# CHAPTER 8 Stocks and Their Valuation

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```					CHAPTER 9
Stocks and Their Valuation

   Features of common stock
   Determining common stock values
   Preferred stock

9-1
Facts about common stock
   Represents ownership
   Ownership implies control
   Stockholders elect directors
   Directors elect management
   Management’s goal: Maximize the
stock price

9-2
Intrinsic Value and Stock Price
   Outside investors, corporate insiders, and
analysts use a variety of approaches to
estimate a stock’s intrinsic value (P0).
   In equilibrium we assume that a stock’s price
equals its intrinsic value.
 Outsiders estimate intrinsic value to help
determine which stocks are attractive to
 Stocks with a price below (above) its
intrinsic value are undervalued
(overvalued).
9-3
Determinants of Intrinsic Value
and Stock Prices (Figure 1-1)

9-4
Different approaches for estimating the
intrinsic value of a common stock

   Dividend growth model
   Corporate value model
   Using the multiples of comparable
firms

9-5
Dividend growth model
   Value of a stock is the present value of the
future dividends expected to be generated by
the stock.

^       D1           D2            D3                  D
P0                                        ... 
(1  rs )1
(1  rs ) 2
(1  rs ) 3
(1  rs ) 

9-6
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:
^    D 0 (1  g)     D1
P0              
rs - g     rs - g
9-7
Future dividends and their
present values
t
\$              D t  D0 ( 1  g )

Dt
0.25           PVD t 
( 1  r )t

P0   PVD t

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

9-9
If rRF = 7%, rM = 12%, and b = 1.2,
what is the required rate of return on
the firm’s stock?
   Use the SML to calculate the required
rate of return (rs):

rs = rRF + (rM – rRF)b
= 7% + (12% - 7%)1.2
= 13%

9-10
If D0 = \$2 and g is a constant 6%,
find the expected dividend stream for
the next 3 years, and their PVs.

0             1           2      3
g = 6%

D0 = 2.00         2.12        2.247   2.382
1.8761
rs = 13%
1.7599
1.6509

9-11
What is the stock’s intrinsic value?
   Using the constant growth model:

ˆ  D1  \$2.12
P0
rs - g 0.13 - 0.06
\$2.12

0.07
 \$30.29

9-12
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.
^     D2     \$2.247
P1        
rs - g 0.13 - 0.06
 \$32.10

   Could also find expected P1 as:
^
P1  P0 (1.06)  \$32.10
9-13
What are 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 (rs)
= Dividend Yield + Capital Gains Yield
= 7.0% + 6.0% = 13.0%

9-14
What would the expected price
today be, if g = 0?
   The dividend stream would be a
perpetuity.

0               1         2           3
rs = 13%
...
2.00     2.00         2.00
^   PMT \$2.00
P0            \$15.38
r   0.13

9-15
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.

9-16
Valuing common stock with
nonconstant growth

0 r = 13% 1               2              3              4
s
...
g = 30%       g = 30%       g = 30%        g = 6%
D0 = 2.00        2.600         3.380         4.394         4.658
2.301
2.647
3.045
4.658
46.114                          \$
P3                      \$66.54
^                        0.13 - 0.06
54.107    = P0
9-17
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%.
9-18
Nonconstant growth:
What if g = 0% for 3 years before long-
run growth of 6%?

0 r = 13% 1                2              3               4
s
...
g = 0%          g = 0%       g = 0%          g = 6%
D0 = 2.00           2.00        2.00          2.00            2.12
1.77
1.57
1.39
2.12
20.99                            \$
P3                       \$30.29
^                          0.13 - 0.06
25.72     = P0
9-19
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%.

9-20
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.

^      D1     D0 ( 1  g )
P0         
rs - g      rs - g
\$2.00 (0.94) \$1.88
                     \$9.89
0.13 - (-0.06) 0.19

9-21
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.
9-22
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
9-23
Applying the corporate value model

   Find the market value (MV) of the firm,
by finding the PV of the firm’s future
FCFs.
   Subtract MV of firm’s debt and preferred
stock to get MV of common stock.
   Divide MV of common stock by the
number of shares outstanding to get
intrinsic stock price (value).
9-24
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.
9-25
Given the long-run gFCF = 6%, and
WACC of 10%, use the corporate value
model to find the firm’s intrinsic value.

0 r = 10%   1    2         3                4
...
g = 6%
-5   10        20              21.20
-4.545
8.264
15.026                               21.20
398.197                   530 =                     = TV3
0.10 - 0.06
416.942

9-26
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
= \$416.94 - \$40
= \$376.94 million
   Value per share = MV of equity / # of shares
= \$376.94 / 10
= \$37.69

9-27
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.
9-28
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, two conditions hold:
   The current market stock price equals its
^
intrinsic value (P0 = P0).
   Expected returns must equal required returns.
^    D1
rs     g         rs  rRF  (rM - rRF )b
P0
9-29
Market equilibrium
   Expected returns are determined by
estimating dividends and expected
capital gains.
   Required returns are determined by
estimating risk and applying the CAPM.

9-30
How is market equilibrium
established?
   If price is below intrinsic value …
   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.

9-31
How are the equilibrium
values determined?
   Are the equilibrium intrinsic value and
expected return estimated by
managers or are they determined by
something else?
   Equilibrium levels are based on the
market’s estimate of intrinsic value and
the market’s required rate of return, which
are both dependent upon the attitudes of
the marginal investor.

9-32
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.
9-33
If preferred stock with an annual
dividend of \$5 sells for \$50, what is the
preferred stock’s expected return?

Vp = D / rp
\$50 = \$5 / rp

^ = \$5 / \$50
rp
= 0.10 = 10%

9-34

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