Ross et al.: Fundamentals
of Corporate Finance, Sixth
Edition, Alternate EditionIII. Valuation of Future
Cash Flows(^274) 8. Stock Valuation © The McGraw−Hill
Companies, 2002
requires. Nonetheless, as we will see, there are cases in which we can come up with the
present value of the future cash flows for a share of stock and thus determine its value.
Cash Flows
Imagine that you are considering buying a share of stock today. You plan to sell the
stock in one year. You somehow know that the stock will be worth $70 at that time. You
predict that the stock will also pay a $10 per share dividend at the end of the year. If you
require a 25 percent return on your investment, what is the most you would pay for the
stock? In other words, what is the present value of the $10 dividend along with the $70
ending value at 25 percent?
If you buy the stock today and sell it at the end of the year, you will have a total of
$80 in cash. At 25 percent:
Present value ($10 70)/1.25 $64
Therefore, $64 is the value you would assign to the stock today.
More generally, let P 0 be the current price of the stock, and assign P 1 to be the price
in one period. If D 1 is the cash dividend paid at the end of the period, then:
P 0 (D 1 P 1 )/(1 R) [8.1]
where Ris the required return in the market on this investment.
Notice that we really haven’t said much so far. If we wanted to determine the value
of a share of stock today (P 0 ), we would first have to come up with the value in one year
(P 1 ). This is even harder to do, so we’ve only made the problem more complicated.
What is the price in one period, P 1? We don’t know in general. Instead, suppose we
somehow knew the price in two periods, P 2. Given a predicted dividend in two periods,
D 2 , the stock price in one period would be:
P 1 (D 2 P 2 )/(1 R)
If we were to substitute this expression for P 1 into our expression for P 0 , we would have:
P 0
Now we need to get a price in two periods. We don’t know this either, so we can pro-
crastinate again and write:
P 2 (D 3 P 3 )/(1 R)
If we substitute this back in for P 2 , we have:P 0
P 3
(1 R)^3
D 3
(1 R)^3
D 2
(1 R)^2
D 1
(1 R)^1
(1 R)^2
D 2
(1 R)^2
D 1
(1 R)^1
D 3 P 3
1 R
P 2
(1 R)^2
D 2
(1 R)^2
D 1
(1 R)^1
P 2
(1 R)^2
D 2
(1 R)^2
D 1
(1 R)^1
D 1
1 R
D 1 P 1
1 R
D 2 P 2
1 R
244 PART THREE Valuation of Future Cash Flows