Question

At time 0, a firm is valued at $1,000 and has no debt. Its equity consists of 100 common shares worth $10 each. The expected rate of return for the firm is 5% in time 1 and 6% in time 2.

At time 1, the firm decides to issue dividends of $2 per share to existing shareholders, by issuing new shares.

How many new shares does it have to issue? What is the issuing price of the new shares?

Answer 1

The share price of the firm at time 1 will be $10.5 and at this price, if the firm issues 19 more shares it will have $200. This raised amount will be sufficient for the dividend payment to all the 100 shareholders. However, the number of shareholders will increase after the share issue. Moreover, it is assumed that the new shareholders will not be entitled to receive the dividends, as only those individuals are entitled to receive the dividend who were the shareholders at the time of announcement.

Company Information Total Amount required for the dividend payment Value of the Compnay Current Share Price Number of outstanding Shares Time 0 $1,000.00 $10.00 100 Before Dividens Value of the firm Share Price Number of Shares $1,050.00 $10.50 100 Time 1 $200.00 After Dividends Amount required for the dividends Dividend Per Share Number of new shares issued to raise the $200 Issuing Price 19 $10.50

x ✓ fx Company Information Total Amount required for the dividend payment Value of the Compnay Current Share Price Number of outstanding Shares 1000 Time 0 10 100 Before Dividens Value of the firm Share Price Number of Shares =D7*(1+0.05) =D12/D14 14 Time 1 100 =D19*D14 After Dividends Amount required for the dividends Dividend Per Share Number of new shares issued to raise the $200 Issuing Price =D18/D13 =D13