Chapter 7: Equity Markets and Stock Valuation
7.1 Common Stock Valuation
•
More Difficult to value
1.
Not even promised cash flows are known in advance
2.
Life of the investment is essentially forever
3.
No way to easily observe the rate of return
•
Cash Flows
o
P
o
= (D
1
+ P
1
) / (1 + R)
o
In 2 periods
P
1
= (D
2
+ P
2
) / (1 + R)
o
So… P
o
= (D
1
/ (1 + R)
1
) + (D
2
/ (1 + R)
2
) + (P
2
/ (1 + R)
2
)
o
No matter what the stock price is, the PV is essentially 0
o
The price of the stock today is equal to the PV of all the future dividends
•
Special Cases
o
Zero Growth
Much like a share of preferred stock
Dividend on a share of preferred stock has zero growth and thus is
constant through time.
So value of a stock is
•
P
o
= (D
1
/ (1 + R)
1
) + (D
2
/ (1 + R)
2
) etc…
Because the dividend is always the same, the stock is viewed as an
ordinary perpetuity with a cash flow equal to D every period
o
Constant Growth
Always grows at a steady rate
D
t
= D
0
X (1 + g)
t
Aka a growing perpetuity
Dividend Growth Model
•
As long as the growth rate (g), is less than the discount rate (R) the
PV of this series of cash flows can be written as
•
P
0
= D
0
X (1 + g) / RG = D
1
/ RG
•
Gives us the stock price at any point in time
•
If the constant growth rate exceeds the discount rate, then the stock
price is infinitely large, because the growth rate is bigger than the
discount rate, then the present value of the dividends keeps getting
bigger
•
Growth rate must be less than the discount rate!!!
Present value of a cash flow = C
o
(1+g)/ (Rg)
o
Nonconstant Growth
Allows for supernormal growth rates over some finite length of time
To see what the stock is worth today we
•
Find out what it will be worth once dividends are paid
•
Calculate the PV of that future price to get today’s price
Value of the stock is the PV of all the future dividends
•
Required Return
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R – g = D
1
/ P
o
o
Total return has 2 components
Dividend yield = a stocks expected cash dividend / current price
Capital gains yield – rate at which a stock price grows, the rate at which
the value of the investment grows
R = Dividend yield + capital gains or
R = D
1
/ P
o
+ g
P
1
= D
1
X (1 + g) / (R g)
7.2 Some Features of Common and Preferred Stock
•
Common Stock – no special preference either in paying dividends or in bankruptcy
•
Shareholder rights
o
Cumulative voting
– permits minority participation (directors elected all at once)
Number of shares owned X number of directors to be elected
1 / (N + 1) percent of the stock plus one share will guarantee you a seat
o
Straight voting
– directors are elected one at a time (50% plus 1 share), can
freeze out minority shareholders
Each shareholder may cast all votes for each member of the board of
directors. Ex. You have 20 shares, each time you can cast 20 votes
o
Staggered elections
Makes it more difficult for a minority to elect a director
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 Spring '08
 TOMNELSON
 Net Present Value

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