Question

Consider a firm that has just paid a dividend of $2. An analyst expects dividends to grow at a rate of 8% per year for the next five years. After that, dividends are expected to grow at a normal rate of 5% per year. Assume that the appropriate discount rate is 7%. How much are the dividends for years 1, 2, and 3?

Answer 1

To calculate the dividends for years 1, 2, and 3, we can use the formula for the present value of dividends. For year 1, the present value is $1.87. For year 2, the present value is $1.99. And for year 3, the present value is $1.83.

Step-by-step explanation:

In order to calculate the dividends for years 1, 2, and 3, we need to apply the formula for the present value of dividends.

The present value of a dividend can be found using the formula PV = D / (1 + r)n, where PV is the present value, D is the dividend, r is the discount rate, and n is the number of periods.

For year 1, the dividend is $2, the discount rate is 7%, and the number of periods is 1. Substituting these values into the formula, we get: PV = 2 / (1 + 0.07)1 = $1.87.

Similarly, for year 2, the dividend is expected to grow at a rate of 8%, so the dividend for year 2 would be $2 * 1.08 = $2.16. Substituting these values into the formula, we get: PV = 2.16 / (1 + 0.07)2 = $1.99.

For year 3, we follow the same process and substitute the values into the formula. Assuming a dividend growth rate of 8%, the dividend for year 3 would be $2 * 1.082 = $2.34. So, the present value for year 3 would be: PV = 2.34 / (1 + 0.07)3 = $1.83.