CHAPTER 8 Stocks and Their Valuation
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Transcript CHAPTER 8 Stocks and Their Valuation
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