Suppose you own $500,000$ shares of common stock in a firm with $40$ million total shares outstanding. The firm announces a plan to sell an additional $5$ million shares through a rights offering. The market value of the stock is $$32\mathrm{.}5$ before the rights offering and the new shares are being offered to existing shareholders at a $$2\mathrm{.}50$ discount. If you exercise your preemptive rights, how many of the new shares can you purchase?

Multiple Choice

$100,000$ shares

$50,000$ shares

$62,500$ shares

$32,500$ shares