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1/1/2007
Chapter 17.
Tool Kit for Capital Structure Decisions:
Extensions
Modigliani and Miller without Taxes
Proposition I.
1.
The weighted average cost of capital is independent of the firm's capital structure.
2.
The WACC of a firm with debt is equal to the unlevered cost of equity.
Proposition II.
Example of an arbitrage opportunity in zerogrowth firms:
Input Data
Firm U
Firm L
No Debt
Some Debt
EBIT
$900,000
$900,000
Debt
$0
$4,000,000
NA
7.5%
10%
10%
Value
of Stock
$9,000,000
$6,000,000
Total Market
Value of Firm
$9,000,000
$10,000,000
Value of Firm = Value of Stock + Value of Debt
Borrow amt.
Invest $100,000
Portfolio of U,
Buy
equal to 10%
in risk free
Debt, and risk
Buy
10% of U
of L's Debt
asset
free asset
10% of L
Cost
$900,000
($400,000)
$100,000
$600,000
$600,000
Income
$90,000
($30,000)
$7,500
$67,500
$60,000
CAPITAL STRUCTURE THEORY: ARBITRAGE PROOFS OF THE MODIGLIANIMILLER MODELS
(Section 17.1)
Franco Modigliani and Merton Miller developed a model to examine the impact of debt on firm value.
In this
first version it is assumed that taxes are zero.
The cost of equity, r
sL
= r
sU
+ Risk premium = r
sU
+ (r
sU
r
d
)(D/S)
Suppose that r
sL
= r
sU
= 10%.
We will show that this leads to an arbitrage opportunity.
rd
rs
Value of Stock = (EBIT  r
d
D)/r
S
Compare an investment in L with a "synthetic" investment that duplicates L's leverage using an investment in
U and borrowing on the investor's own account.
Notice that for the same $600,000 investment, you can get $7,500
more in annual income by forming your own portfolio of U and
"home made debt" than you get from an investment in L.
MM
argue that this won't persistthat investors would buy U and
purchase the portfolio, driving up the price of U.
At the same time,
they would sell their shares of L, driving down its price.
A
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 Spring '10
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