H
AAS
S
CHOOL
OF
B
USINESS
U
NIVERSITY
OF
C
ALIFORNIA
AT
B
ERKELEY
UGBA 103
© A
VINASH
V
ERMA
M
ODIGLIANI
M
ILLER
P
ROPOSITIONS
II:
C
APITAL
B
UDGETING
FOR
THE
L
EVERED
F
IRM
This teaching note assumes familiarity with the material in the text dealing with the
debt policy [Chapters 1719]. In keeping with the text, we shall be denoting cost of
capital by
r
.
1.
While
ModiglianiMiller Proposition I
[MM I] deals with the
relationship between the value of the unlevered and that of the levered
firm,
ModiglianiMiller Proposition II
[MM II] deals with the
relationship among the cost of equity capital, cost of debt capital, and
cost of capital for the firm as a whole, which is related to the expected
return on the assets. As with MM I, there is a taxcorrected version of
MM II.
2.
We saw in the previous note that, according to MM I, under “ideal”
circumstances:
V
V
U
L
=
.
[1]
where
U
V
denotes value of the assets of an unlevered firm, and
L
V
denotes the value of the assets of an otherwise identical levered firm.
By balance sheet identity:
E
D
V
L
+
=
.
[2]
where
D
denotes value of the debt, and
E
value of the equity, of the
levered firm.
1
Now, on the basis of what we learnt in the lecture note
called “CAPM and Capital Budgeting” (or Chapter 9 of the text), we
can estimate the cost of capital for the unlevered firm. When the levered
firm issues debt, the cost of debt capital will be determined by the
market. We want to determine the cost of equity capital for the levered
firm in terms of these two known quantities, the cost of capital for the
unlevered firm, and the cost of debt capital. In order to do that we need
U
V
,
E
and
D
in the same equation. We can get these three in the same
equation by putting equations
[1]
and
[2]
together:
E
D
V
U
+
=
, or
D
V
E
U

=
This enables us to conclude that the equity of the levered firm [Firm
L
]
can be thought of as a portfolio of
V
U
and
D
with a fraction
[
]
E
V
U
invested in the assets of the unlevered firm, and a fraction
[
]
E
D

in
the debt of the levered firm. Therefore, the cost of equity capital, which
is the
expected
(or
required
) return on the equity, will be a weighted
average of the expected returns on the components of the portfolio. Or,
algebraically:
1
Since the levered firm is the only firm here with debt, we need not continue to
distinguish the debt and equity of the levered firm by subscript
L
.
ModiglianiMiller Propositions II
1
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H
AAS
S
CHOOL
OF
B
USINESS
U
NIVERSITY
OF
C
ALIFORNIA
AT
B
ERKELEY
UGBA 103
© A
VINASH
V
ERMA
D
UA
U
E
r
E
D
r
E
V
r
*
*

=
[3]
where
E
r
and
D
r
denote the
expected
return on the equity and on the
debt of the levered firm, and
UA
r
denotes the expected return on the
assets
2
of the unlevered firm.
Substituting
E
D
V
U
+
=
in the numerator of the first term on the right,
and gathering coefficients of the debtequity ratio,
[
]
E
D
, we get:
(
29
D
UA
UA
E
r
r
E
D
r
r

+
=
*
.
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 Spring '08
 MCCULLOUGH
 Net Present Value, Firm, Weighted average cost of capital, ModiglianiMiller propositions, HAAS SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA

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