04/22/2011
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Worksheet for Chapter 15 BOC Questions.
Capital Structure Decisions:
Part 2.
3/17/03
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.
Input Data
Firm U
Firm L
No Debt
Some Debt
EBIT
$500,000
$500,000
Debt
$0
$3,000,000
NA
6.0%
8%
8%
Tax rate
0%
0%
Value
of Stock
$6,250,000
$4,000,000
Total Market
Value of Firm
$6,250,000
$7,000,000
Value of Firm = Value of Stock + Value of Debt
Buy
Borrow amt.
Invest extra
Portfolio of U,
Old
10% of
equal to 10%
$75,000 in risk
Debt, and risk
Investment,
U's Stock
of L's Debt
free asset @ 6%
free asset
10% of L
Cost
$625,000
($300,000)
$75,000
$400,000
$400,000
Income
$50,000
($18,000)
$4,500
$36,500
$32,000
The cost of equity, r
sL
, is found as follows: rsL=
r
sU
+ Risk premium = r
sU
+ (r
sU
-r
d
)(D/S)
Supposethe costs of equity for Firms U and L are as follows: r
sL
= r
sU
= 8%.
k
d
k
s
Value of Stock = (EBIT - r
d
D)/r
S
Now compare an investment in L with a derivative investment which duplicates L's leverage by borrowing and buying U's
stock.
Assume that the investor owns 10% of L's Stock which is sold for $400,000 .
Notice that for the same $400,000 investment, you can get $4,500
more in annual income from a portfolio of U and "homemade
debt" than from an investment in L.
MM argue that this can't
persist--that investors will sell L and buy U to form the portfolio,
driving the price of L down and U up, until the arbitrage
opportunity vanishes.
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