The BMT corporation has a stock price of $$45$ per share, and has $20$ million shares of stock outstanding. During the most recent year, the company had $$100$ million of net income and paid $$40$ million in common stock dividends.

a$)$ Compute BMT$\text{'}$s earnings per share

b$)$ Compute BMT$\text{'}$s dividend payout ratio

c$)$ Compute BMT$\text{'}$s price$-$earnings $($P$/$E$)$ ratio

d$)$ Compute BMT$\text{'}$s market capitalization

e$)$ Compute BMT$\text{'}$s market capitalization category $($small$-,$ mid$-,$ or large$-$cap$)$ must be solved written out and not in excel