approximately 2,000 square feet of living space located in an attractive area with similar homes. The price of the house is $400,000 and she will make an $80,000 down payment. We assume that rents, housing prices, and most of her housing expenses will grow by 4% a year. Although we used monthly data, Table 1 shows an annual summary for selected years.

1. The first column records the years.
2. The rent savings are what the client would have to pay to rent this house. We assume that the rent is initially $2,000 a month and grows by 4% a year. One attractive feature of a house’s implicit rental income is that it is an after-tax cash flow. If you would pay $24,000 a year in after-tax income to rent a house, then home ownership gives you an extra $24,000 in after-tax cash that you otherwise would pay in rent.
3. The third column records the mortgage payments. We assume a 30-year $320,000 mortgage at a fixed 6% interest rate. We report the total payments here and take into account the tax savings after determining the interest portion of the mortgage payment.
4. Annual property taxes are initially $4,000 (1% of the acquisition cost) and grow by 2% a year, as limited by California’s Proposition 13.
5. Mortgage interest and property taxes are an itemized deduction with a tax saving equal to the amount paid multiplied by the client’s marginal tax rate. If the client pays state income taxes that are deductible from federal income taxes, the net marginal tax rate is equal to m = 1 - (1 - f)(1 - s), where f is the marginal federal tax rate and s is the marginal state tax rate. HW’s marginal tax rate m is 35%.
6. Column 6 encompasses utilities, insurance, maintenance and other expenses that HW will make if she buys instead of renting. These are generally not tax-deductible unless part of the home is used for business purposes. Her anticipated total is $8,520 and is projected to grow by 4% a year. If any major remodeling expenses are anticipated, the cash outlays should be recorded in the year they will occur and any effect on the market value of the house should be recorded in column 8.
7. Column 7 is the net cash flow each year if the house is not sold. This net cash flow is the sum of the entries in columns 2-6.
8. For the sale price, we assume that the market value of the house increases at the same 4% rate as does the rental value, and that the brokerage commission and other expenses associated with the sale are equal to 8% of the sale price. Currently, capital gains up to $250,000 for a single person and up to $500,000 for a married couple filing jointly are not taxable; these limits will probably be increased in the future, though tax laws are always difficult to predict. We assume that this client’s capital gain will not be taxed.
9. The mortgage balance is shown with a negative sign since it will be a cash outflow if the house is sold and the mortgage is paid off. The prepayment penalty, if any, should be included if the mortgage is paid off early. This mortgage had no prepayment penalty.
10. Column 10 uses the spreadsheet’s IRR function to calculate the internal rate of return that sets the NPV equal to zero. If, for example, the house is sold in year 5, the IRR is calculated using the $80,000 downpayment in year 0, the net cash flow in column 7 for years 1-4, and a net cash flow in year 5 equal to the sum of columns 7, 8, and 9. Because these are after-tax cash flows, this is an after-tax rate of return.

In our example, the net cash flow is negative for the first 7 years, but the homeowner is building up equity in an appreciating asset and the IRR is positive by the third year. Figure 1 shows the NPVs for 5-, 10-, and 20-year horizons using required returns ranging from 0 to 20%. The NPVs increase with the holding period because (a) the mortgage payments are fixed while the net rental savings grow over time, causing the cash flow to go from negative to increasingly positive; and (b) the homeowner is building up equity in an appreciating asset. The IRRs are where the NPV curves cross the horizontal line at NPV = 0. HW should buy if her after-tax required rate of return is less than the IRR and rent otherwise. In the current financial environment, few investments look so promising.

What a Difference a Model Makes

This example illustrates the weaknesses of simpler approaches. For instance, it is clearly misleading to ignore property taxes, utilities, insurance, and maintenance—which, on an after-tax basis, are approximately two-thirds the size of mortgage payments.

Even if these other expenses are taken into account, it misleading to compare the initial annual cost of home ownership with the initial annual rent. In our example, the annual cash flow is negative the first year, with the rent $3460 less than the mortgage payments plus other expenses. Those who simply compare current rent with current housing expenses would conclude that renting is less expensive. But the rent saving grows over time, while the mortgage payments do not, and the mortgage payments build up equity in an increasingly valuable property. Even with the 8% sales expense, HW can anticipate a double-digit IRR if she lives in the house for more than a few years.

More generally, the after-tax cash flow from buying a house is typically small or negative for the first few years, as the rental savings barely cover (or fail to cover) the costs of home ownership. As time passes, with rent growing and mortgage payments fixed, the after-tax cash flow becomes a substantial positive number. In addition, the homeowner’s equity is growing, but can easily be swamped by substantial selling costs if the house is sold soon after purchase. These transaction costs underlie the generally sound advice that most people should not buy a house unless they plan to keep it for a while.

This cash-flow structure also creates a potentially fatal flaw for analyses that examine just one horizon of, say, 3, 5, or 7 years. Suppose we look at a 5-year horizon and find that the NPV is negative. This doesn’t necessarily mean that the house is a bad investment. Maybe it will be a good investment if we stay in the house for 8 years. Or maybe it won’t. The only way to find out is to look at several horizons. Similarly, suppose we look at a 7-year horizon and find that the NPV is positive. That doesn’t necessarily mean that the house is a good investment if we stay in the house for only 4 years.

What about the house’s P/E? In our example, the current P/E is $400,000/$24,000 = 16.7. Is that high or low? We can’t tell unless we look at the other costs and benefits of home ownership, consider projected growth rates, and compare the IRR to current market interest rates. What about the change in the P/E? This is even less informative. Housing prices happen to have increased much faster than rents in this particular area over the past several years, causing the housing P/E to increase substantially. But an increased P/E doesn’t necessarily mean this house is a bad investment. With our plausible assumptions, this house looks like an excellent investment.

What Matters Most?

Don’t be dismayed by the fact that you cannot provide exact values for the future cash flow. You don’t need to know the values to the last penny. The way to handle imperfect knowledge is to try a range of values. More generally, it is a good idea to do a sensitivity analysis to see whether the buy/rent decision is reasonably robust or depends critically on certain key assumptions. We will show three examples.

First consider mortgage rates of 8% and 10%, in addition to the 6% base case. Figure 2 shows the NPVs for a 10-year horizon and Figure 3 shows the IRRs for horizons up to 30 years. The effects of mortgage rates on the NPVs are very strong because the financial market conditions that increase interest rates also increase the prospective buyer’s required rate of return. Suppose, for example, that the mortgage rate and required return both increase from 6% to 8% and then 10%. The NPV falls from $62,246 (point A) to $9,307 (point B) and then -$34,444 (point C). Two conclusions are apparent: (a) higher interest rates make buying less appealing, and (b) an income approach to valuing a house should take mortgage rates into account.

Now consider 0%, 4%, and 8% growth rates of rent, housing prices, and various expenses. Figure 4 shows the NPVs for a 10-year horizon and Figure 5 shows the IRRs for horizons up to 30 years. The growth rate is clearly a crucial parameter. The purchase of this house will not be financially rewarding unless there will be some growth in rents and housing prices.
The price is also a crucial parameter as there is some price at which this house is too expensive. At $400,000, this house looks like a good investment if rents and prices increase at plausible rates. If the price were $600,000 or $800,000, Figure 6 shows the NPVs for a 10-year horizon and Figure 7 shows the IRRs for horizons up to 30 years. At $800,000, the house loses a lot of its luster.

If HW didn’t have the $80,000 down payment or couldn’t handle the negative cash flow for the first few years or didn’t plan to stay in the house for at least 3 years, we would have advised her not to buy this house. But she could afford it and she planned to stay in the house for at least 6 years.

She decided to buy the house.

References

Detweiler, John H. and Radigan, Ronald E., “Computer-Assisted Real Estate Appraisal: A tool for the Practicing Appraiser,” The Appraisal Journal, 1996, 64: 91-102.

Detweiler, John H. and Radigan, Ronald E., “Computer-Assisted Real Estate Appraisal: A tool for the Practicing Appraiser (2),” The Appraisal Journal, 1999, 67: 280-286.

Feldman, Amy. “A P/E for Your Home?,” Money, July 2003, 107-108

Goodman, Jordan E. Everyone’s Money Book, Chicagp: Dearborn Trade, 2001.

Isakson, Hans R., “The Review of Real Estate Appraisals Using Multiple Regression Analysis,”  The Journal of Real Estate Research, 1998, 15: 177-190.

Joint Center for Housing Studies of Harvard University , The State of the Nation’s Housing,” 2002.

Keown, Arthur J. Personal Finance, Upper Saddle River, New Jersey: Prentice-Hall, 1998, 253-256.

Miller, Ted. Kiplinger’s Practical Guide to Your Money, Kiplinger, 2002.

Nguen, N. and A. Cripps. “Predicting Housing Value: A comparison of Multiple Regression Analysis and Artificial Neural Networks, Journal of Real Estate Research, 2001, 22: 313-336.

Orman, Suze. The Road to Wealth, New York: Riverhead, 2001.

Quinn, Jane Bryant. Making the Most of Your Money, New York: Simon & Schuster, 1997, 1000-1001.

Ramaglia, Judith A., and MacDonald, Diane B. Personal Finance, Cincinnati, Ohio: South-Western, 1999, 250-251.

Table 1 HW’s Buy-Rent Decision, Base Case

Figure 1 NPVs for Different Horizons

Figure 2 NPVs for a 10-year Horizon and Mortgage Rates of 6%, 8%, and 10%

Figure 3 Annual After-Tax IRRs for Mortgage Rates of 6%, 8%, and 10%

Figure 4 NPVs for a 10-year Horizon and Growth Rates of 0%, 4%, and 8%

Figure 5 Annual After-Tax IRRs for Growth Rates of 0%, 4%, and 8%

Figure 6 NPVs for a 10-year Horizon and Prices of $400,000, $600,000, and $800,000

Figure 7 Annual After-Tax IRRs for Prices of $400,000, $600,000, and $800,000