Chapter 13Chapter 13

Equity ValuationEquity Valuation

13-13-22Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

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

• Basic Types of ModelsBasic Types of Models

–Balance Sheet ModelsBalance Sheet Models

–Dividend Discount ModelsDividend Discount Models

–Price/Earning RatiosPrice/Earning Ratios

• Estimating Growth Rates and Estimating Growth Rates and OpportunitiesOpportunities

13-13-33Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Intrinsic Value and Market PriceIntrinsic Value and Market Price

• Intrinsic ValueIntrinsic Value

– Self assigned ValueSelf assigned Value

– Jason: $14, Jamie: $16, Katie: $18Jason: $14, Jamie: $16, Katie: $18

– Variety of models are used for estimationVariety of models are used for estimation

• Market PriceMarket Price

– Consensus value of all potential traders ($16)Consensus value of all potential traders ($16)

• Trading SignalTrading Signal

– IV > MP BuyIV > MP Buy

– IV < MP Sell or Short SellIV < MP Sell or Short Sell

– IV = MP Hold or Fairly PricedIV = MP Hold or Fairly Priced

13-13-44Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Dividend Discount Models:Dividend Discount Models:General ModelGeneral Model

VD

ko

t

tt

( )11

VD

ko

t

tt

( )11

• VV00 = Value of Stock = Value of Stock

• DDt t = Dividend= Dividend• k = required returnk = required return

13-13-55Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

No Growth ModelNo Growth Model

VD

ko

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

• Preferred StockPreferred Stock

13-13-66Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

No Growth Model: ExampleNo Growth Model: Example

EE11 = D = D11 = $5.00 = $5.00

k = .15k = .15

VV00 = $5.00 / .15 = $33.33 = $5.00 / .15 = $33.33

k

DVo

13-13-77Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Constant Growth ModelConstant Growth Model

VoD g

k g

o

( )1Vo

D g

k g

o

( )1

• g = constant perpetual growth g = constant perpetual growth rate rate

Note: D1 = D0(1+g)

13-13-88Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Constant Growth Model: Constant Growth Model: ExampleExample

VoD g

k g

o

( )1Vo

D g

k g

o

( )1

EE11 = $5.00 = $5.00 b = 40%b = 40% k = 15% k = 15%

(1-b) = 60%(1-b) = 60% DD1 1 = $3.00 g = 8%= $3.00 g = 8%

VV00 = 3.00 / (.15 - .08) = $42.86 = 3.00 / (.15 - .08) = $42.86

13-13-99Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Estimating Dividend Growth Estimating Dividend Growth RatesRates

bROEge bROEge

• g = growth rate in g = growth rate in earningsearnings • ROE = Return on Equity for the firmROE = Return on Equity for the firm• b = plowback or retention percentage b = plowback or retention percentage

raterate– (1- dividend payout percentage rate)(1- dividend payout percentage rate)

• d = dividend payout = 1 - bd = dividend payout = 1 - b

13-13-1010Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Constant growthConstant growth

• Rankin Corporation earns a constant Rankin Corporation earns a constant 20% on new equity investment (ROE) 20% on new equity investment (ROE) and pays out a constant 60% of earnings and pays out a constant 60% of earnings as dividends. EPS for the year just as dividends. EPS for the year just ended = $3.00.ended = $3.00.

• The beta of the stock is .90, the expected The beta of the stock is .90, the expected return on the market is 13 percent and Rf return on the market is 13 percent and Rf = 4 percent.= 4 percent.

• Calculate earnings and dividends for the next 4 Calculate earnings and dividends for the next 4 years.years.

13-13-1111Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

RankinRankin

Year ROE b d g Earnings Dividends0 $3.00001 20% 40% 60% 8% $3.2400 $1.94402 20% 40% 60% 8% $3.4992 $2.09953 20% 40% 60% 8% $3.7791 $2.26754 20% 40% 60% 8% $4.0815 $2.4489

13-13-1212Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Rankin continuedRankin continued

• Calculate the growth (percentage Calculate the growth (percentage change) in earnings and dividends.change) in earnings and dividends.

• Calculate the required returnCalculate the required return

–R = Rf + Beta*(Rm-Rf)R = Rf + Beta*(Rm-Rf)

–R = .04 + .9*(.13-.04) = .121R = .04 + .9*(.13-.04) = .121

• Calculate the price (Calculate the price (or valueor value))

–PPtt = D = Dt+1t+1/(k-g)/(k-g)

13-13-1313Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Rankin continuedRankin continued

Year g Dividends Price0 $47.41461 8% $1.9440 $51.20782 8% $2.0995 $55.30443 8% $2.2675 $59.72884 8% $2.4489

Calculate the percentage change in the stock price.

Calculate your HPR if you buy today and hold for one period.

13-13-1414Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Shifting Growth Rate ModelShifting Growth Rate Model

V Dg

k

D g

k g ko o

t

tt

TT

T

( )

( )

( )

( )( )

1

1

1

1

1

1

2

2V D

g

k

D g

k g ko o

t

tt

TT

T

( )

( )

( )

( )( )

1

1

1

1

1

1

2

2

• gg11 = first growth rate = first growth rate

• gg22 = second growth rate = second growth rate

• T = number of periods of growth at gT = number of periods of growth at g11

13-13-1515Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Shifting growthShifting growth

Value at t = 0

D1 D2 D3

Value attime T

DT

……...

Note:value at T

= D T+1/(k-g)

13-13-1616Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Lang CompanyLang Company

• The Lang Company just paid a The Lang Company just paid a dividend of $2dividend of $2

• Dividends are expected to grow at Dividends are expected to grow at a rate of 20% for 3 years and then a rate of 20% for 3 years and then at a constant rate of 5 percent.at a constant rate of 5 percent.

• If your required return is 15%, how If your required return is 15%, how much would you pay for a share of much would you pay for a share of Lang Company stock?Lang Company stock?

13-13-1717Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Shifting Growth Rate Model: Shifting Growth Rate Model: ExampleExample

DD00 = $2.00 g = $2.00 g1 1 = 20% g= 20% g2 2 = 5% = 5%

k = 15% T = 3 Dk = 15% T = 3 D1 1 = 2.40 = 2.40

DD22 = 2.88 D = 2.88 D3 3 = 3.46 D= 3.46 D4 4 = 3.63= 3.63

VV0 0 = D= D11/(1.15) + D/(1.15) + D22/(1.15)/(1.15)22 + D + D33/(1.15)/(1.15)33 + +

DD44 / (.15 - .05) ( (1.15) / (.15 - .05) ( (1.15)33

VV00 = 2.09 + 2.18 + 2.27 + 23.86 = $30.40 = 2.09 + 2.18 + 2.27 + 23.86 = $30.40

13-13-1818Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Multistage or nonconstant growthMultistage or nonconstant growth

• The Wade Company just paid a dividend The Wade Company just paid a dividend of $1.20 per share. Dividends are of $1.20 per share. Dividends are expected to grow at a rate of 10% for 2 expected to grow at a rate of 10% for 2 years, 9 percent for the next 2 years and a years, 9 percent for the next 2 years and a constant 8 percent thereafter. If the constant 8 percent thereafter. If the required return is 13 percent, find value of required return is 13 percent, find value of a share of Wade.a share of Wade.

T

TT

tt

to

k

P

k

DV

)1()1(1

T

TT

tt

to

k

P

k

DV

)1()1(1

13-13-1919Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Specified Holding Period ModelSpecified Holding Period Model

01

12

2

1 1 1V D

kDk

D Pk

N NN

( ) ( ) ( )...

• PPNN = the expected sales price for the = the expected sales price for the

stock at time Nstock at time N

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

13-13-2020Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Partitioning Value: Growth and Partitioning Value: Growth and No Growth ComponentsNo 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 PVGO = Present Value of Growth OpportunitiesOpportunities

• EE11 = Earnings Per Share for period 1 = Earnings Per Share for period 1

13-13-2121Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Partitioning Value: ExamplePartitioning Value: Example

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

• EE11 = $5.00 D = $5.00 D11 = $3.00 k = 15% = $3.00 k = 15%

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

13-13-2222Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

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: ExamplePartitioning 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

13-13-2323Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Price Earnings RatiosPrice Earnings Ratios

• P/E Ratios are a function of two P/E Ratios are a function of two factorsfactors

–Required Rates of Return (k)Required Rates of Return (k)

–Expected growth in DividendsExpected growth in Dividends

• UsesUses

–Relative valuationRelative valuation

–Extensive Use in industryExtensive Use in industry

13-13-2424Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

P/E Ratio: No expected growth P/E Ratio: No expected growth

PE

kP

E k

01

0

1

1

PE

kP

E k

01

0

1

1

• EE11 - expected earnings for next year - expected earnings for next year

– EE11 is equal to D is equal to D11 under no growth under no growth

• k - required rate of returnk - required rate of return

13-13-2525Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

P/E Ratio with Constant GrowthP/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

( )

( )

( )

PD

k g

E b

k b ROE

P

E

b

k b ROE

01 1

0

1

1

1

( )

( )

( )

• b = retention rationb = retention ration

• ROE = Return on EquityROE = Return on Equity

13-13-2626Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Numerical Example: No GrowthNumerical Example: No Growth

EE00 = $2.50 g = 0 k = 12.5% = $2.50 g = 0 k = 12.5%

PP00 = D/k = $2.50/.125 = $20.00 = D/k = $2.50/.125 = $20.00

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

13-13-2727Irwin/McGraw-Hill ©The McGraw-Hill Companies, Inc., 1998

Numerical Example with GrowthNumerical Example with Growth

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

EE1 1 = $2.50 (1 + (.6)(.15)) = $2.73= $2.50 (1 + (.6)(.15)) = $2.73

DD11 = $2.73 (1-.6) = $1.09 = $2.73 (1-.6) = $1.09

k = 12.5% g = 9%k = 12.5% g = 9%

PP00 = 1.09/(.125-.09) = $31.14 = 1.09/(.125-.09) = $31.14

PE = 31.14/2.73 = 11.4PE = 31.14/2.73 = 11.4

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