Alpha Com. just announced its earnings per share of $$6$ yesterday, and the company

currently pays no dividend, but the company plans to pay out its first annual dividend

in $4$ years by distributing $50\%$ of its earnings to shareholders and expects the payout

policy to continue into the foreseeable future.

An analyst expects Alpha's earnings to grow at $12\%$ per year in the following three

years. After that, the earnings will grow at $8\%$ per year for five years and then slow

down to $2\%$ forever. How much is the price of a share of Alpha if the discount rate is

$12\%($EAR$)?$