# Commercial Investment Real Estate September/October 2013 - Page 42

Table 1: Gettel Formula Example M x Rm x DCR = 75% x 6.44% x 1.25 = 6.04% Value NOI M R Variable Calculated \$100,000 — \$7,000 — 75% \$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 cover- age ratio of 1.25. Application of the Gettel formula and its assump- tions are displayed in Table 1. The Investor’s Perspective T e 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 T e 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). T e dif erence is a pretax equity return. T e 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. T e industry averages provided by RealtyRates.com for f rst 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 depos- its 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. T e 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 of ered by a bank); PV = 0 (T e 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% T e 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 of ered as it calculates the loan payof rate. T us 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%. T e loan percentage paid of can be easily calculated by dividing the mortgage constant (less loan interest rate) by the loan amortiza- tion rate for the holding period (less the loan interest rate). T us: 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