Solarpower Systems earned $$$$20$ per share at the beginning of the year and paid out $$$ $8$ in dividends to shareholders$($so$,$Do $=$$$8)$ and retained $12$$ to invest in new projects with an expected return on equity of $21$ percent. In the$$ future, Solarpower expects to retain the same dividend payout$$ ratio, expects to earn a return of $21$ percent on its equity invested in new$$ projects, and will not be changing the number of shares of common stock outstanding.

a$.$Calculate the future growth rate for$$ Solarpower's earnings.

b$.$If the$$ investor's required rate of return for$$ Solarpower's stock is $15$ percent$,$ what would be the price of$$ Solarpower's common$$ stock?

c$.$What would happen to the price of$$ Solarpower's common stock if it raised its dividends to $13$$ and then continued with that same dividend payout ratio$$ permanently? Should Solarpower make this$$ change? $($Assume that the$$ investor's required rate of return remains at $15$percent$.)$

d$.$What would happened to the price of$$ Solarpower's common stock if it lowered its dividends to $$$$2$ and then continued with that same dividend payout ratio$$ permanently? Does the constant dividend growth rate model work in this$$ case? Why or why$$ not? $($Assume that the$$ investor's required rate of return remains at $15$ percent and that all future new projects will earn $21$percent$.)$