Business finance ch 8 stocks and their valuation

CHAPTER 8
Stocks and Their Valuation






Features of common stock
Determining common stock
values
Efficient markets
Preferred stock
8-1


Facts about common stock






Represents ownership
Ownership implies control
Stockholders elect directors
Directors elect management
Management’s goal: Maximize the
stock price

8-2

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.
8-3


Types of stock market
transactions




Secondary market
Primary market
Initial public offering market
(“going public”)

8-4


Different approaches for
valuing common stock




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

8-5


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+ ks ) (1+ ks ) (1+ ks )
(1 + ks )
^

8-6


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:
D0 (1 + g)
D1
P0 =
=

ks - g
ks - g
^

8-7


Future dividends and their
present values
$

Dt = D0 ( 1 + g )

t

Dt
PVDt =
t
(1+ k )

0.25

P0 = ∑ PVDt
0

Years (t)
8-8


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:
 k > g
s


g is expected to be constant forever

8-9


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%

8-10

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

2

2.12

2.247

3
2.382

ks = 13%

1.6509
8-11

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

8-12


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 =
=
ks - g 0.13- 0.06
= $32.10



Could also find expected P1 as:
^

P1 = P0 (1.06)= $32.10
8-13


What is the expected dividend
yield, capital gains yield, and total
return during the first year?




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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%
8-14


What would the expected
price today be, if g = 0?


0

The dividend stream would be a
perpetuity.
ks = 13%

1

2

3

...
2.00

2.00

2.00

PMT $2.00
P0 =
=

= $15.38
k
0.13
^

8-15


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.

8-16


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
46.114
54.107

^

= P0

P 3 =

4.658
0.13 − 0.06

= $66.54
8-17


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%.

8-18


Nonconstant growth:
What if g = 0% for 3 years before
long-run growth of 6%?
0 k = 13% 1
s
g = 0%

D0 = 2.00

2
g = 0%

2.00

3
g = 0%

2.00

4

...

g = 6%

2.00

2.12

1.77
1.57
1.39
20.99
25.72

^

= P0

P 3 =

2.12
0.13 − 0.06

= $30.29
8-19


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%.

8-20


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.

D0 ( 1 + g )
D1
P0 =

=
ks - g
ks - g
^

$2.00(0.94) $1.88
=
=
= $9.89
0.13- (-0.06) 0.19
8-21


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.

8-22


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
8-23


Applying the corporate value
model


Find the market value (MV) of the firm.




Subtract MV of firm’s debt and preferred
stock to get MV of common stock.




Find PV of firm’s future FCFs

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
8-24


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.
8-25