Stock valuation

1. 8-1
CHAPTER 8
Stocks and Their Valuation
 Features of common stock
 Determining common stock values
 Efficient markets
 Preferred stock

2. 8-2
Facts about common stock
 Represents ownership
 Ownership implies control
 Stockholders elect directors
 Directors elect management
 Management’s goal: Maximize the
stock price

3. 8-3
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 stockholders subject to
constraints (environmental, fair hiring, etc.)
and competition.

4. 8-4
Types of stock market
transactions
 Secondary market
 Primary market
 Initial public offering market
(“going public”)

5. 8-5
Different approaches for valuing
common stock
 Dividend growth model
 Corporate value model
 Using the multiples of comparable
firms

6. 8-6
Dividend growth model
 Value of a stock is the present value of the
future dividends expected to be generated by
the stock.











)
k
(1
D
...
)
k
(1
D
)
k
(1
D
)
k
(1
D
P
s
3
s
3
2
s
2
1
s
1
0
^

7. 8-7
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:
g
-
k
D
g
-
k
g)
(1
D
P
s
1
s
0
0
^




8. 8-8
Future dividends and their
present values
t
0
t )
g
1
(
D
D 

t
t
t
)
k
1
(
D
PVD


t
0 PVD
P 

$
0.25
Years (t)
0

9. 8-9
What happens if g > ks?
 If g > ks, the constant growth formula
leads to a negative stock price, which
does not make sense.
 The constant growth model can only be
used if:
 ks > g
 g is expected to be constant forever

10. 8-10
If kRF = 7%, kM = 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 (ks):
ks = kRF + (kM – kRF)β
= 7% + (12% - 7%)1.2
= 13%

11. 8-11
If D0 = $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
2.12

12. 8-12
What is the stock’s market value?
 Using the constant growth model:
$30.29
0.07
$2.12
0.06
-
0.13
$2.12
g
-
k
D
P
s
0



 1

13. 8-13
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 P1 as:
$32.10
0.06
-
0.13
$2.247
g
-
k
D
P
s
2
^
1



$32.10
(1.06)
P
P 0
^
1 


14. 8-14
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 (ks)
= Dividend Yield + Capital Gains Yield
= 7.0% + 6.0% = 13.0%

15. 8-15
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
P
^
0 



16. 8-16
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.

17. 8-17
Valuing common stock with
nonconstant growth
ks = 13%
g = 30% g = 30% g = 30% g = 6%
$
P 
0.06
$66.54
3
4.658
0.13 -

2.301
2.647
3.045
46.114
54.107 = P0
^
0 1 2 3 4
D0 = 2.00 2.600 3.380 4.394
...
4.658

18. 8-18
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 yield
and capital gains yield are not constant,
and capital gains yield ≠ g.
 After t = 3, the stock has constant growth
and dividend yield = 7%, while capital
gains yield = 6%.

19. 8-19
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%
0.06
$ $30.29
P3
2.12
0.13

-

1.77
1.57
1.39
20.99
25.72 = P0
^
0 1 2 3 4
D0 = 2.00 2.00 2.00 2.00
...
2.12

20. 8-20
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 constant
growth and dividend yield = 7%,
while capital gains yield = 6%.

21. 8-21
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.
$9.89
0.19
$1.88
(-0.06)
-
0.13
(0.94)
$2.00
g
-
k
)
g
1
(
D
g
-
k
D
P
s
0
s
1
^
0







22. 8-22
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.

23. 8-23
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

24. 8-24
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 of
shares outstanding to get intrinsic stock price
(value).
 P0 = MV of common stock / # of shares

25. 8-25
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 (TVn) represents value of firm
at the point that growth becomes constant.

26. 8-26
Given the long-run gFCF = 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
...
416.942
-4.545
8.264
15.026
398.197
21.20
530 = = TV3
0.10 0.06
-

27. 8-27
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
= $376.94m / 10m
= $37.69

28. 8-28
Firm multiples method
 Analysts often use the following multiples
to value stocks.
 P / E
 P / CF
 P / Sales
 EXAMPLE: Based on comparable firms,
estimate the appropriate P/E. Multiply this
by expected earnings to back out an
estimate of the stock price.

29. 8-29
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.

-




 )
k
(k
k
k
g
P
D
k RF
M
RF
s
0
1
^
s

30. 8-30
Market equilibrium
 Expected returns are obtained by
estimating dividends and expected
capital gains.
 Required returns are obtained by
estimating risk and applying the CAPM.

31. 8-31
How is market equilibrium
established?
 If expected return exceeds required
return …
 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

32. 8-32
Factors that affect stock price
 Required return (ks) could change
 Changing inflation could cause kRF 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

33. 8-33
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
 Semistrong-form efficiency
 Strong-form efficiency

34. 8-34
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 EMH,
but “technical analysis” is still used.

35. 8-35
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, but superior analysts
can still profit by finding and using
new information

36. 8-36
Strong-form efficiency
 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.

37. 8-37
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 better
understand how individuals and markets
respond to different situations.

38. 8-38
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.

39. 8-39
If preferred stock with an annual
dividend of $5 sells for $50, what is the
preferred stock’s expected return?
Vp = D / kp
$50 = $5 / kp
kp = $5 / $50
= 0.10 = 10%