Chapter 15: Capital Structure:
Basic Concepts
15.1
a.
Since Alpha Corporation is an allequity 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.
ModiglianiMiller 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.
ModiglianiMiller 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).
f.
The initial cost of purchasing 20% of Alpha Corporation’s equity is $20,000, but the cost to an
investor of purchasing 20% of Beta Corporation’s equity is only $15,000 (see part
d
).
In order to purchase $20,000 worth of Alpha’s equity using only $15,000 of his own money, the
investor must borrow $5,000 to cover the difference.
The investor must pay 12% interest on his
borrowings at the end of the year.
B1
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Since the investor now owns 20% of Alpha’s equity, the dollar return on his equity investment at the
end of the year is $70,000 ( = 0.20 * $350,000).
However, since he borrowed $5,000 at 12% per
annum, he must pay $600 (= 0.12 * $5,000) at the end of the year.
Therefore, the cash flow to the investor at the end of the year is $69,400 (= $70,000  $600).
Notice that this amount exactly matches the dollar return to an investor who purchases 20% of
Beta’s equity.
Strategy Summary:
1.
Borrow $5,000 at 12%.
2.
Purchase 20% of Alpha’s stock for a net cost of $15,000 (= $20,000  $5,000 borrowed).
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 Spring '08
 Lim
 Market Value, Firm, Weighted average cost of capital

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