Commercial Investment Real Estate is the magazine of the CCIM Institute, the leading provider of commercial real estate education. CIRE covers market trends, current developments, and business strategies within the commercial real estate field.
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Table 1: Gettel Formula Example M x Rm x DCR = 75% x 6.44% x 1.25 = 6.04% R Variable $100,000 M — 75% NOI — $7,000 Value Calculated $75,000 E — 25% 5.00% — n 30 — Rm — 6.44% Annual $ PMT — $4,831 1.25 — I% DCSR Table 2: Akerson Formula Mortgage Terms Year 1 2 3 4… 10 NOI $7,000 $7,210 $7,426 $7,649 $9,133 DS $4,831 $4,831 $4,831 $4,831 $4,831 Pre-Tax $ CF $2,169 $2,379 $2,595 $2,818 $4,302 Re 8.67% 9.51% 10.38% 11.27% 17.21% Ro 7.00% 7.21% 7.43% 7.65% 9.13% Rm 6.44% 6.44% 6.44% 6.44% 6.44% DCSR 1.449 1.492 1.537 1.583 1.890 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 Te 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 of (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.) 40 September | October | 2013 Te 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). Te diference is a pretax equity return. Te 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. Te industry averages provided by RealtyRates.com for frst 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. Te 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 ofered by a bank); PV = 0 (Te 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% Te 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 ofered as it calculates the loan payof rate. Tus 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%. Te loan percentage paid of 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). Tus: 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% Commercial Investment Real Estate