CHAPTER 8
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
Social/Ethical Question


Should management be equally concerned
about employees, customers, suppliers,
and “the public,” or just the stockholders?
In an enterprise economy, management
should work for stockholders subject to
constraints (environmental, fair hiring, etc.)
and competition.
8-3
Types of stock market
transactions
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Secondary market
Primary market
Initial public offering market
(“going public”)
8-4
Different approaches for valuing
common stock

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Dividend growth model
Corporate value model
Using the multiples of comparable
firms
8-5
Dividend growth model

Value of a stock is the present value of the
future dividends expected to be generated by
the stock.
D3
D1
D2
D
P0 


 ... 
1
2
3
(1  k s ) (1  k s ) (1  k s )
(1  k s )
^
8-6
Constant growth stock

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

If g is constant, the dividend growth formula
converges to:
D0 (1  g)
D1
P0 

ks - g
ks - g
^
8-7
Future dividends and their
present values
$
D t  D0 ( 1  g )
t
Dt
PVDt 
t
(1  k )
0.25
P0   PVDt
0
Years (t)
8-8
What happens if g > ks?


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:


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?

Use the SML 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?

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?


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?

Dividend yield
= D1 / P0 = $2.12 / $30.29 = 7.0%

Capital gains yield
= (P1 – P0) / P0
= ($32.10 - $30.29) / $30.29 = 6.0%

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?

0
The dividend stream would be a
perpetuity.
ks = 13%
1
2
3
...
2.00
2.00
2.00
PMT $2.00
P0 

 $15.38
k
0.13
^
8-15
Supernormal growth:
What if g = 30% for 3 years before
achieving long-run growth of 6%?

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Can no longer use just the constant growth
model to find stock value.
However, the growth does become
constant after 3 years.
8-16
Valuing common stock with
nonconstant growth
0 k = 13% 1
s
g = 30%
D0 = 2.00
2
g = 30%
2.600
3
g = 30%
3.380
4
...
g = 6%
4.394
4.658
2.301
2.647
3.045
P$ 3 
46.114
54.107
^
= P0
4.658
0.13 - 0.06
 $66.54
8-17
Find expected dividend and capital gains
yields during the first and fourth years.

Dividend yield (first year)
= $2.60 / $54.11 = 4.81%
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Capital gains yield (first year)
= 13.00% - 4.81% = 8.19%

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During nonconstant growth, dividend yield
and capital gains yield are not constant,
and capital gains yield ≠ g.
After t = 3, the stock has constant growth
and dividend yield = 7%, while capital
gains yield = 6%.
8-18
Nonconstant growth:
What if g = 0% for 3 years before longrun growth of 6%?
0 k = 13% 1
s
g = 0%
2
g = 0%
D0 = 2.00
2.00
3
g = 0%
2.00
4
...
g = 6%
2.00
2.12
1.77
1.57
1.39
P$ 3 
20.99
25.72
^
= P0
2.12
0.13 - 0.06
 $30.29
8-19
Find expected dividend and capital gains
yields during the first and fourth years.

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%

After t = 3, the stock has constant
growth and dividend yield = 7%,
while capital gains yield = 6%.
8-20
If the stock was expected to have
negative growth (g = -6%), would anyone
buy the stock, and what is its value?

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
8-21
Find expected annual dividend and
capital gains yields.

Capital gains yield
= g = -6.00%
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Dividend yield
= 13.00% - (-6.00%) = 19.00%

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.
8-22
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.
Remember, free cash flow is the firm’s
after-tax operating income less the net
capital investment

FCF = NOPAT – Net capital investment
8-23
Applying the corporate value model
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Find the market value (MV) of the firm.
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Subtract MV of firm’s debt and preferred stock to
get MV of common stock.
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Find PV of firm’s future FCFs
MV of
= MV of – MV of debt and
common stock
firm
preferred
Divide MV of common stock by the number of
shares outstanding to get intrinsic stock price
(value).

P0 = MV of common stock / # of shares
8-24
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.
8-25
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
8-26
If the firm has $40 million in debt and
has 10 million shares of stock, what is
the firm’s intrinsic value per share?
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MV of equity = MV of firm – MV of debt
= $416.94m - $40m
= $376.94 million
Value per share = MV of equity / # of shares
= $376.94m / 10m
= $37.69
8-27
Firm multiples method
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Analysts often use the following multiples
to value stocks.
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P/E
P / CF
P / Sales
EXAMPLE: Based on comparable firms,
estimate the appropriate P/E. Multiply this
by expected earnings to back out an
estimate of the stock price.
8-28
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 )
8-29
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.
8-30
How is market equilibrium
established?
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If expected return exceeds required
return …
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The current price (P0) is “too low” and
offers a bargain.
Buy orders will be greater than sell
orders.
P0 will be bid up until expected return
equals required return
8-31
Factors that affect stock price
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Required return (ks) could change
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Changing inflation could cause kRF to
change
Market risk premium or exposure to
market risk (β) could change
Growth rate (g) could change
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Due to economic (market) conditions
Due to firm conditions
8-32
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
8-33
Weak-form efficiency
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Can’t profit by looking at past trends.
A recent decline is no reason to think
stocks will go up (or down) in the
future.
Evidence supports weak-form EMH,
but “technical analysis” is still used.
8-34
Semistrong-form efficiency
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All publicly available information is
reflected in stock prices, so it doesn’t
pay to over analyze annual reports
looking for undervalued stocks.
Largely true, but superior analysts
can still profit by finding and using
new information
8-35
Strong-form efficiency
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All information, even inside
information, is embedded in stock
prices.
Not true--insiders can gain by
trading on the basis of insider
information, but that’s illegal.
8-36
Is the stock market efficient?
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Empirical studies have been conducted to
test the three forms of efficiency. Most of
which suggest the stock market was:
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Highly efficient in the weak form.
Reasonably efficient in the semistrong form.
Not efficient in the strong form. Insiders could
and did make abnormal (and sometimes
illegal) profits.
Behavioral finance – incorporates elements
of cognitive psychology to better
understand how individuals and markets
respond to different situations.
8-37
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.
8-38
If 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%
8-39