$($Related to Checkpoint $10\mathrm{.}2)($Relative valuation of common stock$)$ Using the P$/$E ratio approach to valuation, calculate the value of a share of stock under the following conditions:

the investor's required rate of return is $12$ percent,

the expected level of earnings at the end of this year $(E_1)$ is $$6,$

the firm follows a policy of retaining $30$ percent of its earnings,

the return on equity $(ROE)$ is $13$ percent, and

similar shares of stock sell at multiples of $8\mathrm{.}642$ times earnings per share.

Now show that you get the same answer using the discounted dividend model.

a$.$ The stock price using the P$/$E ratio valuation method is $ $($Round to the nearest cent.$)$