Question

a company has just paid its dividend. analysts expect the company to pay shareholders $1.00 per share annually for the next five years. after that, the dividend is forecasted to be $1.80 annually forever. given an annual discount rate of 9% compounded annually what is the value of the stock today?

Answer 1

To calculate the value of the stock today using the present discounted value (PDV) method, we need to determine the present value of each future dividend payment and then sum them up.

Step-by-step explanation:

To calculate the value of the stock today using the present discounted value (PDV) method, we need to determine the present value of each future dividend payment and then sum them up. Since the dividends are expected to be $1.00 per share annually for the first five years and $1.80 annually forever after that, we can use the formula for the present value of a growing perpetuity:

Present Value = D / (r - g)

where D is the dividend, r is the discount rate, and g is the growth rate.

For the first five years:

Present Value = $1.00 / (1 + 0.09)1 + $1.00 / (1 + 0.09)2 + $1.00 / (1 + 0.09)3 + $1.00 / (1 + 0.09)4 + $1.00 / (1 + 0.09)5

For the perpetuity:

Present Value = $1.80 / (0.09 - 0)

Adding up the present values gives us the value of the stock today.