A firm with beta $0\mathrm{.}75$ and just distributed all its earnings as dividends $($$$10$ per share$).$ The expected market return is $12\%$ and the risk$-$free rate comfortably sits at $4\%.$

$1.$ Price the stock, if the firm continues to follow the same dividend policy forever. $2.$ Calculate the P$/$E ratio of the firm.

$3.$ Price the stock if the company can retain $20\%$ of its earnings in the future to invest in projects with ROE$=20\%.$ Will the stock price increase or decrease and why?

$4.$ If the company retains its earnings as in $(3),$ find the present value of its growth opportunities and its P$/$E ratio.

$5.$ If the company retains $20\%$ of its earnings but can achieve only ROE $=5\%,$ estimate the price, the present value of its growth opportunities and its P$/$E ratio.