Question 8.4: Chain Reaction, Inc., has been growing at a phenomenal rate ...
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 remains 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 percent 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:
| 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 |
The price at Time 3 can be calculated as:
P_{3} = D_{3} × (1 + g)/(R – g)
where g is the long-run growth rate. So we have:
P_{3} = $10.985 × 1.10/(.20 – .10) = $120.835
To determine the value today, we need the present value of this amount plus the present value of the total dividends:
P_{0}=\frac{D_{1}}{(1+R)^1}+\frac{D_{2}}{(1+R)^2}+\frac{D_{3}}{(1+R)^3}+\frac{P_{3}}{(1+R)^3}=\frac{\$6.50}{1.20}+\frac{8.45}{1.20^2}+\frac{10.985}{1.20^3}+\frac{120.835}{1.20^3}
=\$5.42+5.87+6.36+69.93
=\$87.58
The total value of the stock today is thus $87.58 million. If there were, for example, 20 million shares, then the stock would be worth $87.58/20 = $4.38 per share.