Print EJ Lecture3 · · 2007-11-051 The Capital-Structure Question 2 Financial Leverage and Firm...

Eric JondeauEric Jondeau

Corporate Finance

EMBA in Management & Finance

Eric JondeauEric Jondeau

Lecture 3:

Capital Structure Modigliani and Miller

EMBA in Management & Finance

1 The Capital-Structure Question

2 Financial Leverage and Firm Value

3 Modigliani - Miller Propositions (No Taxes)

4 Modigliani - Miller Propositions (With Taxes)

5 Summary and Conclusions

Eric JondeauEric JondeauEric JondeauEric Jondeau EMBAEMBAEMBAEMBA 3/273/273/273/27

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Outline

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1. The Capital Structure Question• 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.

SB


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.



The Capital Structure Question

CurrentAssets $20,000Debt $0Equity $20,000Debt/Equity ratio 0.00Interest rate n/aShares outstanding 400Share price $50

Proposed$20,000

$8,000$12,000

2/38%240$50

Consider an all-equity firm that is considering going into debt. (Maybe some of the original shareholders want to cash out.)



2. Financial Leverage and Firm Value

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



EPS and ROE under current 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

EPS and ROE under proposed capital structure



EPS and ROE under proposed capital structure

AllAllAllAll----EquityEquityEquityEquityRecession 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

LeveredLeveredLeveredLeveredRecession 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



EPS and ROE under both capital structures

(2.00)

0.00

2.00

4.00

6.00

8.00

10.00

12.00

1,000 2,000 3,000

EPS (dollars) Debt

No DebtBreak-even

point

EBIT in dollars, no taxes

Advantage to debt

Disadvantage to debt

EMBAEMBAEMBAEMBA 10/2710/2710/2710/27Eric JondeauEric JondeauEric JondeauEric Jondeau


Financial leverage and EPS

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



3. Modigliani-Miller Propositions (No Taxes)

Recession Expected ExpansionEPS 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 $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: $800 2$1,200 3

B

S= =



Homemade 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 the some of the firm’s debt gets us to the ROE of the unlevered firm.This is the fundamental insight of MM.



Homemade (Un)Leverage: An Example

• Proposition I– Firm value is not affected by leverage:

• Proposition II– Leverage increases the risk and return to stockholders

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)

SL is the value of levered equity

B is the value of debt

L UV V=

0 0( / )( )S L Br r B S r r= + −

0Expected earnings to unlevered firm

Unlevered equityr =



The MM Propositions I & II (No Taxes)

Shareholders in a levered firm receive Bondholders receive

Total cash flow to all stakeholders:

The present value of this stream of cash flows is VL

Clearly

The present value of this stream of cash flows is VU

BEBIT r B− Br B

( )B BEBIT r B r B− +

( )B BEBIT r B r B EBIT− + =

L UV V=



The MM Proposition I – Derivation

rWACC is constant for a firm regardless of its capital structure. It is therefore equal to the cost of capital for an all-equity firm

Multiply both sides by

0B SB S B B S S B S

r r rS B S S B S S

+ + ++ =+ +

0.WACCr r=

WACC B SB S

r r rB S B S

= ++ +

0B SB S

r r rB S B S

+ =+ +

B S

S

+

0B SB B S

r r rS S

++ =

0 0B SB B

r r r rS S

+ = +0 0( )S B

Br r r r

S= + −



The MM Proposition II – Derivation

Debt-to-equity Ratio (B/S)

Cost of Capitalr (%)

r0

rB

WACC B SL L

B Sr r r

B S B S= +

+ +

0 0( )S BL

Br r r r

S= + −

rB




• Proposition I (with Corporate Taxes)– Firm value increases with leverage:

• Proposition II (with Corporate Taxes)– Some of the increase in equity risk and return is offset

by interest tax shield

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

L U CV V Bτ= +

0 0( / )(1 )( )S L C Br r B S r rτ= + − −



4. Modigliani-Miller Propositions (With Taxes)

Shareholders in a levered firm receive Bondholders receive

Total cash flow to all stakeholders:

The present value of this stream of cash flows is VL

Clearly

The present value of the first term is VU

The present value of the second term is τCB

( ) (1 )B CEBIT r B τ− × − Br B

( ) (1 )B C BEBIT r B r Bτ− × − +

( ) (1 )

(1 ) (1 )

(1 )

B C B

C B C B

C C B

EBIT r B r B

EBIT r B r B

EBIT r B

ττ ττ τ

− × − += × − − × − += × − +

L U CV V Bτ= +EMBAEMBAEMBAEMBA 19/2719/2719/2719/27Eric JondeauEric JondeauEric JondeauEric Jondeau


The MM Proposition I – Derivation

Start with MM Proposition I with taxes:

Since

The cash flows from each side of the balance sheet must equal:

Divide both sides by S

which reduces to

L U CV V Bτ= +

(1 )L U C

U C

V S B S B V B

V S B

ττ

= + ⇒ + = += + −

0

0[ (1 )]S B U C B

S B C C B

Sr Br V r B r

Sr Br S B r B r

ττ τ

+ = ++ = + − +

0[1 (1 )]B B BS B C C BS S Sr r r rτ τ+ = + − +

0 0(1 )( )S C BB

r r r rS

τ= + − −




Cost of Capitalr (%)

r0

rB

0 0(1 )( )S C BL

Br r r r

Sτ= + − −

(1 ) LWACC C B S

L L

SBr r r

B S B Sτ= − +

+ +

0 0( )S BL

Br r r r

S= + −

Debt-to-equity Ratio (B/S)EMBAEMBAEMBAEMBA 21/2721/2721/2721/27Eric JondeauEric JondeauEric JondeauEric Jondeau


The Effect of Financial Leverage with Corp Taxes

All-EquityRecession Expected Expansion

EBIT $1,000 $2,000 $3,000Interest 0 0 0EBT $1,000 $2,000 $3,000Taxes (35%) $350 $700 $1,050Total Cash Flow to S/H $650 $1,300 $1,950

LeveredRecession Expected Expansion

EBIT $1,000 $2,000 $3,000Interest ($8000 at 8% ) $640 $640 $640EBT $360 $1,360 $2,360Taxes (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-τC)+τCrBB $650+$224 $1,300+$224 $1,950+$224

$874 $1,524 $2,174EMBAEMBAEMBAEMBA 22/2722/2722/2722/27Eric JondeauEric JondeauEric JondeauEric Jondeau


Total Cash Flow to Investors Under Each Capital Structure with Corporate 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 isgreater than the equity of the unlevered firm.

S

G

S

G

B

All-equity firm Levered firm




The sum of the debt plus the equity of the levered firm is greater than the equity of the unlevered firm.

This is how cutting the pie differently can make the pie larger:the government takes a smaller slice of the pie!

All-equity firm Levered firm

S

G

S

G

B




• In a world of no taxes, the value of the firm is unaffected by capital structure.

• This is MM Proposition I:

• Proposition I holds because shareholders can achieve any pattern of payouts they desire with homemade leverage.

• In a world of no taxes, MM Proposition II states that leverage increases the risk and return to stockholders

L UV V=

0 0( )S BL

Br r r r

S= + −



Summary: No Taxes

• In a world of taxes, but no bankruptcy costs, the value of the firm increases with leverage.

• This is MM Proposition I:

• Proposition I holds because shareholders can achieve any pattern of payouts they desire with homemade leverage.

• In a world of taxes, MM Proposition II states that leverage increases the risk and return to stockholders.

0 0(1 )( )S C BL

Br r r r

Sτ= + − −

L U CV V Bτ= +



Summary: Taxes

• So far, we have seen MM 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 session is to get comfortable with “MM algebra”.



Prospectus: Bankruptcy Costs

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