Little Oil has 1 million outstanding shares 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 percent a year in
perpetuity. Thus the expected dividend in year 2 is $1.05 million, 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 by a
simultaneous issue of new shares. After that, the total amount paid out each
year will be as previously forecasted, i.e., $1.05 million in year 2 and
increasing by 5 percent a year in each subsequent year. Capital markets are
perfect. The discount rate for equity for this company is 10%.
a) At what price will the new shares be issued in year 1?
b) How many shares will the firm need to issue?
c) What will be the expected payments on these new shares, and what
therefore will be paid out to the old shareholders after year 1?
d) Show that the present value of the cash flows to current shareholders
remains $20 million.
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