$1.$ a public company is expected to pay out $10\%$ of its earnings per share as dividends over the next $3$ years. The other $90\%$ of the earnings will be invested in opening new locations of its chain restaurant. Due to this growth, you expect the company's EPS to be $$5\mathrm{.}00,$ $$7\mathrm{.}00,$ $$12\mathrm{.}00$ and $$15\mathrm{.}00$ in the next four years. After $4$ years, you expect the company to slow down expansion and thus begin paying out $90\%$ of earning as dividends. The remaining $10\%$ will be invested in opening stores that earn a $12\%$ return. Thus, the company's EPS will grow at a rate of $1\mathrm{.}2\%.$ Investors in tech stocks as risky as this companys expect to earn a $10\%$ rate of return.

a$.$ What do you expect the price of the company's stock to be $3$ years from today?

b$.$ What dividends will be paid over the next $3$ years?

c$.$ What do you expect the price of the company's stock to be today?