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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.
(More...)
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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.
(More...)
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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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MM with Zero Taxes (1958)
Proposition I:
VL = VU.
Proposition II:
ksL = ksU + (ksU - kd)(D/S).
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Given the following data, find V, S,
ks, and WACC for Firms U and L.
Firms U and L are in same risk class.
EBITU,L = $500,000.
Firm U has no debt; ksU = 14%.
Firm L has $1,000,000 debt at kd = 8%.
The basic MM assumptions hold.
There are no corporate or personal taxes.
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1. Find VU and VL.
EBIT
$500,000
VU =
=
= $3,571,429.
ksU
0.14
VL = VU = $3,571,429.
Questions: What is the derivation of
the VU equation? Are the MM
assumptions required?
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2. Find the market value of
Firm L’s debt and equity.
VL = D + S = $3,571,429
$3,571,429 = $1,000,000 + S
S = $2,571,429.
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3. Find ksL.
ksL = ksU + (ksU - kd)(D/S)
(
)
$1,000,000
= 14.0% + (14.0% - 8.0%) $2,571,429
= 14.0% + 2.33% = 16.33%.
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4. Proposition I implies WACC = ksU.
Verify for L using WACC formula.
WACC = wdkd + wceks = (D/V)kd + (S/V)ks
$1,000,000
= $3,571,429 (8.0%)
(
)
$2,571,429
+($3,571,429)(16.33%)
= 2.24% + 11.76% = 14.00%.
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Graph the MM relationships between
capital costs and leverage as measured
by D/V.
Without taxes
Cost of
Capital (%)
26
ks
20
WACC
14
kd
8
0
20
40
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60
80
Debt/Value
100 Ratio (%)
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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 kd remains constant, ks
increases with leverage. The
increase in ks is exactly sufficient to
keep the WACC constant.
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Graph value versus leverage.
Value of Firm, V (%)
VU
4
VL
3
Firm value ($3.6 million)
2
1
0
0.5
1.0
1.5
2.0 2.5
Debt (millions of $)
With zero taxes, MM argue that value
is unaffected by leverage.
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Find V, S, ks, and WACC for Firms U and
L assuming a 40% corporate
tax rate.
With corporate taxes added, the MM
propositions become:
Proposition I:
VL = VU + TD.
Proposition II:
ksL = ksU + (ksU - kd)(1 - T)(D/S).
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Notes About the New Propositions
1. When corporate taxes are added,
VL  VU. VL increases as debt is
added to the capital structure, and
the greater the debt usage, the
higher the value of the firm.
2. ksL increases with leverage at a
slower rate when corporate taxes
are considered.
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1. Find VU and VL.
EBIT(1
T)
$500,000(0.6)
VU =
=
= $2,142,857.
ksU
0.14
Note: Represents a 40% decline from the no
taxes situation.
VL = VU + TD = $2,142,857 + 0.4($1,000,000)
= $2,142,857 + $400,000
= $2,542,857.
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2. Find market value of Firm
L’s debt and equity.
VL = D + S = $2,542,857
$2,542,857 = $1,000,000 + S
S = $1,542,857.
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3. Find ksL.
ksL = ksU + (ksU - kd)(1 - T)(D/S)
(
)
$1,000,000
= 14.0% + (14.0% - 8.0%)(0.6) $1,542,857
= 14.0% + 2.33% = 16.33%.
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4. Find Firm L’s WACC.
WACCL = (D/V)kd(1 - T) + (S/V)ks
$1,000,000
= $2,542,857 (8.0%)(0.6)
$1,542,857
+ $2,542,857 (16.33%)
(
(
)
)
= 1.89% + 9.91% = 11.80%.
When corporate taxes are considered, the
WACC is lower for L than for U.
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MM relationship between capital costs
and leverage when corporate taxes are
considered.
Cost of
Capital (%)
ks
26
20
14
8
0
20
40
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60
80
WACC
kd(1 - T)
Debt/Value
100
Ratio (%)
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MM relationship between value and debt
when corporate taxes are considered.
Value of Firm, V (%)
4
VL
3
TD
VU
2
1
Debt
0
0.5
1.0
1.5
2.0
2.5 (Millions of $)
Under MM with corporate taxes, the firm’s value
increases continuously as more and more debt is used.
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Assume investors have the following
tax rates: Td = 30% and Ts = 12%. What
is the gain from leverage according to
the Miller model?
Miller’s Proposition I:
(1 - Tc)(1 - Ts)
VL = VU + 1 (1 - Td)
[
]D.
Tc = corporate tax rate.
Td = personal tax rate on debt income.
Ts = personal tax rate on stock income.
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Tc = 40%, Td = 30%, and Ts = 12%.
[
]
(1 - 0.40)(1 - 0.12)
VL = VU + 1 D
(1 - 0.30)
= VU + (1 - 0.75)D
= VU + 0.25D.
Value rises with debt; each $100 increase
in debt raises L’s value by $25.
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How does this gain compare to the gain
in the MM model with corporate taxes?
If only corporate taxes, then
VL = VU + TcD = VU + 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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If Ts declines, while Tc and Td remain
constant, the slope coefficient (which
shows the benefit of debt) is
decreased.
A company with a low payout ratio
gets lower benefits under the Miller
model than a company with a high
payout, because a low payout
decreases Ts.
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When Miller brought in personal
taxes, the value enhancement of debt
was lowered. Why?
1. Corporate tax laws favor debt over
equity financing because interest
expense is tax deductible while
dividends are not.
(More...)
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2. However, personal tax laws favor
equity over debt because stocks
provide both tax deferral and a lower
capital gains tax rate.
3. This lowers the relative cost of
equity vis-a-vis MM’s no-personaltax world and decreases the spread
between debt and equity costs.
4. Thus, some of the advantage of debt
financing is lost, so debt financing is
less valuable to firms.
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What does capital structure theory
prescribe for corporate managers?
1. MM, No Taxes: Capital structure is
irrelevant--no impact on value or WACC.
2. MM, Corporate Taxes: Value increases,
so firms should use (almost) 100% debt
financing.
3. Miller, Personal Taxes: Value increases,
but less than under MM, so again firms
should use (almost) 100% debt financing.
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Do firms follow the recommendations
of capital structure theory?
Firms don’t follow MM/Miller to 100%
debt. Debt ratios average about 40%.
However, debt ratios did increase
after MM. Many think debt ratios
were too low, and MM led to changes
in financial policies.
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Define financial distress and
agency costs.
Financial distress: As firms use
more and more debt financing, they
face a higher probability of future
financial distress, which brings with
it lower sales, EBIT, and bankruptcy
costs. Lowers value of stock and
bonds.
(More...)
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Agency costs: The costs of
managers not behaving in the best
interests of shareholders and the
resulting costs of monitoring
managers’ actions. Lowers value of
stock and bonds.
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How do financial distress and agency
costs change the MM and Miller
models?
MM/Miller ignored these costs, hence
those models show firm value
increasing continuously with leverage.
Since financial distress and agency
costs increase with leverage, such
costs reduce the value of debt
financing.
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Here’s a valuation model which
includes financial distress and
agency costs:
PV of agency
PV of expected
VL = VU + XD .
costs
fin. distress costs
X represents either Tc in the MM model
or the more complex Miller term.
Now, optimal leverage involves a
tradeoff between the tax benefits of
debt and the costs associated with
financial distress and agency.
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Relationships between capital costs
and leverage when financial distress
and agency costs are considered.
Cost of Capital (%)
ks
WACC
14
kd(1 - T)
4
D*
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Debt ($)
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Relationship between value and
leverage.
Note that value is
maximized and WACC is
minimized at the same
capital structure.
Value of Firm ($)
4
3
2
1
D*
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Debt ($)
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How are financial and business risk
measured in a market risk framework?
ksL = kRF + (kM - kRF)bU
+ (kM - kRF)bU(1 - T)(D/S)
Pure Business Financial
= time + risk
+ risk
.
value premium premium
(Hamada’s equation)
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Hamada’s equation for beta:
bL
=
bU
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+ bU(1 - T)(D/S)
Unlevered
Increased
beta, which
volatility of
= reflects the + the returns
business
to equity
risk of the due to the use
firm
of debt
=
Business
+
risk
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Financial
.
risk
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What is the “pecking order theory”
of capital structure?
Results of a survey by Donaldson and
the asymmetric information theory.
Firms follow a specific financing order:
First use internal funds.
Next, draw on marketable securities.
Then, issue new debt.
Finally, and only as a last resort, issue new
common stock.
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Does the pecking order theory make
sense? Explain.
Is the pecking order theory consistent
with the trade-off theory?
It is consistent with the asymmetric
information theory, in which
managers avoid issuing equity.
It is not consistent with trade-off
theory.
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What is the asymmetric information
theory of capital structure?
Theory recognizes that market
participants do not have
homogeneous expectations-managers typically have better
information than investors.
Thus, financing actions are
interpreted by investors as
signals of managerial
expectations for the future. (More...)
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Managers will issue new common
stock only when no other
alternatives exist or when the stock
is overvalued.
Investors recognize this, so new
stock sales are treated as negative
signals and stock price falls.
Managers do not want to trigger a
price decline, so firms maintain a
reserve borrowing capacity.
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