Capital Structure: Basic Concepts

Chapter 16

Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

16-2

Key Concepts and Skills Understand the effect of financial leverage

(i.e., capital structure) on firm earnings Understand homemade leverage Understand capital structure theories with and

without taxes Be able to compute the value of the unlevered

and levered firm

16-3

Chapter Outline16.1 The Capital Structure Question and The Pie Theory

16.2 Maximizing Firm Value versus Maximizing Stockholder Interests

16.3 Financial Leverage and Firm Value: An Example

16.4 Modigliani and Miller: Proposition II (No Taxes)

16.5 Taxes

16-4

16.1 Capital Structure and the Pie 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 firm’s management 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.

Value of the Firm

S BS BS BS B

16-5

Stockholder InterestsThere are 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.

16-6

Stockholder InterestsAn example: Firm has 10,000 shares. Share price = $25. Debt

has a market value of $100,000.

V = B + S = 100,000 + 10,000 * 25 = 350,000

Now suppose firm borrows another $50,000 and pays it immediately as a special dividend.

B = 100,000 + 50,000 = 150,000

What would be shareholder gain/loss if firm value changes?

16-7

Example cont’dV increases to

$380,000

V stays constant at $350,000

V decreases to $320,000

S $230,000 $200,000 170,000

Shareholder gain from dividend

$50,000 $50,000 $50,000

Capital loss -$20,000 -$50,000 -80,000

Net gain/loss to shareholders

$30,000 0 -30,000

Consider Three Possibilities:

• Changes in capital structure benefit the stockholders if and only if the value of the firm increases. •Managers should choose the capital structure that they believe will have the highest firm value (to make the pie as big as possible).

16-8

16.3 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$12,000

2/38%240$50

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

16-9

EPS and ROE Under Current Structure (un-levered firm)

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

16-10

EPS and ROE Under Proposed Structure (levered firm)

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 1.8% 6.8% 11.8%

ROE 3.0% 11.3% 19.7%

Proposed Shares Outstanding = 240 shares

16-11

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

EBIT in dollars, no taxes

Advantage to debt

Disadvantage to debt

16-12

Assumptions of the M&M 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

16-13

Homemade Leverage: An ExampleRecession 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) 3.0% 11.3% 19.7%We are buying 40 shares of a $50 stock, using $800 in margin. We get the same ROE as if we bought into a levered firm.

Our personal debt-equity ratio is: 32

200,1$

800$

S

B

16-14

Homemade (Un)Leverage: An ExampleRecession Expected Expansion

EPS of Levered Firm $1.50 $5.67 $9.83Earnings 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

16-15

MM Proposition I (No Taxes) We can create a levered or unlevered position

by adjusting the trading in our own account. This homemade leverage suggests that capital

structure is irrelevant in determining the value of the firm:

VL = VU

16-16

16.4 MM Proposition II (No Taxes) 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

16-17

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

16-18

MM Proposition II (No 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

16-19

16.5 MM Propositions I & II (With 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 the

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

16-20

MM Proposition I (With Taxes)

BTVV CUL

BRTBREBIT BCB )1()(

is rsstakeholde all toflowcash totalThe

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(

16-21

MM Proposition II (With 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

16-22

The Effect of Financial Leverage

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(

)( 00 BL

S RRS

BRR

16-23

Total Cash Flow to InvestorsRecession 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

Recession 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 $884+$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

All

Equ

ity

Lev

ered

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Total Cash Flow to Investors

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.

This is how cutting the pie differently can make the pie “larger.” -the government takes a smaller slice of the pie!

S G S G

B

All-equity firm Levered firm

16-25

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

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

In a world of no taxes, M&M Proposition I states that leverage increases the risk and return to stockholders.

)( 00 BL

S RRS

BRR

16-26

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 Proposition II holds because The levered firm pays less in

taxes than does the all-equity firm.. 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

16-27

15-27

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”.

16-28

Quick Quiz Why should stockholders care about

maximizing firm value rather than just the value of the equity?

How does financial leverage affect firm value without taxes? With taxes?

What is homemade leverage? Problems # 16.1, 2, 3, 4, 6, 8, 10, 11