MacKenzie Corporation currently has $10$ million shares of stock outstanding at a price of $$40$ per share. The company would like to raise money and has announced a rights issue. Every existing shareholder will be sent one right per share of stock that he or she owns. The company plans to require five rights to purchase one share at a price of $$40$ per share.

a$.$ Assuming the rights issue is successful, how much money will it raise?

b$.$ What will the share price be after the rights issue? $($Assume perfect capital markets.$)$

Suppose instead that the firm changes the plan so that each right gives the holder the right to purchase one share at $$8$ per share.

c$.$ How much money will the new plan raise?

d$.$ What will the share price be after the rights issue?

e$.$ Which plan is better for the firm's shareholders? Which is more likely to raise the full amount of capital?