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

the investor's required rate of return is $12\mathrm{.}5$ percent,

the expected level of earnings at the end of this year $(E_1)$ is $$14,$

the retention ratio is $30$ percent,

the return on equity $(ROE)$ is $15$ percent $($that is$,$ it can earn $15$ percent on reinvested earnings$),$ and

similar shares of stock sell at multiples of $8\mathrm{.}750$ times earnings per share.

a$.$ What is the expected growth rate for dividends?

$\%($Round to two decimal places.$)$

b$.$ What is the price earnings ratio $(\frac{P}{E_1})?$

$($Round to three decimal places.$)$

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

$ $($Round to the nearest cent.$)$

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

$($Round to the nearest cent.$)$

e$.($i$)$ Using the dividend discount model, what would be the stock price if the company increased its retention rate to $60\%($holding all else constant$)?$

$($Round to the nearest cent.$)$

What would be the $\frac{P}{E}$ ratio $(\frac{P}{E_1})$ if the company increased its retention ratio to $60\%.($holding all else constant$)?$

$($Round to three decimal places.$)$

e$.($ii$)$ Using the dividend discount model, what would be stock price if the company paid out all its earnings in the form of dividends?

$ $($Round to the nearest cent.$)$

What would be the $\frac{P}{E}$ ratio $(\frac{P}{E_1})$ and stock price if the company paid out all its earnings in the form of dividends?

$($Round to three decimal places.$)$