# Cap Rate Calculations Today

## Lenders and investors see ROI differently.

Since the market crash five years ago, CCIMs and other commercial real estate professionals have been asked far too often, “What is it worth?” With a paucity of sales from which to extract investment benchmarks, many of us were limited to guesswork, mathematics, or both. To add to our challenges, credit remained tight, forcing a retreat of some lenders from commercial real estate all together.

When
financing was not at issue, some of us turned to mathematics to explain the
market in a period without empirical transactions. (See “Cap Rate
Calculations,” Sept./Oct. 2009 *CIRE*)
But as we head deeper into recovery and lenders return to the market, let’s
take a closer look at how lenders might “back of the envelope” or underwrite
real estate today by using the Gettel formula to determine capitalization
rates. The information may help us close more escrows in our efforts to
understand the plight of lenders.

## The Lender’s Perspective

In the 2009 article, we discussed L.W. Ellwood’s original cap rate analysis, with its algebraic origins stemming from risk/reward models influenced by mortgage and equity rates of return. The Ellwood formula with its comprehensive algorithms gave way to a streamlined algebraic equation proposed by Charles Akerson, MAI.

With the return of lenders to commercial investment markets, today’s all-cash deals are giving way to leveraged transactions. Let’s look at another formula that is streamlined for quick cap rate calculation based on the most common components in the Ellwood and Akerson formulas: leverage, or loan-to-value ratios; cost of debt, or interest rates; and debt coverage ratios, which is the cash flow available for debt servicing. This is the Gettel formula.

The
Gettel formula explains cap rates in a simplified fashion by examining a
commercial real estate investment from the perspective of a bank lending
committee. In “Good Grief, Another Method of Selecting Capitalization Rates” (*Appraisal
Journal*, 1978, p.98), Ronald Gettel makes the
point that “if the appraiser has credible data on debt coverage factors but
lacks data for a convincing projection of, say, future depreciation or
appreciation, he may feel justified in opting for this simpler method [debt
coverage].” The Gettel formula, which is also known as the debt coverage formula
(*The Appraisal of Real Estate*,
13th edition, p. 508) explains the cap rate as follows:

R = M x Rm x DCSR, whereas:

R = capitalization rate;

M = loan-to-value ratio (percentage of market value that is financed);

Rm = mortgage constant; the “mortgage cap rate” or return on/of a mortgage from annual loan payment divided by the year 1 loan balance; and

DCSR = debt coverage service ratio

Inherent in the Gettel formula are the same risk/reward factors that the Ellwood and Akerson formulas embraced. While Ellwood and Akerson use K-factors or sinking funds to explain the amortization of debt, the build-up of equity, and the constant rate of change in value and income, in Gettel, an assumption of principal pay-down remains a result of amortization of debt. In summary, the Gettel formula yields similar results to Akerson but requires substantially less calculation, as the investor’s rate of return (equity) is less consequential from the lending committee perspective.

Consider the following example. A $100,000 property with $7,000 in annual net operating income can be leveraged at 75 percent for 30 years, due in 10 years, at 5 percent annual interest and at a debt coverage ratio of 1.25. Application of the Gettel formula and its assumptions are displayed in Table 1.

## The Investor’s Perspective

The Gettel formula derives a cap rate (R) of 6.04%, based on the mortgage terms expressed. Given the same terms, what would the Akerson model produce? To process it, a few other items are required: a return on equity (Re), a constant rate of change (CR) in income and value and the side calculations of a sinking fund factor (1/Sn), an amortization rate of the holding period (loan is due in 10 years) and a percentage paid off (based on the holding period). How do we determine the return on equity requirement without using industry reports? Consider the $100,000 property with $7,000 NOI and annual debt service of $4,831 once again, holding all previous mortgage terms constant. (See Table 2: Akerson Formula Mortgage Terms.)

The NOI in Year 1 is $7,000, which escalates at 3.00% per annum (CR) over the 10-year holding period at the consumer price index. Debt service is constant at $4,831 per annum (6.44% Rm x $75,000 loan [M] = $4,831 annual debt service). The difference is a pretax equity return. The Re is calculated by dividing the annual pretax equity return by the equity investment (1-M) or $25,000. In this case, a Re of 8.67% to 17.21% is generated over the holding period. The industry averages provided by RealtyRates.com for first quarter 2013 show most commercial property equity dividend rates or Re ranging from about 10.75% to 17.00%. For purposes of this analysis a Re of 12.00% is assumed.

A sinking fund factor (1/Sn) is an account in which periodic deposits of equal amounts are accumulated in order to pay/amortize a debt or replace depreciating assets with a known replacement cost. It is the compound interest factor that yields the amount per period that will grow (with compounded interest) to the desired reserve (or loan) amount. The sinking fund factor is one of the six functions of a dollar and can be calculated as the present payment per period with the following HP 12C key entries:

n = 10 (10-year holding period/loan expiration with one payment per year assumed);

I% = 12.00% (equity rate is used instead of the interest rate as a sinking fund is a private, noncommercial account that would not be offered by a bank);

PV = 0 (The fund will be fully amortized at the end of the hold);

FV = 1 CHS (calculated on the value of $1 needed in the future); and

Solve for PMT = 0.057 or 5.70%

The loan amortization rate for the holding period is the payment per period on a present value of $1 over the 10-year hold, but at the original loan terms offered as it calculates the loan payoff rate. Thus for the 12C:

n = 10 gn (10-year holding period/loan expiration with 12 payment per year assumed);

I% = 5.00% gi (loan rate is used to determine amortization rate for existing loan);

PV = 1 CHS (loan terms based on the PV of $1 or actual loan amount);

FV = 0 (loan is due in 10 years); and

Solve for PMT = 0.0106 or 1.06% but must be multiplied by 12 given the monthly loan payments, thus PMT = 0.1273 or 12.73%.

The loan percentage paid off can be easily calculated by dividing the mortgage constant (less loan interest rate) by the loan amortization rate for the holding period (less the loan interest rate). Thus:

Rm = ((0.064 or [$4,831 ÷ $75,000]) - .05) = 0.0144; and

AMH = (0.1273 - .05) = 0.0773; So:

0.0144 ÷ 0.0773 = 0.1866 or 18.66%

As shown in Table 3, with the application of the Akerson formula, a cap rate of 6.86% is derived.

## The Difference

The Akerson formula results in a rate that is at least 75 basis points higher than the rate derived by the Gettel formula. The higher Akerson rate is attributed to the investment from a perspective of an individual investor whereas the Gettel formula focuses on the investment from the perspective of a bank lending committee. The Gettel formula is accounting for debt coverage and principal pay-down whereas the Akerson formula accounts for these items as well as equity buildup. Simply put, the contingencies for equity account for roughly 86 basis points of additional risk premium in the Akerson application. In terms of value on the $7,000 NOI, the Gettel formula produces a value of $115,908 and the Akerson formula produces a value of $101,996. Of course both are of nominal difference, yet one is a value to a loan committee based on the property’s ability to pay and the other is a price that buyer would be willing to spend, given these investment criteria.

Which formula is correct? The universal answer is, “It depends.” Of course the results are merely 12 percent apart, but in reality, perhaps both answers are correct. Recall that an appraisal of market value as defined by the Uniform Standards of Professional Appraisal Practice is such only to the intended user. Thus, if your client is a potential buyer, she may provide you with her equity hurdles in addition to costs of debt. Either way, you now have several tools at your disposal, in addition to any sale comparables you analyze, to provide your client or the intended user with credible, quality results founded in generally acceptable appraisal standards.

## Cap Rates at Mid-2013

We’ve refreshed our memory on the anatomy of cap rates and fortunately, this time around, we may soon have data points in the form of sales to support our conclusions. But as a starting point, what are cap rates at mid-2013? Elizabeth Braman, CCIM, JD, of ReadyCap Commercial supplied the following current commercial real estate lending terms in Los Angeles, for first quarter 2013. (See Table 4.)

With these base requirements, the Gettel formula produces the cap rates (some assumptions point-estimated) listed in Table 5. Based on these lending terms, cap rates discussed within loan committees range between 5.00% and 7.00% for all commercial types of real estate in Los Angeles.

“Apartments have better underwriting terms than commercial, generally speaking,” Braman adds, due to the frequency of apartment sales in comparison to other commercial uses. Also LA is a market with limited supply of quality assets and virtually no developable land within city limits for most high-intensity commercial projects. Given these parameters, it is understandable why cap rate thresholds remain low in Southern California.

In lieu of a for-sale sign, an appraisal is the only evidence of market value accepted by third parties in the United States. Valuation is an orderly science and an appraisal is written in conformity with the commonly applied practices and principles of real estate appraisers. Yet like their broker brethren, even appraisers were perplexed when clients asked “How much?” over the past few years. There simply were insufficient data points to suggest a relevant market.

Yet to those armed with CCIM’s CI 101 and CI 103 smarts, the capitalization of income in response to a dearth of data was a natural default. So long as there is leverage, income-producing real estate will be valuable. So long as we continue our studies of investor hurdle rates, both from the perspective of the lender and investor, we’ll have a means of converting stable income streams into value.

**Eric
B. Garfield,** CCIM, MAI, is the director of the
tangible asset valuation practice at WTAS LLC in Los Angeles. Contact him at
eric.garfield@wtas.com.