CHAPTER 9
Stocks and Their Valuation




Features of common stock
Determining common stock values
Efficient markets
Preferred stock
by Donglin Li
9-1
Facts about common stock





Represents ownership
Ownership implies control
Stockholders elect directors
Directors elect management
Management’s goal: Maximize the
stock price
by Donglin Li
9-2
Types of stock market
transactions

Initial public offering market
(“going public”) (Company sells
shares to the public for the 1st times.)

Secondary market (stockholders
sell shares to each other)
by Donglin Li
9-3
Stock Market Transactions

Apple Computer decides to issue additional stock
with the assistance of its investment banker. An
investor purchases some of the newly issued
shares. Is this a primary market transaction or a
secondary market transaction?


Since new shares of stock are being issued, this is a
primary market transaction.
What if instead an investor buys existing shares of
Apple stock in the open market – is this a primary
or secondary market transaction?

Since no new shares are created, this is a secondary
market transaction.
by Donglin Li
9-4
Different approaches for valuing
common stock

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
Dividend growth model
Corporate value model
Using the multiples of comparable
firms
by Donglin Li
9-5
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  rs )
(1  rs )
(1  rs )
(1  rs ) 
^
by Donglin Li
9-6
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 

rs - g
rs - g
^
by Donglin Li
9-7
Future dividends and their
present values
$
D t  D0 ( 1  g )
t
Dt
PVDt 
t
(1  r )
0.25
P0   PVDt
0
Years (t)
by Donglin Li
9-8
What happens if g > rs?


If g > rs, the constant growth formula
leads to a negative stock price, which
does not make sense.
The constant growth model can only be
used if:


rs > g
g is expected to be constant forever
by Donglin Li
9-9
If rRF = 7%, rM = 12%, and b = 1.2,
what is the required rate of return on
the firm’s stock?

Use the SML to calculate the required
rate of return (rs):
rs = rRF + (rM – rRF)b
= 7% + (12% - 7%)1.2
= 13%
by Donglin Li
9-10
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
rs = 13%
1.6509
by Donglin Li
9-11
What is the stock’s intrinsic value?

Using the constant growth model:
ˆP  D1  $2.12
0
rs - g 0.13 - 0.06
$2.12

0.07
 $30.29
by Donglin Li
9-12
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 

rs - g 0.13 - 0.06
 $32.10
Could also find expected P1 as:
^
P1  P0 (1.06)  $32.10
by Donglin Li
9-13
What are 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 (rs)
= Dividend Yield + Capital Gains Yield
= 7.0% + 6.0% = 13.0%
by Donglin Li
9-14
What would the expected price
today be, if g = 0?

0
The dividend stream would be a
perpetuity.
rs = 13%
1
2
3
...
2.00
2.00
2.00
PMT $2.00
P0 

 $15.38
r
0.13
^
by Donglin Li
9-15
Supernormal growth:
What if g = 30% for 3 years before
achieving long-run growth of 6%?


Can no longer use just the constant growth
model to find stock value.
However, the growth does become
constant after 3 years.
by Donglin Li
9-16
Valuing common stock with
nonconstant growth
0 r = 13% 1
s
g = 30%
D0 = 2.00
2
g = 30%
2.600
3
g = 30%
3.380
4
...
g = 6%
4.394
4.658
2.301
2.647
3.045
P$ 3 
46.114
54.107
^
= P0
4.658
0.13 - 0.06
by Donglin Li
 $66.54
9-17
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 

rs - g
rs - g
^
$2.00 (0.94) $1.88


 $9.89
0.13 - (-0.06) 0.19
by Donglin Li
9-18
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 constant
growth, dividend yield and capital gains
yield are constant. Dividend yield is
sufficiently large (19%) to offset a negative
capital gains.
by Donglin Li
9-19
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 firm’s
after-tax operating income less the net
capital investment

FCF = NOPAT – Net capital investment
by Donglin Li
9-20
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
by Donglin Li
9-21
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.
by Donglin Li
9-22
Given the long-run gFCF = 6%, and WACC
(weighted average cost of capital) of 10%,
use the corporate value model to find the
firm’s intrinsic value.
0 r = 10%
1
-5
-4.545
8.264
15.026
398.197
416.942
2
3
10
4
20
...
g = 6%
21.20
21.20
530 =
by Donglin Li
0.10 - 0.06
= TV3
9-23
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
by Donglin Li
9-24
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 per share to back out
an estimate of the stock price.
by Donglin Li
9-25
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, two conditions hold:
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The current market stock price equals its
^
intrinsic value (P0 = P0).
Expected returns must equal required returns.
D1
rs 
g
P0
^

rs  rRF  (rM - rRF )b
by Donglin Li
9-26
Market equilibrium
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Expected returns are obtained by
estimating dividends yield and expected
capital gains yield.
Required returns are obtained by
estimating risk and applying the CAPM.
by Donglin Li
9-27
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
by Donglin Li
9-28
Factors that affect stock price
P0 


D1
rs - g
Required return (rs) could change


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D 0 (1  g)
rs - g
Changing inflation could cause rRF to
change
Market risk premium or exposure to
market risk (β) could change
Growth rate (g) could change


Due to economic (market) conditions
Due to firm conditions
by Donglin Li
9-29
Stock Market Reporting
52 WEEKS
YLD
VOL
NET
HI
LO STOCK SYM DIV % PE 100s HI LO CLOSE CHG
52.75 19.06 Gap Inc GPS 0.09 0.5 15 65172 20.50 19 19.25 -1.75
Gap has
been as
high as
$52.75 in
the last
year.
Gap pays a
dividend of 9
cents/share
Gap ended trading
at $19.25, down
$1.75 from
yesterday’s close
Given the
current price,
the dividend
yield is ½ %
Gap has
been as low
as $19.06 in
the last year.
Given the
current price, the
PE ratio is 15
times earnings
by Donglin Li
6,517,200 shares
traded hands in the
last day’s trading
9-30
Where can you find a stock quote,
and what does one look like?

Stock quotes can be found in a variety of print sources (Wall
Street Journal or the local newspaper) and online sources
(Yahoo!Finance, CNNMoney, or MSN MoneyCentral).
by Donglin Li
9-31
Efficient Capital Markets
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Stock prices are in equilibrium or are “fairly” priced
If this is true, then you should not be able to earn
“abnormal” or “excess” returns, in expectation.
Efficient markets DO NOT imply that investors
cannot earn a positive return in the stock market.
They do mean that, on average, you will earn a
return that is appropriate for the risk undertaken
and there is not a bias in prices that can be
exploited to earn excess returns.
by Donglin Li
9-32
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
by Donglin Li
9-33
Weak-form efficiency


Can’t profit by looking at past price
trends. A recent decline is no reason
to think stocks will go up (or down) in
the future. There is no predictable
price pattern based on price path.
Real world evidence supports weakform EMH, but “technical analysis” is
still used by some people.
by Donglin Li
9-34
Efficient Market Theory

Technical Analysts

Forecast stock prices based on the watching
the fluctuations in historical prices (thus
“wiggle watchers”)
by Donglin Li
9-35
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 in real world, but
superior analysts can still profit by
finding and using new information
by Donglin Li
9-36
Efficient Market Theory
Average Annual Return on 1493 Mutual Funds and the
Market Index
40
30
10
0
-10
Funds
Market
-20
-30
by Donglin Li
19
92
19
77
-40
19
62
Return (%)
20
9-37
Implications of market efficiency

You hear in the news that a medical research
company received FDA approval for one of its
products. If the market is semi-strong
efficient, can you expect to take advantage of
this information by purchasing the stock?

No – if the market is semi-strong efficient, this
information will already have been incorporated
into the company’s stock price. So, it’s probably
too late …
by Donglin Li
9-38
One-year-ahead hedge returns based on capital
investment levels. ©Donglin Li 2004
1 year ahead hedge returns between lowest and highest deciles of investment (d_PPE) firms

Go long the lowest investment
stocks.

Go short the highest investment
stocks.
0.35
0.3
0.25

Hedge Portfolio Return
0.2
12 month size adjusted buy and
hold hedge returns after May each
year.
0.15

0.1
Positive in 36 out of 39 years,
average 12.6%
0.05

0
1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000
Pattern is consistent with
market mispricing.
-0.05
-0.1
Year
by Donglin Li
9-39
Strong-form efficiency


All information, even inside
information, is embedded in stock
prices. That is, one cannot profit
even on private information.
Not true--insiders can gain by
trading on the basis of insider
information, but that’s illegal.
by Donglin Li
9-40
Is the stock market efficient?

Empirical studies have tried to test the
three forms of efficiency.



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.
by Donglin Li
9-41
What Makes Markets Efficient?

There are many investors out there
doing research


As new information comes to market, this
information is analyzed and trades are
made based on this information
Therefore, prices should reflect all available
public information, and almost instantly.
by Donglin Li
9-42
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 preferred
dividend payments without fear of pushing
the firm into bankruptcy.
No voting right.
by Donglin Li
9-43
If preferred stock with an annual
dividend of $5 sells for $50, what is the
preferred stock’s expected return?
Vp = D / rp
$50 = $5 / rp
^r = $5 / $50
p
= 0.10 = 10%
by Donglin Li
9-44
Exercises
1. You purchase a stock expecting the price to rise 10% in
the coming year. After one year, the stock has actually
increased in value by 30%, due primarily to new
information released during the year concerning
unexpectedly higher sales. Which of the following
describes this result?
A) This is a violation of weak form efficiency.
B) This is a violation of semi-strong form efficiency.
C) This is a violation of strong form efficiency.
D) This is not a violation of market efficiency.
by Donglin Li
9-45
2. You track the liquidity of companies and find that you can
consistently earn unusually high returns by purchasing the shares
of firms whose stock price falls below the cash value per share as
indicated on the balance sheet. Which of the following describes
this strategy?
A) This would not be a violation of market efficiency.
B) This would be a violation of weak form efficiency.
C) This would be a violation of semi-strong form efficiency.
by Donglin Li
9-46
3. You have discovered from looking at charts of past stock prices that
if you buy just after a stock price has declined for three
consecutive days, you make money every time! This is clearly a
violation of _________ market efficiency.
A) weak form
B) semi-weak form
C) semi-strong form
D) strong form
by Donglin Li
9-47