Question

1. Mortgage-Equity Approach, Present Value (PV) Approach and Direct-Capitalization Method for calculating the appraised value or Price of a property that generates income. Information: GPI = $500,000 with a growth rate per year of 1.0 % V&C = 5% of GPI and Operating Expenses = 20% of GPI Loan terms are: 6%, 30 years (monthly compounding), LTV=80% Appreciation Rate = 1.0% per year and the holding-period is 3 years IRR to the developer is 18% + (10o- + 3.6 A. Present Value Approach: LTV=80% (1) Calculate the WACC: - Oropulfa 0.003, 360) -0.479640420 = 4.07904 (2) Calculate the Present Value of NOI: N=3 so do 3 years (3) Calculate the Present Value of the Reversion n=3, (4) Appraised Value

Answer 1

Part (1)

Wd = proportion of debt = LTV = 80%

Cost of debt, Kd = Annualized YTM = 12 x Monthly YTM = 12 x RATE (Nper, PMT, PV, FV) = 12 x RATE (12 x 30, 6%/12, -1, 0) = 4.39%

We = proportion of equity = 1 - Wd = 1 - 80% = 20%

Cost of equity, Ke = Developer's IRR = 18%

Hence, WACC = r = Wd x Kd + We x Ke = 80% x 4.39% + 20% x 18% = 7.11%

Part (2)

Please see the table below. Please be guided by the second column titled “Linkage” to understand the mathematics. The last row highlighted in yellow is your answer. Figures in parenthesis, if any, mean negative values. All financials are in $.

Year, N	Linkage	1	2	3
GPI	A	500,000	505,000	510,050
V&C	B = 5% x A	25,000	25,250	25,503
Operating expneses	C = 20% x A	100,000	101,000	102,010
NOI	D = A - B - C	375,000	378,750	382,538
WACC	r	7.11%
PV factor	PVF = (1 + r)^(-N)	0.93362	0.87165	0.81379
Present value of NOI	PV = PVF x D	350,108	330,138	311,306
Total PV of NOI	Sum of all PVs	991,552

Part (3)

If Appraised value is V, then sale value = V x (1 + appreciation rate)N = V x (1 + 3%)3 = 1.0927V

Balance loan amount = - PV (Rate, Nper, PMT, FV) = - PV(4.39%/12, 12 x (30 - 3), 6%/12, 0) =  0.9481 times the original loan amount.

Original loan amount = 80% LTV = 80% x V = 0.8V

Hence, balance loan amount = 0.8V x 0.9481 =  0.7585V

Hence, reversion = Sale value - balance loan amount = 1.0927V - 0.7585V =  0.3343V

PV of reversion = Reversion / (1 + r)N = 0.3343V / (1 + 7.11%)3 =  0.2720V

Part (4)

Appraised Value = V = PV of NOI + PV of reversion = 991,552 +  0.2720V

Hence, V - 0.2720V =  0.7280V = 991,552

Hence, Appraised Value = V = 991,552 / 0.7280 = $ 1,362,052