A firm with $$20$ book equity value per share, and $12\%$ required rate of return from shareholders, intends to maintain a constant dividend payout ratio of $60\%$ and a constant ROE of $10\%$ in the future.$$

$(1)$ What will be next years earnings per share?.

$(2)$ What will be next years dividend per share?$$

$(3)$ What is the sustainable growth rate?$$

$(4)$ What is the reasonable stock price now?$$

$(5)$ If the firm maintains $100\%($rather than $60\%)$ dividend payout ratio in the future, what should be stock price now?$$

$(6)$ Why is the stock price in $(5)$ higher than the stock price in $(4)?$