The Archway Corporation produces PC's. It has grown rapidly and needs to raise $45 million in new equity. It has decided to do this using a rights issue. It currently has 4.5 million shares outstanding at a rights-on price of $40 a share. The issue price it has announced is $30 per share.

(a) If the company anticipates all rights will be exercised, what will be the number of shares the firm needs to issue and what will the ex-rights price be?

(b) Suppose the company anticipates all rights will be exercised but in fact they are not. If the ex-rights price actually turns out to be $37.90 what proportion of rights were actually exercised?

(c) Suppose the company anticipates that 8 percent of the rights will not be exercised. What number of rights should the firm require for the purchase of one share at an issue price of $30 per share if they want the issue to succeed in raising $45 million? What is the ex-rights price if in fact it turns out 14 percent of the rights are not exercised?