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# Imputed Rent: Calculating Return on Home Purchases

I’ve seen a lot of different ways to calculate the rate of return on a home purchase, but my favorite so far is the one William Bernstein provides in The Investor’s Manifesto.

First, he separates the decision to purchase a home from the decision to finance that purchase with borrowing. We calculate the rate of return from the investment itself, then we can determine how borrowing affects that rate of return.

### Calculating Expected Return for a Home Purchase

Bernstein provides the following equation, which (not so coincidentally) looks very much like the Gordon Equation he uses to predict stock market returns:

Expected Return = D + G – C, where

D = imputed rental dividend,
G = inflation-adjusted growth in home value, and
C = costs (insurance, property taxes, and maintenance)

### What the heck is “imputed rental dividend?”

The imputed rental dividend is the payoff from buying the home that comes from not having to pay rent. Remember, for the moment we’re assuming that you pay the whole price up front, so there’s no mortgage payment.

So, for example, if a home had a \$180,000 price and it replaced a \$1,000 monthly rent bill, its imputed rental dividend would be 6.67% annually. (\$12,000 ÷ \$180,000.)

### The Rest of the Calculation

Bernstein assumes property taxes, insurance, and maintenance total approximately 3% of the home’s value each year. Obviously this will vary depending upon circumstances such as location and the age of the home.

Historically, inflation-adjusted home prices have increased at a rate of approximately 1% annually. Of course, it’s not exactly steady on a year-to-year basis, and this figure can also vary dramatically depending upon location.

All together, that gives us the following:

Expected Rate of Return = 6.67% + 1% — 3% = 4.67%

Note: The imputed rental dividend is tax free, as is, for the most part, the capital gain resulting from the sale of a home. As a result, this 4.67% expected annual return is essentially an after-tax return.

### Borrowing for a Home Purchase

Of course, most people don’t purchase their homes entirely with cash. They borrow money. Borrowing money to invest is known as leveraged investing.

As with other leveraged investing scenarios, the fact that you’re borrowing money magnifies your returns (whether good or bad).

• If the return you earn is greater than the interest rate you’re paying, the return on your leveraged investment will be better than it would have been if you’d purchased the investment entirely with cash.
• If the return you earn is less than the interest rate you’re paying, the return on your leveraged investment will be worse than it would have been if you’d purchased the investment entirely with cash.

End result: In our example above, the home purchase only makes sense if our prospective home buyer can take out a mortgage with an after-tax, after-inflation interest rate of below 4.67%.

### Lessons to Be Learned

In my opinion, there are two primary lessons here:

First, if you’re planning on buying a house, go ahead and take a crack at figuring out what your rate of return will be. (And don’t listen to the realtor’s estimates.) If a home is selling for 20 or 25 times its annual rental value, it’s going to be quite difficult to earn a worthwhile rate of return.

Second, this whole calculation is extremely sensitive to the assumptions we make. For example, if our home buyer ends up taking out a mortgage with an after-tax, after-inflation interest rate of 3.5%, she should be in good shape. Borrow money at 3.5%, invest it at 4.67%. Super!

But what if we guessed wrong, and her annual costs of home ownership end up being 4% of the home price instead of 3%? And what if the inflation-adjusted increase in home value ends up being only 0.5% annually instead of 1%? Now she’s borrowing money at 3.5% and investing it at 3.17%. Whoops!

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1. Great example of why you can’t assume that’s it’s always a good idea to buy instead of rent. Good job, Mike!

2. Mike,

The one thing I would add is an example of how to calculate the after-inflation interest rate given a fixed mortgage rate.

-Rick

3. Mike says

Rick:

Good point. The calculation is simply:
Inflation-Adjusted Interest Rate = After-Tax Interest Rate – Rate of Inflation

It’s a bit of a guess though, as there’s no way to know what rate of inflation we’ll see in the future.

That said, we’ve already built an inflation assumption into the expected return calculation when we estimate future inflation-adjusted increases in home values, so just make sure you use the same inflation assumption in each part of the calculation.

4. TFB says

I would be very careful with the assumptions. In many markets the price to annual rent is 20-25 even today. So that 6.67% number becomes 4-5%. Also, you have to use the rent which you otherwise are going to pay if you don’t buy a home, not what the home would rent for. People usually buy a larger or nicer place than what they would rent. If your alternative to buying a home is to stay in the current rental, you should use that rent as the rent savings number.

5. Matt says

With little expertise in this area, but keen interest, I’m wondering how the % of equity factors in here, if at all. For example, if the mortgage is for 60% of the house price vs. 90%.

6. Mike says

TFB: Very good point about making sure to use your current rent when calculating the costs of continuing to rent vs. buying a home. Thanks for mentioning that. 🙂

Matt: The more leveraged the investment (i.e., the greater percentage of it you fund with borrowed money) the more the returns will be magnified.

If your (non-leveraged) return is greater than the rate at which you’re borrowing, more leverage = better returns.

If your (non-leveraged) return is less than the rate at which you’re borrowing, more leverage = worse returns.

7. Monevator says

Well yes, the trouble with that equation is G, the expected rate of change in home value.

How long is a piece of string comes to mind. G will be all over the place, and also presumably most market participants are doing something similar to Bernstein’s equation in their heads, roughly, so there’s an element of feedback involved.

The Economist did a lot of work on rent and house prices throughout the decade; the called the bubble but way too early (as did I) and they expected a far greater correction in prices based on rents (as did I).

Bitter, moi?

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