Chapter 16, Problem 17PS

Repurchases and the DCF model Little Oil has 1 million shares outstanding with a total market value of $20 million. The firm is expected to pay $1 million of dividends next year, and thereafter the amount paid out is expected to grow by 5% a year in perpetuity. Thus, the expected dividend is $1.05 million in year 2, $1.1025 million in year 3, and so on. However, the company has heard that the value of a share depends on the flow of dividends, and therefore, it announces that next year’s dividend will be increased to $2 million and that the extra cash will be raised immediately afterward by an issue of shares. After that, the total amount paid out each year will be as previously forecasted—that is, $1.05 million in year 2 and increasing by 5% in each subsequent year.

1. a. At what price will the new shares be issued in year 1?
2. b. How many shares will the firm need to issue?
3. c. What will be the expected dividend payments on these new shares, and what therefore will be paid out to the old shareholders after year 1?
4. d. Show that the present value of the cash flows to current shareholders remains $20 million.