8-1
Lecture Ten
Cost of Capital From Issuing Stocks or
Stocks and Their Valuation
Determining common stock
values
Efficient markets
Preferred stock
8-2
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.
8-3
For a constant growth stock,
D1  D 0 1  g
2
D2  D 0 1  g
t
D t  D t 1  g
1
If g is constant, then:
D
1

g
D


0
1
P 

0
ks  g
ks  g
8-4
$
D t  D 0 1  g
Dt
PVD t 
t
1

k


0.25
P0   PVD t
0
t
If g > k, P0  !
Years (t)
8-5
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. See slide #8-8.
8-6
Assume beta = 1.2, kRF = 6%, and kM =
11%. What is the required rate of
return on the firm’s stock?
Use the SML to calculate ks:
ks = kRF + (kM - kRF)bFirm
= 6% + (11% - 6%) (1.2)
= 12%.
Also, this is the cost of capital to
the firm from issuing common Stk.
8-7
D0 was $0.25 and g is a constant 6%.
Find the expected dividends for the
next 3 years, and their PVs. ks = 12%.
0
g=6%
1
D0=0.25 0.265
12%
0.2366
0.2239
0.2120
2
0.2809
3
0.2978
4
8-8
What’s the stock’s market value?
D0 = 0.25, ks = 12%, g = 6%.
Constant growth model:
D
$0.
265
1
P0 

ks  g 0.12  0.06
$0.265

 $4.42.
0.06
8-9
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
$0.2809

P1 

k s  g 0.12  0.06
 $4.68.
^
Could also find P1 as follows:
^  P 1  g  $4.42 1.06  $4.68.
P
 

1
0
8 - 10
Find the expected dividend yield,
capital gains yield, and total return
during the first year.
D1 $0.265
Dividend yld 

 6%.
P0
$4.42
 P
P
D1
1
0
Cap. gains yld 
 ks 
 6%.
P0
P0
Total return  6%  6%  12%.
8 - 11
Rearrange model to rate of return form:
D
D
1
1


P0 
to k s 
 g.
ks  g
P0
^
Then, ks = $0.265/$4.42 + 0.06
= 0.06 + 0.06 = 12%.
Again, this is the cost of raising funds
from the sale of common stock.
8 - 12
What would P0 be if g = 0?
The dividend stream would be a
perpetuity.
0
12%
1
2
3
...
0.25
0.25
0.25
PMT $0.25
^
P0 

 $2.08.
k
0.12
8 - 13
If we have supernormal growth of
30% for 3 yrs, then a long-run constant
^
g = 10%, what is P
0? k is still 12%.
Can no longer use constant growth
model.
However, growth becomes constant
after 3 years.
8 - 14
Nonconstant growth followed by constant
growth:
0 k =12%
s
g = 30%
D0 = 0.25
1
2
g = 30%
0.3250
3
g = 30%
0.4225
4
g = 10%
0.5493
...
0.6042
0.2902
0.3368
0.3910
21.5029
22.52
^
= P0
P 3 
0.6042
 $30.21
0 .12  0.10
8 - 15
What is the expected dividend yield
and capital gains yield at t = 0?
At t = 4?
$0.3250
Div. yield0 
 144%.
.
$22.52
Cap. gain0  12%  144%
.
 10.56%.
8 - 16
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 = 10% =
capital gains yield; k = 12%; so D/P =
12% - 10% = 2%.
8 - 17
Suppose g = 0 for t = 1 to 3, and then g
^
is a constant 11%. What is P0?
0
ks=12%
g = 0%
1
2
g = 0%
0.25
0.2232
0.1993
0.1779
19.7519
20.3523
3
g = 0%
0.25
4
g = 11%
0.25
...
0.2775
P  0.2775  27.75.
3
0.01
8 - 18
What is D/P and capital gains yield at
t = 0 and at t = 3?
D1 $0.25
t = 0: P  $20.35 1.23%.
0
CGY 12%1.23% 1077%.
.
t = 3: Now have constant growth
with g = capital gains yield = 11%
and D/P = 1%.
8 - 19
If g = -6%, would anyone buy the
stock? If so, at what price?
Firm still has earnings and still pays
dividends, so P0 > 0:
P  D1  D 0 1  g .
0
ks  g
ks  g
$0.25(0.94)
$0.235


 $1.31.
0.12  ( 0.06)
0.18
8 - 20
What is the annual D/P and capital
gains yield?
Capital gains yield = g = -6.0%,
Dividend yield = 12.0% - (-6.0%)
= 18%.
D/P and cap. gains yield are constant,
with high dividend yield (18%) offsetting
negative capital gains yield.
8 - 21
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.
8 - 22
How is equilibrium established?
D1
If ks =
+ g > ks, then
P0
^
P0 is “too low” (a bargain).
Buy orders > sell orders;
P0 bid up; D1/P0 falls until
D1/P0 + g = ^
ks = ks.
8 - 23
Why do stock prices change?
^
P0 
D1
ki  g
1. ki could change:
ki = kRF + (kM - kRF )bi
kRF = k* + IP
2. g could change due to
economic or firm situation.
8 - 24
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.
8 - 25
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.
8 - 26
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.
8 - 27
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.
8 - 28
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 much money.
3. Have similar access to data.
4. Thus, news is reflected in P0 almost
instantaneously.
8 - 29
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 interest payments on
bonds, companies can omit dividend
payments on preferred stock without
fear of pushing the firm into bankruptcy.
8 - 30
What’s the expected return of preferred
stock with Vps = $50 and annual
dividend = $5?
Vps
$5
 $50  
k
ps
$5

k ps 
 0.10  10.0%.
$50