Question

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 2 percent. If you want to earn 6 percent on investments in common stock, what is the maximum you should pay for this stock?

Answer 1

We should pay $46.50 for this stock.

Step-by-step explanation:

The stock value is the present value of all the future dividends associated with the stock.

Following is the working to calculate the stock value.

Dividend

Year Dividend

_1 ____$1.20

_2 ___ $1.44

_3 ___ $1.73

_4 ___ $2.07

Use following formula to calculate the present value of all the dividends

Present value of Dividend = Dividend value x ( 1 + Expected interest rate )^numbers of years

Now calculate the present value of al the dividends

Year __Working ___________________________ Present values

_1 ____$1.20 x ( 1 + 6% )^-1 ____________________ $1.132

_2 ___ $1.44 x ( 1 + 6% )^-2 ____________________ $1.282

_3 ___ $1.73 x ( 1 + 6% )^-3 ____________________ $1.453

_4 ___ $2.07 x ( 1 + 6% )^-4____________________ $1.640

_5 to onward ___ [$2.07 / ( 6% - 2% )] x ( 1 + 6% )^-4 _ $40.991

Total _____________________________________$46.498

We should pay $46.50 for this stock.