In practice, a common way to value a share of stock when a company pays dividends is to value the dividends over the next five years or so$,$ then find the terminal stock price using a benchmark PE ratio. Suppose a company just paid a dividend of $$1\mathrm{.}95.$ The dividends are expected to grow at $12$ percent over the next five years. In five years, the estimated payout ratio is $40$ percent and the benchmark PE ratio is $37.$

a$.$

What is the target stock price in five years? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ What is the stock price today assuming a required return of $13\mathrm{.}5$ percent on this stock? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$