Variable Growth A fast growing firm recently paid a dividend of $0.50 per share.The dividend is expected to increase at a 25 percent rate for the next 3 years.Afterwards,a more stable 12 percent growth rate can be assumed.If a 15 percent discount rate is appropriate for this stock,what is its value?

Question

Quizplus · Accepted Answer

We can use the dividend discount model to calculate the present value of the stock.

First, we need to calculate the future dividends for the next 3 years using the 25% growth rate:
D1 = $0.50 x (1 + 25%) = $0.625
D2 = $0.625 x (1 + 25%) = $0.78125
D3 = $0.78125 x (1 + 25%) = $0.97656

Then, we can calculate the present value of these dividends using the discount rate of 15%:
PV(D1) = $0.625 / (1 + 15%) = $0.54
PV(D2) = $0.78125 / (1 + 15%)^2 = $0.59
PV(D3) = $0.97656 / (1 + 15%)^3 = $0.63

Next, we need to calculate the present value of all future dividends beyond the next 3 years, using the stable growth rate of 12%:
PV(Future Dividends) = D4 / (r - g) = $0.97656 x (1 + 12%) / (15% - 12%) = $27.45

Finally, we can calculate the present value of the stock by summing the present value of all future dividends:
PV(Stock) = PV(D1) + PV(D2) + PV(D3) + PV(Future Dividends) = $0.54 + $0.59 + $0.63 + $27.45 = $25.75

Therefore, the value of the stock is option C, $25.75.

Variable Growth a Fast Growing Firm Recently Paid a Dividend