Lets say that a company will report $$4$ million in earnings in one year. This companies policy us to pay out $50\%\%$ of it's earnings in dividends $($it just paid out its dividends for this uear$).$ Their ROE is $8\%,$ and required rate of return is $11\%.$ They have $2$ million shares outstanding. Assume that the aforementioned numbers are representative of the foreseeable future

a$)$ What is the company's expected rate of dividend growth?

b$)$ Suppose the boad of directors decidedd to change the dividend policy and pay out $100\%$ of the company's earnings in dividends $($they would pay out the full $$4$ million in dividends next year and mainain this new policy forever$).$ What would be the stock price under this dividend policy? Would shareholders benefit from this decision?