## Mortgage-Equity Approach: Uses BTIRR as the discount rate—WACC would cause the double counting of interest expense BTCF= NOI –DS. Interest expense is part of Debt Service which causes the double-counting issue.

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##### Description

Income Approach Methods to Estimate Appraised Value of a Commercial Property

Income Statement

GPI             Gross Potential Income

-V & C        Vacancy and Collection Losses

EGI             Effective Gross Income

-OE             Operating Expenses

NOI            Net Operating Income

-DS             Debt Service

BTCF           Before ax Cash Flow earned by developer

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.  It is the best approach to use when appraising a commercial real estate property.

Information:

GPI = \$1,200,000 with a growth rate per year of 1.2 %

V&C = 3% of GPI and Operating Expenses = 25% of GPI

Loan terms are: 3%, 30 years (monthly compounding), LTV=90% (Loan to Value)

Appreciation Rate = 1.2% per year and the holding-period is 2 years

BTIRR to the developer is 20% (Before-Tax Internal Rate of Return)

A. Present Value Approach:

(1) Calculate the WACC (Weighted-Average Cost of Capital):

WACC or r = %LTV (1/MPVIFA * 12) + (100-%LTV) BTIRR

r=90(1/MPVIFA.0025, 360   * 12) + 10(.2)

r=90(1/237.1893815   * 12) + 2%

r=90(.004216040 * 12) + 2% or 4.553% + 2% =6.553%   take 3 places after decimal

(2) Calculate the Present Value of NOI:

n                                           1                                             2

GPI                                                   1,200,000 (1.012)                  1,214,400          growth rate in GPI used

-V & C 3%                                             36,000                                     36,432

EGI                                                    1,164,000                                 1,177,968

-OE 25%                                              300,000                                     303,600

NOI                                                       864,000/(1.06553)^1            874,368/(1.06553)^2

PVNOI:                                                 \$ 810,864 + 770,128= \$1,580,992

(3) Calculate the Present Value of the Reversion or Resale Value:

(1 + g)n  V  / ( 1 + r) ^ 2  The holding period in the problem is 2 years.  Number can change per problem

(1.012)^2 V/ (1.06553)^2  = 1.024144V/1.135354   = .90204803V

(4) Appraised Value

1V= PVNOI + PV Resale Price   use WACC as the discount rate

1V=\$1,580,992+.90204803V

V (1-.90204803) + \$1,580,992

V = \$16,140,482

B.  Direct Capitalization Method:   USES r=WACC

NOI year 1/ WACC- growth rate          The model requires that the growth rate (g) for GPI and Resale

Value or Residual Value are the same: only one g rate allowed

\$864,000/.06553-.012   = \$ 16,140,482

The answers for PV Approach and Direct Capitalization Method should match.

Mortgage-Equity Appraised Value will differ due to considering lending conditions.

C. Mortgage-Equity Approach:  Uses BTIRR as the discount rate—WACC would cause the double counting of interest expense   BTCF= NOI –DS.  Interest expense is part of Debt Service which causes the double-counting issue. This approach is used by lenders worldwide.  It is considered better than a simple PV approach, because loan conditions and interest rates are part of the analysis.

(1)    Calculate Max. Loan Amount assuming a DSCR of 1.25x:

Use the NOI calculated for year 1:

Debt-Service Coverage Ratio = NOI year 1 / DS    =1.25

Debt Service is MP * 12 months

DS =   NOI 1/ 1.25 or \$

MP is DS / 12

Maximum Loan is:  MP (MPVIFA .03/12, 30 * 12) or .0025, 360

DS= \$864,000/1.25 = \$691,200

MP=\$691,200/12= \$57,600

Maximum Loan Lender will approve:  \$57,600 (MPVIFA.0025, 360)=

\$57,600(237.1893815) = \$13,662,108

(2)    Calculate the PVBTCF (Present Value of Before-Tax Cash Flow):

1                                                     2

GPI

-V& C                    See prior income statement for numbers

EGI

-OE

NOI                                          \$864,000                                        \$874,368

-DS                                             691,200                                           691,200

BTCF                                          172,800/(1.20)^1                         183,168/(1.20)^2

PVBTCF         \$144,000+127,200=\$271,200