FM11 Ch 17 Capital Structure Decisions_Extensions

17 - 1
CHAPTER 17
Capital Structure Decisions:
Extensions

MM and Miller models

Hamada’s equation

Financial distress and agency costs

Trade-off models

Asymmetric information theory
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Who are Modigliani and Miller (MM)?

They published theoretical papers
that changed the way people thought
about financial leverage.

They won Nobel prizes in economics
because of their work.

MM’s papers were published in 1958
and 1963. Miller had a separate
paper in 1977. The papers differed in
their assumptions about taxes.
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What assumptions underlie the MM
and Miller models?


Firms can be grouped into
homogeneous classes based on
business risk.

Investors have identical
expectations about firms’ future
earnings.

There are no transactions costs.
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
All debt is riskless, and both
individuals and corporations can
borrow unlimited amounts of money
at the risk-free rate.

All cash flows are perpetuities. This
implies perpetual debt is issued,
firms have zero growth, and
expected EBIT is constant over time.
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
MM’s first paper (1958) assumed
zero taxes. Later papers added
taxes.

No agency or financial distress

costs.

These assumptions were necessary
for MM to prove their propositions
on the basis of investor arbitrage.
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Proposition I:
V
L
= V
U
.
Proposition II:
r
sL
= r
sU
+ (r
sU
- r
d
)(D/S).
MM with Zero Taxes (1958)
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Firms U and L are in same risk class.
EBIT
U,L
= $500,000.
Firm U has no debt; r
sU

= 14%.
Firm L has $1,000,000 debt at r
d
= 8%.
The basic MM assumptions hold.
There are no corporate or personal taxes.
Given the following data, find V, S,
r
s
, and WACC for Firms U and L.
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1. Find V
U
and V
L
.
V
U
= = = $3,571,429.
V
L
= V
U
= $3,571,429.
EBIT
r
sU
$500,000
0.14
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V
L
= D + S = $3,571,429
$3,571,429 = $1,000,000 + S
S = $2,571,429.
2. Find the market value of
Firm L’s debt and equity.
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3. Find r
sL
.
r
sL
= r
sU
+ (r
sU
- r
d
)(D/S)
= 14.0% + (14.0% - 8.0%)( )
= 14.0% + 2.33% = 16.33%.
$1,000,000
$2,571,429
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4. Proposition I implies WACC = r
sU
.
Verify for L using WACC formula.
WACC = w

d
r
d
+ w
ce
r
s
= (D/V)r
d
+ (S/V)r
s
= ( )(8.0%)
+( )(16.33%)
= 2.24% + 11.76% = 14.00%.
$1,000,000
$3,571,429
$2,571,429
$3,571,429
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Graph the MM relationships between
capital costs and leverage as measured
by D/V.
Without taxes
Cost of
Capital (%)
26
20
14
8
0 20 40 60 80 100

Debt/Value
Ratio (%)
r
s
WACC
r
d
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
The more debt the firm adds to its
capital structure, the riskier the
equity becomes and thus the higher
its cost.

Although r
d
remains constant, r
s

increases with leverage. The
increase in r
s
is exactly sufficient to
keep the WACC constant.
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Graph value versus leverage.
Value of Firm, V (%)
4
3
2

1
0 0.5 1.0 1.5 2.0 2.5
Debt (millions of $)
V
L
V
U
Firm value ($3.6 million)
With zero taxes, MM argue that value
is unaffected by leverage.
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Find V, S, r
s
, and WACC for Firms U and
L assuming a 40% corporate
tax rate.
With corporate taxes added, the MM
propositions become:
Proposition I:
V
L
= V
U
+ TD.
Proposition II:
r
sL
= r
sU
+ (r

sU
- r
d
)(1 - T)(D/S).
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Notes About the New Propositions
1. When corporate taxes are added,
V
L
≠ V
U
. V
L
increases as debt is
added to the capital structure, and
the greater the debt usage, the
higher the value of the firm.
2. r
sL
increases with leverage at a
slower rate when corporate taxes
are considered.
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1. Find V
U
and V
L
.
Note: Represents a 40% decline from the no
taxes situation.

V
L
= V
U
+ TD = $2,142,857 + 0.4($1,000,000)
= $2,142,857 + $400,000
= $2,542,857.
V
U
= = = $2,142,857.
EBIT(1 - T)
r
sU
$500,000(0.6)
0.14
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V
L
= D + S = $2,542,857
$2,542,857 = $1,000,000 + S
S = $1,542,857.
2. Find market value of Firm
L’s debt and equity.
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3. Find r
sL
.
r
sL
= r

sU
+ (r
sU
- r
d
)(1 - T)(D/S)
= 14.0% + (14.0% - 8.0%)(0.6)( )
= 14.0% + 2.33% = 16.33%.
$1,000,000
$1,542,857
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4. Find Firm L’s WACC.
WACC
L
= (D/V)r
d
(1 - T) + (S/V)r
s
= ( )(8.0%)(0.6)
+( )(16.33%)
= 1.89% + 9.91% = 11.80%.
When corporate taxes are considered, the
WACC is lower for L than for U.
$1,000,000
$2,542,857
$1,542,857
$2,542,857
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Cost of
Capital (%)

26
20
14
8
0 20 40 60 80 100
Debt/Value
Ratio (%)
MM relationship between capital costs
and leverage when corporate taxes are
considered.
r
s
WACC
r
d
(1 - T)
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Value of Firm, V (%)
4
3
2
1
0 0.5 1.0 1.5 2.0 2.5
Debt
(Millions of $)
V
L
V
U
MM relationship between value and debt

when corporate taxes are considered.
Under MM with corporate taxes, the firm’s value
increases continuously as more and more debt is used.
TD
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Assume investors have the following
tax rates: T
d
= 30% and T
s
= 12%. What
is the gain from leverage according to
the Miller model?
Miller’s Proposition I:
V
L
= V
U
+ [1 - ]D.
T
c
= corporate tax rate.
T
d
= personal tax rate on debt income.
T
s
= personal tax rate on stock income.
(1 - T
c

)(1 - T
s
)
(1 - T
d
)
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T
c
= 40%, T
d
= 30%, and T
s
= 12%.
V
L
= V
U
+ [1 - ]D
= V
U
+ (1 - 0.75)D
= V
U
+ 0.25D.
Value rises with debt; each $100 increase
in debt raises L’s value by $25.
(1 - 0.40)(1 - 0.12)
(1 - 0.30)
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How does this gain compare to the gain
in the MM model with corporate taxes?
If only corporate taxes, then
V
L
= V
U
+ T
c
D = V
U
+ 0.40D.
Here $100 of debt raises value by
$40. Thus, personal taxes lowers the
gain from leverage, but the net effect
depends on tax rates.
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