CHAPTER 9
Stocks and Their Valuation


Features of common stock
Stock valuations

Constant dividend growth model
The behavior of dividends and their PV
The model
Applying the model when g>r, g=0 and g<0
Future stock price
Dividend yield and capital gain



Non-constant growth model
Preferred stock
8-1
Facts about common stock

Represents ownership





Ownership implies control
Stockholders elect directors
Directors elect management
Receives cash flow in the form of
dividend
Management’s goal: Maximize the
stock price
8-2
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 rs ) (1 rs )
(1 rs )
(1 rs )
^
8-3
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
8-4
Constant growth stock

If g is constant, the dividend growth formula
converges to:
D0 (1 g) D1
P0 

rs - g
rs - g
^
8-5
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
8-6
If rRF = 7%, rM = 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):
rs = rRF + (rM – rRF)β
= 7% + (12% - 7%)1.2
= 13%
D0 = $2 and g is a constant 6%,
8-7
What is the stock’s market value?

Using the constant growth model:
D1
$2.12
P0 

rs - g 0.13- 0.06
$2.12

0.07
 $30.29
8-8
What would the expected price
today be, if g = -5%?, if g=0?


When g=-5% D1=1.9, P=1.9/(13%+5%)=10.56
When g=0, The dividend stream would be a
perpetuity.
0
rs = 13%
1
2
3
...
2.00
2.00
2.00
PMT $2.00
P0 

 $15.38
r
0.13
^
8-9
Computing other variables
^
P0 



D0 (1 g) D1

rs - g
rs - g
Computing Ks
Computing D
Computing g
8-10
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
8-11
Future stock price

What is the expected market price of the stock
two years from now?
P2,
D3
$2.382
P2 

rs - g 0.13- 0.06
^
 $34.03

What is the expected market price of the stock
years from now?
Pn, n
D0 (1 g) n 1 Dn 1
Pn 

rs - g
rs - g
^
8-12
The growth rate of stock price

What is the % change of stock price from
and from

P1
to
P2
What is the % change of stock price from
Pn+1


P0
to
Pn
to
What is the expected market price of the stock
two years from now?
P1
P2,
P2 =P1 *(1+g)= P0 *(1+g)2
8-13
Dividend Yield and Capital
Gain




P0=D1/(r-g)
k=(D1/P0)+g
Total return=dividend yield + Capital
gain
g is capital gain for constant growth
stock
8-14
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) / $30.29 = 6.0%

Total return (rs)
= Dividend Yield + Capital Gains Yield
= 7.0% + 6.0% = 13.0%
8-15
Supernormal growth:
What if g = 30% for 3 years before
achieving long-run growth of 6%?


Can no longer use just the constant growth
model to find stock value.
However, the growth does become
constant after 3 years.
8-16
Valuing common stock with
nonconstant growth
0 r = 13% 1
s
g = 30%
D0 = 2.00
2
g = 30%
2.600
3
g = 30%
3.380
4
...
g = 6%
4.394
4.658
2.301
2.647
3.045
P$ 3 
46.114
54.107
^
= P0
4.658
0.13 - 0.06
 $66.54
8-17
Nonconstant growth:
What if g = 0% for 3 years before longrun growth of 6%?
0 r = 13% 1
s
g = 0%
2
g = 0%
D0 = 2.00
2.00
3
g = 0%
2.00
4
...
g = 6%
2.00
2.12
1.77
1.57
1.39
P$ 3 
20.99
25.72
^
= P0
2.12
0.13 - 0.06
 $30.29
8-18
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.
8-19
A preferred stock has an annual dividend
of $5, what should the preferred stock
price be if discount rate is 10%?
Vp = D / rp
$50 = $5 / 10%
8-20