Capital Structure

McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

15-1 Capital Structure: Basic Concepts

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


15-2

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, the firm should pick the debt-equity ratio that makes the pie as big as possible.


15-3

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.


15-4

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.)


15-5

EPS and ROE Under Current Capital Structure

Recession Expected ExpansionEBIT $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


15-6

EPS and ROE Under Proposed Capital Structure

Recession Expected ExpansionEBIT $1,000 $2,000 $3,000Interest 640 640 640Net income $360 $1,360 $2,360EPS $1.50 $5.67 $9.83ROA 5% 10% 15%ROE 3% 11% 20%

Proposed Shares Outstanding = 240 shares


15-7

EPS and ROE Under Both Capital Structures

LeveredRecession Expected Expansion

EBIT $1,000 $2,000 $3,000Interest 640 640 640Net income $360 $1,360 $2,360EPS $1.50 $5.67 $9.83ROA 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


15-8

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

EPS

Debt

No Debt

Break-even point

EBI in dollars, no taxes

Advantage to debt

Disadvantage to debt EBIT


15-9

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


15-10

Homemade Leverage: An ExampleRecession Expected Expansion

EPS of Unlevered Firm $2.50 $5.00 $7.50

Earnings for 40 shares $100 $200 $300Less interest on $800 (8%) $64 $64 $64Net Profits $36 $136 $236ROE (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:

32

200,1$800$

SB


15-11

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 other-wise identical levered firm along with the some of the firm’s debt gets us to the ROE of the unlevered firm.This is the fundamental insight of M&M


15-12

The MM Propositions I & II (No Taxes)• Proposition I

– Firm value is not affected by leverageVL = 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 debtSL is the value of levered equity


15-13

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


15-14

The MM Proposition II (No Taxes)

The derivation is straightforward:

SBW ACC rSB

SrSB

Br

0set Then rrW ACC

0rrSB

SrSB

BSB

SSB by sidesboth multiply

0rSSBr

SBS

SSBr

SBB

SSB

SB

0rSSBrr

SB

SB

00 rrSBrr

SB

SB )( 00 BS rrSBrr


15-15 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 c

apita

l: r (

%)

r0

rB

SBW ACC rSB

SrSB

Br

)( 00 BL

S rrSBrr

rB

SB


15-16 The MM Propositions I & II (with Corporate Taxes)• Proposition I (with Corporate Taxes)

– Firm value increases with leverageVL = 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


15-17

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(


15-18

The MM Proposition II (Corp. Taxes)

Start with M&M Proposition I with taxes:

)()1( 00 BCS rrTSBrr

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 rTSBrT

SBr

SBr 0)]1(1[

BTVBS CU

)1( CU TBSV

Which quickly reduces to


15-19 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 rrTSBrr

SL

LCB

LW ACC r

SBSTr

SBBr

)1(


15-20 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 ExpectedExpansionEBIT $1,000$2,000 $3,000Interest ($800 @ 8% ) 640640 640EBT $360$1,360 $2,360Taxes (Tc = 35%) $126$476 $826Total Cash Flow $234+640$468+$640$1,534+$640(to both S/H & B/H): $874$1,524 $2,174EBIT(1-Tc)+TCrBB $650+$224$1,300+$224$1,950+$224

$874$1,524 $2,174


15-21 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


15-22

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 rrSBrr


15-23

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 rrTSBrr


15-24

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.

• The important use of this chapter is to get comfortable with “M&M algebra”.

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Capital Structure

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