Equity ValuationEquity ValuationModelsModels

Chapter 18Chapter 18

Basic Types of Models- Balance Sheet Models

- Dividend Discount Models

- Price/Earning Ratios Estimating Growth Rates and Opportunities

Fundamental Stock Analysis: Fundamental Stock Analysis: Models of Equity ValuationModels of Equity Valuation

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

Intrinsic Value and Market PriceIntrinsic Value and Market Price

VD

ko

t

tt

( )11

VD

ko

t

tt

( )11

V0 = Value of Stock

Dt = Dividendk = required return

Dividend Discount Models:Dividend Discount Models:General ModelGeneral Model

VD

ko

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

Preferred Stock

No Growth ModelNo Growth Model

E1 = D1 = $5.00

k = .15

V0 = $5.00 / .15 = $33.33

VD

ko

No Growth Model: ExampleNo Growth Model: Example

VoD g

k g

o

( )1Vo

D g

k g

o

( )1

g = constant perpetual growth rate

Constant Growth ModelConstant Growth Model

VoD g

k g

o

( )1Vo

D g

k g

o

( )1

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

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

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

Constant Growth Model: ExampleConstant Growth Model: Example

g ROE b g ROE b

g = growth rate in dividendsROE = Return on Equity for the firmb = plowback or retention percentage rate

(1- dividend payout percentage rate)

Estimating Dividend Growth RatesEstimating Dividend Growth Rates

)1()1()1(...2

21

10

kPD

kD

kDV 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

Specified Holding Period ModelSpecified Holding Period Model

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

Partitioning Value: Growth and No Partitioning Value: Growth and No Growth ComponentsGrowth Components

ROE = 20% d = 60% b = 40%

E1 = $5.00 D1 = $3.00 k = 15%

g = .20 x .40 = .08 or 8%

Partitioning Value: ExamplePartitioning Value: Example

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.

Vo = value with growth

NGVo = no growth component value

PVGO = Present Value of Growth Opportunities

Partitioning Value: ExamplePartitioning Value: Example

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

Price Earnings RatiosPrice Earnings Ratios

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

P/E Ratio: No Expected GrowthP/E Ratio: No Expected Growth

PD

k g

E b

k b ROE

P

E

b

k b ROE

01 1

0

1

1

1

( )

( )

( )

PD

k g

E b

k b ROE

P

E

b

k b ROE

01 1

0

1

1

1

( )

( )

( )

b = retention ratio

ROE = Return on Equity

P/E Ratio with Constant GrowthP/E Ratio with Constant Growth

E0 = $2.50 g = 0 k = 12.5%

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

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

Numerical Example: No GrowthNumerical Example: No 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

Numerical Example with GrowthNumerical Example with Growth

Pitfalls in P/E AnalysisPitfalls in P/E Analysis

Use of accounting earnings- Historical costs

- May not reflect economic earnings Reported earnings fluctuate around the

business cycle

Inflation and Equity ValuationInflation and Equity Valuation

Inflation has an impact on equity valuations Historical costs underestimate economic

costs Empirical research shows that inflation has

an adverse effect on equity values- Research shows that real rates of return are

lower with high rates of inflation

Potential Causes of Lower Equity Potential Causes of Lower Equity Values with InflationValues with Inflation

Shocks cause expectation of lower earnings by market participants

Returns are viewed as being riskier with higher rates of inflation

Real dividends are lower because of taxes