09 Chapter model
3/22/2010 7:09
2/14/2006
Chapter 9.
Stocks and Their Valuation
THE DIVIDEND GROWTH MODEL
The basic dividend valuation equation is:
+
+
.
.
.
.
This model is similar to the bond valuation models developed in Chapter 7 in that we employ
discounted cash flow analysis to find the value of a firm's stock.
COMMON STOCK VALUATION
(Section 9.3)
The value of any financial asset is equal to the present value of future cash flows provided by the
asset.
Stocks can be evaluated in two ways:
(1) by finding the present value of the expected future
dividends, or (2) by finding the present value of the firm's expected future free cash flows,
subtracting the value of the debt and preferred stock to find the total value of the common equity,
and then dividing that total value by the number of shares outstanding to find the value per share.
Both approaches are examined in this spreadsheet.
When an investor buys a share of stock, he/she typically expects to receive cash in the form of
dividends and then, eventually, to sell the stock and to receive cash from the sale.
Moreover, the
price any investor receives is dependent upon the dividends the next investor expects to earn, and
so on for different generations of investors.
P
0
=
D
1
D
2
D
n
( 1 + r
s
)
( 1 + r
s
)
2
( 1 + r
s
)
n
The dividend stream theoretically extends on out forever, i.e., n = infinity.
It would not be feasible to
deal with an infinite stream of dividends, but if dividends are expected to grow at a constant rate, we
can use the constant growth equation as developed in the text to find the value.
CONSTANT GROWTH STOCKS (Section 9.4)
In the constant growth model, we assume that the dividend will grow forever at a constant growth
rate.
This is a very strong assumption, but for stable, mature firms, it can be reasonable to assume
that the firm will experience some ups and downs throughout its life but those ups and downs
balance each other out and result in a longterm constant rate.
In addition, we assume that the
required return for the stock is a constant.
With these assumptions, the price equation for a
common stock simplifies to the following expression:
P
0
=
D
1
( r
s
− g )
The longrun growth rate (g) is especially difficult to measure, but one approximates this rate by
multiplying the firm's return on assets by the fraction of earnings retained, ROE x % Earnings
retained.
Generally speaking, the longrun growth rate is likely to fall between 5% and 8%.
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$1.15
g
8%
13.4%
=
=
$1.24
0.054
$23.00
STOCK PRICE SENSITIVITY
Resulting
% Change
Last
Price
$23.00
30%
$0.81
$16.10
15%
$0.98
$19.55
0%
$1.15
$23.00
15%
$1.32
$26.45
30%
$1.50
$29.90
% Change
$23.00
30%
9.38%
$90.00
15%
11.39%
$36.64
0%
13.40%
$23.00
15%
15.41%
$16.76
30%
17.42%
$13.18
% Change
g
$23.00
30%
5.60%
$15.57
15%
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 Spring '10
 woo
 Management, Valuation

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