10.1 Leverage
Financial Leverage
Financial leverage is the use of fixed financial costs to magnify
the effect of changes in EBIT on EPS.
Fixed financial costs can be, for instance, interest payments and
dividends on preferred shares.
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10.1 Leverage
Financial Leverage
Let T denote the tax rate, letI denote interest expense and letNS
denote the number of shares outstanding.
Then earnings per share (EPS) are given by
EPS =(1−T)(EBIT− I)
NS.
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10.1 Leverage
Financial Leverage
At a given EBIT level, how do percentage changes in EBITtranslate into percentage changes in EPS?
∆EPSEPS
=
(1−T)(EBIT′−I)NS −
((1−T)(EBIT−I)
NS
)(1−T)(EBIT−I)
NS
=(1−T)(EBIT′−EBIT)
(1−T)(EBIT− I)
=(1−T)EBIT× EBIT′−EBIT
EBIT
(1−T)(EBIT− I)
=EBIT
EBIT− I× ∆EBIT
EBIT
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10.1 Leverage
Financial Leverage
That is, when EBIT increases by 1%, the percentage increase in
EPS isEBIT
EBIT− I=
EBITEBIT− I
.
This thedegree of financial leverage (DFL) at base level EBIT.
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10.2 The Firm’s Capital Structure
Types of Capital
Assets Debt & Equity
NWC
Fixed Assets
Long-TermDebt (D)
Equity (E)
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10.2 The Firm’s Capital Structure
Capital Structure Theory
Modigliani and Miller’s propositions:
Proposition I: The market value of a firm is constant regardless
of the amount of leverage that it uses to finance its assets.
Proposition II: The expected return on a firm’s equity is an
increasing function of the firm’s leverage.
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10.2 The Firm’s Capital Structure
Capital Structure Theory: M&M Proposition I
The value of a firm is given by the present value of all the cash
flows its assets are expected to generate in the future.
The value of a firm is equal to the value of its assets.
Unlevered Firm: VU = EU
Levered Firm: VL = D + EL.
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10.2 The Firm’s Capital Structure
Capital Structure Theory: M&M Proposition I
M&M Proposition I states that
VU = VL.
Why? Consider an all-equity firm with valueVU = EU .
Suppose there existed a way to finance this firm’s assets with
debt and equity such that
VL = D + EL > VU .
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10.2 The Firm’s Capital Structure
Capital Structure Theory: M&M Proposition I
An arbitrageur could buyα shares of the above firm, place them
in a trust and sell debt and equity claims against these shares in
proportions such that
α(D+EL) > αEU ,
making then a riskless profit.
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10.2 The Firm’s Capital Structure
Capital Structure Theory: M&M Proposition I
Similarly, someone could buy all of the firm’s shares forEU and
modify the firm’s capital stucture to have
VL = D + EL > EU
and then resell the firm for a riskless profit ofVL−VU .
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10.2 The Firm’s Capital Structure
Capital Structure Theory: M&M Proposition I
In a frictionless market, this arbitrage oppotunity would lead to
an increase in the firm’s unlevered equity to the point where
VU = EU = D + EL = VL
for any level ofD andEL.
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10.2 The Firm’s Capital Structure
Capital Structure Theory: M&M Proposition I with Taxes
Consider an unlevered firm, denotedU , that expects constant
earnings before interest and taxes, denotedEBIT, forever.
Each period, if the corporate tax rate isT, shareholders receive
(1−T)EBIT
and the government receives
T×EBIT.
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10.2 The Firm’s Capital Structure
Capital Structure Theory: M&M Proposition I with Taxes
Let EU = VU denote the present value of the payment
(1−T)EBIT forever.
Let GU denote the present value of the paymentT×EBIT
forever.
Let k0 denote the firm’s WACC when unlevered. Then
EU = VU =(1−T)EBIT
k0.
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10.2 The Firm’s Capital Structure
Capital Structure Theory: M&M Proposition I with Taxes
Consider a levered firm, FirmL, with the sameEBIT asU , but
with a perpetual debt issueD with coupon ratei.
Interest payments are tax exempt.
Shareholders receive(1−T)(EBIT− iD) each period forever,
bondholders receiveiD each period forever, and
the government receivesT(EBIT− iD) each period forever.
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10.2 The Firm’s Capital Structure
Capital Structure Theory: M&M Proposition I with Taxes
Each period, the total cash flow to shareholders and bondholders
of Firm L is
(1−T)(EBIT− iD) + iD = (1−T)EBIT + TiD.
The value of the levered firm is then the sum of two perpetuities,
i.e. (1−T)EBIT forever andTiD forever.
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10.2 The Firm’s Capital Structure
Capital Structure Theory: M&M Proposition I with Taxes
As before, the present value of(1−T)EBIT forever isVU .
Discounting the tax shield cash flowsTiD at the bonds’ coupon
ratei, their present value is
TiDi
= TD,
and thus the value of the levered firm is
VL = VU + TD.
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10.2 The Firm’s Capital Structure
Capital Structure Theory: Financial Distress
In a world with uncertainty, however, increasingD also increases
the risk of bankruptcy. Financial distress creates some costs.
Business risk is not affected by the level of debt but has an
impact on the firm’s capability to meet in financial obligations.
Financial risk is directly affected by the firm’s level of debt.
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10.2 The Firm’s Capital Structure
The Optimal Capital Structure
The value of the levered firm can also be obtained using
V =(1−T)EBIT
ka,
whereka is the firm’s cost of capital.
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10.2 The Firm’s Capital Structure
The Optimal Capital Structure
Suppose we have
DD+E ke kd WACC (ka)
0% 13.00% 8.00% 13.00%20% 13.20% 8.20% 12.20%40% 13.80% 8.80% 11.80%50% 14.25% 9.25% 11.75%60% 14.80% 9.80% 11.80%80% 16.20% 11.20% 12.20%
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10.2 The Firm’s Capital Structure
The Optimal Capital Structure
Then the value of the firmV = (1−T)EBITka
, is maximized when
ka is minimized.
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10.2 The Firm’s Capital Structure
The Optimal Capital Structure
Suppose EBIT= 1,000 andT = 40%. Then
DD+E ke kd WACC (ka) V = (1−T)EBIT
ka
0% 13.00% 8.00% 13.00% 46.1520% 13.20% 8.20% 12.20% 49.1840% 13.80% 8.80% 11.80% 50.8550% 14.25% 9.25% 11.75% 51.0660% 14.80% 9.80% 11.80% 50.8580% 16.20% 11.20% 12.20% 49.18
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