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 $1$ million shares through a rights offering. The market value of the stock is $$35$ before the rights offering and the new shares are being offered to existing shareholders at a $$5$ discount. $($LG $8-3)$

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?

c$.$ What is your total inwestment in the firm after the rights offering? How is your imestment split between original shares and new shares?

d$.$ If you decide not to exercise your preemptive rights, what is your investment in the firm after the rights oftering? How is this split between old shares and rights?