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Capital Structure: Part 1
For 9.220, Term 1, 2002/03
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Outline
1. Introduction
2. Theories of Capital Structure
a) Modigliani and Miller – No tax
b) M&M with Corporate Tax
3. Summary and Conclusions (so far)
Introduction
 Definition: Capital Structure is the mix of
financial securities used to finance the firm.
 Our goal is to see if there is an optimal way for
firms to finance.
 Should a firm have a higher or lower D/E ratio.
 What factors affect the optimal D/E choice?
 In order to optimize the D/E ratio, our overall
goal is to maximize the total value of the firm
and thus maximize expected shareholder wealth.

Modigliani and Miller – No Tax Case
 M&M began looking at capital
structure in a very simplified world so
that we would know what does or
does not matter.
 Assume no taxes
 No transaction costs
 Including no bankruptcy costs
 Investors can borrow/lend at the same rate
(the same as the firm).
 No information asymmetries
 A fixed investment policy by the firm
M&M No Tax: Result
 A change in capital structure does not
matter to the overall value of the
firm. The total cash flows produced
are the same, thus the total value of
the cash flows is the same.
 It doesn’t matter if the cash flows
from the firm to its security holders
are called debt or equity cash flows.
M&M – No Tax Case
Equity,
$1,000,
100%
Debt,
$300, 30%
Equity,
$700, 70%
Equity,
$400, 40%
Debt,
$600, 60%
The M&M Propositions I & II (No Taxes)
 Proposition I
 Firm value is not affected by leverage
VL = V U
 Proposition II
 Leverage increases the risk and return to
stockholders
rs = r0 + (B / SL) (r0 - rB)
rB is the interest rate (cost of debt)
rs is the return on (levered) equity (cost of equity)
r0 is the return on unlevered equity (cost of capital)
B is the value of debt
SL is the value of levered equity
M&M Proposition I (No Taxes)
The derivation is straightforward:
Shareholde rs in a levered firm receive
Bondholder s receive
EBIT  rB B
rB B
Thus, the total cash flow to all stakeholde rs is
( EBIT  rB B)  rB B
The present value of this stream of cash flows is VL
Clearly
( EBIT  rB B)  rB B  EBIT
The present value of this stream of cash flows is VU
VL  VU
M&M Proposition II (No Taxes)
The derivation is straightforward:
B
S
rW ACC 
 rB 
 rS
BS
BS
B
S
 rB 
 rS  r0
BS
BS
Then set rWACC  r0
BS
multiply both sides by
S
BS
B
BS
S
BS

 rB 

 rS 
r0
S
BS
S
BS
S
B
BS
 rB  rS 
r0
S
S
B
B
 rB  rS  r0  r0
S
S
B
rS  r0  (r0  rB )
S
Exercise
 Suppose the firm is currently all equity
financed and the total value of the firm is
$90 million. E[Requity] is 18%. Also,
suppose Rf = 4% and E[RM] = 14%.
1. What is the value of the equity and the
total value of the firm if the capital
structure is changed to include $30 million
of debt? If E[Rdebt] is 6%, then what is the
new E[Requity]? What is the WACC?
Compare the beta of the levered equity to
the unlevered equity. What is the weighted
beta of the firms securities?
2. Redo 1 with $60 million of debt.
Cost of capital: r (%)
The Cost of Equity & Debt, and the WACC:
M&M Proposition II with No Corporate Taxes
r0
rS  r0 
rW ACC 
B
 (r0  rB )
SL
B
S
 rB 
 rS
BS
BS
rB
rB
Debt-to-equity Ratio B
S
M&M with Corporate Taxes
 When corporate taxes are introduced, then
debt financing causes a positive benefit to
the value of the firm.
 The reason for this is that debt interest
payments reduce taxable income and thus
reduce taxes.
 Thus with debt, there is more after-tax cash flow
available to security holders (equity and debt)
than there is without debt.
 Thus the value of the equity and debt securities
combined is greater.
M&M with Corporate Taxes
TC = 40% in this example
Tax, $400,
40%
Equity,
$600, 60%
Equity,
$420, 42%
Tax, $280,
28%
Tax, $160,
16%
Equity,
$240, 24%
Debt,
$300, 30%
Debt,
$600, 60%
M&M Proposition I (with Corporate Taxes)
Proposition I (with Corporate Taxes)
 Firm value increases with leverage
VL = VU + TC B

M&M Proposition I (with Corp. Taxes)
Shareholde rs in a levered firm receive
Bondholder s receive
( EBIT  rB B)  (1  TC )
rB B
Thus, the total cash flow to all stakeholde rs is
( EBIT  rB B)  (1  TC )  rB B
The present value of this stream of cash flows is VL
Clearly ( EBIT  rB B)  (1  TC )  rB B 
 EBIT  (1  TC )  rB B  (1  TC )  rB B
 EBIT  (1  TC )  rB B  rB BTC  rB B
The present value of the first term is VU
The present value of the second term is TCB
VL  VU  TC B
M&M Proposition II (with Corp. Taxes)
 Proposition II (with Corporate Taxes)
 This proposition is similar to Prop. II in the no
tax case, however, now the risk and return of
equity does not rise as quickly as the
debt/equity ratio is increased because low-risk
tax cash flows are saved.
 Some of the increase in equity risk and return is
offset by interest tax shield
rS = r0 + (B/S)×(1-TC)×(r0 - rB)
rB is the interest rate (cost of debt)
rS is the return on equity (cost of equity)
r0 is the return on unlevered equity (cost of capital)
B is the value of debt
S is the value of levered equity
Exercise
 Suppose the firm is currently all equity
financed and the total value of the firm is
$90 million. E[Requity] is 18%. Also,
suppose that TC = 40%, Rf = 4% and
E[RM] = 14%.
1. What is the value of the equity and the
total value of the firm if the capital
structure is changed to include $30 million
of debt? If E[Rdebt] is 6%, then what is the
new E[Requity]? What is the new WACC?
2. Redo 1 with $60 million of debt.
The Effect of Financial Leverage on the
Cost of Debt and Equity Capital
Cost of capital: r
(%)
rS  r0 
B
 (1  TC )  (r0  rB )
SL
r0
rW ACC 
B
SL
 rB  (1  TC ) 
 rS
BSL
B  SL
rB
Debt-to-equity
ratio (B/S)
Summary and Conclusions
 At this point, it appears clear that an
increase in the debt/equity ratio increases
the risk of the equity.
 With corporate taxes, it also appears that
the value of the firm increases as the
amount of debt used increases (due to
taxes being saved).
 However, in reality, we don’t see 100% debt
financing, so there must be other factors that
affect the firm’s optimal capital structure.
 The next lecture addresses these other factors
and extends the theory.