Currently, a company's EBIT $($earnings before interest and tax$)$ is $1000.$The company expects a $5\%$ perpetual growth rate starting from the next year. WACC is constantly $8\%$ and there are no taxes. Current dividend payout ratio is $55\%,$ meaning that the firm retains $45\%$ of its earnings for reinvestment purposes. Now the company decides to double its dividend payout without changing investment policy $($reinvestment amount remains constant$)$ and raise additional shares to meet the existing reinvestment need. Current shares outstanding is $1000.$ Assuming no interest payment or tax expenses, calculate the following:

A$.$ Value to the firm $($note: based constant growth model for free cash flow to the firm$).(2$ marks$)$

B$.$ Price per share after dividend payout is doubled. $(2$ marks$)$

C$.$ Dividend per share after dividend payout is doubled. $(2$ marks$)$

D$.$ Total value per share after dividend payout is doubled. $(2$ marks$)$

E$.$ If the company decides to cut dividend payout by half without changing investment policy, how much will be the total value per share after dividend is cut? $(2$ marks$)$