Corporate Finance - MSc in Finance (BGSE) Albert Banal · PDF fileCorporate Finance - MSc in...

Chapter 1: The Modigliani-Miller Propositions, Taxesand Bankruptcy Costs

Corporate Finance - MSc in Finance (BGSE)

Albert Banal-Estañol

Universitat Pompeu Fabra and Barcelona GSE

Albert Banal-Estañol (UPF and BGSE) Chapter 1 1 / 34

Corporate Finance - MSc in Finance (BGSE)

In this chapter...

The Modigliani and Miller irrelevance results

Taxes

Bankruptcy costs

Main conclusions


Corporate Finance - MSc in Finance (BGSE) The Modigliani and Miller irrelevance results

The Modigliani and Miller (MM) irrelevance results

The Modigliani-Miller results state that, if...

A1 Total cash �ows available for distribution to all debt and equity holders donot depend on the capital structure

A2 Capital markets are perfect

A3 Information is perfect

A4 Arbitrage opportunities are absent

...then....

1. (P1) A �rm�s debt-equity ratio does not a¤ect its market value

2. (P2) A �rm�s leverage has no e¤ect on its weighted average cost of capital



MM Proposition 1: An example

Consider a one-period economy in which two �rms, U and L, provide thesame payo¤s or cash �ows at the end of the period:

Firm U Firm LPayo¤ in good state 160 160Payo¤ in bad state 50 50

But...

Firm U is �nanced by equity only, which gets all cash �ows.Firm L is �nanced by debt and equity and its cash �ows are dividedbetween these two classes of claims.Still, the sum of cash �ows of L�s debt and equity holders is identical tothe payo¤s U�s equity holders

Claim: Their value at the beginning of the period must be the same

The total value of Firm L�s debt and equity must equal the value ofFirm U�s equity.




Let�s assume the following regarding how �rm L is �nanced:

Firm L�s debt promises e60 and has market value of e50Firm L�s equity has market value of e50The value of Firm L is then:

VL = DL + EL = 50+ 50 = 100.

Suppose that the value of Firm U is di¤erent from 100, say, 105.




We could carry out the following arbitrage strategy:

1 Sell (short) Firm U at 1052 Buy Firm L�s equity at 503 Buy Firm L�s bond at 50

The resulting cash �ows look as follows:Current cash �ow is 105 - 50 - 50 = 5Future cash �ow is

Good state Bad stateLong Firm L�s equity 100 0Long Firm L�s bond 60 50Short Firm U�s equity -160 -50

Net 0 0

Arbitrage opportunity! This will happen as long as VL 6= VUAlbert Banal-Estañol (UPF and BGSE) Chapter 1 6 / 34


MM Proposition 1: Intuition

This means that the value of the �rm (total size of the pie) isindependent of its capital structure (how the total pie is shared)

Hence, the �nancial manager should not worry about considerationsother than cash-�ows from the operating activities

She should worry only about identifying whether particular investmentprojects have positive NPVs and undertaking them.



Proof of Proposition 1Setup and notation

Consider a two-dates economy (t = 0, 1), with 2 �rms (i = 1, 2)which have identical cash �ows x at t = 1 (uncertain at t = 0)Firm 1 is unlevered and �rm 2 is leveredAll shareholders are protected by limited liability

Denote:B: repayment promised to debtholders at t = 1E and D market value of 2�s equity and debt at t = 0

Value at t = 0 Payo¤ at t = 1Debt �rm 2 D minfB, xgEquity �rm 2 E maxfx � B, 0gMarket value �rm 2 V2 = D + E xMarket value �rm 1 V1 = U x

P1 claims that V1 = V2 even if B > 0Albert Banal-Estañol (UPF and BGSE) Chapter 1 8 / 34


Proof of Proposition 1Benchmark: total payments as a function of x at t=1

1 2 3 4 5

2

0

2

4

x

Total payments (equity and debt) independent of capital structure (A1)Suppose that B = 2. Clearly, B might not be repaid; debt may be riskyAlbert Banal-Estañol (UPF and BGSE) Chapter 1 9 / 34


Proof of Proposition 1Payments to debtholders as a function of x at t=1 (B=2)

1 2 3 4 5

2

0

2

4

x



Proof of Proposition 1Payments to equityholders as a function of x at t=1 (B=2)

1 2 3 4 5

2

0

2

4

x



Proof of Proposition 1

Strategy:

Suppose that V1 6= V2 and show that, if A1-A3 hold, there arearbitrage opportunities (contradicting A4)If V1 < V2, sell short equity and debt of �rm 2 and buy equity of 1If V1 > V2, buy equity and debt of �rm 2 and sell short equity of 1That is, buy undervalued securities and sell-short overvalued ones

What if V1 < V2?

Transaction At t = 0 At t = 1Sell α of D αD �α minfB , xgSell α of E αE �α maxfx � B , 0gBuy α of U �αU αx

Sum αD + αE � αU = α(V2 � V1) > 0 0

Arbitrage opportunity!!




Prop 1 states that if two �rms are equal except for the corporatestructure: U = E +D, where U is the value of the unlevered �rm andE and D are the equity and debt values of the levered one

De�ne: Expected return on...

equity for the unlevered �rm: RU � E (x)/Udebt for the levered �rm: RD � E (minfB, xg)/Dequity for the levered �rm: RE � E (maxfx � B, 0g)/E

But then...

URU = E (x), DRD = E (minfB, xg) and ERE � E (maxfx � B, 0g)But E (x) = E (minfB, xg) + E (maxfx � B, 0g), henceURU = DRD + ERERearranging, and using that U = E +D,

RU =D

D + ERD +

ED + E

RE (1)




Denote the asset value as A and the return on assets as RA � E (x)/AIn an unlevered �rm, all cash �ows of its assets are paid out to itsequity holders:

Hence A = U = E +D (for any D, E )and therefore RA � E (x)/A = E (x)/U = RU

Substituting RU = RA and rearranging (1)

RE = RA +DE(RA � RD )

That is, insofar as debt is riskless, the expected return on equity of alevered �rm is a positive and linearly increasing function of thedebt-to-equity ratio, expressed in market values

This rate of increase is given by the spread between the expectedreturn on assets and the expected return on debt



Implications of Proposition 2

As shown earlier, projects�cash �ows should be appropiately discounted:

what is the return the �rm can receive on alternative investments thatbear the same risks?(�cost of capital� as it measures the opportunity cost of the funds)use this return as the discount rate to compute the net present value

If the �rm�s assets have same risk as project evaluated. . .

and �rm is unlevereduse equity cost of capital as the cost of capital for the project



Implications of Proposition 2

For a levered �rm, equity cost of capital is. . .

higher than cost of capital of the assets,and therefore of the project

But we can compute asset returns by substituting RU = RA in (1)

RA =D

D + E| {z }Proportion in Debt

RD +E

D + E| {z }Proportion in Equity

RE � Rwacc (2)

The weighted average cost of capital (the expected return for an investorthat holds all the equity and all the debt of a levered �rm) for any leverageratio (for any D, E ) is constant (RA is constant)

Firm�s WACC is independent of capital structure!


Corporate Finance - MSc in Finance (BGSE) Taxes

Corporate taxes

MM: without taxes (and without bankruptcy costs, etc,.):

companies should be indi¤erent between debt and equity

All else equal, the objective should be to minimise the tax bill:

Interest rates are usually tax deductible at the corporate level!Advantage to debt as a form of �nancingPersonal tax on equity is higher than the personal tax on debt!Advantage to equity �nancing and partially (but notcompletely o¤setting) the e¤ect of corporate taxationIn practice, managers pay great attention to the tax implications

Suppose �rst that. . .

companies are taxed but. . .investors are not (e.g. pension funds) (we will come back later to that)



Example: DF Builders

What was the amount available to investors in 2005?Would it have been higher or lower without leverage?



What is the value of the �tax shield�?

Consider two �rms, U and L,...

with identical, pre-tax, expected annual cash �ows x t , t = 1...Firm U is 100% equity �nancedFirm L maintains debt level D and pays perpetual interest rate rDThe corporate tax is τc and ignore personal taxes for now



The expected annual after-tax cash �ows of �rms U and L are

(1� τc )x t

and(1� τc ) (x t � rDD) + rDD = (1� τc )x t + τc rDD

They di¤er by the�debt tax shield� created by the tax-deductibility

Since it is the same in every period, it is a �perpetuity�, and therefore

VL = VU +τc rDDrD

= VU + τcD

Risk of the �rst part of the cash �ow of L is identical to that ofU, thus the same discount rate appliesThe discount rate for the cash �ows to the debt holders is thesame as the required rate of return on debt, rD .



Personal Taxes

So far, we have only considered corporate taxes� which favor debtover equity

Therefore the optimal capital structure should be 100% debtBut most investors are also taxed when they receive cash

Debt and equity also face di¤erential taxation at the personal level:

Interest income from debt taxed as income (τd )Equity investors pay taxes on dividends & capital gains (τe )

Typically. . .

Capital gains are taxed at lower rates than dividends or interestsCapital gains (and therefore taxes on them) might be deferred

As a result: τe < τd



What is the value of the �tax shield�?

Assuming all shareholders have same tax rates, cash �ows for U are

(1� τc )(1� τe )x t

and for L are:

(1� τc )(1� τe ) (x t � rDD) + (1� τd )rDD

= (1� τc )(1� τe )x t + [(1� τd )� (1� τc )(1� τe )] rDD

Discounted at the after-tax rate rD (1� τd ), PV of second term isτgD, where

τg = 1�(1� τc )(1� τe )

(1� τd )

and thereforeVL = VU + τgD



Relative advantage formula (RAF)

Debt is preferred over equity if and only if τg > 0 or i¤

RAF � (1� τd )

(1� τc )(1� τe )> 1

For example,

if corporate tax is 35% (τc = 35%)if personal income tax is 40% (τd = 40%)if there are no dividends and capital gains are not deferred and ifcapital gains tax is 20% (τe = 20%)

... then...

τg = 1�0.65 0.80.6

= 0.13 and RAF � 0.60.65 � 0.8 = 1.15

For every euro in permanent debt, value increases by 13c


Corporate Finance - MSc in Finance (BGSE) Bankruptcy costs

Bankruptcy costs

Debt might have an important disadvantage:

high debt levels increase the chance of �nancial distress

This is only important if bankruptcy a¤ects revenues or costs

Direct costs:

legal process of restructuring (court costs, advisory fees)on average 2-3% of the assetsExamples:

Enron $30m per month, $750 in totalWorldcom (reorganisation to become MCI) $657mUnited Airlines, 8.6m per month for legal and professional servicesrelated to chapter 11 reorganisation

Indirect costs:

Loss of customers, suppliers,. . . (see next slide)



Some indirect costs of �nancial distress

Loss of customers:

Bankruptcy may enable �rms to walk away from future commitments(support, future upgrades,. . . )

Loss of suppliers:

Bankruptcy may enable �rms not to pay for inventorySwissair forced to shut because suppliers refuse to fuel planes

Loss of employees:

Fear of job securityPaci�c Gas and Electric Co. paid to retain 17 key employees

Loss of receivables:

Debtors might have an opportunity to avoid obligations

Fire sales of assets:

Companies need to sell assets quickly to raise cash



Summing up: the Trade-O¤ Theory

Tax bene�ts vs costs of �nancial distress costs:

VL = VU + PV (interest tax shield)� PV (�nancial distress costs)

To determine the PV(Financial distress costs), need to compute. . .

1. Probability, which:

increases with the amount of a �rm�s liabilities, relative to assetsincreases with the volatility of a �rm�s cash �ows and asset valuesincreases with the strength of the competitors

2. Magnitude of costs once in distress, which depends on industry:

Technology: high (loss of customers, key personnel, lack of tangibleassets being liquidated)Real estate: low (assets can (in normal times) be sold relatively easily)



Practical implications

Firms with high prob. of distress should minimise costs of distress:

Avoid too much debtBut also, if debt is need it, use easy-to-reorganize debt structureBanks rather than many bondholdersFew rather than many banksFew rather than many classes of debt

In general �rms with mostly intangible assets have high distress costs

!Follow conservative debt �nancing policies

In contrast, �rms with mostly tangible assets have low distress costs

!Load up on debt to get the tax shield



Optimal leverage



Empirical Evidence

1 Firms that produce steady cash �ows (e.g. utilities), and have easilyredeployable assets that they can use as collateral (e.g. aircraft or realestate) have high debt ratios

2 Risky �rms, with little current cash �ows, and �rms with intangibleassets (e.g. with high R&D and advertising) tend to have low leverage

3 Companies whose value consists largely of intangible growth options(high market-to-book ratios and heavy R&D spending) have lowerleverage ratios

4 Most pro�table companies tend not to borrow as much: they rely oninternally generated funds



Debt to Equity RatiosSource: Grinblatt and Titman



Measures of net worth by industry in the US�1985Source: White (1991)


Corporate Finance - MSc in Finance (BGSE) Main conclusions

Main Conclusions

1 In absence of neutral taxes and bankruptcy costs (and otherimperfections), a �rm�s value is independent of its capital structureand �nancing decisions are irrelevant

2 However, the real world is di¤erent

1 Resources taken away as taxes depends debt/equity mix

* In the presence of corporate taxes, with interest expensesbeing tax deductible, a �rm�s value increases with itsdebt/equity ratio

* Personal taxes favour equity over debt and partially o¤setthe e¤ect of corporate taxes

2 Firm value may be lost in bankruptcy, and leverage increases thelikelihood

* When bankruptcy is costly, there may exist an optimalcapital structure with a mixture of debt and equity


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