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Price of Stock

29. Cellular Systems paid a $3 dividend last year. The dividend is expected to grow at a constant rate of 5 percent over the next two years. The required rate of return is 12 percent (this will also serve as the discount rate in this problem).
Round all values to three places to the right of the decimal point where appropriate.

a. Compute the anticipated value of the dividends for the next three years.
That is, compute D1, D2, and D3; for example, D1 is $3.15 ($3.00 _ 1.05).
Round all values throughout this problem to three places to the right of the decimal point.

b. Discount each of these dividends back to the present at a discount rate of
12 percent and then sum them.

c. Compute the price of the stock at the end of the third year (P3).

d. After you have computed P3, discount it back to the present at a discount rate of 12 percent for three years.

e. Add together the answers in part b and part d to get P0, the current value of the stock. This answer represents the present value of the first three periods of dividends, plus the present value of the price of the stock after three periods (which, in turn, represents the value of all future dividends).

f. Use Formula 10-9 to show that it will provide approximately the same answer as part e.

For Formula 10-9 use D1 _ $3.15, Ke _ 12 percent, and g _ 5 percent.
(The slight difference between the answers to part e and part f is due to

Solution Preview

a. Compute the anticipated value of the dividends for the next three years.
That is, compute D1, D2, and D3; for example, D1 is $3.15 ($3.00 _ 1.05).
Round all values throughout this problem to three places to the right of the
decimal point.

The dividends over the three years would grow at 5% each. The initial dividend is $3.
Year 1 Dividend D1 = 3 X 1.05 = 3.15
Year 2 Dividend D2 = 3.15 x 1.05 = 3.308
Year 3 Dividend D3 = 3.308X1.05 = 3.473

b. Discount each of these dividends back to the present at a discount rate of
12 ...

Solution Summary

The solution explains the calculation of anticipated dividends and the price of stock as the present value of all dividends.

$2.19