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Chapters 15&16
The Capital Structure Questions
The balance sheet of the firm(market values):
Debt (B)
Assets (V)
Equity (S)
We can write: V = B + S
Or, draw a pie:
B
S
Two questions:
1. Should the management aim at maximizing V or S?
2. What is the debt to equity ratio (B/S) that will maximize S?
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Is There An Optimal Capital Structure?
Modigliani & Miller (MM) Proposition I (No Taxes)
 Firm value is not affected by financial leverage:
VL = VU
MM assume (among other things):
 No risk of default
 Perpetual Cash Flows
 Firms and investors can borrow/lend at the same rate
 No taxes
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Proving MM Proposition I (No Taxes)
 Consider two firms, identical in every way except that one is levered
and the other is all equity (unlevered):
Assets
Equity
Debt
Cost of Debt
Unlevered
VU = $1,000,000
SU = $1,000,000
BU = 0
Levered
VL = ?
SL = ?
BL = $400,000
rB = 5%
 Recall: Firms and investors can borrow/lend at the same rate, and
there are no taxes
 The (uncertain) dollar return on the firm’s assets is given by Y
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Consider the following two investment strategies:
Strategy A
Buy 10% of SL
Dollar Investment
0.1SL = 0.1(VL - BL)
Total CF from A
0.1(VL - BL)
Dollar Return
0.1(Y - rBBL)
= 0.1(Y - 0.05%400,000)
0.1Y - 2,000
Strategy B
1) Buy 10% of VU
Dollar Investment
0.1VU
Dollar Return
0.1Y
2) Borrow 10% of BL
- 0.1BL
Total CF from B
0.1(VU - BL)
- 0.1rBBL
= - 0.1% 0.05%400,000
= - 2,000
0.1Y - 2,000
Since the dollar return from A and B is identical, the initial cost of both strategies
must be identical, thus 0.1(VL - BL) = 0.1(VU - BL), and VL = VU
MM Proposition I (No Taxes):
Firm value is not affected by leverage (VL = VU )
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The Value of a Levered Firm Under
MM Proposition I with No Corporate Taxes
Value of
the firm
(VL )
VU
VL = VU
Debt-equity ratio (B/S)
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MM Proposition II (No Taxes)
The cost of equity and financial leverage:
A. Because of Prop. I, the WACC must be constant. With no taxes,
WACC = rU = (S/A) % rS + (B/A) % rB,
where A = S + B
where rU is the constant return on the firm’s assets
B. Solve for rS to get MM Prop. II (No Taxes):
rS = rU + (rU - rB) % (B/S)
Cost of equity has two parts:
1. rU and “business” risk
the risk inherent in the firm’s operations (beta of assets)
2. B/S and “financial” risk
extra risk from using debt financing
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The Cost of Equity, the Cost of Debt, and the Weighted
Average Cost of Capital: MM Proposition II with No
Corporate Taxes
Cost of
capital
rS = rU + (rU – rB) x (B/S)
WACC = rU
rB
Debt-equity ratio (B/S)
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Debt, Taxes, and Firm Value
 The interest tax shield and firm value
For simplicity: (1) perpetual cash flows
(2) no depreciation
(3) no fixed asset or NWC spending
A firm is considering going from zero debt to $400 at 10%:
EBIT
Interest
Tax (40%)
Net income
Cash flow from
assets (EBIT-Taxes)
Firm U
(unlevered)
$200
0
$80
$120
$120
Firm L
(levered)
$200
$40
$64
$96
+$16
$136
Tax saving = $16 = 0.4 % $40 = TC % rB % B
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Debt, Taxes, and Firm Value (concluded)
What’s the link between debt and firm value?
Since interest creates a tax deduction, borrowing creates an
interest tax shield. Its value is added to the value of the
firm.
PV(perpetual tax savings) = $16/0.1= $160
= (TC % rB % B)/rB = TC B
MM Proposition I (with taxes):
VL = VU + TC B
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The Value of a Levered Firm Under
MM Proposition I with Corporate Taxes
Value of
the firm
(VL )
VL = VU + TC B
Present value of tax
shield on debt
VU
VU
Total Debt (B)
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Debt, Taxes, and the WACC
Taxes and firm value: an example
 EBIT = $100
 TC
= 30%
 rU
= 12.5%
Q. Suppose debt goes from $0 to $100 at 10%, what
happens to equity value, S?
VU
= EBIT(1 - TC) / rU =
VL =
SL = VL - B = $
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Debt, Taxes, and the WACC (concluded)
 WACC and the cost of equity (MM Proposition II with taxes) With taxes:
Recall: WACC = (S/A) % rS + (B/A) % rB % (1-TC)
 MM Proposition II (with taxes):
rS = rU + (rU - rB) % (B/S) % (1 - TC )
 In the above example:
rs =
WACC =
 The WACC decreases as more debt financing is used
=> since WACC is a discount rate for future cash flows, the optimal
capital structure is all debt!
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Taxes, the WACC, and Proposition II
Cost of capital
rS
rU
rU
WACC
rB (1 – TC)
Debt-Equity Ratio (B/S)
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Financial Distress
 MM with taxes
VL = VU + TC B
debt provides tax benefits to the firm => the firm should
borrow an infinite amount
 In reality
 the firm has to pay interest and principal to bondholders
regardless of profitability
 if the firm defaults on a payment to its bondholders, it
will enter a phase of financial distress (e.g. Eaton’s), or
 ultimately, if financial distress persists, the firm will
declare bankruptcy
 there are costs involved in both financial distress and
bankruptcy
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Costs of Financial Distress
 Direct Costs
 Legal and administrative costs (e.g. lawyers, accounting, expert
witnesses)
 Indirect Costs
 Impaired ability to conduct business (e.g. lost sales)
 Agency costs In financial distress, stockholders may engage in
 Selfish strategy 1: Incentive to take large risks
 Selfish strategy 2: Incentive toward underinvestment
 Selfish Strategy 3: Milking the property (liquidating dividend, or
Increase perks to owners/management )
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Selfish Strategy 3: Milking the Property
Liquidating dividends
 Such tactics are often illegal
Increase perks to owners/management
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The Firm Value, Tax-Shield of Debt, and Financial Distress Costs
 The Value of a levered firm:
VL = VU + TC B - PV[expected costs of financial distress]
 For firms with a low financial leverage, the probability of default is close to
zero, and
PV[expected costs of financial distress] { 0
a $1 increase in debt, will increase tax benefits (and the firm value) at a constant
rate of TC
 For highly levered firms, the probability of default is positive, and
PV[expected costs of financial distress] > 0
a $1 increase in debt, will
 increase tax benefits at a constant rate of TC
 increase costs of financial distress at increasing rates
Conclusion - increase debt as long as tax benefits exceed the PV
of the costs of financial distress (up to the optimal level of debt: B*)
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The Optimal Capital Structure and the Value of the Firm
Value of
the firm
(VL )
VL = VU + TC
Present value of tax
shield on debt
Maximum
firm value VL*
B
Financial
distress costs
Actual firm value
VU
VU = Value of firm
with no debt
Total Debt (B)
B*
Optimal Level of Debt
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The Optimal Capital Structure and the Cost of Capital
WACC = (S/V) % rS + (B/V) % rB %
(1-TC) +Premium for Costs of Financial Distress
Cost of
capital
(%)
rS
rU
WACC
rB (1 – TC)
rU
Minimum
cost of capital WACC*
Debt/equity ratio (B/S)
(B/S) *
Optimal Leverage Ratio
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