CHAPTER 8
Stocks and Their Valuation
Features of common stock
Determining common stock
values
Facts about common stock
Represents ownership
Ownership implies control
Stockholders elect directors
Directors elect management
Management’s goal: Maximize the
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
Types of stock market
transactions
Secondary market
Primary market
Initial public offering market
Different approaches for
valuing common stock
Dividend growth model
Corporate value model
Using the multiples of
Dividend growth model
Value of a stock is the present value of
the future dividends expected to be generated by the stock.
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:
D g)
(1 D
Future dividends and their
present values
t 0
t D (1 g)
D
t t
t
) k 1
(
D PVD
$
What happens if g > k
s?
If g > k
s, the constant growth
formula leads to a negative stock
price, which does not make sense.
The constant growth model can
only be used if:
k
s > g
If k
RF= 7%, k
M= 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 (k
s):
k
s= k
RF+ (k
M– k
RF)β
If D
0= $2 and g is a constant 6%,
find the expected dividend
stream for the next 3 years, and
their PVs.
1.8761 1.7599 D0 = 2.00
1.6509
ks = 13%
g = 6%
0 1
2.247 2
2.382 3
What is the stock’s market
value?
Using the constant growth model:
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.
Could also find expected P
1 as:
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 (k
What would the expected
price today be, if g = 0?
The dividend stream would be a
perpetuity.
2.00 2.00 2.00
0 1 2 3
ks = 13%
...
$15.38 0.13
$2.00 k
PMT
Supernormal growth:
What if g = 30% for 3 years before
achieving long-run growth of 6%?
Can no longer use just the constant
growth model to find stock value.
However, the growth does become
Valuing common stock with
nonconstant growth
ks = 13%
g = 30% g = 30% g = 30% g = 6%
P 4.658 $66.54 2.301
2.647 3.045 46.114
0 1 2 3 4
D0 = 2.00 2.600 3.380 4.394
...
Find expected dividend and capital
gains yields during the first and
fourth years.
Dividend yield (first year)
= $2.60 / $54.11 = 4.81%
Capital gains yield (first year)
= 13.00% - 4.81% = 8.19%
During nonconstant growth, dividend
Nonconstant growth:
What if g = 0% for 3 years before
long-run growth of 6%?
ks = 13%
g = 0% g = 0% g = 0% g = 6%
$30.29
P 2.12 1.77
1.57 1.39 20.99
0 1 2 3 4
D0 = 2.00 2.00 2.00 2.00
...
Find expected dividend and capital
gains yields during the first and
fourth years.
Dividend yield (first year)
= $2.00 / $25.72 = 7.78%
Capital gains yield (first year)
= 13.00% - 7.78% = 5.22%
After t = 3, the stock has
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.
Find expected annual dividend
and capital gains yields.
Capital gains yield
= g = -6.00%
Dividend yield
= 13.00% - (-6.00%) = 19.00%
Since the stock is experiencing
Corporate value model
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
Applying the corporate value
model
Find the market value (MV) of the firm.
Find PV of firm’s future FCFs
Subtract MV of firm’s debt and preferred
stock to get MV of common stock.
MV of = MV of – MV of debt and
common stock firm preferred
Divide MV of common stock by the number
Issues regarding the
corporate value model
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 (TV
Given the long-run g
FCF= 6%, and
WACC of 10%, use the corporate
value model to find the firm’s
intrinsic value.
g = 6% k = 10%
21.20
0 1 2 3 4
-5 10 20
...
-4.545 8.264
If the firm has $40 million in debt
and has 10 million shares of stock,
what is the firm’s intrinsic value per
share?
MV of equity = MV of firm – MV of debt
= $416.94m - $40m = $376.94 million
Value per share = MV of equity / # of
shares
Firm multiples method
Analysts often use the following
multiples to value stocks.
P / E
P / CF
P / Sales
EXAMPLE: Based on comparable firms,
What is market
equilibrium?
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.
g
k
k
(k
k
)
P
D
k
s RF M RF0 1 ^
Market equilibrium
Expected returns are obtained by
estimating dividends and expected
capital gains.
Required returns are obtained by
How is market equilibrium
established?
If expected return exceeds
required return …
The current price (P
0
) is “too low”
and offers a bargain.
Buy orders will be greater than sell
orders.
P
0
will be bid up until expected
Factors that affect stock
price
Required return (k
s
) could change
Changing inflation could cause k
RF to
change
Market risk premium or exposure to
market risk (β) could change
What is the Efficient Market
Hypothesis (EMH)?
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
Weak-form efficiency
Weak-form efficiency
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
Semistrong-form efficiency
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
Strong-form efficiency
All information, even inside
information, is embedded in
stock prices.
Not true--insiders can gain by
Is the stock market
efficient?
Empirical studies have been conducted to
test the three forms of efficiency. Most of which suggest the stock market was:
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
Preferred stock
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
If preferred stock with an annual
dividend of $5 sells for $50, what is
the preferred stock’s expected
return?
V
p= D / k
p$50= $5 / k
pk
p= $5 / $50
