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{.}27.$ The dividends are expected to grow at $12$ percent over the next five years. In five years, the estimated payout ratio will be $30$ percent and a benchmark PE will be $22.$ The required return is $14$ percent.

a$.$ What is the target stock price in five years?

b$.$ What is the stock price today?