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SFU Bus413 Fall 2011

Does Debt Policy Matter?

Lecture 14

Chapter 17

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Topics Covered

• Leverage in a Competitive Tax Free Environment Modigliani-Miller theorem 1

• Financial Risk and Expected Returns

and Modigliani-Miller theorem 2

• The Weighted Average Cost of Capital

2

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Motivation

• Financing: Your firm needs to raise capital for amajor new investment.

Should it obtain financing through the issuance of newdebt? New equity? What kind of debt? What kind of

equity? How will the stock market react your decision?What price should the levered equity sell for? Which isthe best capital structure choice for the entrepreneur?

3

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Why Capital Structure is Irrelevant (for theFirm Value)

• The main conclusion of this chapter: in perfect capital markets , capital structure does not affectthe firm’s market value.

• Intuition:

The value of the firm is determined by the value of theassets (the left half of the balance sheet)

• The value of the assets is the sum of the DCFs of theproject

• The discount rate is also determined by asset (project’s)

characteristics because the cost of capital is determined byasset characteristics

4

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The Modigliani-Miller Theorem IAssumptions

• Assume Perfect Capital Markets1. No taxes

2. No transactions costs.

3. Firm’s cash flows and decisions are not affectedby the choice of financial structure.

4. Symmetric information.

No agency costs

5. No arbitrage (prices are fair, equal to PV offuture cash flows).

5

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Assumptions 1, 2, and 4

• No taxes.• No costs of financial distress or bankruptcy costs.

• No issuance costs.

• No security trading costs.

• Symmetric information: Every agent has the

same information. Nobody knows more thananybody else.

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Assumption 3 means

• (Assumption 3: Firm’s cash flows and decisions are notaffected by the choice of financial structure)

• Financial structure does not affect

investment policy of the firm.

managerial effort.

corporate governance, compensation of management,

and managerial behavior. bargaining power of firm.

competitive dynamics between firms.

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The Modigliani-Miller Theorem I

• ASSUME:1. No taxes

2. No transactions costs.

3. Firm’s cash flows and decisions are not affected by the choice of

financial structure.4. Symmetric information.

5. No arbitrage

•

THEN: The total market value of the firm is notaffected by how the firm is financed.

8

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Intuition and Implications of M&M I

• The size of a pie is independent of how it is sliced

• Value comes from project choice on the LHS of

the balance sheet (from project CFs), not fromfinancing on the RHS of the balance sheet

• The value of an asset is preserved regardless ofthe type of claims against it (debt or equity)

9

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Intuition of M&M 1 : “pie theory”

10

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Derivation of M&M1(Can We Create Value by Splitting a Pie?)

11

U L V V

1) Let V U be the value of unlevered

firm; it is equal to earnings ( EBIT).

Dr Dr EBIT isersstakehold allto flowcashtotaltheThus,

D D )(

The PV of this stream of cash flows is the value of levered firm V L .

EBIT Dr Dr EBIT Clearly

D D )(

Consequently,

Dr EBIT D Dr D

2) In a levered firm, Shareholders receive Bondholders receive

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12

All Equity Financed

201510%5(%)sharesonReturn

2.001.501.00$.50shareperEarnings

2,0001,5001,000$500IncomeOperatingD C B A:Outcomes

10,000$SharesofValueMarket

$10shareperPrice

1,000sharesofNumber

Data

The

Expected

outcome

Effect of Debt on EPSExample: Macbeth Spot Removers

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13

Issue $5000

debt and

repurchase

500 shares,i.e., do Leveraged

Recapitalization.

Result:

50% Debt, 50% Equity.

Let rd = 10%.30 20100%(%) shares on Return

321$0shareperEarnings

500,11,000500$0earningsEquity

500500500$500Interest000,21,5001,000$500IncomeOperating

CBA

Outcomes

5,000$debtof ueMarket val

5,000$Sharesof ValueMarket

$10shareperPrice

500sharesof Number

Data

D

Example - Macbeth (contd.)

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14

Example - Borrowing and EPS at Macbeth

Borrowing increases expected EPS whenIncome is greater than $1000. Borrowingdecreases expected EPS when Income isless than $1000.

The steeper black line means thesame fluctuations in OI lead to

greater fluctuations in EPS in themore levered firm, i.e. EPS are riskier in the levered firm.

Leverage increases the risk of

equity, even when there is no risk that the firm can default. Thus,while debt may be cheaper thanequity, its use raises the cost ofcapital for equity.

Expected

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Homemade Leverage: Intuition for M&M

• Homemade Leverage When investors use leverage in their own portfolios to

adjust the leverage choice made by the firm.

• MM demonstrated that if investors would prefer analternative capital structure to the one the firm haschosen, investors can borrow or lend on their ownand achieve the same result.

15

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16

Debt replicated by investors.- The Firm is All Equity Financed;

- Borrow $10 and invest $20 in two shares.

30 20100%(%)investment on Return

3.002.001.000$investmentonearningsNet

1.001.001.00$1.0010%@Interest:LESS

4.003.002.00$1.00sharestwoonEarnings

DCBA

Outcomes

Homemade Leverage. Macbeth Example

The 20% return here is the same as for the levered firm.

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• Leverage increases the risk of the firm’s equity. Investors in a levered firm will require a higher

expected return to compensate for the increased risk.

MM’s first proposition can be used to derive an

explicit relationship between leverage and the equitycost of capital (which is MM Proposition 2).

Start with definitions.

• Note that the numerator below is often just Net Income

The Effect of Leverage on Risk and Return

securitiesallofvaluemarket

incomeoperatingexpected ArROAassetsonreturnExpected

17

equityofvaluemarket

incomeoperatingexpected ErROEequityonreturnExpected

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•

From

•

obtain

Derivation ofModigliani-Miller Proposition II

E D E r

E D Dr r

E D A

18

E D

r r r r D A A E

Since assets=equity in an unlevered firm, the return on unlevered equity r U in this firm is the return on assets: r U = r A .

Then the return on levered equity r E is

E

Dr r r r DU U E

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• The relation between Leverage and the EquityCost of Capital

MM Proposition II:

•The cost of capital of levered equity is equal to the cost ofcapital of unlevered equity plus a premium that isproportional to the market value debt-to-equity ratio.

• Cost of Capital of Levered Equity

Modigliani-Miller II (cont'd)

E

Dr r r r DU U E

19

The amount of the premium depends on the amount of leverage,measured by the firm’s market value debt-equity ratio, D/E.

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M&M Proposition II in action: Macbeth

20

15.000,10

1500

rr AU

securitiesallofvaluemarket

incomeoperatingexpected

20%or20.

5000500010.15.15.

E r

Expected return on unlevered equity:

Expected return on levered equity: E

Dr r r r DU U E

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Leverage and Risk: Macbeth Example

21

Leverage increases not only the return, but also the risk of Macbeth shares (If OI declines, ROE declines by more in a

levered firm):

Scenario:

Operating Income Decline

ChangesFrom: $1500 To: $500

All equity

EPS ($) 1.50 0.50

Return onequity

15% 5% -10%

50% debt

EPS ($) 2 0

Return on

equity

20% 0 -20%

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Leverage and Returns.Example: Increasing Leverage may affect rd

%75.12100

7015

100

305.7

A

E D A

r

E D

E r

E D

Dr r

22

Asset Value 100 Debt (D) 30

Equity (E) 70

Asset Value 100 Firm Value (V) 100

Let r d = 7.5%, and r e = 15%.

Market Value Balance Sheet

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Leverage and Returns Example (contd.)

%0.16

100

60

100

40

875.775.12

e

e

r

r

23

What happens to r e when the firm borrows more, resulting in a

higher cost of borrowing? - Let r d = 7.5% change to 7.875%.

re = ??

Market Value Balance SheetAsset Value 100 Debt (D) 40

Equity (E) 60

Asset Value 100 Firm Value (V) 100

Both required returns on debt and equity increase.

Note that rA is constant above because assets are unaffected.

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Unlevered Firm’s Weighted Average Cost of Capital

• If a firm is unlevered, all of the free cashflows generated by its assets are paid out toits equity holders.

The market value, risk, and cost of capital for the firm’s

assets and its equity coincide, and therefore,

24

U A r r

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Levered Firm’s Weighted Average Cost of Capital

• If a firm is levered, project return rA is equal to thefirm’s weighted average cost of capital.

Weighted Average Cost of Capital (No Taxes ) definition

We also know that COC of assets is

Therefore,

25

E D

E r E D

Dr r E D A

U AWACC r r r

E D E r

E D Dr r

E DWACC

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Leverage and WACC (cont'd)

• With perfect capitalmarkets, a firm’s

WACC is independentof its capital structureand is equal to itsequity cost of capital ifit is unlevered, whichmatches the cost of

capital of its assets.

• Debt-to-Value Ratio - thefraction of a firm’s enterprise

value that corresponds todebt. 26

UE AWACC r r r

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27

Cost of Equity, Cost of Debt, and the WACC:MM II assuming No Corporate Taxes

Debt-to-equity

Ratio

C o s t

o f c a p i t a l : r

( % )

r U

r D

E DWACC r E D

E r

E D

Dr

)( DU U E r r E

Dr r

r D

E

D

Assume (just for now) that debt is risk-free : rd

does notincrease with leverage.

27

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28

r

DE

rD

rE

M&M Proposition II with Risky Debt (rD changeswith leverage)

rWACC=rA

Risk free

debt

Risky debt

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Levered and Unlevered Betas

•

The effect of leverage on the risk of a firm’s securities can also beexpressed in terms of betas:

= =

+ +

+

• Unlevered Beta (bU or bUE)

A measure of the risk of a firm as if it did not have leverage, whichis equivalent to the beta of the firm’s assets: bA=bU

• If your goal is to estimate the beta for an investment

project, first, you should calculate the unlevered betas offirms with comparable investments (using the formulaabove). Then apply the effects of your firm’s leverage:

= + ( − )

29

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Example: Unlevered Beta

• Problem You are managing a food company. Estimates of equity

betas and market debt-equity ratios for severalcomparable stocks are shown below.

Which firm has riskier assets?

30

Name Equity Beta Debt-Equity Ratio Debt Beta

Kraft Foods Inc. 0.65 0.35 0.10

H.J. Heinz Co. 0.79 2.23 0.27Lancaster Colony 0.87 0.00 0.00

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Example: Unlevered Beta

•

Solution Since = (Assets=Equity in a firm with no debt), we just need tocalculate the unlevered beta for each of the firms.

= =

+ +

+

31

Name Equity Beta E/(E+D) Debt Beta D/(E+D) βU=βA

Kraft Foods Inc. 0.65 74.07% 0.10 25.93% 0.51

H.J. Heinz Co. 0.79 30.96% 0.27 69.04% 0.43

Lancaster Colony 0.87 100.00% 0.00 0.00% 0.87

The upshot: levered equity beta is not appropriate to compare riskacross firms; we need to remove the effects of financing, i.e. unlever the

betas.

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MM and (Unsatisfied) Clienteles (p.432)

•

If corporations can borrow more cheaply than someindividual investors, the perfect market assumptions areviolated. Then, there can be a clientele of such investorswho would pay a premium for shares of levered firms.

17.5.f. Borrowing increases the firm value if there is a clientele ofinvestors with a reason to prefer debt.

True or False?

• Unsatisfied clienteles appear due to temporary marketimperfections (e.g., interest-rate ceilings, constraints forsmall investors, which lead to temporary profits fromissuing additional debt in floating-rate notes, creation of

money market funds). 32

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33

Summary. M&M without Taxes

• In a world of no taxes and perfect capital markets, thevalue of the firm is unaffected by capital structure.

• This is M&M Proposition I:

V L

= V U

• In a world of no taxes, M&M Proposition II states that

leverage increases the risk and return to stockholders

E

Dr r r

E

Dr r r r DU U D A A E )()(

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