15-0 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Corporate Finance Ross Westerfield Jaffe Sixth Edition 15 Chapter Fifteen Capital Structure:

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McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited

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.”