15-0
Chapter Fifteen
Capital Structure:
Basic
Corporate
Finance
Ross Westerfield Jaffe
Concepts


15
Sixth Edition
Prepared by
Gady Jacoby
University of Manitoba
and
Sebouh Aintablian
American University of
Beirut
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15-1
Chapter Outline
15.1 The Capital-Structure Question and The Pie Theory
15.2 Maximizing Firm Value versus Maximizing
Stockholder Interests
15.3 Financial Leverage and Firm Value: An Example
15.4 Modigliani and Miller: Proposition II (No Taxes)
15.5 Taxes
15.6 Summary and Conclusions
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15.1 The Capital-Structure Question and The Pie Theory
• The value of a firm is defined to be the sum of the
value of the firm’s debt and the firm’s equity.
• V=B+S
• If the goal of the
management of the firm is to
make the firm as valuable as
possible, then the firm should
pick the debt-equity ratio that
makes the pie as big as
possible.
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S
B
Value of the Firm
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The Capital-Structure Question
There are really two important questions:
1. Why should the stockholders care about
maximizing firm value? Perhaps they should be
interested in strategies that maximize shareholder
value.
2. What is the ratio of debt-to-equity that maximizes
the shareholder’s value?
As it turns out, changes in capital structure benefit the
stockholders if and only if the value of the firm
increases.
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15.3 Financial Leverage, EPS, and ROE
Consider an all-equity firm that is considering going into
debt. (Maybe some of the original shareholders want to cash
out.)
Assets
Debt
Equity
Debt/Equity ratio
Interest rate
Shares outstanding
Share price
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Current
$20,000
$0
$20,000
0.00
n/a
400
$50
Proposed
$20,000
$8,000
$12,000
2/3
8%
240
$50
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15-5
EPS and ROE Under Current Capital Structure
EBIT
Interest
Net income
EPS
ROA
ROE
Recession
$1,000
0
$1,000
$2.50
5%
5%
Expected Expansion
$2,000
$3,000
0
0
$2,000
$3,000
$5.00
$7.50
10%
15%
10%
15%
Current Shares Outstanding = 400 shares
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EPS and ROE Under Proposed Capital Structure
EBIT
Interest
Net income
EPS
ROA
ROE
Recession
$1,000
640
$360
$1.50
5%
3%
Expected Expansion
$2,000
$3,000
640
640
$1,360
$2,360
$5.67
$9.83
10%
15%
11%
20%
Proposed Shares Outstanding = 240 shares
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EPS and ROE Under Both Capital Structures
All-Equity
Recession
EBIT
$1,000
Interest
0
Net income
$1,000
EPS
$2.50
ROA
5%
ROE
5%
Current Shares Outstanding = 400 shares
EBIT
Interest
Net income
EPS
ROA
ROE
Levered
Recession
$1,000
640
$360
$1.50
5%
3%
Expected
$2,000
0
$2,000
$5.00
10%
10%
Expansion
$3,000
0
$3,000
$7.50
15%
15%
Expected
$2,000
640
$1,360
$5.67
10%
11%
Expansion
$3,000
640
$2,360
$9.83
15%
20%
Proposed Shares Outstanding = 240 shares
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Financial Leverage and EPS
12.00
Debt
10.00
EPS
8.00
6.00
4.00
No Debt
Advantage
to debt
Break-even
point
2.00
0.00
1,000
(2.00)
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Disadvantage
to debt
2,000
3,000
EBIT
EBI in dollars, no taxes
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Assumptions of the Modigliani-Miller Model
•
•
•
•
Homogeneous Expectations
Homogeneous Business Risk Classes
Perpetual Cash Flows
Perfect Capital Markets:
–
–
–
–
–
Perfect competition
Firms and investors can borrow/lend at the same rate
Equal access to all relevant information
No transaction costs
No taxes
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Homemade Leverage: An Example
EPS of Unlevered Firm
Recession Expected Expansion
$2.50
$5.00
$7.50
Earnings for 40 shares
Less interest on $800 (8%)
Net Profits
ROE (Net Profits / $1,200)
$100
$64
$36
3%
$200
$64
$136
11%
$300
$64
$236
20%
We are buying 40 shares of a $50 stock on margin. We get the
same ROE as if we bought into a levered firm.
Our personal debt equity ratio is:
B $800
S
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
$1,200
2
3
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Homemade (Un)Leverage: An Example
EPS of Levered Firm
Earnings for 24 shares
Plus interest on $800 (8%)
Net profits
ROE (Net profits / $2,000)
Recession Expected Expansion
$1.50
$5.67
$9.83
$36
$64
$100
5%
$136
$64
$200
10%
$236
$64
$300
15%
Buying 24 shares of an otherwise identical levered firm along
with some of the firm’s debt gets us to the ROE of the
unlevered firm.
This is the fundamental insight of M&M
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The MM Propositions I & II (No Taxes)
• Proposition I
– Firm value is not affected by leverage
VL = VU
• 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
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The MM 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
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15.4 The MM 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
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B
rS  r0  (r0  rB )
S
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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: r (%)
15-15
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
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15.5 Taxes
The MM Propositions I & II (with Corporate Taxes)
• Proposition I (with Corporate Taxes)
– Firm value increases with leverage
VL = VU + TC B
• Proposition II (with Corporate Taxes)
– 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
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The MM Proposition I (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
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VL  VU  TC B
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The MM Proposition II (Corp. Taxes)
VL  VU  TC B
Start with M&M Proposition I with taxes:
Since
VL  S  B  S  B  VU  TC B
VU  S  B(1  TC )
The cash flows from each side of the balance sheet must equal:
SrS  BrB  VU r0  TC BrB
SrS  BrB  [S  B(1  TC )]r0  TC rB B
Divide both sides by S
rS 
B
B
B
rB  [1  (1  TC )]r0  TC rB
S
S
S
Which quickly reduces to
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B
rS  r0   (1  TC )  (r0  rB )
S
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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)
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Total Cash Flow to Investors Under
Each Capital Structure with Corp. Taxes
All-Equity
EBIT
Interest
EBT
Taxes (Tc = 35%
Total Cash Flow to S/H
Recession
$1,000
0
$1,000
$350
Expected
$2,000
0
$2,000
$700
Expansion
$3,000
0
$3,000
$1,050
$650
$1,300
$1,950
Expected
$2,000
640
$1,360
$476
$468+$640
$1,524
$1,300+$224
$1,524
Expansion
$3,000
640
$2,360
$826
$1,534+$640
$2,174
$1,950+$224
$2,174
Levered
EBIT
Interest ($800 @ 8% )
EBT
Taxes (Tc = 35%)
Total Cash Flow
(to both S/H & B/H):
EBIT(1-Tc)+TCrBB
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Recession
$1,000
640
$360
$126
$234+640
$874
$650+$224
$874
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Total Cash Flow to Investors Under
Each Capital Structure with Corp. Taxes
All-equity firm
S
G
Levered firm
S
G
B
The levered firm pays less in taxes than does the allequity firm.
Thus, the sum of the debt plus the equity of the levered
firm is greater than the equity of the unlevered firm.
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Summary: No Taxes
• In a world of no taxes, the value of the firm is unaffected by
capital structure.
• This is M&M Proposition I:
VL = VU
• Prop I holds because shareholders can achieve any pattern of
payouts they desire with homemade leverage.
• In a world of no taxes, M&M Proposition II states that
leverage increases the risk and return to stockholders
B
rS  r0   (r0  rB )
SL
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Summary: Taxes
• In a world of taxes, but no bankruptcy costs, the value of the
firm increases with leverage.
• This is M&M Proposition I:
VL = VU + TC B
• Prop I holds because shareholders can achieve any pattern of
payouts they desire with homemade leverage.
• In a world of taxes, M&M Proposition II states that leverage
increases the risk and return to stockholders.
B
rS  r0   (1  TC )  (r0  rB )
SL
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Prospectus: Bankruptcy Costs
• So far, we have seen M&M suggest that financial
leverage does not matter, or imply that taxes cause
the optimal financial structure to be 100% debt.
• In the real world, most executives do not like a
capital structure of 100% debt because that is a state
known as “bankruptcy.”
• In the next chapter we will introduce the notion of a
limit on the use of debt: financial distress.
• Use this chapter to get comfortable with “M&M
algebra.”
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