Question

The Liberty Corporation has 120,000 shares outstanding with a current market price of $8.10 per share. The company needs to raise an additional $36,000 to finance new expenditures, and has decided on a rights issue. The issue will allow current stockholders to purchase one additional share for 20 rights at a subscription price of $6 per share. Suppose that the company was also considering structuring the rights issue to allow for an additional share to be purchased for 10 rights at a subscription price of $3. Prove that a stockholder with 100 shares would be indifferent between purchasing a new share for 10 rights at $3 or purchasing a new share for 20 rights at $6.

Answer 1

It is assumed that 1 share = 1 right

Structure 1 : one additional share for 20 rights at a subscription price of $6 per share

For a shareholder with 100 shares, the number of shares that can be purchased  = number of shares / number of rights required to purchase one share

number of shares that can be purchased  = 100 / 20 = 5

Total purchase amount = number of shares that can be purchased * subscription price per share

Total purchase amount = 5 * $6 = $30

The Total purchase amount is same in both structures - $30

Hence the shareholder will be indifferent between the two strutures

Structure 2 : one additional share for 10 rights at a subscription price of $6 per share

For a shareholder with 100 shares, the number of shares that can be purchased  = number of shares / number of rights required to purchase one share

number of shares that can be purchased  = 100 / 10 = 10

Total purchase amount = number of shares that can be purchased * subscription price per share

Total purchase amount = 10 * $3 = $30