Chapter 1: The Modigliani-Miller Propositions, Taxes
and Bankruptcy Costs
Corporate Finance - MSc in Finance (BGSE)
Albert Banal-Estañol
Universitat Pompeu Fabra and Barcelona GSE
Albert Banal-Estañol (UPF and BGSE)
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In this chapter...
The Modigliani and Miller irrelevance results
Taxes
Bankruptcy costs
Main conclusions
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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 do
not depend on the capital structure
A2 Capital markets are perfect
A3 Information is perfect
A4 Arbitrage opportunities are absent
...then....
. (P1) A …rm’s debt-equity ratio does not a¤ect its market value
. (P2) A …rm’s leverage has no e¤ect on its weighted average cost of capital
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The Modigliani and Miller irrelevance results
MM Proposition 1: An example
Consider a one-period economy in which two …rms, U and L, provide the
same payo¤s or cash ‡ows at the end of the period:
Payo¤ in good state
Payo¤ in bad state
Firm U
160
50
Firm L
160
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 divided
between these two classes of claims.
Still, the sum of cash ‡ows of L’s debt and equity holders is identical to
the 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 of
Firm U’s equity.
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The Modigliani and Miller irrelevance results
MM Proposition 1: An example
Let’s assume the following regarding how …rm L is …nanced:
Firm L’s debt promises e60 and has market value of e50
Firm L’s equity has market value of e50
The 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.
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The Modigliani and Miller irrelevance results
MM Proposition 1: An example
We could carry out the following arbitrage strategy:
1
2
3
Sell (short) Firm U at 105
Buy Firm L’s equity at 50
Buy Firm L’s bond at 50
The resulting cash ‡ows look as follows:
Current cash ‡ow is 105 - 50 - 50 = 5
Future cash ‡ow is
Long Firm L’s equity
Long Firm L’s bond
Short Firm U’s equity
Net
Good state
100
60
-160
0
Bad state
0
50
-50
0
Arbitrage opportunity! This will happen as long as VL 6= VU
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The Modigliani and Miller irrelevance results
MM Proposition 1: Intuition
This means that the value of the …rm (total size of the pie) is
independent of its capital structure (how the total pie is shared)
Hence, the …nancial manager should not worry about considerations
other than cash-‡ows from the operating activities
She should worry only about identifying whether particular investment
projects have positive NPVs and undertaking them.
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The Modigliani and Miller irrelevance results
Proof of Proposition 1
Setup 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 levered
All shareholders are protected by limited liability
Denote:
B: repayment promised to debtholders at t = 1
E and D market value of 2’s equity and debt at t = 0
Debt …rm 2
Equity …rm 2
Market value …rm 2
Market value …rm 1
Value at t = 0
D
E
V2 = D + E
V1 = U
Payo¤ at t = 1
minfB, x g
maxfx B, 0g
x
x
P1 claims that V1 = V2 even if B > 0
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The Modigliani and Miller irrelevance results
Proof of Proposition 1
Benchmark: total payments as a function of x at t=1
4
2
0
1
2
3
4
5
x
-2
Total payments (equity and debt) independent of capital structure (A1)
Suppose that B = 2. Clearly, B might not be repaid; debt may be risky
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The Modigliani and Miller irrelevance results
Proof of Proposition 1
Payments to debtholders as a function of x at t=1 (B=2)
4
2
0
1
2
3
4
5
x
-2
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The Modigliani and Miller irrelevance results
Proof of Proposition 1
Payments to equityholders as a function of x at t=1 (B=2)
4
2
0
1
2
3
4
5
x
-2
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The Modigliani and Miller irrelevance results
Proof of Proposition 1
Strategy:
Suppose that V1 6= V2 and show that, if A1-A3 hold, there are
arbitrage opportunities (contradicting A4)
If V1 < V2 , sell short equity and debt of …rm 2 and buy equity of 1
If V1 > V2 , buy equity and debt of …rm 2 and sell short equity of 1
That is, buy undervalued securities and sell-short overvalued ones
What if V1 < V2 ?
Transaction
Sell α of D
Sell α of E
Buy α of U
Sum
αD + αE
At t = 0
αD
αE
αU
αU = α(V2
V1 ) > 0
At t = 1
α minfB, x g
α maxfx B, 0g
αx
0
Arbitrage opportunity!!
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The Modigliani and Miller irrelevance results
Proof of Proposition 2
Prop 1 states that if two …rms are equal except for the corporate
structure: U = E + D, where U is the value of the unlevered …rm and
E 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 )/U
debt for the levered …rm: RD
E (minfB, x g)/D
equity for the levered …rm: RE
E (maxfx B, 0g)/E
But then...
URU = E (x ), DRD = E (minfB, x g) and ERE
E (maxfx
But E (x ) = E (minfB, x g) + E (maxfx B, 0g), hence
URU = DRD + ERE
Rearranging, and using that U = E + D,
RU =
Albert Banal-Estañol (UPF and BGSE)
B, 0g)
D
E
RD +
R
D +E
D +E E
(1)
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The Modigliani and Miller irrelevance results
Proof of Proposition 2
Denote the asset value as A and the return on assets as RA
E (x )/A
In an unlevered …rm, all cash ‡ows of its assets are paid out to its
equity 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 +
D
(RA
E
RD )
That is, insofar as debt is riskless, the expected return on equity of a
levered …rm is a positive and linearly increasing function of the
debt-to-equity ratio, expressed in market values
This rate of increase is given by the spread between the expected
return on assets and the expected return on debt
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The Modigliani and Miller irrelevance results
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 that
bear 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 unlevered
use equity cost of capital as the cost of capital for the project
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The Modigliani and Miller irrelevance results
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
+ E}
|D {z
Proportion in Debt
RD +
E
+ E}
|D {z
RE
Rwacc
(2)
Proportion in Equity
The weighted average cost of capital (the expected return for an investor
that holds all the equity and all the debt of a levered …rm) for any leverage
ratio (for any D , E ) is constant (RA is constant)
Firm’s WACC is independent of capital structure!
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Albert Banal-Estañol (UPF and BGSE)
The Modigliani and Miller irrelevance results
Chapter 1
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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 …nancing
Personal tax on equity is higher than the personal tax on debt
!Advantage to equity …nancing and partially (but not
completely o¤setting) the e¤ect of corporate taxation
In 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)
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Taxes
Example: DF Builders
What was the amount available to investors in 2005?
Would it have been higher or lower without leverage?
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Taxes
Chapter 1
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Taxes
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 …nanced
Firm L maintains debt level D and pays perpetual interest rate rD
The corporate tax is τ c and ignore personal taxes for now
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Taxes
The expected annual after-tax cash ‡ows of …rms U and L are
(1
τ c )x t
and
(1
τ c ) (x t
rD D ) + rD D = (1
τ c )x t + τ c rD D
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 +
τ c rD D
= VU + τ c D
rD
Risk of the …rst part of the cash ‡ow of L is identical to that of
U, thus the same discount rate applies
The discount rate for the cash ‡ows to the debt holders is the
same as the required rate of return on debt, rD .
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Taxes
Personal Taxes
So far, we have only considered corporate taxes— which favor debt
over equity
Therefore the optimal capital structure should be 100% debt
But 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 (τ d )
Equity investors pay taxes on dividends & capital gains (τ e )
Typically. . .
Capital gains are taxed at lower rates than dividends or interests
Capital gains (and therefore taxes on them) might be deferred
As a result: τ e < τ d
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Taxes
What is the value of the “tax shield”?
Assuming all shareholders have same tax rates, cash ‡ows for U are
(1
τ c )(1
τ e )x t
and for L are:
(1
= (1
τ c )(1
τ e ) (x t
rD D ) + (1
τ c )(1
τ e )x t + [(1
τd )
τ d )rD D
(1
τ c )(1
τ e )] rD D
Discounted at the after-tax rate rD (1 τ d ), PV of second term is
τ g D, where
(1 τ c )(1 τ e )
τg = 1
(1 τ d )
and therefore
VL = VU + τ g D
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Taxes
Relative advantage formula (RAF)
Debt is preferred over equity if and only if τ g > 0 or i¤
RAF
(1 τ d )
>1
(1 τ c )(1 τ e )
For example,
if corporate tax is 35% (τ c = 35%)
if personal income tax is 40% (τ d = 40%)
if there are no dividends and capital gains are not deferred and if
capital gains tax is 20% (τ e = 20%)
... then...
τg = 1
0.65 0.8
= 0.13 and RAF
0.6
0.6
= 1.15
0.65 0.8
For every euro in permanent debt, value increases by 13c
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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 assets
Examples:
Enron $30m per month, $750 in total
Worldcom (reorganisation to become MCI) $657m
United Airlines, 8.6m per month for legal and professional services
related to chapter 11 reorganisation
Indirect costs:
Loss of customers, suppliers,. . . (see next slide)
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Bankruptcy costs
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 inventory
Swissair forced to shut because suppliers refuse to fuel planes
Loss of employees:
Fear of job security
Paci…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
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Bankruptcy costs
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 assets
increases with the volatility of a …rm’s cash ‡ows and asset values
increases 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 tangible
assets being liquidated)
Real estate: low (assets can (in normal times) be sold relatively easily)
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Bankruptcy costs
Practical implications
Firms with high prob. of distress should minimise costs of distress:
Avoid too much debt
But also, if debt is need it, use easy-to-reorganize debt structure
Banks rather than many bondholders
Few rather than many banks
Few 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
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Bankruptcy costs
Optimal leverage
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Bankruptcy costs
Empirical Evidence
1
Firms that produce steady cash ‡ows (e.g. utilities), and have easily
redeployable assets that they can use as collateral (e.g. aircraft or real
estate) have high debt ratios
2
Risky …rms, with little current cash ‡ows, and …rms with intangible
assets (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 lower
leverage ratios
4
Most pro…table companies tend not to borrow as much: they rely on
internally generated funds
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Bankruptcy costs
Debt to Equity Ratios
Source: Grinblatt and Titman
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Bankruptcy costs
Measures of net worth by industry in the US–1985
Source: White (1991)
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Main conclusions
Main Conclusions
1
In absence of neutral taxes and bankruptcy costs (and other
imperfections), a …rm’s value is independent of its capital structure
and …nancing decisions are irrelevant
2
However, the real world is di¤erent
1
2
Resources taken away as taxes depends debt/equity mix
* In the presence of corporate taxes, with interest expenses
being tax deductible, a …rm’s value increases with its
debt/equity ratio
* Personal taxes favour equity over debt and partially o¤set
the e¤ect of corporate taxes
Firm value may be lost in bankruptcy, and leverage increases the
likelihood
* When bankruptcy is costly, there may exist an optimal
capital structure with a mixture of debt and equity
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