A stock just paid an annual dividend of $$2\mathrm{.}7.$ The dividend is expected to grow by $9\%$ per year for the next $3$ years. The growth rate of dividends will then fall steadily $($linearly$)$ from $9\%$ after $3$ years to $6\%$ in year $6.$The required rate of return is $12\%.$

In $6$ years, the P$/$E ratio is expected to be $17$ and the payout ratio to be $80\%.$ What is the value of the stock when using the P$/$E ratio?