If P
1
is the price per share at t = 1, then:
V
1
= P
1
×
(1,000,000 + N) = $21,000,000
and:
P
1
×
N = $1,000,000
From the first equation:
(1,000,000
×
P
1
) + (N
×
P
1
) = 21,000,000
Substituting from the second equation:
(1,000,000
×
P
1
) + 1,000,000 = 21,000,000
so that P
1
= $20.00
b.
With P
1
equal to $20, and $1,000,000 to raise, the firm will sell 50,000 new
shares.
c.
The expected dividends paid at t = 2 are $1,050,000, increasing by 5% in
each subsequent year.
With 1,050,000 shares outstanding, dividends per
share are: $1 at t = 2, increasing by 5% in each subsequent year.
Thus,
total dividends paid to old shareholders are: $1,000,000 at t = 2,
increasing by 5% in each subsequent year.
d.
For the current shareholders:
5.
From Question 4, the fair issue price is $20 per share.
If these shares are
instead issued at $10 per share, then the new shareholders are getting a
bargain, i.e., the new shareholders win and the old shareholders lose.
As pointed out in the text, any increase in cash dividend must be offset by a
stock issue if the firm’s investment and borrowing policies are to be held
constant.
If this stock issue cannot be made at a fair price, then shareholders
are clearly not indifferent to dividend policy.