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Part $1$

$$DFB$,$ Inc. expects earnings next year of $ $5\mathrm{.}67$ per$$ share, and it plans to pay a $ $3\mathrm{.}44$ dividend to shareholders$($assume that is one year from$$ now$).$ DFB will retain $ $2\mathrm{.}23$ per share of its earnings to reinvest in new projects that have an expected return of $15\mathrm{.}5\%$ per year. Suppose DFB will maintain the same dividend payout$$ rate, retention$$ rate, and return on new investments in the future and will not change its number of outstanding shares. Assume next dividend is due in one year.

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

b$.$ If$$ DFB$\text{'}$s equity cost of capital is $12\mathrm{.}6\%,$ what price would you estimate for DFB stock$$ today?

c$.$ Suppose instead that DFB paid a dividend of $ $4\mathrm{.}44$ per share at the end of this year and retained only $ $1\mathrm{.}23$ per share in earnings. That$$ is$,$ it chose to pay a higher dividend instead of reinvesting in as many new projects. If DFB maintains this higher payout rate in the$$ future, what stock price would you estimate for the firm$$ now? Should DFB raise its$$ dividend?