This document discusses common stock valuation models. It begins by explaining the dividend growth model and its assumptions for valuing constant growth stocks. It then discusses handling non-constant growth periods and the free cash flow method. It also covers market equilibrium, how it is established, and the efficient market hypothesis which suggests stock prices reflect all available information.

1. Chapter 10
Stocks and Their
Valuation
taufikur@ugm.ac.id

2. Legal Rights and Privileges
of Common Stockholders
 Represents ownership.
 Ownership implies control.
 Stockholders elect directors.
 Directors elect management.
 Management’s goal: Maximize stock price.
 Social/Ethical Question
Should management be equally concerned about employees,
customers, suppliers, “the public,” or just the stockholders?
In enterprise economy, work for stockholders subject to
constraints (environmental, fair hiring, etc.) and competition.

3. Types of Common Stocks
 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.

4. The Market for Common Stock
 Closely Held Corporations
 Publicly Owned Corporations
 Types of Stocks Market Transaction
Secondary Market
Primary Market
Going Public
Initial Public Offering Market

5. Definitions of Terms Used in Stock Valuation Model
 Stock market price 
 Intrinsic (theoretical) value of stock 
 Expected rate of growth in dividend per share  g
 Required rate of return 
 Expected rate of return 
 Expected Dividend yield 
 Expected Capital gain yield 
 Expected total return  = +
P0
rs
^
rs D
1
P0
P1 – P0
P0
^
^
r s P1 – P0
P0
^
D
1
P0
P
0
^

6. ( ) ( ) ( )
D
k
D
k
D
k
s s s
P0
2
2
3
3
1 1 1
=
( )
D
ks
1
1
1+
+
+
+
+
+ +
+


. . .
One whose dividends are expected to
grow forever at a constant rate, g.
Stock Value = PV of Dividends
What is a constant growth stock?
Dividend growth model
^

7. For a Constant Growth Stock
(Constant Growth/Gordon Model)
D1 = D0(1 + g)1
D2 = D0(1 + g)2
Dt = D0(1 + g)t
P0 = = .
If g is constant, then:
D0(1 + g)
rs - g
D1
rs - g
^

8. Example
 RT & T just paid a dividend of $1.15, its stock has a
required rate of return, ks, of 13,4%, and investors expect
the dividend to grow at a constant 8 % rate in the future.
 The estimated dividend one year hence would be
 D1 = $1.15(1.08) = $1.24
 D2 = $1.34
 D5 = $1.69
 Using Gordon Model, we can know the intrinsic value of
stock (P0)=
 P0 = $1.15 (1.08) = $23
0.134 – 0.08
^
^

9. ( )t
0
t g
1
D
D +
=
( )t
t
t
r
D
PVD
+
=
1
t
0
PVD
P 
=
$
1.15
Years (t)
0
PV D1 = 1.10
Present Values of Dividends of a Constant Growth Stock

10. What happens if g > ks?
 If rs< g, get negative stock price, which
is nonsense.
 We can’t use model unless (1) rs> g and
(2) g is expected to be constant forever.
.
D
r g
g
s
1
=
-
>
requires r s
P0
^

11. Assume beta = 1.2, rRF = 7%, and rM =
12%. What is the required rate of return
on the firm’s stock?
rs= rRF + (rM – rRF)bFirm
= 7% + (12% – 7%) (1.2)
= 13%.
Use the SML to calculate ks:

12. 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 1
2.247
2
2.382
3
g = 6%
1.8761
1.7599
D0 = 2.00
1.6509
13%
2.12

13. = =
What’s the stock’s market value?
D0 = 2.00, rs = 13%, g = 6%.
Constant growth model:
P0 = =
D1
rs – g 0.13 – 0.06
$2.12
$2.12
0.07
$30.29.

14.  D1 will have been paid, so expected dividends
are D2, D3, D4 and so on. Thus,
Could also find P1 as follows:
ks – g 0.13 – 0.06
P1 = =
What is the stock’s market value
one year from now, P1?
^
^
^
D2 $2.247
^
= $32.10.
P1 = P0(1.06) = $32.10.

15. Find the expected dividend yield,
capital gains yield, and total return
during the first year.
Dividend yld = = =
Cap gains yld = =
Total return = 7.0% + 6.0% = 13.0%.
D1
P0
P1 – P0
P0
^
$30.29
$2.12
7.0%.
$32.10 – $30.29
$30.29
= 6.0%.

16. Rearrange model to rate of return form:
.
P
D
r g
D
P
g
s
0
1 1
0
=
-
= +
to r s
Then, rs = $2.12/$30.29 + 0.06
= 0.07 + 0.06 = 13%.
^
^ ^

17. P0 = = = $15.38.
What would P0 be if g = 0?
The dividend stream would be a
perpetuity.
2.00 2.00
2.00
0 1 2 3
13% ...
^ PMT
r
$2.00
0.13
^

18. For a Constant Growth Stock
 The following conditions must hold:
1. The dividend is expected to grow forever at a
constant rate, g
2. The stock price is expected to grow at this same
rate
3. The expected dividend yield is a constant
4. The expected capital gain yield is also a constant,
and it is equal to g
5. The expected total rate of return, , is equal to the
expected dividend yield plus the expected growth
rate: = dividend yield + g
^
r s
^
r s

19.  Can no longer use constant growth model.
 However, growth becomes constant after 3 years
(terminal/horizon date: the date when the growth rate
becomes constant)
 3 Steps for nonconstant growth:
 Find the PV of the dividends during the period of
nonconstant growth
 Find the price of the stock at the end of the noncontstant
growth period, at which point has become a constant
growth stock, and discount this price back to the present
 Add this two components to find the intrinsic value of the
stock, P0
If we have supernormal growth of 30%
for 3 years, then a long-run constant
g = 6%, what is P0? k is still 13%.
^
^

20. Nonconstant growth followed by constant
growth:
0
2.301
2.647
3.045
46.116
1 2 3 4
rs = 13%
54.109 = P0
g = 30% g = 30% g = 30% g = 6%
D0 = 2.00 2.600 3.380 4.394 4.658
$ .
. .
$66.54
P3
4.658
13 0 06
=
-
=
0
...
^

21. What is the expected dividend yield
and capital gains yield at t = 0?
At t = 4?
Div. yield0 = = 4.81%.
Cap. gain0 = 13.00% – 4.81% = 8.19%.
$2.60
$54.11

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; r = 13%; so D/P = 13% –
6% = 7%.

23. 25.72
Suppose g = 0 for t = 1 to 3, and then
g is a constant 6%. What is P0?
0
1.77
1.57
1.39
20.99
1 2 3 4
ks=13%
g = 0% g = 0% g = 0% g = 6%
2.00 2.00 2.00 2.00 2.12
.
$
P3
2.12
0 07
30.29.
= =
^
...

24. t = 3: Now have constant growth
with g = capital gains yield = 6% and
D/P = 7%.
$2.00
$25.72
What is D/P and capital gains yield at
t = 0 and at t = 3?
t = 0:
D1
P0
= = 7.78%.
CGY = 13% – 7.78% = 5.22%.

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:
( )
$
P
D
r g
D g
r g
s s
0
1 0 1
=
-
=
+
-
$2.00(0.94) $1.88
0.13 – (-0.06) 0.19
= = = $9.89.

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.

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.

28.  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/number of shares.
Using the Free Cash Flow Method
^

29.  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.
Issues Regarding the Free Cash
Flow Method
(More...)

30.  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.
FCF Method Issues Continued

31. 416.942
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
-4.545
8.264
15.026
398.197
1 2 3 4
r = 10%
g = 6%
-5 10 20 21.20
21.20
0.04
...
*TV3 represents the terminal value of
the firm, at t = 3.
530 = = *TV3

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/number of shares
= $376.94/10
= $37.69.

33. 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:
What is market equilibrium?
rs = D1/P0 + g = rs = rRF + (rM – rRF)b.
^

34. rs = D1/P0 + g = rs = rRF + (rM – rRF)b.
^
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.

35. How is equilibrium established?
If ks = + g > ks, then
P0 is “too low” (a bargain).
Buy orders > sell orders;
P0 bid up; D1/P0 falls until
D1/P0 + g = ks = ks.
^
^
D1
P0

36. Why do stock prices change?
1. ki could change:
ki = rRF + (rM – rRF )bi.
rRF = k* + IP.
2. g could change due to
economic or firm situation.
P0 =
^ D1
ri – g

37. 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.
The Price: reflects all publicly
available information on each
security

38. 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.

39. 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.

40. 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.

41. 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.
3. Have similar access to data.
4. Thus, news is reflected in P0 almost
instantaneously.

42. Preferred Stock
 Hybrid security.
 Similar to bonds in that preferred stockholders
receive a fixed dividend 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.

43. What’s the expected return of preferred
stock with Vp = $50 and annual dividend =
$5?
%.
0
.
10
10
.
0
50
$
5
$
5
$
50
$
=
=
=
=
=
p
p
p
r
r
V