CHAPTER FIFTEEN
DIVIDEND DISCOUNT
MODELS
1
CAPITALIZATION OF INCOME
METHOD
• THE INTRINSIC VALUE OF A STOCK
– represented by present value of the income
stream
2
CAPITALIZATION OF INCOME
METHOD
• formula

Ct
V 
t
t 1 (1  k )
where
Ct = the expected cash flow
t = time
k = the discount rate
3
CAPITALIZATION OF INCOME
METHOD
• NET PRESENT VALUE
– FORMULA
NPV = V - P
4
CAPITALIZATION OF INCOME
METHOD
• NET PRESENT VALUE
– Under or Overpriced?
• If NPV > 0
underpriced
• If NPV < 0
overpriced
5
CAPITALIZATION OF INCOME
METHOD
• INTERNAL RATE OF RETURN (IRR)
– set NPV = 0, solve for IRR, or
– the IRR is the discount rate that makes the NPV
=0
6
CAPITALIZATION OF INCOME
METHOD
• APPLICATION TO COMMON STOCK
– substituting
V
D1
(1  k )1



 (1  k )
t 1
D2
(1  k ) 2
 ... 
D
(1  k ) 
Dt
t
determines the “true” value of one share
7
CAPITALIZATION OF INCOME
METHOD
• A COMPLICATION
– the previous model assumes dividends can be
forecast indefinitely
– a forecasting formula can be written
Dt = Dt -1 ( 1 + g t )
where g t = the dividend growth rate
8
THE ZERO GROWTH MODEL
• ASSUMPTIONS
– the future dividends remain constant such that
D1 = D2 = D3 = D4 = . . . = DN
9
THE ZERO GROWTH MODEL
• THE ZERO-GROWTH MODEL
– derivation

V 
 (1  k )
D0
t 1
 
D0
 D0 
t
(
1

k
)
 t 1

t



10
THE ZERO GROWTH MODEL
• Using the infinite series property, the model
reduces to



t 1
1
1

t
k
(1  k )
• if g = 0
11
THE ZERO GROWTH MODEL
• Applying to V
D1
V 
k
12
THE ZERO GROWTH MODEL
• Example
– If Zinc Co. is expected to pay cash dividends of
$8 per share and the firm has a 10% required
rate of return, what is the intrinsic value of the
stock?
8
V 
.10
 $80
13
THE ZERO GROWTH MODEL
• Example(continued)
If the current market price is $65, the stock is
underpriced.
Recommendation:
BUY
14
CONSTANT GROWTH MODEL
• ASSUMPTIONS:
– Dividends are expected to grow at a fixed rate,
g such that
D0 (1 + g) = D1
and
D1 (1 + g) = D2
or D2 = D0 (1 + g)2
15
CONSTANT GROWTH MODEL
• In General
Dt = D0 (1 + g)t
16
CONSTANT GROWTH MODEL
• THE MODEL:

V 

t 1
D0 (1  g )
t
(1  k ) t
D0 = a fixed amount
  (1  g ) t
V D 
0
t
 t 1 (1  k )

17



CONSTANT GROWTH MODEL
• Using the infinite property series,
if k > g, then

(1  g ) t
 (1  k )
t 1
t
1 g

kg
18
CONSTANT GROWTH MODEL
• Substituting
 1 g 
V  D0 

k  g 
19
CONSTANT GROWTH MODEL
• since D1= D0 (1 + g)
D1
V
kg
20
THE MULTIPLE-GROWTH
MODEL
• ASSUMPTION:
– future dividend growth is not constant
• Model Methodology
– to find present value of forecast stream of
dividends
– divide stream into parts
– each representing a different value for g
21
THE MULTIPLE-GROWTH
MODEL
– find PV of all forecast dividends paid up to and
including time T denoted VTT
VT 
D0

t
t 1 (1  k )
22
THE MULTIPLE-GROWTH
MODEL
• Finding PV of all forecast dividends paid
after time t
– next period dividend Dt+1 and all thereafter are
expected to grow at rate g
 1 

VT  DT 1 
kg
23
THE MULTIPLE-GROWTH
MODEL
VT 


1
 VT 
T 
 (1  k ) 
DT 1

T
(k  g )(1  k )
24
THE MULTIPLE-GROWTH
MODEL
• Summing VT- and VT+
V=
VT- +
VT+
T
DT
DT 1


t
T
(k  g )(1  k )
t 1 (1  k )
25
MODELS BASED ON P/E
RATIO
• PRICE-EARNINGS RATIO MODEL
– Many investors prefer the earnings multiplier
approach since they feel they are ultimately
entitled to receive a firm’s earnings
26
MODELS BASED ON P/E
RATIO
• PRICE-EARNINGS RATIO MODEL
– EARNINGS MULTIPLIER:
= PRICE - EARNINGS RATIO
=
Current Market Price
following 12 month earnings
27
PRICE-EARNINGS RATIO
MODEL
• The Model is derived from the Dividend
Discount model:
D1
P0 
kg
28
PRICE-EARNINGS RATIO
MODEL
• Dividing by the coming year’s earnings
D1
P0
E1

E1
kg
29
PRICE-EARNINGS RATIO
MODEL
• The P/E Ratio is a function of
– the expected payout ratio ( D1 / E1 )
– the required return (k)
– the expected growth rate of dividends (g)
30
THE ZERO-GROWTH MODEL
• ASSUMPTIONS:
• dividends remain fixed
• 100% payout ratio to assure zero-growth
31
THE ZERO-GROWTH MODEL
• Model:
1
V E0 
k
32
THE CONSTANT-GROWTH
MODEL
• ASSUMPTIONS:
• growth rate in dividends is
constant
• earnings per share is constant
• payout ratio is constant
33
THE CONSTANT-GROWTH
MODEL
• The Model:
 1  ge 
V

 P
E0
 k  ge 
where ge = the growth rate in earnings
34
SOURCES OF EARNINGS
GROWTH
• What causes growth?
• assume no new capital added
• retained earnings used to pay firm’s new investment
• If pt = the payout ratio in year t
• 1-pt = the retention ratio
35
SOURCES OF EARNINGS
GROWTH
• New Investments:
I t  (1  pt ) Et
36
SOURCES OF EARNINGS
GROWTH
• What about the return on equity?
Let rt = return on equity in time t
rt I t is added to earnings per
share in year t+1 and thereafter
37
SOURCES OF EARNINGS
GROWTH
• Assume constant rate of return
Et 1  Et  rt I t
 Et  1  rt (1  pt )
38
SOURCES OF EARNINGS
GROWTH
• IF
Et  Et 1 (1  get )
• then
Et 1  Et (1  g et 1 )
39
SOURCES OF EARNINGS
GROWTH
• and
g et 1  rt (1  pt )
40
SOURCES OF EARNINGS
GROWTH
• If the growth rate in earnings per share
get+1
is constant, then rt and pt are constant
41
SOURCES OF EARNINGS
GROWTH
• Growth rate depends on
– the retention ratio
– average return on equity
42
SOURCES OF EARNINGS
GROWTH
• such that


1
V  D1 

 k  r (1  p) 
43