Chapter 16 ACTSC372

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© 2011 McGraw–Hill Ryerson Limited

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Chapter 16

Capital Structure: Basic Concepts

Instructor: Fan YangACTSC 372Winter 2015

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Chapter Outline

• The Capital-Structure Question and The Pie Theory

• The Impact of Financial Leverage on the– Firm Value– EPS– ROE

• Modigliani and Miller (MM): Propositions I and II– No Taxes– With Taxes

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The Capital-Structure Question and The Pie Theory• Recall that the firm’s mix of securities is known as

its capital structure.• 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

Three key questions:• What should the management do to

maximize shareholders’ interest?• Does a change in capital structure

affect the value of the firm?• Does it exist an optimal debt to equity

ratio (B/S) or debt to asset ratio (B/V ) that maximizes shareholders’ interest?

Value of the Firm

S BBS BS B

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Maximizing Firm Value versus Maximizing Stockholder Interests

• Management is appointed by the shareholders and hence should attempt to maximize shareholders’ interests• this in turn should maximize market values of

the equity•

Maximizing Shareholders’ Interests

Maximizing Equity

Maximizing Firm Value• Since debt (interest) payments are fixed

• shareholders only receive the residual cash flows

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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.)

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EPS and ROE Under Both Capital StructuresAll-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

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 3.0% 11.3% 19.7%

Proposed Shares Outstanding = 240 shares

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Break-Even Analysis

(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

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Break-Even Analysis (Cont.)

• Is leverage always beneficial to the shareholders?• It depends on EBIT• EBIT > break-even point,• leverage increases EPS & ROE• EBIT < break-even point, leverage decreases

EPS & ROE• In any case, financial leverage increases the

volatility of EPS and ROE,• increases the risk of equity (higher slope)

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Modigliani and Miller (1958)• Assumptions:

– 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

• Modigliani & Miller (MM) Proposition I (no taxes):VL = VU

• VU (VL) is the value of the unlevered (levered) firm

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Proof of MM Proposition I (No Taxes)• Consider Two firms: U and L, both with identical EBIT

– Firm U is an unlevered firm, and firm L is a levered firm

• Need to show a firm cannot change its total value by merely changing the proportions of its capital structure

• Key idea of the proof: Through “homemade leverage”, individuals (or investors) can either duplicate or undo the effects of corporate leverage

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Proof of MM Proposition I (No Taxes) (cont.)• Consider the following two strategies:

– Strategy X: Invest 𝛼𝛼 proportion of 𝑆𝑆𝐿𝐿 (by buying the appropriate number of shares)

– Strategy Y: Invest 𝛼𝛼 proportion of 𝑆𝑆𝑈𝑈 and borrow proportion of 𝐵𝐵𝐿𝐿. (The Homemade Leverage Portfolio)

• We must have 𝑉𝑉𝑈𝑈 = 𝑉𝑉𝐿𝐿 to avoid arbitrage!• Homemade Leverage: investor can replicate the levered firm

by borrowing and taking appropriate position in unlevered firm (and vice versa)

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Implications of MM Proposition I (No Taxes)

• the value of the firm is independent of the firm’s capital structure– capital structure is irrelevant

• capital restructuring does not (in itself) create value

• Investment decision does not depend on the source of funding

• 𝑟𝑟𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊 is constant for a given firm, regardless of capital structure (no taxes)

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Required Return to Equity holders with Leveraging

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• 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

MM Proposition II (No Taxes)

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MM Proposition II (No Taxes)

The derivation is straightforward:

SBWACC rSB

SrSB

Br ×+

+×+

= 0set Then rrWACC =

0rrSB

SrSB

BSB =×

++×

+ SSB +by sidesboth multiply

0rSSBr

SBS

SSBr

SBB

SSB

SB+

=×+

×+

+×+

×+

0rSSBrr

SB

SB+

=+×

00 rrSBrr

SB

SB +=+× )( 00 BS rrSBrr −+=

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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

SBWACC rSB

SrSB

Br ×+

+×+

=

)( 00 BL

S rrSBrr −×+=

rB

SB

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What Determines the Cost of Capital?

• MM argues that the firm’s overall cost of capital cannot be reduced as debt is substituted for equity, even though debt appears to be cheaper than equity– as firm adds debt, more projects are financed by lower-cost

debt– but the remaining equity becomes more risky, hence cost of

equity capital rises– MM proves that these two effects exactly offset each other!

• return of equity compensates for two sources of risk:– business risk - equity risk that comes from the nature of the

firm’s operating activities (reflected in 𝛽𝛽𝑈𝑈)– financial risk - extra risk from using debt financing

(measured by 𝐵𝐵𝑆𝑆

(𝛽𝛽𝑈𝑈-𝛽𝛽𝐵𝐵))

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An Example (No Taxes)• An all-equity firm has 10 million shares outstanding with

– share price $20,– equity beta = 1.0

• The firm plans to issue $50 million of 10% debt and use the proceeds to pay a dividend to shareholders

• Given 𝑟𝑟𝑓𝑓= 6% and market risk premium of 8%• What is the effect of this capital restructuring on:

– (a) the value of the firm,– (b) the 𝑟𝑟𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊

– (c) the required return on equity– (d) the equity beta– (e) the wealth of the firm’s shareholders?

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Solution

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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(

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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

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The Effect of Financial Leverage on the Cost of Debt and Equity Capital with Corporate Taxes

Debt-to-equityratio (B/S)

Cost of capital: r(%)

r0

rB

)()1( 00 BCL

S rrTSBrr −×−×+=

SL

LCB

LWACC r

SBSTr

SBBr ×

++−××

+= )1(

)( 00 BL

S rrSBrr −×+=

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

LeveredRecession Expected Expansion

EBIT $1,000 $2,000 $3,000Interest ($8000 @ 8% ) 640 640 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

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

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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.

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

S G

All-equity firm Levered firm

S G

B

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Summary: 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 −×+=

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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

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

)()1( 00 BCL

S rrTSBrr −×−×+=

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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”.

Chapter 16 ACTSC372

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Transcript of Chapter 16 ACTSC372