DFB$,$ Inc.,expects earnings this year of $$5\mathrm{.}19$ per share, and it plans to pay a $$2\mathrm{.}81$ dividend to

shareholders. DFB will retain $$2\mathrm{.}38$ per share of its earnings to reinvest in new projects that

have an expected return of $15\mathrm{.}1\%$ 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?

$($c$)$ Suppose instead that DFB paid a dividend of $$3\mathrm{.}81$ per share this year and retained only $$1\mathrm{.}38$

per share in earnings. If DFB maintains this higher payout rate in the future, what stock price

would you estimate for the firm now? Should DFB raise its dividend?