Company F does not pay any dividends because it is expanding rapidly and needs to retain all of its earnings. However, investors expect the company to begin paying dividends, with the first dividend of $$0\mathrm{.}50$ coming $3$ years from today. The dividend should grow rapidly $-$ at a rate of $80\%$ per year $-$ during Years $4$ and $5.$ After Year $5,$ the company should grow at a constant rate of $7\%$ per year. If the required return on the stock is $16\%,$ what is the value of the stock today?