DFB$,$ Inc., expects earnings at the end of this year of $$5$ per share, and it plans to pay a $$3$ dividend at that time. DFB will retain $$2$ per share of its earnings to reinvest in new projects with an expected return of $15\%$ per year. Suppose DFB will maintain the same dividend payout rate, retention rate, and return on new investments in the future and will not change its number of outstanding shares.

a$)$ What growth rate of earnings would you forecast for DFB$?$

b$)$ If DFB$\text{'}$s equity cost of capital is $12\%,$ what price would you estimate for DFB stock today?

c$)$ Suppose DFB instead paid a dividend of $$4$ per share at the end of this year and retained only $$1$ per share in earnings. If DFB maintains this higher payout rate in the future, what stock price would you estimate now? Should DFB raise its dividend?