Suppose a stock has just paid a $10 per share dividend. The dividend is projected to grow at 15% for the next year, then 10% for one year, then 8% for two years, and then 5% indefinitely. The required return is 7%.

Remember that all prices are ex-dividend, that time 0 dividend does not go to the purchaser and is hence not included in the price calculation.

Time 0 | 1 | 2 | 3 | 4 | 5 | 6
Growth Rate | 15% | 10% | 8% | 8% | 5% | 5%
Dividend | 10 | 11.5 | 12.65 | 13.66 | 14.75 | 15.49 | 16.27

What is the stock's ex-dividend price at time 1 (that is one period from today, and does not include the $11.50 dividend paid one year from now)?

Explanation: Time 4 dividend of $14.75 grows at a constant rate of 5% forever, so we can apply the growing perpetuity formula to it to get the price at time 3 equal to $737.75. Discount this price (by 2 periods, not 3) to get it back from time 3 to time 1. Add discounted values of individual dividends of $12.65, and $13.66 to get price today.