Question

A firm recently paid a $0.50 annual dividend. The dividend is expected to increase by 9 percent in each of the next four years. In the fourth year, the stock price is expected to be $70. If the required rate for this stock is 12 percent, what is its value? Hint: Think about the stock price of $70 in Year 4 (P4) as the present values of all future dividends from years 5 onwards.

a. $16.67
b. $22.88
c. $46.36
d. $51.58
e. $72.51

Answer 1

The value of the stock is $46.36.

Step-by-step explanation:

To calculate the value of the stock, we need to find the present value of all the future dividends. The annual dividend is currently $0.50 and it is expected to increase by 9 percent each year for the next four years. In the fourth year, the stock price is expected to be $70.

We can use the formula for the present value of a growing perpetuity to calculate the present value of the future dividends. The formula is: PV = D / (r - g), where PV is the present value, D is the dividend, r is the required rate of return, and g is the growth rate. Using this formula, we can calculate the present value of each year's dividend and add them together to get the total present value.

PV = $0.50 / (0.12 - 0.09) + $0.50 * 1.09 / (0.12 - 0.09)^2 + $0.50 * 1.09^2 / (0.12 - 0.09)^3 + $70 * 1.09^3 / (0.12 - 0.09)^4 = $46.36

Therefore, the value of the stock is $46.36.