The question is incomplete. The complete question is,
Presently, Stock A pays a dividend of $1.00 a share, and you expect the dividend to grow rapidly for the next four years at 20 percent. Thus the dividend payments will be
Year Dividend
1 $1.20
2 1.44
3 1.73
4 2.07
After this initial period of super growth, the rate of increase in the dividend should decline to 8 percent. If you want to earn 12 percent on investments in common stock, what is the maximum you should pay for this stock?
Answer:
The maximum that should be paid for the stock today is $40.29
Step-by-step explanation:
We will use the two stage dividend growth model of DDM to calculate the price of the stock today. The DDM values the stock based on the present value of the expected future dividends from the stock. The formula for price under the two stage model is,
P0 = D1 / (1+r) + D2 / (1+r)^2 + ... + Dn / (1+r)^n + [Dn * (1+g2) / (r - g2)] / (1+r)^n
P0 = 1.2 / (1+0.12) + 1.44 / (1+0.12)^2 + 1.73 / (1+0.12)^3 + 2.07 * (1+0.12)^4 +
[2.07 * (1+0.08) / (0.12 - 0.08)] / (1+0.12)^4
P0 = $40.2853 rounded off to $40.29