Chapter 16: Capital Structure:
Basic Concepts
16.1
a.
Since Alpha Corporation is an all-equity firm, its value is equal to the market value of its
outstanding
shares.
Alpha has 5,000 shares of common stock outstanding, worth $20 per share.
Therefore, the value of Alpha Corporation is $100,000 (= 5,000 shares * $20 per
share).
b.
Modigliani-Miller Proposition I states that in the absence of taxes, the value of a levered
firm equals the value of an otherwise identical unlevered firm.
Since Beta Corporation is
identical to Alpha Corporation in every way except its capital structure and neither firm
pays taxes, the value of the two firms should be equal.
Modigliani-Miller Proposition I (No Taxes):
V
L
=V
U
Alpha Corporation, an unlevered firm, is worth $100,000 = V
U
.
Therefore, the value of Beta Corporation (V
L
) is $100,000.
c.
The value of a levered firm equals the market value of its debt plus the market value of its
equity.
V
L
= B + S
The value of Beta Corporation is $100,000 (V
L
), and the market value of the firm’s debt is
$25,000 (B).
The value of Beta’s equity is: S
= V
L
– B
= $100,000 - $25,000
=
$75,000
Therefore, the market value of Beta Corporation’s equity (S) is $75,000.
d.
Since the market value of Alpha Corporation’s equity is $100,000, it will cost
$20,000
(=
0.20 * $100,000) to purchase 20% of the firm’s equity.
Since the market value of Beta Corporation’s equity is $75,000, it will cost
$15,000
(= 0.20
* $75,000) to purchase 20% of the firm’s equity.
e.
Since Alpha Corporation expects to earn $350,000 this year and owes no interest payments,
the dollar return to an investor who owns 20% of the firm’s equity is expected to be
$70,000
(= 0.20 * $350,000) over the next year.
While Beta Corporation also expects to earn $350,000 before interest this year, it must pay
12% interest on its debt.
Since the market value of Beta’s debt at the beginning of the year
is $25,000, Beta must pay $3,000 (= 0.12 * $25,000) in interest at the end of the year.
Therefore, the amount of the firm’s earnings available to equity holders is $347,000 (=
$350,000 - $3,000). The dollar return to an investor who owns 20% of the firm’s equity is
$69,400
(= 0.20 * $347,000).
Answers to End-of-Chapter Problems
B-214