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CHAPTER SEVENTEENTHE VALUATION
OF COMMON STOCK
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CAPITALIZATION OF INCOME METHOD THE INTRINSIC VALUE OF A STOCK
•represented by present value of the income stream
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CAPITALIZATION OF INCOME METHOD formula
where Ct = the expected cash flow
t = time k = the discount rate
1 )1(ttk
CV
t
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CAPITALIZATION OF INCOME METHOD NET PRESENT VALUE
•FORMULA
NPV = V - P
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CAPITALIZATION OF INCOME METHOD NET PRESENT VALUE
•Under or Overpriced?
If NPV > 0 underpriced
If NPV < 0 overpriced
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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
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CAPITALIZATION OF INCOME METHOD APPLICATION TO COMMON STOCK
•substituting
determines the “true” value of one share
)1(...
)1()1( 22
11
k
D
k
D
k
DV
1 )1(tt
t
k
D
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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
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THE ZERO GROWTH MODEL ASSUMPTIONS
•the future dividends remain constant such that
D1 = D2 = D3 = D4 = . . . = DN
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THE ZERO GROWTH MODEL THE ZERO-GROWTH MODEL
•derivation
1
0
)1(ttk
DV
1
00
)1(ttk
DD
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THE ZERO GROWTH MODEL Using the infinite series property,
the model reduces to
if g = 0
kktt
1
)1(
1
1
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THE ZERO GROWTH MODEL Applying to V
k
DV 1
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THE ZERO GROWTH MODEL Example
•If Zinc Co. is expected to pay cash dividends of $8 per share and the firm has a 10% required rate of return, what is the intrinsic value of the stock?
10.
8V
80$
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THE ZERO GROWTH MODEL Example(continued)
If the current market price is $65, the stock is underpriced.
Recommendation: BUY
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CONSTANT GROWTH MODEL ASSUMPTIONS:
•Dividends are expected to grow at a fixed rate, g such that
D0 (1 + g) = D1
andD1 (1 + g) = D2
or D2 = D0 (1 + g)2
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CONSTANT GROWTH MODEL In General
Dt = D0 (1 + g)t
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CONSTANT GROWTH MODEL THE MODEL:
D0 = a fixed amount
1
0
)1(
)1(
tt
t
k
gDV
10
)1(
)1(
tt
t
k
gDV
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CONSTANT GROWTH MODEL Using the infinite property series,
if k > g, then
gk
g
k
g
tt
t
1
)1(
)1(
1
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CONSTANT GROWTH MODEL
Substituting
gk
gDV
10
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CONSTANT GROWTH MODEL since D1= D0 (1 + g)
gk
DV
1
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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
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THE MULTIPLE-GROWTH MODEL
•find PV of all forecast dividends paid up to and including time T denoted VT-
T
ttT k
DV
1
0
)1(
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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
gkDV TT
11
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THE MULTIPLE-GROWTH MODEL
TTT kVV
)1(
1
TT
kgk
D
)1)((1
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THE MULTIPLE-GROWTH MODEL Summing VT- and VT+
V = VT- + VT+
TT
T
tt
T
kgk
D
k
D
)1)(()1(1
1
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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
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MODELS BASED ON P/E RATIO PRICE-EARNINGS RATIO MODEL
•EARNINGS MULTIPLIER:
= PRICE - EARNINGS RATIO
= Current Market Price following 12 months earnings
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PRICE-EARNINGS RATIO MODEL The Model is derived from the
Dividend Discount model:
gk
DP
1
0
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PRICE-EARNINGS RATIO MODEL Dividing by the coming year’s
earnings
gk
ED
E
P
1
1
1
0
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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)
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THE ZERO-GROWTH MODEL ASSUMPTIONS:
dividends remain fixed100% payout ration to assure zero-
growth
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THE ZERO-GROWTH MODEL Model:
kEV
10
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THE CONSTANT-GROWTH MODEL ASSUMPTIONS:
growth rate in dividends is constant
earnings per share is constantpayout ratio is constant
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THE CONSTANT-GROWTH MODEL The Model:
where ge = the growth rate in earnings
e
e
gk
gP
E
V 1
0
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SOURCES OF EARNINGS GROWTH What causes growth?
assume no new capital addedretained earnings use to pay firm’s new
investment
If pt = the payout ratio in year t
1-pt = the retention ratio
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SOURCES OF EARNINGS GROWTH New Investments:
ttt EpI )1(
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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
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SOURCES OF EARNINGS GROWTH Assume constant rate of return
tttt IrEE 1
)1(1 ttt prE
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SOURCES OF EARNINGS GROWTH IF
then
)1(1 ettt gEE
)1( 11 ettt gEE
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SOURCES OF EARNINGS GROWTH and
)1(1 ttet prg
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SOURCES OF EARNINGS GROWTH If the growth rate in earnings
per share get+1
is constant,then rt and pt are constant
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SOURCES OF EARNINGS GROWTH Growth rate depends on
•the retention ratio
•average return on equity
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SOURCES OF EARNINGS GROWTH such that
)1(
11 prkDV
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END OF CHAPTER 17