Corporate finance 7e ross ch15

Chapter Outline15.1 The Capital-Structure Question and The Pie Theory 15.2 Maximizing Firm Value versus Maximizing Stockholder Interests15.3 Financial Leverage and Firm Value: An Example

15

Capital Structure:

Basic Concepts

Chapter Outline

15.1 The Capital-Structure Question and The Pie Theory

15.2 Maximizing Firm Value versus Maximizing

Stockholder Interests15.3 Financial Leverage and Firm Value: An Example

15.4 Modigliani and Miller: Proposition II (No Taxes)

15.5 Taxes

15.6 Summary and Conclusions

15.1 The Capital-Structure Question and The Pie Theory

15.2 Maximizing Firm Value versus Maximizing

Stockholder Interests15.3 Financial Leverage and Firm Value: An Example

15.4 Modigliani and Miller: Proposition II (No Taxes)

15.5 Taxes

15.6 Summary and Conclusions

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

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, the the

firm should pick the debt-equity

ratio that makes the pie as big as

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

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

Financial Leverage, EPS, and ROE

240

$50

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

EPS and ROE Under Current Capital

EPS and ROE Under Proposed Capital

EPS and ROE Under Both Capital Structures

Financial Leverage and EPS

(2.00) 0.00 2.00 4.00 6.00 8.00 10.00 12.00

EBIT in dollars, no taxes

Advantage

to debt Disadvantage

to debt

Assumptions of the Modigliani-Miller

Model

Homogeneous Expectations Homogeneous Business Risk Classes Perpetual Cash Flows

Perfect Capital Markets:

Perfect competitionFirms and investors can borrow/lend at the same rateEqual access to all relevant information

No transaction costs

No taxes

Homogeneous Expectations Homogeneous Business Risk Classes Perpetual Cash Flows

Perfect Capital Markets:

Perfect competitionFirms and investors can borrow/lend at the same rateEqual access to all relevant information

No transaction costs

No taxes

Homemade Leverage: An Example

Recession Expected Expansion

EPS of Unlevered Firm $2.50 $5.00 $7.50

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

2 200

, 1

Homemade (Un)Leverage:

An Example

RecessionExpectedExpansion

EPS of Levered Firm $1.50$5.67$9.83

Earnings for 24 shares $36$136$236

Plus interest on $800 (8%) $64$64 $64

ROE (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

RecessionExpectedExpansion

EPS of Levered Firm $1.50$5.67$9.83

Earnings for 24 shares $36$136$236

Plus interest on $800 (8%) $64$64 $64

Net Profits $100$200$300

ROE (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

The MM Propositions I & II (No Taxes)

r B is the interest rate (cost of debt)

r s 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

S is the value of levered equity

B is the value of debt

The MM Proposition I (No Taxes)

receive firm

levered a

in rs

Shareholde

B

r B

receive s

Bondholder

The derivation is straightforward:

B r B

r EBIT  B )  B(

is rs stakeholde all

to flow cash

total the

Thus,

The present value of this stream of cash flows is V L

EBIT B

r B

r EBIT  B )  B  (

Clearly

The present value of this stream of cash flows is V U

The MM Proposition II (No Taxes)

The derivation is straightforward:

S B

S B

S r

S B

S r

S B

both multiply

0

r S

S

B r

S B

S S

S

B r

S B

B S

S

B

S B

S B r

r S

B

S B

B r

r S

The Cost of Equity, the Cost of Debt, and the Weighted Average Cost

of Capital: MM Proposition II with No Corporate Taxes

WACC r

S B

S r

S B

r B

S B

The MM Propositions I & II

(with Corporate Taxes)

Proposition I (with Corporate Taxes)

Firm value increases with leverage

V L = V U + T C B

Proposition II (with Corporate Taxes)

Some of the increase in equity risk and return is offset by interest tax shield

r S = r 0 + (B/S)×(1-T C )×(r 0 - r B )

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 debt

S is the value of levered equity

Proposition I (with Corporate Taxes)

Firm value increases with leverage

V L = V U + T C B

Proposition II (with Corporate Taxes)

Some of the increase in equity risk and return is offset by interest tax shield

r S = r 0 + (B/S)×(1-T C )×(r 0 - r B )

r B is the interest rate (cost of debt)

r S is the return on equity (cost of equity)

r0 is the return on unlevered equity (cost of capital)

B is the value of debt

S is the value of levered equity

The MM Proposition I (Corp Taxes)

B T

V

VL  U  C



) 1

( ) (

receive firm

levered a

in rs Shareholde

Bondholder

B r T

B r EBIT  B )  ( 1  C )  B(

is rs stakeholde all

to flow cash

total the

Clearly

The present value of the first term is V U

The present value of the second term is T C B

B r T

B r T

EBIT   C  B   C  B

B r BT

r B r T

EBIT   C  B  B C  B

The MM Proposition II (Corp Taxes)

Start with M&M Proposition I with taxes:

) (

) 1

B T V

V L  U  C

Since V L S B

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

B C

U B

S Br V r T Br

B r T r

T B

S Br

Sr S  B  [  ( 1  C )] 0  C B

Divide both sides by S

B C C

B

S

B r

T S

B r

S

B

r   [ 1  ( 1  )] 0 

B T V

B

S   U  C



) 1

The Effect of Financial Leverage on the Cost of Debt and

Equity Capital with Corporate Taxes

) 1

S L

L C

B L

S B

S T

r S B

Total Cash Flow to Investors Under Each Capital Structure with Corp Taxes

Total Cash Flow to S/H $650 $1,300 $1,950

LeveredRecession ExpectedExpansion

Interest ($800 @ 8% ) 640640 640

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

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)+T C r B B $650+$224$1,300+$224$1,950+$224

$874$1,524 $2,174

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

B

All-equity firm Levered firm

Total Cash Flow to Investors Under Each Capital Structure with Corp Taxes

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!

B

All-equity firm Levered firm

) 1

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

In the real world, most executives do not like a capital structure of 100% debt because that is a state known as