## Calculating a Derivative Capitalization Rate

How do you know what an income property is worth? How do you know that if you pay X amount for a property that you can get the return you desire on your investment? Is there some way to calculate the maximum you can pay for an investment and still achieve your investment goals? Do you know how to get the answers to these questions? This article is written to give you a valuable tool to use in answering the critical questions regarding the value of an income property.

Among the many tools used by investors to gauge the worth of an income property, one of the most popular is a capitalization rate, aka cap rate. But as it is typically used, it is probably the one most misused concept in the real estate investment business. While brokers, sellers and lenders alike are fond of quoting deals based on the “cap rate”, the way it is typically used they are really shortcutting the true use of a valuable tool.

The typical way a broker prices a property is to take the Net Operating Income (NOI), divide it by the sales price, and voila!, there’s the cap rate. Example: Say the property has an NOI of $125,000, and the price is $1,125,000. Then

$125,000/ $1,125,000 = 11.1% cap rate.

But what does that number tell you? Does it tell you what your return will be if you use financing? No. Does it take into account the different finance terms available to different investors? No. Then just what does it show?

What the cap rate represents as used above is merely the projected return for one year as if the property were bought with all cash. Not many of us buy property for all cash, so we have to break the deal down, usually by trial and error, to find the cash on cash return on our actual investment using leverage (debt). Then we calculate the debt service, subtract it from the Net Operating Income, and then calculate our return. If the debt terms change, or loan to value, or our return requirement, then the whole calculation has to be performed again. That’s not exactly an efficient use of time or knowledge.

Brokers are also fond of quoting a “market cap rate.” This is an effort to legitimize an assumption, but it is flawed in its source.

As a comparison tool it is almost impossible by any means to find out what other properties have sold for on the basis of the cap rate. In order to correctly calculate a cap rate, and get an apples-to-apples comparison, we must know the correct income and expenses for the property, and that the calculations of each were done in the same way as will be explained below. This information is not part of any public record. The only way to access the information would be to contact a principal in the deal, and that just isn’t done because the information is generally held in the strictest confidence. A broker may have the details pertaining to several deals in the marketplace, and with enough information about enough deals the information may rise to the level of a market cap rate. But very few brokers are involved in enough deals in one market to have that much information. So the conventional wisdom becomes a range of cap rates for property types, which may or may not apply to the property you are looking at, and certainly does not take into account your own return requirements.

So what do you do when you’ve found a property that looks promising, and the broker tells you the cap rate is 11.1% and you better act fast? How do you know if it is worth pursuing? For years I would immediately jump in the car, go take a look, and then start crunching numbers making assumption after assumption to arrive at some estimate of value. The truth is I was guessing. I wasn’t looking at the right numbers, and I spent a lot of time guessing. There is a better way. It is not a magic bullet, but it does give an investor a powerful tool to use in gauging value.

**What’s it Worth to YOU?**

The real question in valuation is not how much I, or any other investor, or even an appraiser value a property at, nor the value from a cap rate estimated in the market, but rather the value at which YOU can attain YOUR investment goals, that is reflective of YOUR borrowing power, and gives you an intelligent starting point for the analysis. I can give you a tool that will give you that answer. I promise you if you learn how to do this it will give you a leg up on 90% of the brokers and investors out there.

First, we have to become conversant with the terminology.

Critical to this calculation is that the NOI (Net Operating Income) is figured consistently with industry norms. The generally accepted definition of NOI is:

Gross Income – Operating Expenses = NOI

Please note that the operating expenses do not include debt service, or the interest component of debt service.

Obviously, the income and expenses must be verified, or all calculations that flow from them will be flawed. Verifying the income is usually easier than the expenses. Rent roll analysis and a contract contingency for tenant estoppel letters at closing can settle the income stream conclusively.

On the expense side, normal due diligence includes verifying with third party suppliers as many of the expenses as possible. Care must be taken in evaluating the operating expenses to uncover any anomalies that may exist under the present ownership. Owners often take a management fee that may or may not be market based; maintenance expenses may or may not include labor charges; items such as “office expense” or “professional fees” or “auto expense” may or may not be property specific. In short, before accepting the NOI presented, effort must be made to understand what is behind the numbers. This is known as “normalizing” the numbers. You can also tweak the numbers to reflect the way you will own and manage the property. No two investors will own and operate a property the same way. It is entirely possible for two investors to look at the same property and come up with two different NOIs, and two widely divergent values, and both are right.

That’s why appraisers use comparable sales, replacement value and the income approach as part of a three-pronged methodology in estimating value. They are charged with making the appraisal representative of the market conditions and the typical requirements of investors and lenders active in the market. The third method, the income approach, is usually given the most weight. That method is also known as the “band of investment” method of estimating the present value of future cash flows. That method addresses the return required on both equity and debt, and leads to what can be called a derived capitalization rate.

### Deriving Your Cap Rate

After I am reasonably certain that the NOI is accurate the best way to get an initial value indication is to use a “derived” capitalization rate. That requires two more pieces of information. You have to know the terms of financing available to you and the return you want on your investment. We can then use these terms for both debt and equity to indicate the value at one precise point in time–the instance of when the operating numbers are calculated–to derive the cap rate that reflects those terms. (The value in future years is another discussion.)

Deriving a cap rate works like a weighted average, using the known required terms of debt and equity capital.

**The Bank’s Return: the Loan Constant**

Let’s start with the finance piece. We need to know the terms of the financing available, and from that we can develop what is known as the loan constant, also called a mortgage constant.

The loan’s constant, when multiplied by the loan amount, gives the payment needed to fully repay the debt over the specified amortization period. IT IS NOT AN INTEREST RATE, but a derivative of a specific interest rate AND amortization period. When deriving a cap rate, one must use the constant since it encompasses amortization and rate, rather than just the rate. Using just the interest rate would indicate an interest only payment and distort the overall capitalization process.

The formula for developing a constant is:

Annual Debt Service/Loan Principal Amount = Loan Constant

You can use ANY principal amount for the calculation, then calculate the debt service and complete the formula. The constant will be the same for any loan amount. For example, say your bank says they will generally make an acquisition loan at a two points over prime, with twenty-year amortization, with a maximum loan amount of 75% of the lower of cost or value.

Say prime is at its current 4.5%. That means the loan will have a 6.5% interest rate. Using a payment calculator or loan chart, find the payment for those terms. On a loan for $10,000, the annual debt service required is $894.72. Divide that by $10,000 to find the constant.

894.72/10,000= .08947

Using these terms, the loan constant for that loan would be .08947 (I usually round to four or five digits… depending on the level of exactitude desired, you can use as many as you like.) The answer will be the same if you use $100,000 or any other number as the principal amount. (One hint though: do not use a principal number with less than five digits, because the rounding will affect the outcome.)

You might note here that the mortgage constant is basically the lender’s cap rate on his piece of the investment. Both the mortgage constant and “cash-on-cash” rates for equity are “cap” rates in their basic forms. A cap rate is any rate that capitalizes a single year’s income into value (as opposed to a yield rate).

### Your Return: Cash-on-Cash Return

The next step is to provide for the return on the equity.

Start with the return you want on your money: Say the cash-on-cash return you are seeking is 20%. The “cash-on-cash” rate is also known variously as the equity dividend rate, equity cap rate, and cash-throw-off rate. It represents the “cap” rate to the equity position, and to be consistent we will call it the equity constant. If an investor puts in $30,000 and requires a 20% pre-tax return, then his annual cash in the pocket after paying the mortgage (but before income taxes) would have to be $6,000.

In this case, the equity constant is .20.

### Put It All Together: Weighted Average

Each of these cap rates is then weighted based on the loan-to-value ratio of each of the debt and equity positions to build the “overall cap rate”. The formula looks like this:

(LTV debt ratio x mortgage constant) + (LTV equity ratio x equity constant) = derived cap rate

To finish the example, using the mortgage terms given above, and the desired 20% cash on cash return, the following would be the “overall cap rate” with a 75% loan-to-value on the debt component:

(.75 x 0.08947) + (.25 x 0.20) = .1171

or

.0671 + .05 = .1171

To convert to a percentage, move the decimal two places, and therefore, under the stated conditions, the required cap rate for the property (income stream) is 11.71%. Using the normalized NOI figure, then the indicated value is calculated with this formula:

NOI/Cap Rate = Maximum Purchase Price

For the original deal above, the value would be calculated thusly to attain the desired return:

$125,000/11.71% = $1, 067,464

The asking price of $1,125,000 is very close (within 10%) to the indicated value of $1,067,464. This is a deal that would definitely be worth taking a look at. Had the deal been priced at a 10% cap rate, or $1,250,000, then I might still take a run at it since the indicated value is within ten to fifteen percent of the asking price. In a normal market, California aside, most sellers do not expect the property to sell for the asking price.

### Not a Magic Bullet

Now please note that I said at the beginning that this is a starting point. It is not the end-all-and-be-all of valuation, nor should it be. That doesn’t exist.

Many factors can influence the value of an income property both up and down. Some of the most important include deferred maintenance; security of the income stream (strength of the tenants and length of the leases); comparable sales in the area; general economic and market conditions; and local market conditions. These factors speak to the relative risk and effort involved in the continuance of the income stream. As risk or effort increases, so does the investor’s required return on equity. Increase the required equity return and the cap rate changes, and so does the value. At this point you literally write your own paycheck.

This is a powerful tool if understood and applied correctly. Play around with some alternative scenarios of returns, loan terms and rates, etc. and you will see the effect of changing different parts of deal structure. You should also now see why it is so critical to verify EXISTING income and expense BEFORE establishing value. This little exercise also shows why I harp all the time on no two investors coming up with the same value for the same property.

DO NOT however, use this as a “magic bullet”, and stop your analysis after the calculation. I cannot stress enough the importance of performing thorough due diligence in commercial income properties. That alone is what determines the difference between being a true “investor”, and the next “don’t wanter” seller.

My thanks to several people who posted valuable input on the commercial newsgroup at CRE Online. They include Paul Ness, MAI, Jim Rayner, and Jerry Menke.