Chapter 18

Equity Valuation

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Fundamental Stock Analysis: Models of Equity

Valuation

• Basic Types of Models• Balance Sheet Models• Dividend Discount Models• Price/Earning Ratios

• Estimating Growth Rates and Opportunities

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Dividend Discount Models:General Model

VD

ko

t

tt

( )11

VD

ko

t

tt

( )11

• V0 = Value of Stock• Dt = Dividend• k = required return

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No Growth Model

VD

ko

• Stocks that have earnings and dividends that are expected to remain constant

• Preferred Stock

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No Growth Model: Example

E1 = D1 = $5.00

k = .15

V0 = $5.00 / .15 = $33.33

VD

ko

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Constant Growth Model

VoD g

k g

o

( )1Vo

D g

k g

o

( )1

• g = constant perpetual growth rate

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Constant Growth Model: Example

VoD g

k g

o

( )1Vo

D g

k g

o

( )1

E1 = $5.00b = 40% k = 15%

(1-b) = 60% D1 = $3.00 g = 8%

V0 = 3.00 / (.15 - .08) = $42.86

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Estimating Dividend Growth Rates

g ROE b g ROE b

• g = growth rate in dividends

• ROE = Return on Equity for the firm

• b = plowback or retention percentage rate• (1- dividend payout percentage rate)

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Estimating Growth via historical info.

• Dividend in 2000 was $1.

• Dividend in 2006 was $1.80

• Growth is (1.80/1)^(1/6)-1 = 10.29%

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Specified Holding Period Model

01

12

2

1 1 1V D

kDk

D Pk

N NN

( ) ( ) ( )...

• PN = the expected sales price for the stock at time N

• N = the specified number of years the stock is expected to be held

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Partitioning Value: Growth and No Growth Components

VE

kPVGO

PVGOD g

k g

E

k

o

o

1

11( )

( )

VE

kPVGO

PVGOD g

k g

E

k

o

o

1

11( )

( )

• PVGO = Present Value of Growth Opportunities

• E1 = Earnings Per Share for period 1

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Partitioning Value: Example

• ROE = 20% d = 60% b = 40%

• E1 = $5.00 D1 = $3.00 k = 15%

• g = .20 x .40 = .08 or 8%

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

V

NGV

PVGO

o

o

3

15 0886

5

1533

86 33 52

(. . )$42.

.$33.

$42. $33. $9.

V

NGV

PVGO

o

o

3

15 0886

5

1533

86 33 52

(. . )$42.

.$33.

$42. $33. $9.

Partitioning Value: Example

VVoo = value with growth = value with growth

NGVNGVoo = no growth component value = no growth component value

PVGO = Present Value of Growth OpportunitiesPVGO = Present Value of Growth Opportunities

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A much better model is to apply discount models to FCFE which may more accurately reflect a firms value.

FCFE = Net Income + depreciation – Cap. Expend. – change in working capital – principal debt repayments + new debt issues.

Apply model as per usual.

Free Cash Flow to Equity

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• If the firm finances a fixed percentage of its capital spending and investments in working capital with debt, the calculation of FCFE is simplified. Let DR be the debt ratio, debt as a percentage of assets. In this case, FCFE can be written as

• FCFE = NI – (1 – DR)(Capital Spending + change in Working Capital – Depreciation)

• When building FCFE valuation models, the logic, that debt financing is used to finance a constant fraction of investments, is very useful. This equation is pretty common.

Free Cash Flow to Equity

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

http://faculty.etsu.edu/trainor/FNCE%203300/Lowes.doc

Another interesting site you may want to use:

http://caps.fool.com/Ticker.aspx?source=icaedilnk9950012&ticker=LOW

Let’s look at an example

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• FCFF = EBIT(1-tax rate) + Dep. – Cap. Expenditures – Change in WC – Change in other assets.

• Again, proceed as normal(replace dividends with FCFF) but discount at firms cost of capital.

• You find value of firm. To find value of equity, simply subtract off debt.

Free Cash flow to the Firm

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Price Earnings Ratios

• P/E Ratios are a function of two factors• Required Rates of Return (k)• Expected growth in Dividends

• Uses• Relative valuation• Extensive Use in industry

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

P/E Ratio: No expected growth

PE

kP

E k

01

0

1

1

PE

kP

E k

01

0

1

1

• E1 - expected earnings for next year

• E1 is equal to D1 under no growth

• k - required rate of return

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

P/E Ratio with Constant Growth

)(

1

)(

)1(

1

0

110

ROEbk

b

E

P

ROEbk

bE

gk

DP

)(

1

)(

)1(

1

0

110

ROEbk

b

E

P

ROEbk

bE

gk

DP

• b = retention ration• ROE = Return on Equity

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Numerical Example: No Growth

E0 = $2.50 g = 0 k = 12.5%

P0 = D/k = $2.50/.125 = $20.00

PE = 1/k = 1/.125 = 8

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Numerical Example with Growth

b = 60% ROE = 15% (1-b) = 40%

E1 = $2.50 (1 + (.6)(.15)) = $2.73

D1 = $2.73 (1-.6) = $1.09

k = 12.5% g = 9%

P0 = 1.09/(.125-.09) = $31.14

PE = 31.14/2.73 = 11.4

PE = (1 - .60) / (.125 - .09) = 11.4

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Pitfalls in Using PE Ratios

• Flexibility in reporting makes choice of earnings difficult

• Pro forma earnings may give a better measure of operating earnings

• Problem of too much flexibility

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Other types of Valuation

• Use Price/sales

• Price/Cash flow

• All relative valuation models rely on the market to be fairly valued. What is a good Price/Sales ratio? Relies on comparisons which may or may not be valued accurately.