Question $3$: Stock Valuation $(45$ points$)$

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 D$1,$ D$2$ and D$3)?$ Assume

no change in the future dividend forecasts or the discount rate.