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.