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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 projects1. new vs. established structures--different risks from being leased up

2. non-viable structures: e.g., the World Trade Center in Kansas City

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2. Income or Cap Rate Approach

a. capitalizes cash flow as perpetuity via a cap rate1. V=I/r

where V=property value, I=stabilized income flow, r=cap rate

b. cap rates vs. discount rates1. 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 CapitalizationV = NOI / R

2. Present Value MethodV = NOI / (r-g)

r = “competitive” discount rate

g = growth rate

R = r-g

3. Mortgage/Equity MethodV = D + E

D = mortgage debt

E = equity

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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

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==>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 analysis1. HPi = jXij i

where HP is the price of the ith home,

X is the vector of house traits

is the regression intercept term

is the coefficient vector of trait prices

is the error term

2. = 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 approacha. 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

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Linear Regression

SALES PRICE f SQUARE FEET

Y SALES PRICE

X PROPERTY SIZE SF

Y X

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Linear Regression

• Linear model is estimated by least squares– Ordinary Least Squares (OLS)

X X X Y1

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Regression StatisticsMultiple R 74%R Square 54%Adjusted R Square 54%Standard Error 35510.7554Observations 746

ANOVAdf SS MS F Significance F

Regression 1 1.11775E+12 1.118E+12 886.39 0.0000Residual 744 9.38194E+11 1.261E+09Total 745 2.05594E+12

Coefficients Standard Error t Stat P-value Lower 95%Intercept -21542.26 4064.70 -5.30 0.00 -29521.9X Variable 1 51.71 1.74 29.77 0.00 48.3

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Regression Equation

Y X 21542 5171. *

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X Variable 1 Line Fit Plot

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X Variable 1

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Predicted Y

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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..

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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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