Okay, for those of you interesting in the whole “Buy vs. Rent” thing, I found a new study that seems to provide a good way of comparing the costs of both.

A Formula

The formula for the annual cost of home ownership, also known in the housing literature as the “imputed rent,� is the sum of six components representing both costs and offsetting benefits.

# The first component is the cost of foregone interest that the homeowner could have earned by investing in something other than a house.

# The second component is the one-year cost of property taxes.

# The third component is actually an offsetting benefit to owning, namely, the tax deductibility of mortgage interest and property taxes for filers who itemize on their federal income taxes.

# The fourth term reflects maintenance costs.

# The fifth term is the expected capital gain (or loss) during the year.

# The sixth term represents an additional risk premium to compensate homeowners for the higher risk of owning vs. renting.

The sum of these six components gives the total annual cost of home ownership.

Equilibrium in the housing market implies that the expected annual cost of owning a house should not exceed the annual cost of renting.

Using the above equation, we can summarize this logic by equating annual rent with the annual cost of ownership.

For the purpose of illustrating how the user cost model works, suppose the following:

(i) the risk-free 10-year interest rate 5.125 percent;
(ii) the (30-year fixed) mortgage rate is 6.21 percent;
(iii) the annual depreciation rate 2.5 percent (Harding, Rosenthal and Sirmans
(2004);
(iv) the marginal tax rate of the typical home buyer is 25 percent;
(v) the property tax rate is 1.11 percent (Boston’s residential tax rate is $11.07 per $1,000 of assessed value, for fiscal year 2006 (however, we’re ignoring Boston’s huge $1,000 residential exemption, which would lower your property tax, considerably);
(vi) the risk premium is = 2.0 percent; and
(vii) the long-run appreciation rate of housing prices is 2.0 percent: which is made up of an expected rate of inflation of 2.0 percent plus a real expected appreciation rate of housing of 0.0 percent. (Inflation was running 3.5% during the first quarter, 2006, but it will probably slow down, to a more manageable 2.0% or so, over the coming months.) (The appreciation rate of housing was actually an average of 1.8% for the years 1980-2004, but I made it zero for this example, because I knew if I said prices would continue to increase, people would say I was living in a fantasy world, even though prices have continued to rise, each quarter, and are expected to continue to rise, by 5%, this coming year.)

Under these assumptions, the predicted user cost is 6.9075 percent: that is, for every dollar of price, the owner pays 6.9075 cents per year in cost. Leaving aside other differences between renting and owning, people should be willing to pay up to 14.48 times (1/0.069075) the market rent to purchase a house.

Hence, for example, a two-bedroom apartment that rents for $2,400/month ($28,800/year) should sell for up to $417,024.

A one-bedroom apartment that rents for $1,800/month ($21,600/year) should sell for up to $312,768.

Okay, so condo prices in most of Boston are higher than that.

Overpriced? Perhaps. We’re only talking one point in time, of course. Interest rates, both Treasury Bonds and mortgage loan rates, can go up (and down), offsetting each other, but affecting the outcome of this calculation.

More important, if you play with the inflation/appreciation number, you get a wide range of results.

For example, if we add back in the historical rate of appreciation, 1.8%, you get a much lower cost of ownership (5.1075 percent). Using these numbers, a person should be willing to pay 19.58 times the market rent to purchase a house.

Hence, for example, a two-bedroom apartment that rents for $2,400/month ($28,800/year) should sell for up to $563,904.

A one-bedroom apartment that rents for $1,800/month ($21,600/year) should sell for up to $422,928.

This price-to-rent ratio provides a ceiling against which housing prices can be judged “too high� or “too low.�

If price multiplied by the user cost exceeds the market rent, housing is relatively costly.

Source: Federal Reserve Bank of New York Study (warning, .pdf)

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