A company’s dividend is expected to grow at 20% for the next six years. After that, the growth is expected to be 3% forever. If the required return is 10%, what is the value of the stock at time 6? The dividend just paid was $1

To calculate the value of the stock at time 6, we first need to calculate the dividends for the first six years and the dividend in the seventh year.

Step 1: Calculate the dividends for the first six years The dividend growth rate for the first six years is 20%. So, the dividends for the first six years would be:

Year 1: $1 * 1.20 =$1.20 Year 2: $1.20 * 1.20 =$1.44 Year 3: $1.44 * 1.20 =$1.73 Year 4: $1.73 * 1.20 =$2.07 Year 5: $2.07 * 1.20 =$2.49 Year 6: $2.49 * 1.20 =$2.98

Step 2: Calculate the dividend for the seventh year The growth rate after the sixth year is expected to be 3% forever. So, the dividend in the seventh year would be:

Year 7: $2.98 * 1.03 =$3.07

Step 3: Calculate the value of the stock at time 6 The value of the stock at time 6 would be the present value of the dividends from year 7 onwards, discounted back to year 6 at the required return of 10%. This is a perpetuity, and the formula for the present value of a perpetuity is D/(r-g), where D is the dividend, r is the required return, and g is the growth rate. So, the value of the stock at time 6 would be:

Value at time 6 = $3.07 / (0.10 - 0.03) =$43.86

So, the value of the stock at time 6 is $43.86.