Download FIN 303 Chap 9 Fall 2009

CHAPTER 9
Stocks and Their Valuation


Methods for valuing common stock
Preferred stock
We WILL cover Sections 9-1 through 9-5 (pages 269-283) and Section 9-8
(Preferred Stock, pages 291-292).
In the interest of time, we will NOT cover (and will NOT be on the final exam)
Sections 9-6 and 9-7.
Practice problems: Please work end of Chapter 9: 2,3,6,8,10,11, and 13.
9-1
Different approaches for estimating what you
think a share of a company’s common stock
is worth



Dividend growth model
Corporate value model (We’ll skip this.)
Using the multiples of comparable firms
Note: The value you put on the stock could be different
from its current price in the market.
Example: Suppose IBM is trading for $84/share. But you
estimate it is worth $100/share. Based on that belief,
you might buy IBM stock. You’d be betting others would
figure out you are right and buy IBM stock. If you are
right, as others buy IBM, the price could increase.
9-2
Dividend growth model:
This is a popular method for estimating the
value or worth of common




Value of a stock (in $/share) is the present value of the
future dividends expected to be generated by the stock.
P0 is price you estimate it is worth now.
Dt is the dividend ($/share) you expect the company
will pay shareholders at time “t”.
rs is the rate of return you require to invest in the stock.
D3
D1
D2
D
P0 


 ... 
1
2
3
(1  rs )
(1  rs )
(1  rs )
(1  rs ) 
^
9-3
If we believe the dividend will grow at a
constant rate, we can use the “Constant
Growth” version of the Dividend Growth Model

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 (i.e., approximately equals):
D0 (1  g)
D1
P0 

rs - g
rs - g
^
9-4
Constant Growth Model (continued):
What if growth (g) > required return (rs)?
^
P0


D 0 (1  g)
D1


rs - g
rs - g
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
9-5
CAPM/Security Market Line/Beta approach for
estimating required rate of return (rs):
If rRF = 7%, rM = 12%, and beta (b) = 1.2, what is
the required rate of return on the firm’s stock?
rs
= rRF + (rM – rRF)(b)
= 7% + (12% - 7%)(1.2)
= 13%
9-6
Suppose D0 = $2 (paid now) and you
believe g will be a constant 6%. The PVs of
the dividends today plus first 3 years are:
0
g = 6%
D0 = 2.00
1.8761
1.7599
1
2
2.12
2.247
3
2.382
rs = 13%
1.6509
9-7
Suppose D0 = $2 (paid yesterday) and you
believe g will be a constant 6%. What is the
stock’s intrinsic value? (We exclude D0.)

Using the constant growth model:
ˆP  D1  $2.12
0
rs - g 0.13 - 0.06
$2.12

0.07
 $30.29
9-8
What is the expected market price of the
stock, one year from now?


We assume 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
9-9
What would we estimate for the value of the
stock if g = 0?

0
The dividend stream would be a
perpetuity.
rs = 13%
1
2
3
...
2.00
2.00
2.00
PMT $2.00
P0 

 $15.38
r
0.13
^
9-10
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 

rs - g
rs - g
^
$2.00 (0.94) $1.88


 $9.89
0.13 - (-0.06) 0.19
9-11
Firm multiples method using financial ratios



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.
Chartered Financial Analysts often use include this analysis as
part of their valuations of stock. They themselves often refer to
the multiples approach as more of an art than a science.
9-12
Use a little algebra to rewrite the Constant
Growth Model with required return on the lefthand side of the equation:
D1
P0 
rs - g
• Multiply both sides of the equation by (rs - g),
Divide both sides by P0 , and
Add g to both sides.
D1
rs 
g
P0
This expression says that if we expect Dividends
will grow at constant growth rate g and we pay P0 ,
we expect our return (per period) will equal rs.
9-13
What is market equilibrium (using the Constant
Growth Model and CAPM/SML/Beta approach)?


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 what the
“marginal investor” thinks it is worth.

Expected returns must equal required returns.
D1
rs 
g
P0
^

rs  rRF  (rM  rRF )b
9-14
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.
9-15
If preferred stock with an annual dividend of
$5 sells for $50, what is the preferred stock’s
expected return? (This is just a perpetuity.)
Vp = D / rp
$50 = $5 / rp
^rp
= $5 / $50
= 0.10 = 10%
9-16