Chapter 12

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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Intrinsic Value and Market Price

• Intrinsic Value• Self assigned Value• Variety of models are used for estimation

• Market Price• Consensus value of all potential traders

• Trading Signal• IV > MP Buy• IV < MP Sell or Short Sell• IV = MP Hold or Fairly Priced

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Dividend Discount Models:General Model

VDk

ot

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

( )1

• g = constant perpetual growth rate

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Constant Growth Model: Example

VoD 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 = 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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Shifting Growth Rate Model

V Dg

k

D g

k g ko o

t

tt

TT

T

( )

( )

( )

( )( )

1

1

1

1

1

1

2

2

• g1 = first growth rate

• g2 = second growth rate

• T = number of periods of growth at g1

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Shifting Growth Rate Model: Example

D0 = $2.00 g1 = 20% g2 = 5%

k = 15% T = 3 D1 = 2.40

D2 = 2.88 D3 = 3.46 D4 = 3.63

V0 = D1/(1.15) + D2/(1.15)2 + D3/(1.15)3 +

D4 / (.15 - .05) ( (1.15)3

V0 = 2.09 + 2.18 + 2.27 + 23.86 = $30.40

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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

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Partitioning Value: Growth and No Growth Components

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%

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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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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

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P/E Ratio: No expected growth

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

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P/E Ratio with Constant Growth

PD

k g

E b

k b ROE

P

E

b

k b ROE

01 1

0

1

1

1

( )

( )

( )

• b = retention ration• ROE = Return on Equity

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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 Valuation Ratios & Approaches

• Price-to-book• Price-to-cash flow• Price-to-sales• Present Value of Free Cash Flow