### Chapter 9

9-1
CHAPTER 9
Stocks and Their Valuation
Features of common stock
Determining common stock
values
Efficient markets
Preferred stock
9-2
Represents ownership.
Ownership implies control.
Stockholders elect directors.
Directors elect management.
Management’s goal: Maximize
stock price.
9-3
Social/Ethical Question
Should management be equally
customers, suppliers, “the public,”
or just the stockholders?
In enterprise economy, work for
stockholders subject to constraints
(environmental, fair hiring, etc.) and
competition.
9-4
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.
9-5
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.
9-6
Average Initial Returns on IPOs in
Various Countries
100%
75%
50%
25%
9-7
Different Approaches for Valuing
Common Stock
Dividend growth model
Free cash flow method
Using the multiples of comparable
firms
9-8
Stock Value = PV of Dividends
P 0 
D1

D2

D3
1  k  1  k  1  k 
1
s
2
s
s
3
. . .
D
1  k 

s
What is a constant growth stock?
One whose dividends are expected to
grow forever at a constant rate, g.
9-9
For a Constant Growth Stock
D1 = D0(1 + g)1
D2 = D0(1 + g)2
Dt = Dt(1 + g)t
If g is constant, then:
D0(1 + g)
D1
P0 =
=
.
ks - g
ks - g
^
9 - 10
\$
Dt  D0 1  g
t
Dt
PVD t 
t
1  k 
0.25
P0   PVD t
0
If g > k, P0  !
Years (t)
9 - 11
What happens if g > ks?
P 0 
D1
requires k s  g.
ks  g
If ks< g, get negative stock price,
which is nonsense.
We can’t use model unless (1) ks> g
and (2) g is expected to be constant
forever.
9 - 12
Assume beta = 1.2, kRF = 7%, and kM =
12%. What is the required rate of
return on the firm’s stock?
Use the SML to calculate ks:
ks= kRF + (kM – kRF)bFirm
= 7% + (12% – 7%) (1.2)
= 13%.
9 - 13
D0 was \$2.00 and g is a constant 6%.
Find the expected dividends for the
next 3 years, and their PVs. ks = 13%.
0
g = 6%
1
D0 = 2.00 2.12
13%
1.8761
1.7599
1.6509
2
2.247
3
2.382
9 - 14
What’s the stock’s market value?
D0 = 2.00, ks = 13%, g = 6%.
Constant growth model:
D1
\$2.12
P0 =
=
ks – g
0.13 – 0.06
=
\$2.12
0.07
= \$30.29.
9 - 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
\$2.247
P1 =
=
ks – g
0.13 – 0.06
= \$32.10.
^
^ as follows:
Could also find P
1
^ = P (1.06) = \$32.10.
P
1
0
9 - 16
Find the expected dividend yield,
capital gains yield, and total return
during the first year.
D1
\$2.12
Dividend yld =
=
= 7.0%.
P0
\$30.29
^
P1 – P0 \$32.10 – \$30.29
Cap gains yld =
=
\$30.29
P0
= 6.0%.
Total return = 7.0% + 6.0% = 13.0%.
9 - 17
Rearrange model to rate of return form:
D
D
1
1




 g.
P0
to k s
ks  g
P0
^
Then, ks = \$2.12/\$30.29 + 0.06
= 0.07 + 0.06 = 13%.
9 - 18
^
What would P0 be if g = 0?
The dividend stream would be a
perpetuity.
0
13%
1
2
3
...
2.00
2.00
2.00
PMT
\$2.00
P0 =
=
= \$15.38.
k
0.13
^
9 - 19
If we have supernormal growth of 30%
for 3 years, then a long-run constant
^
g = 6%, what is P0? k is still 13%.
Can no longer use constant growth
model.
However, growth becomes constant
after 3 years.
9 - 20
Nonconstant growth followed by constant
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 
46.116
54.109
^
= P0
4.658
.
 \$66.54
0 .13  0.06
9 - 21
What is the expected dividend yield
and capital gains yield at t = 0?
At t = 4?
\$2.60
Div. yield0 =
= 4.81%.
\$54.11
Cap. gain0 = 13.00% – 4.81% = 8.19%.
9 - 22
During nonconstant growth, D/P and
capital gains yield are not constant,
and capital gains yield is less than g.
After t = 3, g = constant = 6% =
capital gains yield; k = 13%; so D/P =
13% – 6% = 7%.
9 - 23
Suppose g = 0 for t = 1 to 3, and then g
^
is a constant 6%. What is P0?
0
ks=13%
g = 0%
2.00
1
2
g = 0%
2.00
1.77
1.57
1.39
20.99
25.72
3
g = 0%
2.00
4
g = 6%
2.00
...
2.12
2.12
 
 30.29.
P
3
0.07
9 - 24
What is D/P and capital gains yield at
t = 0 and at t = 3?
t = 0:
D1 \$2.00
=
= 7.78%.
P0 \$25.72
CGY = 13% – 7.78% = 5.22%.
t = 3: Now have constant growth
with g = capital gains yield = 6% and
D/P = 7%.
9 - 25
If g = -6%, would anyone buy the
stock? If so, at what price?
Firm still has earnings and still pays
dividends, so P0 > 0:

 g
D
1
D
0
1
0 =
=
P
ks  g
ks  g
\$2.00(0.94)
\$1.88
=
=
= \$9.89.
0.13 – (-0.06)
0.19
9 - 26
What is the annual D/P and capital
gains yield?
Capital gains yield = g = -6.0%,
Dividend yield= 13.0% – (-6.0%) = 19%.
D/P and cap. gains yield are constant,
with high dividend yield (19%) offsetting
negative capital gains yield.
9 - 27
Free Cash Flow Method
The free cash flow method suggests
that the value of the entire firm
equals the present value of the firm’s
free cash flows (calculated on an
after-tax basis).
Recall that the free cash flow in any
given year can be calculated as:
NOPAT – Net capital investment.
9 - 28
Using the Free Cash Flow Method
Once the value of the firm is estimated,
an estimate of the stock price can be
found as follows:
MV of common stock (market
capitalization) = MV of firm – MV of
debt and preferred stock.
^
P = MV of common stock/# of shares.
9 - 29
Issues Regarding the Free Cash Flow
Method
Free cash flow method is often
preferred to the dividend growth
model--particularly for the large
number of companies that don’t pay
a dividend, or for whom it is hard to
forecast dividends.
(More...)
9 - 30
FCF Method Issues Continued
Similar to the dividend growth model,
the free cash flow method generally
assumes that at some point in time,
the growth rate in free cash flow will
become constant.
Terminal value represents the value
of the firm at the point in which
growth becomes constant.
9 - 31
FCF estimates for the next 3 years are
-\$5, \$10, and \$20 million, after which
the FCF is expected to grow at 6%.
The overall firm cost of capital is 10%.
0
k = 10%
1
2
3
4
g = 6%
-5
-4.545
8.264
15.026
398.197
416.942
10
20
...
21.20
21.20
530 =
= *TV3
0.04
*TV3 represents the terminal value of
the firm, at t = 3.
9 - 32
If the firm has \$40 million in debt and
has 10 million shares of stock, what is
the price per share?
Value of equity = Total value – Value of debt
= \$416.94 – \$40
= \$376.94 million.
Price per share = Value of equity/# of shares
= \$376.94/10
= \$37.69.
9 - 33
Using the Multiples of Comparable
Firms to Estimate Stock Price
 Analysts often use the following multiples
to value stocks:
P/E
P/CF
P/Sales
P/Customer
 Example: Based on comparable firms,
estimate the appropriate P/E. Multiply this
by expected earnings to back out an
estimate of the stock price.
9 - 34
What is market equilibrium?
In equilibrium, stock prices are stable.
There is no general tendency for
people to buy versus to sell.
In equilibrium, expected returns must
equal required returns:
^
ks = D1/P0 + g = ks = kRF + (kM – kRF)b.
9 - 35
Expected returns are obtained by
estimating dividends and expected
capital gains (which can be found
using any of the three common stock
valuation approaches).
Required returns are obtained from
the CAPM.
^
ks = D1/P0 + g = ks = kRF + (kM – kRF)b.
9 - 36
How is equilibrium established?
D1
If ks =
+ g > ks, then
P0
^
P0 is “too low” (a bargain).
P0 bid up; D1/P0 falls until
D1/P0 + g = ^
ks = ks.
9 - 37
Why do stock prices change?
D1
P0 =
ki – g
^
1. ki could change:
ki = kRF + (kM – kRF )bi.
kRF = k* + IP.
2. g could change due to
economic or firm situation.
9 - 38
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 better
information.
9 - 39
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.
9 - 40
2. Semistrong-form EMH:
All publicly available
information is reflected in
stock prices, so doesn’t pay to
pore over annual reports
looking for undervalued
stocks. Largely true, but
superior analysts can still
profit by finding and using new
information.
9 - 41
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.
9 - 42
Markets are generally efficient
because:
1. 15,000 or so trained analysts; MBAs,
CFAs, Technical PhDs.
2. Work for firms like Merrill, Morgan,
Prudential, which have a lot of money.
4. Thus, news is reflected in P0 almost
instantaneously.
9 - 43
Preferred Stock
Hybrid security.
Similar to bonds in that preferred
that must be paid before dividends can
be paid on common stock.
However, unlike interest payments on
bonds, companies can omit dividend
payments on preferred stock without
fear of pushing the firm into bankruptcy.
9 - 44
What’s the expected return of preferred
stock with Vp = \$50 and annual
dividend = \$5?
\$5
Vp  \$50 
kˆ p
ˆk  \$5  0.10  10.0%.
p
\$50