Ross et al.: Fundamentals
of Corporate Finance, Sixth
Edition, Alternate EditionIII. Valuation of Future
Cash Flows(^280) 8. Stock Valuation © The McGraw−Hill
Companies, 2002
P 3 D 3 (1 g)/(Rg)
$2.50 1.05/(.10 .05)
$52.50
We can now calculate the total value of the stock as the present value of the first three
dividends plus the present value of the price at Time 3, P 3 :
P 0
$.91 1.65 1.88 39.44
$43.88
The value of the stock today is thus $43.88.52.50
1.10^3
2.50
1.10^3
2
1.10^2
$1
1.10
P 3
(1 R)^3
D 3
(1 R)^3
D 2
(1 R)^2
D 1
(1 R)^1
250 PART THREE Valuation of Future Cash Flows
FIGURE 8.1
(^012345)
$1 $2 $2.50 $2.50
X 1.05
Time
Dividends $2.50
X 1.05^2
Nonconstant growth Constant growth @ 5%
Nonconstant Growth
Supernormal Growth
Chain Reaction, Inc., has been growing at a phenomenal rate of 30 percent per year because
of its rapid expansion and explosive sales. You believe that this growth rate will last for three
more years and that the rate will then drop to 10 percent per year. If the growth rate then re-
mains at 10 percent indefinitely, what is the total value of the stock? Total dividends just paid
were $5 million, and the required return is 20 percent.
Chain Reaction’s situation is an example of supernormal growth. It is unlikely that a 30 per-
cent growth rate can be sustained for any extended length of time. To value the equity in this
company, we first need to calculate the total dividends over the supernormal growth period:
The price at Time 3 can be calculated as:
P 3 D 3 (1 g)/(Rg)
where gis the long-run growth rate. So we have:
P 3 $10.985 1.10/(.20 .10) $120.835
Year Total Dividends (in millions)
1 $5.00 1.3 $ 6.500
2 6.50 1.3 8.450
3 8.45 1.3 10.985
EXAMPLE 8.4