ROI Formula: Lenders vs. Investors

08 Jan ROI Formula: Lenders vs. Investors

 

CAP Rate Calculations; The ROI Formula Lens of Lenders vs Investors

 
After the 2007 market crash, CCIMs  and  other  commercial  real estate  professionals were often asked, ‘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. This article presents a variation on the usual ROI formula and analyzes the concept of return on investment (ROI) from lender vs. investor perspectives.

The Lender’s Perspective
In the 2009 article, we discussed L.W. Ellwood’s original ROI formula 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 stream­ lined 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 ROI 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 ROI 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 ROI 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.

Table 1: Gettel Formula Example

 

The Investor’s Perspective
The Gettel ROI 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.)

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 cover- age ratio of 1.25. Application of the Gettel formula and its assumptions are displayed in Table 1.

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%

The Difference
The Akerson ROI 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.

 

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

Which ROI 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.

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.

This article on ROI Formula is written by Eric B. Garfield, CCIM, MAl and reprinted with permission from Commercial Investment Real Estate Magazine, the magazine of the CCIM Institute. 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.

Editor’s notes:

1. To see an update on using 2013 CAP rates for different asset classes, see original CCIM version of this article

2. For further reading on the ROI Formula by Ronald E Gettel see:

See Ronald E. Gettel, “Gettel’s Method”, Real Estate Guidelines & Rules of Thumb, McGraw- Hill, 1976, p.136

See Ronald E. Gettel, “Good Grief, Another Method of Selecting Capitalization Rates,” The Appraisal Journal, January 1978

See “Debt Coverage Formula” The Appraisal of Real Estate, Eighth Edition, American Institute of Real Estate Appraisers of the National Association of Realtors, 1983, p.394