Derived Capitalization Rate

In an earlier article (How to Estimate Resale Value Using "Cap" Rates) we discussed income capitalization in general terms. It would not be unreasonable to ask, "Where do cap rates come from?" If the stork doesn't bring them, who does? Typically, the marketplace drives cap rates. Investors tend to keep tabs on what rate fellow investors are achieving and are reluctant to settle for anything less favorable. The rate that prevails for a particular type of income property (e.g., office, retail, etc.) in a particular market is called the Market Cap Rate.

You can further dissect an investor's cap-rate expectation, however, using an approach called "Band of Investment" or "Derived Cap Rate." The Derived Cap Rate breaks the calculation of the return into two components: financing and equity. The lender gets a return on the financing; the investor gets a return on the equity. The Derived Cap Rate is the weighted average of the two.

A simple example should illustrate the process. Examine this calculation:

0.80 x 0.10785939 = 0.086287514 financing cap rate
0.20 x 0.12000000 = 0.024000000 equity cap rate
= 0.110287514 derived cap rate


You are purchasing a property with 20% equity and 80% financing. You find that loans are available for 15 years at 7%. Start with the financing component, the so-called "lender's cap rate." To do so, it's necessary to introduce a new term here: Mortgage Constant. The Mortgage Constant equals the payment amount on a loan of $1 at a given rate and term.

There are tables of mortgage constants where you can look up the answer. You can also use a spreadsheet, of course, to calculate the payment on a $1 loan, but be sure to format the results to display about 8 to 10 decimal places. If you try this with a calculator, use $1,000,000 as the amount instead of $1 so that you can display a meaningful number of digits. Then move the decimal point 6 places to the left.

Whichever method you use, you should end up with 0.00898828. That's the monthly payment on $1 at 7% for 15 years, aka the monthly Mortgage Constant.

But you're dealing with annual cap rates, so you need to multiply the monthly Mortgage Constant by 12 to find the annual constant of 0.10785939. (Rounding may affect this slightly.) This is the lender's cap rate. Since the lender is contributing 80% of the money to this deal, multiply that by 0.80 to get the lender's portion of the Derived Cap Rate.

What is the investor's cap rate? The classic approach is to specify a "risk-adjusted safe rate." The logic here is that you take a safe rate such as the current T-Bill and then bump it up to account for the risks and travails of being a real estate investor. With a T-Bill you always get paid and the Treasury Secretary never calls you in the middle of the night to tell us the toilets are stopped up. Multiply the investor's desired rate by 0.20 to determine the investor's portion of the Derived Cap Rate.

But bump it up how high? You may detect some circumlocution in our attempt to derive a cap rate that is more objective than the Market Cap Rate, because ultimately you need to make a subjective judgment as to how much of a risk adjustment you're going to make. Investors are competitive creatures, and as suggested above, they are not going to settle for less than everyone else in is getting in their; and although you might want even more than that, wanting and expecting are two different things. It comes down to this: Your risk adjustment is typically market-driven, so you probably end up right back with something close to the Market Cap Rate. To put it another way, you should not be too surprised to find that the prevailing market rate is what it is because the market has taken into account both the typical current cost of financing and the current expectations regarding an acceptable risk-adjusted return.

Does this mean your entire derivation exercise was pointless? Not really, because you can use this technique to see how cap rates might be affected in a different financing environment, or with a shifting tolerance for risk.

You can also run this process backwards if you want to discern some useful information: namely, what kind of cash-on-cash return are investors in your market getting?

Consider the example above, but this time solve for a different variable. If you know that the Market Cap Rate is 11% and that the typical financing available is for 7%, 15 years with an 80% loan-to-value ratio, you can disassemble the weighted average to find out what the equity cap rate is. By doing so, you surmise that investors in your market are expecting to achieve a 12% cash-on-cash return in the first year of ownership. Now you have one more yardstick you can apply as you evaluate potential income property investments.

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