7-1
CHAPTER 7
Stocks and Their Valuation
Features of common stock
Determining common stock
values
Efficient markets
Preferred stock
7-2
Common Stock: Owners, Directors,
and Managers
Represents ownership.
Ownership implies control.
Stockholders elect directors.
Directors hire management.
Since managers are “agents” of
shareholders, their goal should be:
Maximize stock price.
7-3
What’s classified stock? How might
classified stock be used?
Classified stock has special provisions.
Could classify existing stock as
founders’ shares, with voting rights but
dividend restrictions.
New shares might be called “Class A”
shares, with voting restrictions but full
dividend rights.
7-4
What is tracking stock?
The dividends of tracking stock are tied
to a particular division, rather than the
company as a whole.
Investors can separately value the
divisions.
Its easier to compensate division
managers with the tracking stock.
 But tracking stock usually has no
voting rights, and the financial
disclosure for the division is not as
regulated as for the company.
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When is a stock sale an initial public
offering (IPO)?
A firm “goes public” through an IPO
when the stock is first offered to the
public.
Prior to an IPO, shares are typically
owned by the firm’s managers, key
employees, and, in many situations,
venture capital providers.
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What is a seasoned equity offering
(SEO)?
A seasoned equity offering occurs
when a company with public stock
issues additional shares.
After an IPO or SEO, the stock trades
in the secondary market, such as the
NYSE or Nasdaq.
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Different Approaches for Valuing
Common Stock
Dividend growth model
Using the multiples of comparable
firms
Free cash flow method (covered in
Chapter 15)
7-8
Stock Value = PV of Dividends
Pˆ0 
D3
D1
D2
D


...
1
2
3

1  rs  1  rs  1  rs 
1  rs 
What is a constant growth stock?
One whose dividends are expected to
grow forever at a constant rate, g.
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For a constant growth stock,
D1  D0 1  g
2
D2  D 0 1  g
t
D t  D t 1  g
1
If g is constant, then:
D0 1  g 
D1
ˆ
P0 

rs  g
rs  g
7 - 10
$
D t  D 0 1  g
t
0.25
Dt
PVDt 
1  r t
P0   PVDt
0
If g > r, P0  !
Years (t)
7 - 11
What happens if g > rs?
Pˆ0 
D1
requires rs  g .
rs  g
If rs< g, get negative stock price,
which is nonsense.
We can’t use model unless (1) g  rs
and (2) g is expected to be constant
forever. Because g must be a longterm growth rate, it cannot be  rs.
7 - 12
Assume beta = 1.2, rRF = 7%, and RPM =
5%. What is the required rate of return
on the firm’s stock?
Use the SML to calculate rs:
rs = rRF + (RPM)bFirm
= 7% + (5%) (1.2)
= 13%.
7 - 13
D0 was $2.00 and g is a constant 6%.
Find the expected dividends for the
next 3 years, and their PVs. rs = 13%.
0
g=6%
1
D0=2.00 2.12
13%
1.8761
1.7599
1.6508
2
2.2472
3
2.3820
4
7 - 14
What’s the stock’s market value?
D0 = 2.00, rs = 13%, g = 6%.
Constant growth model:
D0 1  g 
D1
ˆ
P0 

rs  g
rs  g
$2.12
$2.12
=
=
$30.29.
0.13 - 0.06
0.07
7 - 15
What is the stock’s market value one
^
year from now, P1?
D1 will have been paid, so expected
dividends are D2, D3, D4 and so on.
Thus,
D2
P1 = rs - g
= $2.2427 = $32.10
0.07
7 - 16
Find the expected dividend yield and
capital gains yield during the first year.
D1
$2.12
Dividend yield =
=
= 7.0%.
P0
$30.29
^
P1 - P0
$32.10 - $30.29
CG Yield =
=
P0
$30.29
= 6.0%.
7 - 17
Find the total return during the
first year.
Total return = Dividend yield +
Capital gains yield.
Total return = 7% + 6% = 13%.
Total return = 13% = rs.
For constant growth stock:
Capital gains yield = 6% = g.
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Rearrange model to rate of return form:

D
D1
1
ˆ
P0 
to r s 
 g.
rs  g
P0
^
Then, rs = $2.12/$30.29 + 0.06
= 0.07 + 0.06 = 13%.
7 - 19
What would P0 be if g = 0?
The dividend stream would be a
perpetuity.
0 r =13%
s
1
2
3
2.00
2.00
2.00
PMT $2.00
P0 =
=
= $15.38.
r
0.13
^
7 - 20
If we have supernormal growth of
30% for 3 years, then a long-run
^
constant g = 6%, what is P0? r is
still 13%.
Can no longer use constant growth
model.
However, growth becomes constant
after 3 years.
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Nonconstant growth followed by constant
growth:
0 r =13%
s
1
g = 30%
D0 = 2.00
2
g = 30%
2.60
3
g = 30%
3.38
4
g = 6%
4.394
4.6576
2.3009
2.6470
3.0453
$4.6576
P̂3 
 $66.5371
0.13  0.06
46.1135
54.1067
^
= P0
7 - 22
What is the expected dividend yield and
capital gains yield at t = 0? At t = 4?
At t = 0:
D1
$2.60
Dividend yield =
=
= 4.8%.
P0
$54.11
CG Yield = 13.0% - 4.8% = 8.2%.
(More…)
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During nonconstant growth, dividend
yield and capital gains yield are not
constant.
If current growth is greater than g,
current capital gains yield is greater
than g.
After t = 3, g = constant = 6%, so the t
t = 4 capital gains gains yield = 6%.
 Because rs = 13%, the t = 4 dividend
yield = 13% - 6% = 7%.
7 - 24
Is the stock price based on
short-term growth?
The current stock price is $54.11.
The PV of dividends beyond year 3 is
$46.11 (P^3 discounted back to t = 0).
The percentage of stock price due to
“long-term” dividends is:
$46.11
$54.11 = 85.2%.
7 - 25
If most of a stock’s value is due to longterm cash flows, why do so many
managers focus on quarterly earnings?
Sometimes changes in quarterly
earnings are a signal of future
changes in cash flows. This would
affect the current stock price.
Sometimes managers have bonuses
tied to quarterly earnings.
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Suppose g = 0 for t = 1 to 3, and then g
^
is a constant 6%. What is P0?
0
rs=13%
g = 0%
1
2
g = 0%
2.00
1.7699
1.5663
1.3861
20.9895
25.7118
3
g = 0%
2.00
4
g = 6%
2.00
...
2.12
P  2.12  30.2857
3
0.07
7 - 27
What is dividend yield and capital
gains yield at t = 0 and at t = 3?
D1 2.00
t = 0: P  $25.72 7.8%.
0
CGY = 13.0% - 7.8% = 5.2%.
t = 3: Now have constant growth
with g = capital gains yield = 6% and
dividend yield = 7%.
7 - 28
If g = -6%, would anyone buy the
stock? If so, at what price?
Firm still has earnings and still pays
^
dividends, so P0 > 0:
ˆP  D0 1  g   D1
0
rs  g
rs  g
$2.00(0.94) $1.88
=
=
= $9.89.
0.13 - (-0.06) 0.19
7 - 29
What are the annual dividend
and capital gains yield?
Capital gains yield = g = -6.0%.
Dividend yield = 13.0% - (-6.0%)
= 19.0%.
Both yields are constant over time, with
the high dividend yield (19%) offsetting
the negative capital gains yield.
7 - 30
Using the Stock Price Multiples to
Estimate Stock Price
 Analysts often use the P/E multiple (the price
per share divided by the earnings per share)
or the P/CF multiple (price per share divided
by cash flow per share, which is the earnings
per share plus the dividends per share) to
value stocks.
 Example:
Estimate the average P/E ratio of
comparable firms. This is the P/E multiple.
Multiply this average P/E ratio by the
expected earnings of the company to
estimate its stock price.
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Using Entity Multiples
 The entity value (V) is:
the market value of equity (# shares of
stock multiplied by the price per share)
plus the value of debt.
 Pick a measure, such as EBITDA, Sales,
Customers, Eyeballs, etc.
 Calculate the average entity ratio for a
sample of comparable firms. For example,
V/EBITDA
V/Customers
7 - 32
Using Entity Multiples (Continued)
 Find the entity value of the firm in question.
For example,
Multiply the firm’s sales by the V/Sales
multiple.
Multiply the firm’s # of customers by the
V/Customers ratio
 The result is the total value of the firm.
 Subtract the firm’s debt to get the total value
of equity.
 Divide by the number of shares to get the
price per share.
7 - 33
Problems with Market Multiple Methods
 It is often hard to find comparable firms.
 The average ratio for the sample of
comparable firms often has a wide range.
For example, the average P/E ratio might
be 20, but the range could be from 10 to 50.
How do you know whether your firm
should be compared to the low, average, or
high performers?
7 - 34
Why are stock prices volatile?
^
D
P  r 1g
0 s
 rs = rRF + (RPM)bi could change.
 Inflation expectations
 Risk aversion
 Company risk
 g could change.
7 - 35
Stock value vs. changes in rs and g
D1 = $2, rs = 10%, and g = 5%:
P0 = D1 / (rs-g) = $2 / (0.10 - 0.05) = $40.
rs
9%
10%
11%
What if rs or g change?
g
g
g
4%
5%
6%
40.00
50.00
66.67
33.33
40.00
50.00
28.57
33.33
40.00
7 - 36
Are volatile stock prices consistent
with rational pricing?
 Small changes in expected g and rs
cause large changes in stock prices.
 As new information arrives, investors
continually update their estimates of
g and rs.
 If stock prices aren’t volatile, then
this means there isn’t a good flow of
information.
7 - 37
What is market equilibrium?
In equilibrium, stock prices are stable.
There is no general tendency for
people to buy versus to sell.
^
The expected price, P, must equal the
actual price, P. In other words, the
fundamental value must be the same as
the price.
(More…)
7 - 38
In equilibrium, expected returns must
equal required returns:
^
rs = D1/P0 + g = rs = rRF + (rM - rRF)b.
7 - 39
How is equilibrium established?
^
^
If rs = D1 + g > rs, then P0 is “too low.”
P0
If the price is lower than the fundamental
value, then the stock is a “bargain.”
Buy orders will exceed sell orders, the
price will be bid up, and D1/P0 falls until
D1/P0 + g = ^rs = rs.
7 - 40
Why do stock prices change?
D1
P0 
ri  g
^
 ri = rRF + (rM - rRF )bi could change.
 Inflation expectations
 Risk aversion
 Company risk
 g could change.
7 - 41
What’s the Efficient Market
Hypothesis (EMH)?
Securities are normally in
equilibrium and are “fairly priced.”
One cannot “beat the market”
except through good luck or inside
information.
(More…)
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1. Weak-form EMH:
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.
7 - 43
2. Semistrong-form EMH:
All publicly available
information is reflected in
stock prices, so it doesn’t pay
to pore over annual reports
looking for undervalued
stocks. Largely true.
7 - 44
3. Strong-form EMH:
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.
7 - 45
Markets are generally efficient
because:
1. 100,000 or so trained analysts--MBAs,
CFAs, and PhDs--work for firms like
Fidelity, Merrill, Morgan, and
Prudential.
2. These analysts have similar access to
data and megabucks to invest.
3. Thus, news is reflected in P0 almost
instantaneously.
7 - 46
Preferred Stock
Hybrid security.
Similar to bonds in that preferred
stockholders receive a fixed dividend
which must be paid before dividends
can be paid on common stock.
However, unlike bonds, preferred stock
dividends can be omitted without fear
of pushing the firm into bankruptcy.
7 - 47
What’s the expected return on
preferred stock with Vps = $50 and
annual dividend = $5?
V ps  $50 
$5

r ps

r ps
$5

 0.10  10.0%.
$50