The fast-growing firm of GoodCoffee Inc. is planning its first issue of public stock. The firm will pay out its first dividend of $1 one year from today. Analysts expect annual dividends to grow at a rate of 12% per year for each of the following two years (year 2 and year 3). After that, the dividends will grow at a constant rate of 7% indefinitely. Investors require a 10% return from holding GoodCoffee stock.

a) What price should GoodCoffee Inc. set for its new stock?

b) What is the stock price at the end of year 3 (after paying out the first three dividends)? Assume no change in the future dividend forecasts or the discount rate.