CHAPTER 17 Capital Structure Decisions: Extensions

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Copyright © 2002 by Harcourt Inc. All rights reserved.

CHAPTER 17Capital Structure Decisions:

Extensions

MM and Miller models

Hamada’s equation

Financial distress and agency costs

Trade-off models

Asymmetric information theory

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Who are Modigliani and Miller (MM)?

They published theoretical papers that changed the way people thought about financial leverage.

They won Nobel prizes in economics because of their work.

MM’s papers were published in 1958 and 1963. Miller had a separate paper in 1977. The papers differed in their assumptions about taxes.

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What assumptions underlie the MMand Miller models?

Firms can be grouped into homogeneous classes based on business risk.

Investors have identical expectations about firms’ future earnings.

There are no transactions costs.

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All debt is riskless, and both individuals and corporations can borrow unlimited amounts of money at the risk-free rate.

All cash flows are perpetuities. This implies perpetual debt is issued, firms have zero growth, and expected EBIT is constant over time.

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MM’s first paper (1958) assumed zero taxes. Later papers added taxes.

No agency or financial distress costs.

These assumptions were necessary for MM to prove their propositions on the basis of investor arbitrage.

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Proposition I:

VL = VU.

Proposition II:

ksL = ksU + (ksU - kd)(D/S).

MM with Zero Taxes (1958)

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Firms U and L are in same risk class.

EBITU,L = $500,000.

Firm U has no debt; ksU = 14%.

Firm L has $1,000,000 debt at kd = 8%.

The basic MM assumptions hold.

There are no corporate or personal taxes.

Given the following data, find V, S,ks, and WACC for Firms U and L.

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1. Find VU and VL.

VU = = = $3,571,429.

VL = VU = $3,571,429.

Questions: What is the derivation of the VU equation? Are the MM assumptions required?

EBITksU

$500,0000.14

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VL = D + S = $3,571,429

$3,571,429 = $1,000,000 + S

S = $2,571,429.

2. Find the market value of Firm L’s debt and equity.

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3. Find ksL.

ksL = ksU + (ksU - kd)(D/S)

= 14.0% + (14.0% - 8.0%)( )= 14.0% + 2.33% = 16.33%.

$1,000,000$2,571,429

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4. Proposition I implies WACC = ksU. Verify for L using WACC formula.

WACC = wdkd + wceks = (D/V)kd + (S/V)ks

= ( )(8.0%)

+( )(16.33%)

= 2.24% + 11.76% = 14.00%.

$1,000,000$3,571,429

$2,571,429$3,571,429

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Graph the MM relationships between capital costs and leverage as measured

by D/V.

Without taxesCost of Capital (%)

26

20

14

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0 20 40 60 80 100Debt/Value Ratio (%)

ks

WACC

kd

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The more debt the firm adds to its capital structure, the riskier the equity becomes and thus the higher its cost.

Although kd remains constant, ks increases with leverage. The increase in ks is exactly sufficient to keep the WACC constant.

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Graph value versus leverage.

Value of Firm, V (%)

4

3

2

1

0 0.5 1.0 1.5 2.0 2.5Debt (millions of $)

VLVU

Firm value ($3.6 million)

With zero taxes, MM argue that value is unaffected by leverage.

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Find V, S, ks, and WACC for Firms U and L assuming a 40% corporate

tax rate.

With corporate taxes added, the MM propositions become:

Proposition I:

VL = VU + TD.

Proposition II:

ksL = ksU + (ksU - kd)(1 - T)(D/S).

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Notes About the New Propositions

1. When corporate taxes are added,VL VU. VL increases as debt is added to the capital structure, and the greater the debt usage, the higher the value of the firm.

2. ksL increases with leverage at a slower rate when corporate taxes are considered.

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1. Find VU and VL.

Note: Represents a 40% decline from the no taxes situation.

VL = VU + TD = $2,142,857 + 0.4($1,000,000)

= $2,142,857 + $400,000

= $2,542,857.

VU = = = $2,142,857.EBIT(1 - T)ksU

$500,000(0.6)0.14

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VL = D + S = $2,542,857

$2,542,857 = $1,000,000 + S

S = $1,542,857.

2. Find market value of Firm L’s debt and equity.

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3. Find ksL.

ksL = ksU + (ksU - kd)(1 - T)(D/S)

= 14.0% + (14.0% - 8.0%)(0.6)( ) = 14.0% + 2.33% = 16.33%.

$1,000,000$1,542,857

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4. Find Firm L’s WACC.

WACCL= (D/V)kd(1 - T) + (S/V)ks

= ( )(8.0%)(0.6)

+( )(16.33%)

= 1.89% + 9.91% = 11.80%.When corporate taxes are considered, the WACC is lower for L than for U.

$1,000,000$2,542,857

$1,542,857$2,542,857

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Cost of Capital (%)

26

20

14

8

0 20 40 60 80 100Debt/Value Ratio (%)

MM relationship between capital costs and leverage when corporate taxes are

considered.

ks

WACCkd(1 - T)

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Value of Firm, V (%)

4

3

2

10 0.5 1.0 1.5 2.0 2.5

Debt(Millions of $)

VL

VU

MM relationship between value and debt when corporate taxes are considered.

Under MM with corporate taxes, the firm’s value increases continuously as more and more debt is used.

TD

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Assume investors have the following tax rates: Td = 30% and Ts = 12%. What is the gain from leverage according to

the Miller model?

Miller’s Proposition I:

VL = VU + [1 - ]D.

Tc = corporate tax rate.Td = personal tax rate on debt income.Ts = personal tax rate on stock income.

(1 - Tc)(1 - Ts)(1 - Td)

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Tc = 40%, Td = 30%, and Ts = 12%.

VL = VU + [1 - ]D

= VU + (1 - 0.75)D

= VU + 0.25D.

Value rises with debt; each $100 increase in debt raises L’s value by $25.

(1 - 0.40)(1 - 0.12)(1 - 0.30)

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How does this gain compare to the gain in the MM model with corporate taxes?

If only corporate taxes, then

VL = VU + TcD = VU + 0.40D.

Here $100 of debt raises value by $40. Thus, personal taxes lowers the gain from leverage, but the net effect depends on tax rates.

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If Ts declines, while Tc and Td remain constant, the slope coefficient (which shows the benefit of debt) is decreased.

A company with a low payout ratio gets lower benefits under the Miller model than a company with a high payout, because a low payout decreases Ts.

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When Miller brought in personaltaxes, the value enhancement of debt

was lowered. Why?

1. Corporate tax laws favor debt over equity financing because interest expense is tax deductible while dividends are not.

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2. However, personal tax laws favor equity over debt because stocks provide both tax deferral and a lower capital gains tax rate.

3. This lowers the relative cost of equity vis-a-vis MM’s no-personal-tax world and decreases the spread between debt and equity costs.

4. Thus, some of the advantage of debt financing is lost, so debt financing is less valuable to firms.

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What does capital structure theoryprescribe for corporate managers?

1. MM, No Taxes: Capital structure is irrelevant--no impact on value or WACC.

2. MM, Corporate Taxes: Value increases, so firms should use (almost) 100% debt financing.

3. Miller, Personal Taxes: Value increases, but less than under MM, so again firms should use (almost) 100% debt financing.

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Firms don’t follow MM/Miller to 100% debt. Debt ratios average about 40%.

However, debt ratios did increase after MM. Many think debt ratios were too low, and MM led to changes in financial policies.

Do firms follow the recommendationsof capital structure theory?

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Define financial distress andagency costs.

Financial distress: As firms use more and more debt financing, they face a higher probability of future financial distress, which brings with it lower sales, EBIT, and bankruptcy costs. Lowers value of stock and bonds.

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Agency costs: The costs of managers not behaving in the best interests of shareholders and the resulting costs of monitoring managers’ actions. Lowers value of stock and bonds.

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How do financial distress and agency costs change the MM and Miller

models?

MM/Miller ignored these costs, hence those models show firm value increasing continuously with leverage.

Since financial distress and agency costs increase with leverage, such costs reduce the value of debt financing.

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Here’s a valuation model which includes financial distress and

agency costs:

X represents either Tc in the MM model or the more complex Miller term.

Now, optimal leverage involves a tradeoff between the tax benefits of debt and the costs associated with financial distress and agency.

VL = VU + XD - - .PV of expected

fin. distress costsPV of agency

costs

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Cost of Capital (%)

14

4

Debt ($)

Relationships between capital costs and leverage when financial distress

and agency costs are considered.

ks

WACC

kd(1 - T)

D*

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Relationship between value and leverage.

Value of Firm ($)

Debt ($)

4

3

2

1

Note that value is maximized and WACC is minimized at the same capital structure.

D*

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How are financial and business risk measured in a market risk framework?

ksL = kRF + (kM - kRF)bU

+ (kM - kRF)bU(1 - T)(D/S)

= + + .

(Hamada’s equation)

Puretimevalue

Businessrisk

premium

Financialrisk

premium

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Hamada’s equation for beta:

bL = +

= +

= + .

bU

Unlevered beta, which reflects the business risk of the

firm

Business risk

bU(1 - T)(D/S)

Increased volatility of the returnsto equity

due to the use of debt

Financialrisk

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Results of a survey by Donaldson and the asymmetric information theory.

Firms follow a specific financing order:First use internal funds.Next, draw on marketable securities.Then, issue new debt.Finally, and only as a last resort, issue new

common stock.

What is the “pecking order theory”of capital structure?

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Does the pecking order theory make sense? Explain.

Is the pecking order theory consistent with the trade-off theory?

It is consistent with the asymmetric information theory, in which managers avoid issuing equity.

It is not consistent with trade-off theory.

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Theory recognizes that market participants do not have homogeneous expectations--managers typically have better information than investors.

Thus, financing actions are interpreted by investors as signals of managerial expectations for the future.

What is the asymmetric information theory of capital structure?

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Managers will issue new common stock only when no other alternatives exist or when the stock is overvalued.

Investors recognize this, so new stock sales are treated as negative signals and stock price falls.

Managers do not want to trigger a price decline, so firms maintain a reserve borrowing capacity.

CHAPTER 17 Capital Structure Decisions: Extensions

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