Stocks and Their Valuation
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Features of common stock
Determining common stock values
Efficient markets
Preferred stock
8-1
Facts about common stock
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Represents ownership
Ownership implies control
Stockholders elect directors
Directors elect management
Management’s goal: Maximize the
stock price
8-2
Types of stock market
transactions
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Secondary market
Primary market
Initial public offering market
(“going public”)
8-3
Different approaches for valuing
common stock
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Dividend growth model
Corporate value model
Using the multiples of comparable
firms
8-4
Terms used in stock valuation
Dt = Dividend expected to receive at the
end of year t.
 Po = Actual market price of the stock
today
^
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P t = Expected price of the stock at the
end of year t
^
 P 0 =Intrinsic or theoretical value
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8-5
Terms used in stock valuation
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g= Expected growth rate in dividends.
Ks=
^
Required rate of return
K s= Expected rate of return
Ks= Actual or realized rate of return
D1/P0 =Dividend Yield during the coming year
(P1-P0)/P0 = Capital Gain Yield.
8-6
Dividend growth model
Value of a stock is the present value of the
future dividends expected to be generated by
the stock.
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^
P0 
D1
(1  k s )1

D2
(1  k s ) 2

D3
(1  k s )3
 ... 
D
(1  k s ) 
8-7
Constant growth stock
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A stock whose dividends are expected to
grow forever at a constant rate, g.
D1 = D0 (1+g)1
D2 = D0 (1+g)2
Dt = D0 (1+g)t
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If g is constant, the dividend growth formula
converges to:
D0 (1  g)
D1
P0 

ks - g
ks - g
^
8-8
What happens if g > ks?
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If g > ks, the constant growth formula
leads to a negative stock price, which
does not make sense.
The constant growth model can only be
used if:
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ks > g
g is expected to be constant forever
8-9
If kRF = 7%, kM = 12%, and β = 1.2,
what is the required rate of return on
the firm’s stock?
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Use the CAPM to calculate the required
rate of return (ks):
ks = kRF + (kM – kRF)β
= 7% + (12% - 7%)1.2
= 13%
8-10
If D0 = $2 and g is a constant 6%,
find the expected dividend stream for
the next 3 years, and their PVs.
0
g = 6%
D0 = 2.00
1.8761
1.7599
1
2
2.12
2.247
3
2.382
ks = 13%
1.6509
8-11
What is the stock’s market value?
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Using the constant growth model:
D1
$2.12
P0 

k s - g 0.13 - 0.06
$2.12

0.07
 $30.29
8-12
What is the expected market price
of the stock, one year from now?
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D1 will have been paid out already. So,
P1 is the present value (as of year 1) of
D2, D3, D4, etc.
^
D2
$2.247
P1 

k s - g 0.13 - 0.06
 $32.10
Could also find expected P1 as:
^
P1  P0 (1.06)  $32.10
8-13
What is the expected dividend yield,
capital gains yield, and total return
during the first year?
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Dividend yield
= D1 / P0 = $2.12 / $30.29 = 7.0%
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Capital gains yield
= (P1 – P0) / P0
= ($32.10 - $30.29) / $30.29 = 6.0%
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Total return (ks)
= Dividend Yield + Capital Gains Yield
= 7.0% + 6.0% = 13.0%
8-14
What would the expected price
today be, if g = 0?
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0
The dividend stream would be a
perpetuity.
ks = 13%
1
2
3
...
2.00
2.00
2.00
PMT $2.00
P0 

 $15.38
k
0.13
^
8-15
Self testing:1
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Cook company is expected to pay a $0.50
per share dividend at the end of the year.
The dividend is expected to grow at a
constant rate of 7% per year. The required
rate of return on the stock,Ks, is 15%.
What is the value per share of the
company’s stock?
8-16
Self testing:2
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Dozier Corporation’s share currently sell for
$20 per share. The stock just paid a
dividend of $1 per share. The dividend is
expected to grow at a constant rate of 10%
a year. What stock price is expected 1 year
from now? What is the required rate of
return on the company’s stock?
8-17
Supernormal/Nonconstant growth:
What if D0 = $2 & g = 30% for 3 years
before achieving long-run growth of 6%?
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Can no longer use just the constant growth
model to find stock value.
However, the growth does become
constant after 3 years.
Required Return is 13%
8-18
Valuing common stock with
nonconstant growth
0 k = 13% 1
s
g = 30%
D0 = 2.00
2
g = 30%
2.600
3
g = 30%
3.380
4
...
g = 6%
4.394
4.658
2.301
2.647
3.045
P$ 3 
46.114
54.107
^
= P0
4.658
0.13 - 0.06
 $66.54
8-19
Find expected dividend and capital gains
yields during the first and fourth years.
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Dividend yield (first year)
= $2.60 / $54.11 = 4.81%
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Capital gains yield (first year)
= 13.00% - 4.81% = 8.19%
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During nonconstant growth, dividend yield
and capital gains yield are not constant,
and capital gains yield ≠ g.
After t = 3, the stock has constant growth
and dividend yield = 7%, while capital
gains yield = 6%.
8-20
Nonconstant growth:
What if g = 0% for 3 years before longrun growth of 6%?
0 k = 13% 1
s
g = 0%
2
g = 0%
D0 = 2.00
2.00
3
g = 0%
2.00
4
...
g = 6%
2.00
2.12
1.77
1.57
1.39
P$ 3 
20.99
25.72
^
= P0
2.12
0.13 - 0.06
 $30.29
8-21
Find expected dividend and capital gains
yields during the first and fourth years.
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Dividend yield (first year)
= $2.00 / $25.72 = 7.78%
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Capital gains yield (first year)
= 13.00% - 7.78% = 5.22%
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After t = 3, the stock has constant
growth and dividend yield = 7%,
while capital gains yield = 6%.
8-22
If the stock was expected to have
negative growth (g = -6%), would anyone
buy the stock, and what is its value?
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The firm still has earnings and pays
dividends, even though they may be
declining, they still have value.
D0 ( 1  g )
D1
P0 

ks - g
ks - g
^
$2.00 (0.94) $1.88


 $9.89
0.13 - (-0.06) 0.19
8-23
Find expected annual dividend and
capital gains yields.
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Capital gains yield
= g = -6.00%
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Dividend yield
D1 / P0 = $1.88/$9.89 = 19.00%
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Since the stock is experiencing constant
growth, dividend yield and capital gains
yield are constant. Dividend yield is
sufficiently large (19%) to offset a negative
capital gains.
8-24
Corporate value model
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Also called the free cash flow method.
Suggests the value of the entire firm
equals the present value of the firm’s
free cash flows.
Free cash flow is the firm’s after-tax
operating income less the net capital
investment
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FCF = NOPAT – Net capital investment
8-25
Issues regarding the
corporate value model
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Often preferred to the dividend growth
model, especially when considering number
of firms that don’t pay dividends or when
dividends are hard to forecast.
Similar to dividend growth model, assumes at
some point free cash flow will grow at a
constant rate.
Terminal value (TVn) represents value of firm
at the point that growth becomes constant.
8-26
Given the long-run gFCF = 6%, and
WACC of 10%, use the corporate value
model to find the firm’s intrinsic value.
0 k = 10%
1
-5
-4.545
8.264
15.026
398.197
416.942
2
10
3
4
20
...
g = 6%
21.20
21.20
530 =
0.10 - 0.06
= TV3
8-27
What is market equilibrium?
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In equilibrium, stock prices are stable and
there is no general tendency for people to
buy versus to sell.
In equilibrium, expected returns must equal
required returns.
D1
ks 
g
P0
^

k s  k RF  (k M - k RF )
8-28
Market equilibrium
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Expected returns are obtained by
estimating dividends and expected
capital gains.
Required returns are obtained by
estimating risk and applying the CAPM.
8-29
What is the Efficient Market
Hypothesis (EMH)?
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Securities are normally in equilibrium
and are “fairly priced.”
Investors cannot “beat the market”
except through good luck or better
information.
Levels of market efficiency
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Weak-form efficiency
Semistrong-form efficiency
Strong-form efficiency
8-30
Weak-form efficiency
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The weak form of the EMH states that
all information contained in past price
movements is fully reflected in current
market prices.
8-31
Semistrong-form efficiency
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The semistrong-form of the EMH
states that current market prices
reflect all publicly available
information.
8-32
Strong-form efficiency
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The strong form of the EMH states
that current market prices reflect all
related information, whether publicly
available or privately held.
8-33
Preferred stock
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Hybrid security
Like bonds, preferred stockholders
receive a fixed dividend that must be
paid before dividends are paid to
common stockholders.
However, companies can omit
preferred dividend payments without
fear of pushing the firm into
bankruptcy.
8-34
If a preferred stock with an annual
dividend of $5 sells for $50, what is the
preferred stock’s expected return?
Vp = D / kp
$50 = $5 / kp
kp = $5 / $50
= 0.10 = 10%
8-35