Stocks and Their Valuation
• Features of common stock
• Determining common stock values
• Efficient markets
Facts about common stock
•
•
•
•
•
Represents ownership
Ownership implies control
Stockholders elect directors
Directors elect management
Management’s goal: Maximize the stock
price
Types of stock market
transactions
• Secondary market
• Primary market
• Initial public offering market (“going
public”)
Different approaches for valuing
common stock
• Dividend growth model
• Corporate value model
Dividend growth model
• Value of a stock is the present value of the
future dividends expected to be generated by
the stock.
D3
D1
D2
D
P0 


 ... 
1
2
3

(1  k s ) (1  k s ) (1  k s )
(1  k s )
^
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:
D0 (1  g)
D1
P0 

ks - g
ks - g
^
Future dividends and their present
values
$
D t  D0 ( 1  g )
t
Dt
PVDt 
t
(1  k )
0.25
P0   PVDt
0
Years (t)
What would the expected price
today be, if g = 0?
• The dividend stream would be a
perpetuity.
0
ks = 13%
1
2
...
2.00
2.00
PMT $2.00
P0 

 $15.38
k
0.13
^
3
2.00
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%
If D0 = $2 and g is a constant 6%, find
the expected dividend stream for the
next 3 years, and their PVs.
0
g = 6%
D0 = 2.00
1.8761
1.7599
1.6509
1
2
2.12
2.247
ks = 13%
3
2.382
What is the stock’s market value?
• Using the constant growth model:
D1
$2.12
P0 

ks - g
0.13 - 0.06
$2.12

0.07
 $30.29
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 

k s - g 0.13 - 0.06
 $32.10
^
• Could also find expected P1 as:
^
P1  P0 (1.06)  $32.10
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) / $30.29 = 6.0%
• Total return (ks)
= Dividend Yield + Capital Gains Yield
= 7.0% + 6.0% = 13.0%
Supernormal growth:
What if g = 30% for 3 years before
achieving long-run growth of 6%?
• Can no longer use just the constant growth
model to find stock value.
• However, the growth does become constant
after 3 years.
Valuing common stock with
nonconstant growth
0 k = 13% 1
s
g = 30%
D0 = 2.00
2
g = 30%
2.600
3
g = 30%
3.380
4
...
g = 6%
4.394
4.658
2.301
2.647
3.045
P$ 3 
46.114
54.107
^
= P0
4.658
0.13 - 0.06
 $66.54
Find expected dividend and capital gains
yields during the first and fourth years.
• Dividend yield (first year)
= $2.60 / $54.11 = 4.81%
• Capital gains yield (first year)
= 13.00% - 4.81% = 8.19%
• During nonconstant growth, dividend yield and
capital gains yield are not constant, and capital
gains yield ≠ g.
• After t = 3, the stock has constant growth and
dividend yield = 7%, while capital gains yield =
6%.
Nonconstant growth:
What if g = 0% for 3 years before long-run
growth of 6%?
0 k = 13% 1
s
g = 0%
2
g = 0%
D0 = 2.00
2.00
3
g = 0%
2.00
4
...
g = 6%
2.00
2.12
1.77
1.57
1.39
P$ 3 
20.99
25.72
^
= P0
2.12
0.13 - 0.06
 $30.29
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%.
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.
D0 ( 1  g )
D1
P0 

ks - g
ks - g
^
$2.00 (0.94) $1.88


 $9.89
0.13 - (-0.06) 0.19
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
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
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.
Given the long-run gFCF = 6%, and
WACC of 10%, use the corporate value
model to find the firm’s intrinsic value.
0 k = 10%
1
-5
-4.545
8.264
15.026
398.197
416.942
2
10
3
4
20
...
g = 6%
21.20
21.20
530 =
0.10 - 0.06
= TV3
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
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.
D1
ks   g
P0
^

k s  k RF  (k M - k RF )
Market equilibrium
• Expected returns are obtained by
estimating dividends and expected capital
gains.
• Required returns are obtained by
estimating risk and applying the CAPM.
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
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
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
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.
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
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.