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Copyright 2002 by Harcourt Inc. All rights reserved.

CHAPTER 17Capital Structure Decisions:

Extensions

MM and Miller models

Hamadas equation

Financial distress and agency costsTrade-off models

Asymmetric information theory

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Who are Modigliani and Miller (MM)?

They published theoretical papersthat changed the way people thoughtabout financial leverage.

They won Nobel prizes in economicsbecause of their work.

MMs papers were published in 1958and 1963. Miller had a separatepaper in 1977. The papers differed intheir assumptions about taxes.

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What assumptions underlie the MM

and Miller models?

Firms can be grouped into

homogeneous classes based onbusiness risk.

Investors have identical

expectations about firms futureearnings.

There are no transactions costs.(More...)

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All debt is riskless, and bothindividuals and corporations canborrow unlimited amounts of moneyat the risk-free rate.

All cash flows are perpetuities. Thisimplies perpetual debt is issued,firms have zero growth, and

expected EBIT is constant over time.

(More...)

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MMs first paper (1958) assumedzero taxes. Later papers addedtaxes.

No agency orfinancial distresscosts.

These assumptions were necessary

for MM to prove their propositionson 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 ofthe VU equation? Are the MM

assumptions required?

EBITksU

$500,0000.14

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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 measuredby D/V.

Without taxesCost of

Capital (%)

26

20

14

8

0 20 40 60 80 100Debt/ValueRatio (%)

ks

WACCkd

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The more debt the firm adds to itscapital structure, the riskier theequity becomes and thus the higher

its cost.

Although kd remains constant, ks

increases with leverage. The

increase in ks is exactly sufficient tokeep 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 valueis unaffected by leverage.

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Find V, S, ks, and WACC for Firms U

and L assuming a 40% corporatetax 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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VL = D + S = $2,542,857

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

S = $1,542,857.

2. Find market value of Firm

Ls 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 Ls 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, theWACC is lower for L than for U.

$1,000,000

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

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Value of Firm, V (%)

4

3

2

1

0 0.5 1.0 1.5 2.0 2.5Debt

(Millions of $)

VL

VU

MM relationship between value and debt

when corporate taxes are considered.

Under MM with corporate taxes, the firms valueincreases 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%. Whatis the gain from leverage according tothe Miller model?

Millers 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 Ls 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?

Ifonly corporate taxes, then

VL = VU + TcD = VU + 0.40D.

Here $100 of debt raises value by

$40. Thus, personal taxes lowers thegain from leverage, but the net effectdepends on tax rates.

(More...)

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If Ts declines, while Tc and Td remainconstant, the slope coefficient(which shows the benefit of debt) isdecreased.

A company with a low payout ratiogets lower benefits under the Millermodel than a company with a high

payout, because a low payoutdecreases Ts.

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When Miller brought in personal

taxes, the value enhancement of debtwas lowered. Why?

1. Corporate tax laws favor debt overequity financing because interestexpense is tax deductible while

dividends are not.

(More...)

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2. However, personal tax laws favor

equity over debt because stocksprovide both tax deferral and alower capital gains tax rate.

3. This lowers the relative cost ofequity vis-a-vis MMs no-personal-tax world and decreases the spreadbetween debt and equity costs.

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

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What does capital structure theory

prescribe 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% debtfinancing.

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

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Firms dont follow MM/Miller to 100%debt. Debt ratios average about 40%.

However, debt ratios did increaseafter MM. Many think debt ratios

were too low, and MM led to changesin financial policies.

Do firms follow the recommendations

of capital structure theory?

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Define financial distress and

agency costs.

Financial distress: As firms usemore and more debt financing, theyface a higher probability of futurefinancial distress, which brings with

it lower sales, EBIT, and bankruptcycosts. Lowers value of stock andbonds.

(More...)

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Agency costs: The costs ofmanagers not behaving in the bestinterests of shareholders and theresulting costs of monitoring

managers actions. Lowers value ofstock and bonds.

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How do financial distress and agency

costs change the MM and Millermodels?

MM/Miller ignored these costs, hencethose models show firm valueincreasing continuously withleverage.

Since financial distress and agencycosts increase with leverage, suchcosts reduce the value of debt

financing.

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Heres a valuation model which

includes financial distress andagency costs:

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

Now, optimal leverage involves atradeoff between the tax benefits ofdebt and the costs associated withfinancial distress and agency.

VL

= VU

+ XD - - .PV of expected

fin. distress costs

PV of agency

costs

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Cost of Capital (%)

14

4

Debt ($)

Relationships between capital costs

and leverage when financial distressand 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

21

Note that value ismaximized and WACC is

minimized at the samecapital structure.

D*

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Hamadas equation for beta:

bL = +

= +

= + .

bU

Unleveredbeta, which

reflects thebusinessrisk of the

firmBusiness

risk

bU(1 - T)(D/S)Increased

volatility of

the returnsto equity

due to the

use of debtFinancial

risk

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Results of a survey by Donaldson andthe 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 newcommon 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 consistentwith the trade-off theory?

It is consistent with theasymmetric information theory, inwhich managers avoid issuing

equity.

It is not consistent with trade-offtheory.

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