Chapter 9 Stocks and Their Valuation 277All active investors hope to be better than average—they hope to identify
stocks whose intrinsic values exceed their current prices and whose expected re-
turns (expected by this investor) exceed the required rate of return. Note, though,
that about half of all investors are likely to be disappointed. A good understanding
of the points made in this chapter can help you avoid being disappointed.
9-4a Expected Dividends as the Basis for Stock Values
In our discussion of bonds, we used Equation 7-1 to! nd the value of a bond; the
equation is the present value of interest payments over the bond’s life plus the
present value of its maturity (or par) value:
VB! INT
(1 " rd)^1
" INT
(1 " rd)^2
"... " INT
(1 " rd)N
" M
(1 " rd)N
Stock prices are likewise determined as the present value of a stream of cash " ows,
and the basic stock valuation equation is similar to the one for bonds. What are the
cash " ows that a corporation will provide to its stockholders? To answer that ques-
tion, think of yourself as an investor who buys the stock of a company that is
expected to go on inde! nitely (for example, GE). You intend to hold it (in your
family) forever. In this case, all you (and your heirs) will receive is a stream of divi-
dends; and the value of the stock today can be calculated as the present value of an
in! nite stream of dividends:
Value of stock! Pˆ 0! PV of expected future dividends
!
D 1
_______
(1 " rs)^1
"D 2
_______
(1 " rs)^2
"... "
D#
_______
(1 " rs)#! ∑
t! 1#
Dt
_______
(1 " rs)t
9-1What about the more typical case, where you expect to hold the stock for a
! nite period and then sell it—what will be the value of Pˆ 0 in this case? Unless the
company is likely to be liquidated or sold and thus disappears, the value of the stock
is again determined by Equation 9-1. To see this, recognize that for any individual
investor, the expected cash " ows consist of expected dividends plus the expected
sale price of the stock. However, the sale price to the current investor depends on
the dividends some future investor expects, and that investor’s expected sale price
is also dependent on some future dividends, and so forth. Therefore, for all present
and future investors in total, expected cash " ows must be based on expected future
dividends. Put another way, unless a! rm is liquidated or sold to another concern,
the cash " ows it provides to its stockholders will consist only of a stream of divi-
dends. Therefore, the value of a share of stock must be established as the present
value of the stock’s expected dividend stream.^4
(^4) The general validity of Equation 9-1 can also be con! rmed by asking yourself the following question: Suppose I
buy a stock and expect to hold it for 1 year. I will receive dividends during the year plus the value Pˆ 1 when I sell it
at the end of the year. But what will determine the value of Pˆ 1? The answer is that it will be determined as the
present value of the dividends expected during Year 2 plus the stock price at the end of that year, which, in turn,
will be determined as the present value of another set of future dividends and an even more distant stock price.
This process can be continued ad in! nitum, and the ultimate result is Equation 9-1.
We should note that investors periodically lose sight of the long-run nature of stocks as investments and
forget that in order to sell a stock at a pro! t, one must! nd a buyer who will pay the higher price. If you analyze a
stock’s value in accordance with Equation 9-1, conclude that the stock’s market price exceeds a reasonable value,
and buy the stock anyway, you would be following the “bigger fool” theory of investment—you think you may be
a fool to buy the stock at its excessive price; but you also believe that when you get ready to sell it, you can! nd
someone who is an even bigger fool. The bigger fool theory was widely followed in the summer of 2000, just
before the stock market crashed.