AAA Corporation expects to haves earnings this coming year of $$100$ per share. The firm plans to retain all of its earnings for the next two years. For the subsequent two years, the firm will retain $50\%$ of its earnings. It will then retain $20\%$ of its earnings from that point onward. Each year, retained earnings will be invested in new projects with an expected return of $25\%$ per year. Any earnings that are not retained will be out as dividends. All earnings growth comes from the investment of retained earnings. Cost of capital is $10\%.$ Which of the following statements are correct. Select all that apply.

a$)$ EPS in year $6$ is $175\mathrm{.}78$

b$)$ EPS in year $5$ is $197\mathrm{.}75$

c$)$ Dividends in year $5$ are $158\mathrm{.}20$

d$)$ EPS is year $4$ is $125\mathrm{.}00$

e$)$ Price today, rounded to dollars, is $2277$ f$)$ EPS in year $1$ is $125$