Practice Problems – Chapter 16
1)
Assume perfect capital markets. An
all-equity firm has $6,000 in cash and assets worth $28,000. The firm has 1,200 shares outstanding, and no investment
opportunities.
a)
If the firm pays no dividend today, what is the stock price and the wealth of
stockholders?
b)
If the firm pays a dividend of $6,000 today,
i) what is the stock price before the dividend?
ii) what is the stock price after the dividend?
iii) what is the wealth of stockholders after the dividend?
c)
If the firm pays a dividend of $9,000 today,
i) what is the stock price before the dividend?
ii) what is the stock price after the dividend?
iii) how many new shares must be issued?
iv) how does the dividend affect stockholder wealth?
2)
Online Dating Services Inc. is an all-equity firm with the following
assets and investment opportunity:
Cash
$ 1,200
Other Assets
$22,000
Project with an investment of
$ 3,500
and an NPV of
$ 1,000
The
firm has decided to pay a dividend of $1 per share on its 4000 existing shares.
Any new capital required will be raised by issuing new shares.
Assume that all three actions occur simultaneously -- dividend payment,
issue of new shares and investing in the project. Assuming perfect capital
markets,
a)
What is the wealth of stockholders before and after these actions?
b)
How many new shares are issued?
3)
Assume perfect capital markets. R
and D are all-equity firms identical in all respects, except that D makes cash
payouts to stockholders through dividends, and R through stock repurchases.
Both firms have 1,000 shares outstanding, and the following assets and
investment opportunities:
Cash
$1,500
Other Assets
$7,750
Project A with Investment of
$1,000
and an NPV of
$ 425
Project B with Investment of
$ 800
and an NPV of
$ 325
a)
Firm D pays a dividend of $2 per share and invests in both projects, by
issuing new shares. Assume that all
these actions occur simultaneously. Compute
the following (where cum-dividend means before these actions and ex-dividend
means after these actions):
cum-dividend stock price and value of equity
ex-dividend stock price and value of equity
number of new shares issued
cum-dividend
and ex-dividend wealth of the original stockholders
the fraction of the shares the original stockholders own at the end
b)
Firm R repurchase shares worth $2,000 at the current market
price and invests in both projects, by issuing new shares.
Assume that all these actions occur simultaneously.
Compute the following (where initial means before these actions and final
means after these actions):
initial and final stock price
number of shares repurchased and number of new shares issued
initial
and final value of equity
change
in wealth of the original stockholders
the fraction of the shares the original stockholders own at the end
Which
of these numbers will change if the amount of the repurchase is increased?
4)
C. L. Computer Corp. is an all-equity firm which is fortunate enough to
operate in perfect capital markets. The firm
has 10,000 shares outstanding, and the following assets and investment
opportunities:
Cash
$ 8,000
Other Assets
$240,000
A project with Investment of
$ 5,000
and an NPV of
$ 900
a)
Suppose the firm pays a dividend of 75 cents per share, and invests in the
project, by issuing new shares. Assume
that all these actions occur simultaneously.
Compute the following (where cum-dividend means before these actions and
ex-dividend means after these actions):
cum-dividend stock price and value of equity
ex-dividend stock price and value of equity
number of new shares issued
cum-dividend and ex-dividend wealth of the original stockholders
the fraction of the shares the original stockholders own at the end
Which
of these numbers will change if the amount of the dividend is increased?
b)
Suppose that instead of paying a dividend, the firm uses the $8,000 cash to
repurchase shares at the current market price, and it invests in the project by
issuing new shares. Assume that all
these actions occur simultaneously. Compute
the following (where initial means before these actions and final means after
these actions):
initial and final stock price
number of shares repurchased and number of new shares issued
initial and final value of equity
change in wealth of the original stockholders
the fraction of the shares the original stockholders own at the end
5)
Mark the following statements with a T or an F to indicate
whether they are true or false (no explanations required or considered):
a)
It is not possible to make a pure dividend policy change; when you try to
change the dividend keeping the investment decision constant, the firm’s
capital structure necessarily changes.
b)
When a firm increases its dividend, stockholders are receiving a higher
return; hence the firm’s cost of equity increases.
c)
The reluctance of managers to cut dividends leads to a situation where
dividends reflect nor just current earnings but expected future earnings as
well; the market then punishes you for cutting dividends by reducing your stock
price.
d)
Dividends are typically increased when earnings go up and managers are
confident that earnings will remain at this higher level.
e)
An earnings announcement tells the market whether earnings went up or
down; the accompanying dividend announcement clarifies whether the earnings
change is temporary or permanent.
f)
In perfect capital markets, when a firm pays a dividend, the stock price
falls by exactly the amount of the dividend.
g)
If a firm is paying out $2 million to its stockholders, the stock price
will fall by the same amount whether the $2 million is paid out through a
dividend or a stock repurchase.
h)
In PCM, stockholders who do not need cash from their portfolios may not
care whether a firm pays dividends or not, but stockholders who need cash from
their portfolio for living expenses prefer dividend paying firms.
i)
Corporations do not pay taxes on their dividend income, so they are
indifferent between dividend income and capital gains income.
j)
In perfect capital markets, stockholders are indifferent between buying
shares in the unlevered firm or borrowing
money to buy shares in an otherwise identical levered firm.