DISCOUNTED DIVIDEND VALUATION

PresenterVenueDate

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DISCOUNTED CASH FLOW MODELS

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CHOICE OF DISCOUNTED CASH FLOW MODELS

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VALUING COMMON STOCK USING A MULTI-PERIOD DDM

EXAMPLE: VALUING COMMON STOCK USING A MULTPERIOD DDM

0 1 2 3

D $1.00 $1.05 $1.10

P $20.00

EXAMPLE: VALUING COMMON STOCK USING A MULTPERIOD DDM

0 2 3

0

$1.00 $1.05 $21.101.10 1.10 1.10

$17.63

V

V

VALUING COMMON STOCK USING THE GORDON GROWTH MODEL

0 10

(1 )

D g D

Vr g r g

EXAMPLE: VALUING COMMON STOCK USING THE GORDON GROWTH MODEL

Risk-free rate 3.0%

Equity risk premium 6.0%

Beta 1.20

Current dividend $2.00

Dividend growth rate 5.0%

Current stock price $24 .00

VALUING COMMON STOCK USING THE GORDON GROWTH MODEL

0$2.00(1 0.05) $2.10 $40.38

0.102 0.05 0.102 0.05

V

CAPM: = 3% + 1.2(6%) = 10.2%r

EXAMPLE: VALUING PREFERRED STOCK

0$2.00 $19.61

0.102 0

V

EXAMPLE: CALCULATING THE IMPLIED GROWTH RATE USING THE GORDON GROWTH MODEL

$2.00(1 )$240.102

2.448 24 2.00(1 )26 0.448

1.72%

gg

g gg

g

Using the previous common stock example and the current stock price of $24, what is the implied growth rate?

CALCULATING THE IMPLIED REQUIRED RETURN USING THE GORDON GROWTH MODEL

10

1

0

DV

r gD

r gP

EXAMPLE: CALCULATING THE IMPLIED REQUIRED RETURN USING THE GORDON GROWTH MODEL

Using the previous common stock example and the current stock price of $24, what is the implied required return?

1

0

2.10 0.0524

8.75% 5% 13.75%

Dr g

P

r

r

PRESENT VALUE OF GROWTH OPPORTUNITIES

10

10

PVGO

PVGO

EV

rE

Pr

PRESENT VALUE OF GROWTH OPPORTUNITIES

10

0

1 1

PVGO

1 PVGO

EV

rPE r E

EXAMPLE: PRESENT VALUE OF GROWTH OPPORTUNITIES

Stock price $80 .00

Expected earnings $5 .00

Required return on stock 10%

EXAMPLE: PRESENT VALUE OF GROWTH OPPORTUNITIES

10PVGO

5PVGO $80 $300.10

EP

r

EXAMPLE: PRESENT VALUE OF GROWTH OPPORTUNITIES

0

0

1 PVGO

1 300.10 5

16 10 6

PE r EPE

USING THE GORDON GROWTH MODEL TO DERIVE A JUSTIFIED LEADING P/E

10

0 1 1

1

0

1

1

DV

r gP D EE r gP bE r g

USING THE GORDON GROWTH MODEL TO DERIVE A JUSTIFIED TRAILING P/E

00

0 0 0

0

0

0

(1 )

(1 )

(1 )(1 )

D gV

r gP D g EE r gP b gE r g

EXAMPLE: USING THE GORDON GROWTH MODEL TO DERIVE A JUSTIFIED P/E

Stock price $50 .00

Trailing earnings per share $4 .00

Current dividends per share $1.60

Dividend growth rate 5.0%

Required return on stock 9.0%

EXAMPLE: USING THE GORDON GROWTH MODEL TO DERIVE A JUSTIFIED LEADING P/E

0

1

0

1

1

$1.60 $4.00 10.00.09 0.05

P bE r gPE

EXAMPLE: USING THE GORDON GROWTH MODEL TO DERIVE A JUSTIFIED TRAILING P/E

0

0

0

0

(1 )(1 )

($1.60 / $4.00)(1.05) 10.500.09 0.05

Actual P/E = $50.00/$4.00 = 12.50

P b gE r gPE

ISSUES USING THE GORDON GROWTH MODEL

StrengthsSimple and applicable to

stable, mature firms

Can be applied to entire markets

g can be estimated using macro data

Can be applied to firms that repurchase stock

Limitations

Not applicable to non-dividend-paying firms

g must be constant

Stock value is very sensitive to r – g

Most firms have nonconstant growth in dividends

CHOICE OF DISCOUNTED CASH FLOW MODELS

• Rapidly earnings• Heavy reinvestment• Small or no

dividends

Growth

• Earnings growth slows

• Capital reinvestment slows

• FCFE & dividends

Transition • ROE = r

• Earnings & dividends growth matures

• Gordon growth model useful

Maturity

GENERAL TWO-STAGE DDM

0 00

1

1 1 1

1 1

t nnS S Lt n

t L

D g D g gV

r r r g

EXAMPLE: GENERAL TWO-STAGE DDM

Current dividend = $2.00Growth Current dividend = $2.00Growth for next three years = 15 percentLong-term growth = 4 percentRequired return = 10 percentfor next three years = 15 percentLong-term growth = 4 percentRequired return = 10 percent

EXAMPLE: GENERAL TWO-STAGE DDM

Step 1: Calculate the first three dividends:• D1 = $2.00 x (1.15) = $2.30• D2 = $2.30 x (1.15) = $2.6450• D3 = $2.6450 x (1.15) = $3.0418

Step 2: Calculate the year 4 dividend:• D4 = $3.0418 x (1.04) = $3.1634

Step 3: Calculate the value of the constant growth dividends:• V3 = $3.1634 / (0.10 – 0.04) = $52.7237

EXAMPLE: GENERAL TWO-STAGE DDM

0 2 3 3

0

$2.30 $2.6450 $3.0418 $52.7237V1.10 1.10 1.10 1.10

V $46.17

EXAMPLE: GENERAL TWO-STAGE DDM

• Using the previous example, now we’ll use the trailing P/E to determine the terminal value

• The D4 is $3.1634• Assume also that the projected P/E is 13.0 in year 4 and

that the firm will pay out 60 percent of earnings as dividends

• Year 4 earnings are then $3.1634 / 0.60 = $5.2724• The stock price in year 4 is then $5.2724 × 13 = $68.54

EXAMPLE: GENERAL TWO-STAGE DDM

0 2 3 3

0

$2.30 $2.6450 $3.0418 $3.1634 $68.541.10 1.10 1.10 1.10

$55.54

V

V

TWO-STAGE H-MODEL

0 00

1

L S L

L

D g D H g gV

r g

EXAMPLE: TWO-STAGE H-MODEL

Current dividend $3.00gs 20%gL 6%H 5Required return on stock 10%Current stock price $120

EXAMPLE: TWO-STAGE H-MODEL

0 00

0

0

1

$3 1 0.06 $3 5 0.20 0.06

0.10 0.06

$79.50 $52.50 $132.00

L S L

L

D g D H g gV

r g

V

V

SOLVING FOR THE REQUIRED RETURN USING THE TWO-STAGE H-MODEL

0

01

3 1 0.06 5 0.20 0.06 0.06 10.40%120

L S L LD

r g H g g gP

r

EXAMPLE: THREE-STAGE MODEL

• Firm pays a current dividend of $1.00• Growth rate is 20 percent for next two years• Growth then declines over six years to stable rate of 5 percent

• Required return is 10 percent• Current stock price is $50

THREE-STAGE MODEL

Assumes three distinct growth stages:• First stage of growth• Second stage of growth• Stable-growth phase

H-model can be used for last two stages if growth declines linearly

2

0 1 2

2 2

2 2

0

$1 1.20 $1 1.20

1.10 1.106$1 1.20 0.20 0.05 $1 1.20 1.052

1.10 0.10 0.05 1.10 0.10 0.05

$1.09 $1.19 $10.71 $24.99 $37.98

V

V

THREE-STAGE MODEL EXAMPLE

ESTIMATING THE GROWTH RATE

Industry or Macroeconomic

Average

g = b × ROE• DuPont formula• ROE = r• ROE = industry ROE

THE SUSTAINABLE GROWTH RATE

g b ROE

THE DUPONT MODEL

Net income Total assetsROE = Total assets Shareholders' equity

Net income Sales Total assetsROE = Sales Total assets Shareholders' equity

Net income Dividends Net income Sales Total assetsNet income Sales Total assets Equity

g

EXAMPLE: DUPONT MODEL

Net profit margin 5.00%

Total asset turnover 1.5

Equity multiplier 2.0

Retention ratio 60%

EXAMPLE: DUPONT MODEL

Net income Dividends Net income Sales Total assetsNet income Sales Total assets Equity

0.60 5% 1.5 2.0

9.0%

g

g

g

• Dividend discount models, free cash flow models, residual income models

• Dividend models most appropriate for• Mature, profitable, dividend-paying firms• Noncontrolling shareholder perspective

Choice of Discounted Cash Flow Models

• Assumes constant g and r > g• Applicable to mature, stable firms• Estimated value very sensitive to r – g denominator

Gordon Growth Model

SUMMARY

• Preferred stock valuation where g = 0• PVGO – Value from future growth• Justified leading and trailing P/Es• Implied r and g

Uses of Gordon Growth Model

• Growth• Transition• Maturity

Phases of Growth

SUMMARY

• General two-stage model: growth abruptly declines• H-model: growth gradually declines• Three-stage model: can utilize general or H-model

Multistage Models

• g = Retention ratio × ROE• DuPont analysis:

• ROE = Profit margin × Asset turnover × Equity multiplier

Sustainable Growth Rate

SUMMARY