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Corporate Finance Ross Westerfield Jaffe Sixth Edition
15Chapter Fifteen
Capital Structure: Basic Concepts
Prepared by
Gady JacobyUniversity of Manitoba
and
Sebouh AintablianAmerican University of Beirut
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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
Value of the Firm
S B
• 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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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
CurrentAssets $20,000Debt $0Equity $20,000Debt/Equity ratio 0.00Interest rate n/aShares outstanding 400Share price $50
Proposed$20,000$8,000
$12,0002/38%240$50
Consider an all-equity firm that is considering going into debt. (Maybe some of the original shareholders want to cash out.)
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EPS and ROE Under Current Capital Structure
Recession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest 0 0 0
Net income $1,000 $2,000 $3,000
EPS $2.50 $5.00 $7.50
ROA 5% 10% 15%
ROE 5% 10% 15%
Current Shares Outstanding = 400 shares
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EPS and ROE Under Proposed Capital Structure
Recession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest 640 640 640
Net income $360 $1,360 $2,360
EPS $1.50 $5.67 $9.83
ROA 5% 10% 15%
ROE 3% 11% 20%
Proposed Shares Outstanding = 240 shares
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EPS and ROE Under Both Capital Structures
LeveredRecession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest 640 640 640
Net income $360 $1,360 $2,360
EPS $1.50 $5.67 $9.83
ROA 5% 10% 15%
ROE 3% 11% 20%
Proposed Shares Outstanding = 240 shares
All-EquityRecession Expected Expansion
EBIT $1,000 $2,000 $3,000Interest 0 0 0Net income $1,000 $2,000 $3,000EPS $2.50 $5.00 $7.50ROA 5% 10% 15%ROE 5% 10% 15%Current Shares Outstanding = 400 shares
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Financial Leverage and EPS
(2.00)
0.00
2.00
4.00
6.00
8.00
10.00
12.00
1,000 2,000 3,000
EP
S
Debt
No Debt
Break-even point
EBI in dollars, no taxes
Advantage to debt
Disadvantage to debt EBIT
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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
Recession Expected Expansion
EPS of Unlevered Firm $2.50 $5.00 $7.50
Earnings for 40 shares $100 $200 $300
Less interest on $800 (8%) $64 $64 $64
Net Profits $36 $136 $236
ROE (Net Profits / $1,200) 3% 11% 20%
We are buying 40 shares of a $50 stock on margin. We get the same ROE as if we bought into a levered firm.
Our personal debt equity ratio is:3
2200,1$
800$
S
B
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Homemade (Un)Leverage: An Example
Recession Expected ExpansionEPS of Levered Firm $1.50 $5.67 $9.83
Earnings for 24 shares $36 $136 $236Plus interest on $800 (8%) $64 $64 $64Net profits $100 $200 $300ROE (Net profits / $2,000) 5% 10% 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)
UL VV
BrEBIT Breceive firm levered ain rsShareholde
BrB
receive sBondholderThe derivation is straightforward:
BrBrEBIT BB )(
is rsstakeholde all toflowcash total theThus,
The present value of this stream of cash flows is VL
EBITBrBrEBIT BB )(
Clearly
The present value of this stream of cash flows is VU
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15.4 The MM Proposition II (No Taxes)
The derivation is straightforward:
SBWACC rSB
Sr
SB
Br
0set Then rrWACC
0rrSB
Sr
SB
BSB
S
SB by sidesboth multiply
0rS
SBr
SB
S
S
SBr
SB
B
S
SBSB
0rS
SBrr
S
BSB
00 rrS
Brr
S
BSB )( 00 BS rr
S
Brr
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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
Debt-to-equity Ratio
Cos
t of
capi
tal:
r (%
)
r0
rB
SBWACC rSB
Sr
SB
Br
)( 00 BL
S rrS
Brr
rB
S
B
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15.5 TaxesThe 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 shieldrS = 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 debtS is the value of levered equity
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The MM Proposition I (Corp. Taxes)
BTVV CUL
)1()(
receive firm levered ain rsShareholde
CB TBrEBIT BrB
receive sBondholder
BrTBrEBIT BCB )1()(
is rsstakeholde all toflowcash total theThus,
The present value of this stream of cash flows is VL
BrTBrEBIT BCB )1()(Clearly
The present value of the first term is VU
The present value of the second term is TCB
BrTBrTEBIT BCBC )1()1(
BrBTrBrTEBIT BCBBC )1(
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The MM Proposition II (Corp. Taxes)
Start with M&M Proposition I with taxes:
)()1( 00 BCS rrTS
Brr
BTVV CUL
Since BSVL
The cash flows from each side of the balance sheet must equal:
BCUBS BrTrVBrSr 0
BrTrTBSBrSr BCCBS 0)]1([
Divide both sides by S
BCCBS rTS
BrT
S
Br
S
Br 0)]1(1[
BTVBS CU
)1( CU TBSV
Which quickly reduces to
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The Effect of Financial Leverage on the Cost of Debt and Equity Capital
Debt-to-equityratio (B/S)
Cost of capital: r(%)
r0
rB
)()1( 00 BCL
S rrTS
Brr
SL
LCB
LWACC r
SB
STr
SB
Br
)1(
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Total Cash Flow to Investors Under Each Capital Structure with Corp. Taxes
All-EquityRecession Expected Expansion
EBIT $1,000 $2,000 $3,000Interest 0 0 0EBT $1,000 $2,000 $3,000Taxes (Tc = 35% $350 $700 $1,050
Total Cash Flow to S/H $650 $1,300 $1,950
LeveredRecession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest ($800 @ 8% ) 640 640 640
EBT $360 $1,360 $2,360
Taxes (Tc = 35%) $126 $476 $826
Total Cash Flow $234+640 $468+$640 $1,534+$640
(to both S/H & B/H): $874 $1,524 $2,174
EBIT(1-Tc)+TCrBB $650+$224 $1,300+$224 $1,950+$224
$874 $1,524 $2,174
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Total Cash Flow to Investors Under Each Capital Structure with Corp. Taxes
The levered firm pays less in taxes than does the all-equity firm.
Thus, the sum of the debt plus the equity of the levered firm is greater than the equity of the unlevered firm.
S G S G
B
All-equity firm Levered 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
)( 00 BL
S rrS
Brr
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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.
)()1( 00 BCL
S rrTS
Brr
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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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