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Overhead Set#2:
VALUATION APPROACHES
• 3 Approaches to Valuation:
– Cost Approach
– Income Approach
– Sales Comparison or Market Approach
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1. Cost Approach
a. cost of duplicating property minus depreciation
b. most fruitful in engineering or cost-to-cure cases
c. potential problems in ranking projects
1. new vs. established structures--different risks from being leased up
2. non-viable structures: e.g., the World Trade Center in Kansas City
2:3
2. Income or Cap Rate Approach
a. capitalizes cash flow as perpetuity via a cap rate
1. V=I/r
where V=property value, I=stabilized income flow, r=cap rate
b. cap rates vs. discount rates
1. cap rate reflects purely real estate/property factors
a. e.g., site-specific factors, property-type issues, property-specific
factors
2. discount rates reflect opportunity cost of capital as learned in
introductory finance
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2. Income or Cap Rate Approach
1. Direct Capitalization
V = NOI / R
2. Present Value Method
V = NOI / (r-g)
r = “competitive” discount rate
g = growth rate
R = r-g
3. Mortgage/Equity Method
V=D+E
D = mortgage debt
E = equity
2:5
Cap Rate Example
Building Cash Flow = $100,000/yr for 25 yrs.
Loan Amount = $700,000 at 10% for 25 yrs.
Pmt = $77,177.65
Required Rate of Return = 15%
Investor’s Cash Flow = $100,000 - $77,177 = $22,882.35
Present Value = $147,915
Value = $700,000 + $147,915 = $847,915
IRR = 10.91%
Cap Rate = NOI/V = $100,000/$847,915 = 11.79%
Assumption: NOI remains level
2:6
==>old exam question on meaning of cap rates
• Assume that AA noncallable corporate bonds with ten
years to maturity currently are yielding 10%. Further
assume that the real estate cap rate is 7% for an entirely
owner-occupied office building with a standard lease
whose occupant also has a AA credit rating. [If the
building owner were to come to you and propose a
sale/leaseback with a ten year term, you would consider
the AA corporate bond rate as more appropriate than the
real estate cap rate for determining the present value of
the cash flows on the sale/leaseback.]
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2. Income or Cap Rate Approach
c. potential problems if cash flows are not stable-large differences in PVs of equal dollar flows if one is cyclical and
the other is not
d. potential problems from no attempt to differentiate among
the components of cash flow by risk level
e. in practice, often very ad hoc assumptions made in
determining I
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3. Market Approach
a. identify comparable properties and value accordingly
b. how should this be implemented empirically?
e.g., how to value a warehouse in terms of its value for conversion to
condominiums?
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4. Mass Appraisal (Hedonic)
(means implicit in the Greek)
a. used first by consultants to the auto industry
b. simple regression analysis
1. HPi = a + bjXij + ei ,
where HP is the price of the ith home,
X is the vector of house traits
a is the regression intercept term
b is the coefficient vector of trait prices
e is the error term
2. b = HP/X
the marginal effect of a small change in trait j on home price HP
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4. Mass Appriasal (Hedonic)
3. Potential problems with the statistical approach
a. specification error--never know all the relevant traits
b. some traits very hard to quantify--e.g., style features
c. changes in trends in neighborhood from which sample of
comparables is drawn
in absence of transactions-based prices, any approach
gives you at best an educated guess about asset value;
market approach is the best from a conceptual perspective
(simple market approach valuation now required in house
appraisals by secondary market agencies)
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Linear Regression
• Simple Real Estate Example:
– We wish to explain/predict the price of single family homes (find
their value).
– Dependent Variable (Y) = Sales Price
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Linear Regression
• Independent Variable (X):
• What causes sales prices to vary?
– Size of property?
– Test to see if sales prices change as property size changes.
– X = size in square feet.
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Linear Regression
• SCATTER PLOT:
– diagram that plots the relationship between two variables
– In our case, we wish to plot the relationship between sales price
and property size.
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Scatter Plot of Sales Price v. Property Size
500000
450000
400000
350000
Price ($)
300000
250000
200000
150000
100000
50000
0
0
1000
2000
3000
4000
Size (square feet)
5000
6000
2:15 7000
Linear Regression
SALES PRICE  f  SQUARE FEET
Y  SALES PRICE
X  PROPERTY SIZE  SF 
Y  a + b X + e
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Linear Regression
• Linear model is estimated by least squares
– Ordinary Least Squares (OLS)
b   X X  X Y
1
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Regression Statistics
Multiple R
74%
R Square
54%
Adjusted R Square
54%
Standard Error
35510.7554
Observations
746
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
SS
MS
1 1.11775E+12 1.118E+12
744 9.38194E+11 1.261E+09
745 2.05594E+12
Coefficients Standard Error
-21542.26
4064.70
51.71
1.74
t Stat
-5.30
29.77
F
886.39
Significance F
0.0000
P-value
0.00
0.00
Lower 95%
-29521.9
48.3
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Regression Equation
Y   21542 + 51.71 * X
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X Variable 1 Line Fit Plot
500000
450000
400000
350000
Y
300000
Y
250000
Predicted Y
200000
150000
100000
50000
0
0
1000
2000
3000
4000
5000
6000
7000
X Variable 1
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Multiple Regression
• Add independent variables to model to
explain more of the price.
–
–
–
–
–
# of bedrooms
# of bath rooms
year built
location
amenities
• fireplace, garage, deck, etc..
2:21
Multiple Regression
• Problem: Collinearity
– As you add variables, some of the independent variables may be
collinear with each other.
• Example: As the number of bed rooms increases, you expect the
number of bathrooms to increase as well.
• This will bias your regression equation. (Makes it difficult to support
the results in court.)
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Example
• Factors that influence warehouse valuation.
–
–
–
–
–
–
–
building size
office space
ceiling height
doors (dock and drive-in)
rail service
sprinklers
age
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