Transcript Discounted Dividend Valuation (Ch. 3)

DISCOUNTED DIVIDEND
VALUATION
Presenter
Venue
Date
DISCOUNTED CASH FLOW MODELS
2
CHOICE OF DISCOUNTED CASH FLOW
MODELS
3
VALUING COMMON STOCK USING
A MULTI-PERIOD DDM
4
EXAMPLE: VALUING COMMON STOCK USING
A MULTPERIOD DDM
0
D
P
1
2
3
$1.00
$1.05
$1.10
$20.00
EXAMPLE: VALUING COMMON STOCK USING
A MULTPERIOD DDM
$1.00 $1.05 $21.10
V0 


2
3
1.10 1.10
1.10
V0  $17.63
VALUING COMMON STOCK USING
THE GORDON GROWTH MODEL
D0 (1  g )
D1
V0 

r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
Dividend growth rate
Current stock price
$2.00
5.0%
$24 .00
VALUING COMMON STOCK USING
THE GORDON GROWTH MODEL
CAPM: r = 3% + 1.2(6%) = 10.2%
$2.00(1  0.05)
$2.10
V0 

 $40.38
0.102  0.05
0.102  0.05
EXAMPLE: VALUING PREFERRED STOCK
$2.00
V0 
 $19.61
0.102  0
EXAMPLE: CALCULATING THE IMPLIED GROWTH
RATE USING THE GORDON GROWTH MODEL
Using the previous common stock example and the current stock price of $24,
what is the implied growth rate?
$2.00(1  g )
$24 
0.102  g
2.448  24 g  2.00(1  g )
26 g  0.448
g  1.72%
CALCULATING THE IMPLIED REQUIRED RETURN
USING THE GORDON GROWTH MODEL
D1
V0 
r g
D1
r 
 g
P0
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?
D1
r 
g
P0
2.10
r 
 0.05
24
r  8.75%  5%  13.75%
PRESENT VALUE OF GROWTH
OPPORTUNITIES
E1
V0 
 PVGO
r
E1
PVGO  P0 
r
PRESENT VALUE OF GROWTH
OPPORTUNITIES
E1
 PVGO
V0 
r
P0 1 PVGO
 
E1
E1 r
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
E1
PVGO  P0 
r
5
PVGO  $80 
 $30
0.10
EXAMPLE: PRESENT VALUE OF GROWTH
OPPORTUNITIES
P0 1 PVGO
 
E r
E
P0
1
30


E 0.10 5
16  10  6
USING THE GORDON GROWTH MODEL TO
DERIVE A JUSTIFIED LEADING P/E
D1
V0 
rg
P0
D1 E1

E1
rg
P0
1 b

E1
rg
USING THE GORDON GROWTH MODEL TO
DERIVE A JUSTIFIED TRAILING P/E
D 0 (1  g )
V0 
rg
P0
D 0 (1  g ) E0

E0
rg
P0
(1  b )(1  g )

E0
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
P0
1 b

E1
rg
P0
$1.60 $4.00

 10.0
E1
0.09  0.05
EXAMPLE: USING THE GORDON GROWTH
MODEL TO DERIVE A JUSTIFIED TRAILING P/E
P0
(1  b)(1  g )

E0
rg
P0
($1.60 / $4.00)(1.05)

 10.50
E0
0.09  0.05
Actual P/E = $50.00/$4.00 = 12.50
ISSUES USING THE GORDON GROWTH MODEL
Strengths
Limitations
Simple and applicable to
stable, mature firms
Not applicable to nondividend-paying firms
Can be applied to entire
markets
g must be constant
g can be estimated using
macro data
Stock value is very sensitive
to r – g
Can be applied to firms that
repurchase stock
Most firms have nonconstant
growth in dividends
CHOICE OF DISCOUNTED CASH FLOW
MODELS
• Rapidly  earnings
• Heavy reinvestment
• Small or no dividends
Growth
Transition
• Earnings growth
slows
• Capital reinvestment
slows
• FCFE & dividends 
• ROE = r
• Earnings & dividends
growth matures
• Gordon growth model
useful
Maturity
GENERAL TWO-STAGE DDM
n
D0 1  gS 
t 1
1  r 
V0  
t
t
D0  1  g S   1  g L 
n

1  r    r  gL 
n
EXAMPLE: GENERAL TWO-STAGE DDM
Current dividend = $2.00
Growth Current dividend = $2.00
Growth for next three years = 15 percent
Long-term growth = 4 percent
Required return = 10 percent
for next three years = 15 percent
Long-term growth = 4 percent
Required 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
$2.30 $2.6450 $3.0418 $52.7237
V0 



1.10
1.102
1.103
1.103
V0  $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
$2.30 $2.6450 $3.0418 $3.1634  $68.54
V0 



1.10
1.102
1.103
1.103
V0  $55.54
TWO-STAGE H-MODEL
 D0  1  g L     D0  H  g S  g L 
V0 
r  gL
EXAMPLE: TWO-STAGE H-MODEL
Current dividend
$3.00
gs
20%
gL
H
Required return on stock
Current stock price
6%
5
10%
$120
EXAMPLE: TWO-STAGE H-MODEL
 D0  1  g L     D0  H  g S  g L  
V0 
r  gL
$3  1  0.06    $3  5  0.20  0.06  
V0 
0.10  0.06
V0  $79.50  $52.50  $132.00
SOLVING FOR THE REQUIRED RETURN USING
THE TWO-STAGE H-MODEL
 D0 

r    1  g L   H   g S  g L    g L
 P0 

 3 

1  0.06   5   0.20  0.06    0.06  10.40%
r  

 120 

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
THREE-STAGE MODEL EXAMPLE
$1 1.20  $1 1.20 
V0 


1
2
1.10
1.10
2 6
$1 1.20       0.20  0.05
2
2
1.10  0.10  0.05
2
$1 1.20  1.05
2

1.10  0.10  0.05
2
V0  $1.09  $1.19  $10.71  $24.99  $37.98
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

Total assets
 Net income  
ROE = 


 Total assets   Shareholders' equity 

Sales
Total assets
 Net income 

ROE = 



Sales
Total
assets
Shareholders'
equity




 Net income  Dividends   Net income   Sales
  Total assets 
g 


 




Net
income
Sales
Total
assets
Equity






 
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 assets 
g 

   Total assets    Equity 
Net
income
Sales
 


 
 
g   0.60    5%   1.5    2.0 
g  9.0%
SUMMARY
Choice of Discounted Cash Flow Models
• Dividend discount models, free cash flow models,
residual income models
• Dividend models most appropriate for
• Mature, profitable, dividend-paying firms
• Noncontrolling shareholder perspective
Gordon Growth Model
• Assumes constant g and r > g
• Applicable to mature, stable firms
• Estimated value very sensitive to r – g denominator
SUMMARY
Uses of Gordon Growth Model
•
•
•
•
Preferred stock valuation where g = 0
PVGO – Value from future growth
Justified leading and trailing P/Es
Implied r and g
Phases of Growth
• Growth
• Transition
• Maturity
SUMMARY
Multistage Models
• General two-stage model: growth abruptly declines
• H-model: growth gradually declines
• Three-stage model: can utilize general or H-model
Sustainable Growth Rate
• g = Retention ratio × ROE
• DuPont analysis:
• ROE = Profit margin × Asset turnover × Equity
multiplier