Since its inception five years ago,Companioni Gyms has not paid a dividend to its common stockholders,and it does not expect to pay a dividend for the next five years.Beginning six years from today,however,Companioni Gyms expects to pay a $2 dividend,which,from that point on,will increase by 10 percent per year forever.Stocks with similar risks have a required rate of return equal to 15 percent.What should be the market price of Companioni's common stock?
A) $19.89
B) $22.87
C) $17.29
D) $44.00
E) There is not enough information to answer this question.

Question

Quizplus · Accepted Answer

The market price of Companioni's common stock can be calculated using the Gordon Growth Model (also known as the Dividend Discount Model for a perpetually growing dividend). The model is P = D / (r - g), where P is the price, D is the dividend, r is the required rate of return, and g is the growth rate. In this case, the first dividend ($2) is expected 6 years from now and will grow at 10% (0.10) annually thereafter. The required rate of return is 15% (0.15). However, since the first dividend is 6 years away, we first calculate the present value of the stock at year 5 (just before the first dividend) as D1 / (r - g) = $2 / (0.15 - 0.10) = $40. This value is then discounted back to the present value using the formula PV = FV / (1 + r)^n, where FV is the future value ($40), r is the required rate of return (0.15), and n is the number of periods (5 years). Thus, the present value is $40 / (1 + 0.15)^5, which approximately equals $19.89.

Since Its Inception Five Years Ago,Companioni Gyms Has Not Paid