Leverage and Capital Structure
Ross Chapter 16
Spring 2005
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.
10.1 Leverage
Financial Leverage
Let T denote the tax rate, let I denote interest expense and let NS 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 EBIT translate into percentage changes in EPS?
∆EPS EPS = (1−T )(EBIT0−I) NS − ³ (1−T )(EBIT−I) NS ´ (1−T )(EBIT−I) NS = (1 − T ) (EBIT0− EBIT) (1 − T )(EBIT − I) = (1 − T )EBIT × EBIT0−EBIT EBIT (1 − T )(EBIT − I) = EBIT EBIT − I × ∆EBIT EBIT
10.1 Leverage
Financial Leverage
That is, when EBIT increases by 1%, the percentage increase in EPS is
EBIT
EBIT − I =
EBIT EBIT − I.
This the degree 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-Term Debt (D)
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
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 value VU = 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 buy α 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,
10.2 The Firm’s Capital Structure
Capital Structure Theory: M&M Proposition I
Similarly, someone could buy all of the firm’s shares for EU and
modify the firm’s capital stucture to have VL = D + EL > EU
and then resell the firm for a riskless profit of VL−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
10.2 The Firm’s Capital Structure
Capital Structure Theory: M&M Proposition I with Taxes Consider an unlevered firm, denoted U , that expects constant earnings before interest and taxes, denoted EBIT , forever. Each period, if the corporate tax rate is T , 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 payment T × EBIT
forever.
Let k0 denote the firm’s WACC when unlevered. Then
EU = VU = (1 − T )EBIT k0
10.2 The Firm’s Capital Structure
Capital Structure Theory: M&M Proposition I with Taxes
Consider a levered firm, Firm L, with the same EBIT as U , but with a perpetual debt issue D with coupon rate i.
Interest payments are tax exempt.
Shareholders receive (1 − T )(EBIT − iD) each period forever, bondholders receive iD each period forever, and
the government receives T (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 and TiD forever.
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 is VU.
Discounting the tax shield cash flows TiD at the bonds’ coupon rate i, their present value is
TiD
i = T D, and thus the value of the levered firm is
VL = VU + T D.
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10.2 The Firm’s Capital Structure
Capital Structure Theory: Financial Distress
In a world with uncertainty, however, increasing D 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.
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
,
where ka 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 D D+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%
10.2 The Firm’s Capital Structure
The Optimal Capital Structure
Then the value of the firm V = (1−T )kEBIT
a , 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 and T = 40%. Then
D D+E ke kd WACC (ka) V = (1−T )EBIT ka 0% 13.00% 8.00% 13.00% 46.15 20% 13.20% 8.20% 12.20% 49.18 40% 13.80% 8.80% 11.80% 50.85 50% 14.25% 9.25% 11.75% 51.06 60% 14.80% 9.80% 11.80% 50.85 80% 16.20% 11.20% 12.20% 49.18