$($Common stock valuation$)$ Assume the following:

$$the investor's required rate of return is

$14\mathrm{.}5\%$

$$the expected level of earnings at the end of this year

$($E$1)$ is $$8,$

$$the retention ratio is $40\%$

$$the return on equity $($ROE$)$ is $12\%($that is$,$ it can earn

$12\%$ on reinvested earnings$),$ and

$$similar shares of stock sell at multiples of $6\mathrm{.}185$

times earnings per share.

Questions:

a$.$Determine the expected growth rate for dividends.

b$.$Determine the price earnings ratio $($P$/$E$1).$

c$.$What is the stock price using the P$/$E ratio valuation method?

d$.$What is the stock price using the dividend discount model?

e$.$What would happen to the P$/$E ratio $($P$/$E$1)$ and stock price if the company increased its retention rate to $75\%($holding all else constant$)?$ What would happen to the P$/$E ratio $($P$/$E$1)$ and stock price if the company paid out all its earnings in the form of dividends?

f$.$ What have you learned about the relationship between the retention rate and the P$/$E ratios?