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Presently, Stock A pays a dividend of $2.00 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?

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Answer:

In order to find the price of a stock which has different growth rate at different periods, we need to find the price at a time when the growth rate slows down after the initial burst of growth and is stable, in this case its in the 4th period.

Year 4 dividend = 2.07

Growth rate (G)= 8%

Required return (R)= 12%

DDM formula for stock price = D*(1+G)/R-G

2.07*(1+0.08)/0.04

=55.89

The maximum that you should be willing to pay for the stock 4 years from now is $55.89 but in order to find out what the maximum we should pay for the stock now, we need to discount this price 4 years back to the present value using the required return of 12 %

so 55.89/1.12^4=35.52

The maximum that you should be willing to pay for the stock now is $35.52

Explanation:

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