Suppose you own $50,000$ shares of common stock in a firm with $2\mathrm{.}5$ million total shares outstanding. The firm announces a plan to sell an additional $1$mllion shares through a rights offering. The market value of the stock is $$33$ before the rights offering and the new shares are being offered to existing shareholders at a $$3$ discount.

a$.$ If you exercise your preemptive rights, how many of the new shares can you purchase?

b$.$ What is the market value of the stock after the rights offering? $($Enter your answer in millions rounded to $1$ decimal place. $($e$.$g$.,32\mathrm{.}1))$

c$-1.$ What is your total investment in the firm after the rights offering? $($Do not round intermediate calculations. Enter your answer in millions rounded to $2$ decimal places. $($e$.$g$.,32\mathrm{.}16))$

c$-2.$ If you exercise your preemptive right how many original shares and how many new shares do you have?

d$-1.$ If you decide not to exercise your preemptive rights, what is your investment in the firm after the rights offering? $($Do not round intermediate calculations. Enter your answer in millions rounded to $3$ decimal places. $($e$.$g$.,32\mathrm{.}161))$

d$-2.$ If you sell your rights rather than use them, how much money will you receive from the rights sale and what is the total value of your proceeds from the sale of the rights offering plus your investment in the firm? $($Enter your answer in millions rounded to $3$ decimal places. $($e$.$g$.,32\mathrm{.}161))$