Modigliani-Miller Theorem

Under some assumptions, corporate financial policy is

IRRELEVANT.

• Financing decisions are irrelevant.

• Capital structure is irrelevant.

• Dividend policy is irrelevant.

• Cash management is irrelevant.

• Risk management policy is irrelevant.

• Cross shareholdings are irrelevant.

• Diversification is irrelevant.

• Etc.

The Original Propositions

• MM-Proposition I (MM 1958)

A firm’s total market value is independent

of its capital structure.

• MM-Proposition II (MM 1958)

A firm’s cost of equity increases with its

debt-equity ratio.

• Dividend Irrelevance (MM 1961)

A firm’s total market value is independent

of its dividend policy.

• Investor Indifference (Stiglitz 1969)

Individual investors are indifferent to the

firms’ financial policy.

Assumptions

• Frictionless markets: No transaction costs, etc.

• Competitive markets: Individuals and firms are price-

takers.

• Individuals and firms can undertake financial transac-

tions at the same prices (e.g., borrow at the same

rate).

• All agents have the same information.

• No taxes.

• A firm’s cashflows do not depend on its financial policy

(e.g., no bankruptcy costs).

MM as a No-Arbitarge Argument

• Value additivity:

– No arbitrage Profits in Equilibrium

– Value additivity: If A and B are cashflow streams,

no arbitrage =⇒

V (A + B) = V (A) + V (B) .

• Firm value:

– A firm’s value ≡ the sum of the values of all its

financial claims.

– The cashflows received by all its claims must add

up to the total cashflow that assets generate.

– Value additivity. ⇒ The firm’s value must equal

that of the assets’ cashflow stream.

• Identical firm:

– Consider an identical firm with a different financial

policy.

– Assets being identical, they generate the same

cashflow stream. ⇒ Firm value is the same.

Model

2 Firms: 1, 2

• At t = 1, 2, ..., both firms yield the same (random)

CF X.

• At t = 0, they have different capital structures:

– Firm 1 has equity and a constant level of risk-free

debt.

– Firm 2 has no debt.

• At t = 0,

– Risk-free rate: r.

– Market value of firm i’s debt: Di.

– Market value of firm i’s equity: Ei.

– Total market value of firm i: Vi = Di + Ei.

• Hence, at t:

– Firm 1’s debtholders receive: rD1.

– Firm 1’s equityholders receive: X − rD1.

– Firm 2’s equityholders receive: X .

Step 1: It cannot be that V2 > V1.

• Suppose V2 > V1.

• An investor could:

– Short sell a fraction α of firm 2’s shares for αV2.

– Use the proceeds to buy a fraction αV2/V1 of firm

1’s debt and equity as:

αV2 =

αV2

V1

·D1 +

αV2

V1

· E1.

• At t, the investor would receive:

−αX +

αV2

V1

rD1 +

αV2

V1

· (X − rD1)

= α

−1 +V2

V1

X > 0

for all X.

• ⇒ An arbitrage opportunity exists.

• Intuition: Arbitrageurs can “undo firm 1’s lever-

age” by buying equal proportions of its debt and equity

so that interest paid and received cancel out.

Step 2: It cannot be that V1 > V2.

• Suppose V1 > V2.

• An investor could:

– Short sell a fraction α of firm 1’s shares for αE1.

– Borrow αD1.

– Use the proceeds to buy a fraction αV1/V2 of firm

2’s shares as:

αE1 + αD1 =

αV1

V2

· V2.

• At t, the investor would receive:get αV1

V2X and pay

interests rαD1:

−α (X − rD1)− rαD1 +

αV1

V2

X = α

−1 +V1

V2

X > 0

for all X.

• ⇒ An arbitrage opportunity exists.

• Intuition: Arbitrageurs can “lever up” firm 2 by

borrowing on individual accounts (homemade lever-

age).

MM and the Cost of Capital

Proposition II: A firm’s cost of equity increases

with its debt-equity ratio.

• Intuition: Raising debt makes existing equity more

risky, hence more costly.

• Note: Debt makes equity riskier even if it is riskfree,

i.e., this is not (only) about default risk.

• Use the notion of a firm’s WACC

Proof:

• The firm’s Weighted Average Cost of Capital (WACC)

is:

WACC =D

D + Er +

E

D + ErE

where:

– r is the cost of risk-free debt, i.e., its return.

– rE is the cost of equity, i.e., its expected return.

• This can be rewritten as:

rE = (WACC− r)D

E+ WACC.

• By Proposition I, the WACC is independent of D/E.

⇒ rE is linear in D/E.

• Note:In practice, WACC > r (i.e., rE > r) essentially

for all firms. ⇒ rE increases with D/E.

But we all know that debt is cheaper than equity —-

• Isn’t debt cheaper than equity?

– Interest rates on corporate debt ' 5%.

– Equity earnings/price ratios (then the conventional

measure of the cost of equity capital) ' 20%.

• MM’s Proposition II shows that there is no contradic-

tion.

• By issuing debt at 5% the firm would increase the

riskiness of equity.

• Difference between rE and r is irrelevant!

But, some people value dividend streams.

Financial Structure does matter

• Heterogenous investors value the same cash flow streams

differently.

• ⇒ Financial policy choices affect the match between

securities and heterogenous preferences.

• ⇒ Financial policy can affect firm value.

Argument: An all-equity firm doesn’t exploit the de-

mands for risky and safe securities.

It may be worth more by separating riskier from safer cash

flow streams (e.g., into debt and equity) so that investors

can focus on their preferred security.

Intuition for MM:

• MM show that this theory is flawed (Win-Win Fal-

lacy).

• Investors’ preferences are over cashflows, not securi-

ties.

• They are not limited to the securities issued by firms.

• If investors can trade at the same prices as firms, they

won’t pay a premium for the firm to trade for them.

• MM do not assume away heterogeneity.

• The match between preferences and cash flow streams

need not be organized by the firms.

• There is no value to financial marketing.

MM DIVIDEND POLICY IRRELEVANCE

Proposition: A firm’s value is independent of

its dividend policy.

• Each “period”, the firm:

– Invests and retains cash (Investment Policy).

– Raises new capital (Financing Policy).

– Pays some dividends (Payout Policy).

• Accounting identity: Taking investment as given, a

change in payout has to be met by a change in fi-

nancing.

• For instance:

– A dividend increase can be financed with a new

debt issue.

– A dividend decrease can be met by a retirement

of debt.

• Existing shareholders and new investors form a “closed

system”.

⇒ The total value of their claims is unaffected (value

conservation).

• New investors are competitive.

⇒ The value of their claims is unchanged.

⇒ The value of the current shareholders’ claims is

unchanged.

Important because....

• For the study of dividend policy:

– Why do firms pay dividends?

• For the other MM propositions:

– The arbitrage proof relies on firms generating iden-

tical cashflows.

– But shareholders receive dividends, not cashflows.

– Do dividends have to be identical too?

Another Argument........

Dividends are safer than future payments. ⇒ Don’t they

increase firm value?

• MM show that this theory is flawed

USING MM SENSIBLY

• Financial decisions do matter.

• So what do we make of the irrelevance result?

– Avoid the fallacies

– Organize your thoughts.

Main insight:

• Value is created only by real assets

• If Financial Policy is unrelated to Investment Policy,

then it is irrelevant: It merely divides a “pie” of fixed

size.

• Serves as a benchmark: If we know what does not

matter, we may be able to infer what does.

How can financial decisions affect the size of

the pie?

• Investors cannot undertake the same financial trans-

actions as firms

– Taxes,

– transaction costs and short-sale constraints,

– bankruptcy costs,

– information asymmetries,

– Moral hazard

The Static Tradeoff Theory

Main idea:

• Capital structure matters because:

– Debt has a tax advantage over equity.

– Debt involves bankruptcy costs.

• Trade-off. ⇒Optimal capital structure (firm-

specific).

DEBT TAX SHIELD

• At the corporate level:

– Interest payments are tax deductible.

– Dividends and retained earnings are taxed.

• Consider a firm that:

– generates cashflow X in t = 0, 1, 2...

– has a constant level of riskfree debt D.

• Notation:

– Riskfree rate: r.

– Corporate tax rate: τ .

• Each period, the after tax cashflow is:

(1− τ ) (X − rD)︸ ︷︷ ︸to equityholders

+ rD︸ ︷︷ ︸to debtholders

• Rewrite as:

(1− τ ) X︸ ︷︷ ︸all equity firm

+ τrD︸ ︷︷ ︸tax shield

Proposition (MM with corporate taxes):

• The value of a levered firm equals that

of an unlevered firm plus that of the in-

terest tax shield.

• Here:

V (D) = V (0) + τD.

Proof:

• By value additivity:

V (D) = V (0) + V (Tax Shield Perpetuity).

• Moreover, the value of the tax reduction is:

V (Tax Shield Perpetuity) =τrD

r= τD.

• Intuition: In effect, the government pays a fraction

τ of the interest. Investors cannot get such a tax

break on homemade leverage. Hence, they will pay a

premium for levered firms.

• Note: If the government’s tax claim is included, MM

Proposition I holds: Firm Value+V (Taxes) is inde-

pendent of capital structure.

BANKRUPTCY COSTS

• Debt implies a risk of bankruptcy.

• Bankruptcy costs:

– Administrative and court cost, legal and advisory

fees.

– Resources spent by management and creditors deal-

ing with bankruptcy.

– Mismanagement by judges (blocking/delaying non-

routine expenditures).

– In US, average time spent in bankruptcy: 20 months.

• Note: This violates the MM assumption that cash-

flows are independent of financial policy.

STATIC TRADE-OFF THEORY

• As leverage increases:

– Tax shield increases.

– Expected bankruptcy costs increase:

∗ Probability of bankruptcy increases.

∗ Costs when in bankruptcy increase (most likely).

• Optimal leverage (ratio) trades-off these costs and

benefits.

• Remarks/Implications:

– Optimal leverage should be firm-specific.

– Static trade-off: Observed capital structures should

be close to the target, hence relatively stable.

– This contrasts with other theories of capital struc-

ture.

– As firms strive to approach a target capital struc-

ture, we might observe mean-reversion (to the tar-

get).

ISSUES

The tax effect can be substantial.

• Consider a firm with constant riskfree cash flow X :

V (100%) = V (0%) + τV (100%)

⇒ V (0%)

V (100%)= 1− τ ' 60%.

• Note: Many firms’ effective tax rate is below the

statutory tax rate due to tax credits, etc.

• Therefore, tax effect’s order of magnitude is much

lower.

Direct bankruptcy costs are generally too

small to offset the potentially big tax gains.

• Direct bankruptcy costs can amount to $100Ms, but

should be compared to firm value.

• Large firms: Small fraction of firm value when enter-

ing bankruptcy (e.g. 5%, see Warner (1977), Weiss

(1990)).

• Smaller firms: Higher fraction (e.g., 20%).

• These overestimate the relevant cost.

– Need the expected cost as a fraction of firm value

at the time when capital structure is decided.

– Caveat 1: Firm value is low near bankruptcy. ⇒5% is an overestimate.

– Caveat 2: Ex-ante distress probability is small.

⇒ For many firms, STO suggest that high

leverage is optimal.

⇒ Firms tend to be less leveraged than pre-

dicted by STO.

⇒ Does not count growth options

PERSONAL TAXES

Main idea: For personal taxes, equity has an

advantage over debt.

• Classical tax systems: (e.g., US).

– Interests and dividends are taxed as ordinary in-

come.

– Capital gains are taxed at a lower effective rate:

∗ Sometimes, lower tax rate

∗ Capital gains can be deferred (6= dividends and

interests). ⇒ Earn the time value.

– However, some dividend exclusion (e.g. 70%) for

corporations.

• Imputation systems: (e.g., most of Europe).

– Tax credits for recipients of dividends (= fraction

of corporate tax) reduce the double taxation of

dividends.

• At the personal level:

– Tax rate on debt: τD.

– Tax rate on equity (dividend + capital gains): τE.

• Each period, the cashflow after corporate and personal

taxes is:

(1− τE) (1− τ ) (X − rD)︸ ︷︷ ︸to equityholders

+ (1− τD) rD︸ ︷︷ ︸to debtholders

• Rewritten as:

(1− τE) (1− τ ) X︸ ︷︷ ︸all-equity firm

+ [(1− τD)− (1− τE) (1− τ )] rD︸ ︷︷ ︸tax impact of debt

Proposition (MM with corporate and personal

taxes):

V (D) = V (0) +

1− (1− τ ) (1− τE)

(1− τD)

D.

Debt vs. Equity

• Debt tax shield:

(1− τ )(1− τE)

1− τD.

• Effective τE increases with the payout ratio.

• If τD ' τE (e.g. equity pays large dividends):

– We can ignore personal taxes.

– We are back to MM with corporate taxes

V (D) = V (0) + τD.

– Debt has a strong tax advantage over equity.

• ⇒ Dividend Puzzle: Tax-disadvantage relative to debt

and capital gains.

• If τE < τD (e.g. equity can avoid large dividends):

– Equity does not look as bad.

– Debt’s tax shield is less than τD.

• If (1−τ)(1−τE)1−τD

> 1:

– Debt has a negative tax shield.

– Equity has a tax advantage over debt.

THE MILLER EQUILIBRIUM

Miller (1977).

• Capital structure is:

– Uniquely determined at the aggregate

level.

– Irrelevant at the firm level.

• With τE = 0 (for simplicity), a firm prefers debt to

equity iff τ > τD.

• If all firms face the same τ and all investors the same

τD, all firms issue the same claim, i.e., no debt-equity

mix.

• Assume instead investors with heterogenous personal

tax rates τ iD.

• Additional assumptions:

– Firms’ cashflow is certain (debt is riskfree).

– No short sales.

• Yield on tax-exempt (e.g., municipal) bonds: r0.

Demand for corporate debt:

• Investors can always buy tax-exempt bonds offering a

return r0.

– For r < r0, no investor wants corporate debt.

– For r = r0, tax-exempt institutions hold corporate

debt (horizontal stretch).

– For r > r0, tax-paying investor i holds corporate

debt iff:

r0 ≤(1− τ i

D

)r.

Supply of corporate debt:

• Paying a return r0 to equityholders costs firms r01

(1−τ).

– For r > r01

(1−τ), firms issue no debt, only equity.

– For r < r01

(1−τ), firms issue only debt, no equity.

– For r = r01

(1−τ), firms are indifferent between issu-

ing debt and equity (⇒ Perfectly elastic supply).

Equilibrium:

• There are gains from trade (i.e., from issuing debt)

until the marginal investor’s tax rate is τmD = τ .

• If the debt supply exceeded D∗, r would be driven

above r01

(1−τ), and vice versa if less than D∗ were

issued.

Implications

• Capital structure is irrelevant at the firm

level:

V (D) = V (0) +

1− (1− τ )

(1− τmD )

D = V (0).

• Unique aggregate debt-equity ratio: In equi-

librium, aggregate debt is such that the marginal in-

vestor is indifferent between debt and equity, i.e.,

(1− τmD ) = (1− τ ).

• The equilibrium aggregate debt level depends on:

– Tax rates.

– Funds available to investors in each tax bracket.

• Clientele effect:

– Investors with τD > τmD hold only equity and tax-

exempt bonds.

– Investors with τD < τmD hold only corporate bonds.

Relevance

• This is plausible only if the effective personal tax rate

on equity is substantially lower than rate on interest.

• Although τE < τD, corporate tax advantage of debt

seems to exceed personal tax disadvantage for most

investors,

• i.e., Aren’t many investors with

(1− τD) < (1− τ )(1− τE)

• No strong clientele effect:

– Highly taxed individuals do not only hold equity.

– Tax-exempt institutions do not only invest in cor-

porate bonds.

NON-DEBT TAX SHIELDS

• Many firms cannot fully exploit the tax deductibility

of interests because of:

– Negative earnings (EBITDA).

– Non-debt tax shields: Depreciation, tax credits,

etc.

• Tax Loss Carry Forwards (TLCF):

– Several years, but most firms continue to have

losses for several years.

– ⇒ They lose the time value of the debt tax shield.

• Implication:

– Other things equal, the expected tax rate decreases

with leverage.

– The marginal debt tax shield decreases

with leverage.

BOTTOM LINE

• Taxes favor debt for most firms, but beware of partic-

ular cases.

• It is still standard to use τD to evaluate the debt tax

shield.

• Somewhat overstated.

• Definitely NOT OK for non-tax paying firms.

MODELS BASED ON INCENTIVE

PROBLEMS

• Moral hazard.

• Moral hazard and credit rationing.

• Jensen and Meckling (1976).

– Effort problem.

– Risk-shifting problem.

INCENTIVE ISSUES

Main idea:

• Conflicts of interests between the party mak-

ing operating decisions (≡ insider) and out-

side investors.

• Outside financing involves costs due to Moral

Hazard:

– Deviations from value maximization.

– Credit rationing: Some valuable projects

cannot be financed.

– Costs incurred to prevent the above such

as:

∗ Monitoring

∗ Bonding.

• Role for internal funds.

Model

• Three dates (t = 0, 1, 2), no discounting, and univer-

sal risk-neutrality.

• An entrepreneur has a project.

• At t = 0: Financing.

– Needs to invest I > 0.

– Entrepreneur’s resources available: W .

• At t = 1: Moral hazard.

– The entrepreneur is key to the project.

– He can choose an “effort” level e ∈ {0, 1}.– Cost c (0) = 0 and c(1) = c.

• At t = 2: Cash flow.

– X ∈{XL, XH

}with ∆X ≡ XH −XL > 0,

– and Pr[X = XH

]≡ θ + e ·∆θ.

Assumption (*): e = 1 is efficient, i.e.,

∆θ∆X > c.

Assumption: The project’s value is positive if e = 1,

i.e.,

V1 ≡ XL + (θ + ∆θ) ∆X − I − c > 0.

• “Effort” is a metaphor

• The incentives of the party taking operating decisions

depends on his claims.

• Therefore, the pie size is affected by how it is split.

⇒ Violates one MM assumption.

Financial Contracts

• Financial claims are promises of payments at t = 2,

contingent on X :

RL if X = XL and RH ≡ RL + ∆R if X = XH .

• Limited liability:

RL ≤ XL and RH ≤ XH

Examples:

• Debt with face value K:

RL = min{XL, K} and RH = min{XH , K}.

• Fraction β of equity:

RL = βXL and RH = βXH .

• Call option on the firm’s equity with strike K:

RL = max{XL −K, 0} and RH = max{XH −K, 0}.

• Etc.

Remark:

• If XL = 0, all contracts are linear (in cashflows):

RL = 0 and RH ≥ 0.

• There is no difference between debt, equity, etc.

• Useful modelling trick when one wants to concentrate

on internal vs. external finance as opposed to the type

of external finance.

First Best

If W ≥ I, the entrepreneur should:

• Invest I and exert e = 1.

What if W < I?

• The entrepreneur needs to raise at least (I −W ).

• He can sell a claim (RL, RH).

• Competitive investors are willing to pay

RL + (θ + ∆θ)∆R.

Assumption (for now): XL = 0.

• The entrepreneur raises at least (I−W ) with a claim

such that:

RH ≥ RHmin ≡

I −W

θ + ∆θ.

• Note: Possible since RHmin ≤ XH .

• For instance, he can sell a claim to the entire cash

flow, i.e., RH = XH .

• Irrespective of W , the entrepreneur can always finance

the project.

• MM applies: Firm value is independent of whether

and how much the project if funded internally vs. ex-

ternally.

• True if there is no incentive problem, i.e., effort is

contractible or not costly.

Moral Hazard

Assumption: Effort is costly (i.e., c > 0) and non-

contractible.

• conflict + non-contractibility creates an incentive prob-

lem.

• For instance:

– Suppose that the entrepreneur sells the entire cash-

flow at t = 0.

– He has no incentives to incur a cost c(e) > 0 at

t = 1.

– Investors are willing to pay less for the firm’s claims.

• At t = 1, the entrepreneur chooses e = 1 iff:

∆θ(XH −RH) ≥ c or RH ≤ RH

max ≡ XH − c/∆θ.

• But financing the project (given e = 1) requires:

RH ≥ RHmin ≡ (I −W )/(θ + ∆θ).

• Hence, the first best is obtained iff:

RHmin ≤ RH

max.

Note: If the entrepreneur were not key to the project,

he could sell it to an investor who would run the project

(i.e., choose e).

Implications

• Role of internal funds:

– The condition is more likely to be satisfied when

W is large.

– Firms with more internal funds are less constrained

in their investment policy.

What if RHmin > RH

max?

• The project’s value for e = 0 is:

V0 ≡ XL + θ∆X − I.

• Credit rationing:

– Suppose V0 < 0.

– The entrepreneur cannot raise (I −W ), irrespec-

tive of RH .

• Deviation from value maximization:

– Suppose V0 > 0.

– The entrepreneur can raise (I − W ) but fails to

use these funds optimally.

Commitment Problem

• The entrepreneur’s payoff is:

Firm value − Net payment to competitive investor(s)︸ ︷︷ ︸=0

.

⇒ He is best-off maximizing firm value, so e = 1.

• Ultimately, the entrepreneur bears the costs of moral

hazard.

• However, once some claims are sold to investors, his

incentives are determined only by the claims that he

retains.

Costly commitment:

• To commit to e = 1, the entrepreneur is willing to pay

up to:

V1 −max{V0, 0}.

• Monitoring by a blockholder, a bank, an auditor,

etc...

• Bonding: Contractual commitment not to take cer-

tain actions (even if potentially valuable): Loan ear-

marking, etc.

Important Remark: Effort is a Metaphor

• The entrepreneur allocates the firm’s resources (in-

cluding but not only his labor) between activities gen-

erating:

– Security benefits, accruing to the firm’s claimhold-

ers,

– Private benefits, accruing to the entrepreneur

only.

• Note: Private benefits are negative private costs.

⇒ c(e) is the entrepreneur’s opportunity cost of not

getting private benefits.

⇒ Effort is efficient. ⇔ Private benefits are ineffi-

cient.

Examples:

• Future investment/funding decisions (Debt overhang).

• Empire building: Managers like large firms. Power?

Insurance?

• Entrenchment activities (Shleifer and Vishny 1989).

• Career concerns.

• Sustain family control (Is managerial talent heredi-

tary?).

• Perks, pet projects, etc. (Nabisco)

• Assets sold in sweetheart deals or for window dressing.

• “Time”: Work versus golf or outside jobs.

CAPITAL STRUCTURE

Jensen and Meckling (1976).

Main idea:

• Conflicts of interests:

– Between inside and outside equityhold-

ers.

– Between equityholders and debtholders.

• Specific costs:

– Outside equity ⇒ Low “effort.”

– Debt ⇒ Risk-shifting (aka asset substi-

tution).

• Optimal capital structure minimizes these

agency costs.

Model

Same as before except:

• XL > 0, to be able to discuss financing choices.

• I > XL, for simplicity.

• W = 0, for simplicity.

First-Best: Modigliani-Miller

• Financing choices are irrelevant in the absence of Moral

Hazard (i.e., if c = 0 or e is contractible).

• Say the entrepreneur chooses to raise exactly:

I = RL + (θ + ∆θ) ∆R.

• He can issue debt with face value K = XL+I −XL

θ + ∆θ,

i.e.,

RL = min{XL, K} = XL RH = min{XH , K} = K.

• Alternatively he can issue equity: Sell a fraction

β =I

XL + (θ + ∆θ)∆X

of existing shares, i.e.,

RL = βXL RH = βXH .

• Intuition: Competitive investors. ⇒ Irrespective of

financing, the entrepreneur receives the project’s en-

tire value.

Optimality of Debt

• At t = 1, the entrepreneur chooses e = 1 iff:

∆θ (∆X −∆R) ≥ c or ∆R ≤ ∆maxR ≡ ∆X − c/∆θ.

• Debt is the contract making this constraint least se-

vere, i.e., binding for a smallest set of parameters as,

it solves:

min(RL,RH)

∆R

RL ≤ XL RH ≤ XH

I ≤ RL + (θ + ∆θ) ∆R

• Debt is an optimal response to the effort problem:

Projects that can be funded (e.g., with equity) can

also be debt financed but the reverse is not true.

• Intuition: The optimal (debt) contract maximizes

the fraction of the return from effort that accrues to

the entrepreneur. Hence, it maximizes his incentive to

exert effort.

Cost of Debt: “Risk-Shifting”

• Same model except for Moral hazard at t = 1.

• Two mutually exclusive projects generating X ∈ {0, X̂, 2X̂}at t = 2.

Pr[X = 2X̂ ] Pr [X = 0]

Project A: θ1 θ2

Project B: θ1 + ∆1 θ2 + ∆2

with 0 < ∆1 < ∆2 and θ1 + ∆1 + θ2 + ∆2 < 1.

• Assume that Project A’s value is positive, i.e.,

(1 + θ1 − θ2)X̂ − I > 0.

First Best

• Project B’s value is

(1 + θ1 + ∆1 − θ2 −∆2)X̂ − I.

• This is less than Value(Project A), the difference be-

ing:

(∆2 −∆1)X̂ > 0.

• ⇒ I should be used for Project A.

Debt Finance?

• Suppose that I is raised in debt with face value K.

• Assume (for simplicity) that K > X̂, i.e.,

(1− θ2)X̂ < I.

• The entrepreneur gets a positive payoff only when

X = 2X̂ .

• With Project A, he gets:

θ1(2X̂ −K).

• With Project B, he gets:

(θ1 + ∆1)(2X̂ −K).

⇒ Once I has been raised, the entrepreneur picks

Project B.

Equity Finance?

• Suppose I has been raised in equity.

• Once I raised and invested, the entrepreneur gets a

fixed share of cash flows.

• ⇒ He maximizes expected cash flows.

• ⇒ He undertakes Project A.

• Equity is optimal since it induces no distortion in in-

vestment.

Intuition

• The difference between Project A and Project B has

two parts.

• An increase in θ1 and θ2 by ∆1 which preserves the

mean:

∆12X̂ − 2∆1X̂ + ∆1 · 0 = 0

but increases the variance.

• An increase in θ2 by (∆2 − ∆1) which decreases the

mean:

−(∆2 −∆1)X̂ + (∆2 −∆1) · 0 < 0.

Debt:

• Risky debt’s payoff is concave in cash flows.

⇒ Levered equity’s payoff is convex in cash flows.

⇒ Equityholders have an incentive to take excessive

risk.

• Value of call option increases with volatility. ⇒Risk-

shifting problem.

Equity:

• The entrepreneur and the investors have the same

claims. ⇒ No conflict.

• Linear claims. ⇒ No risk-shifting.

• Note: Equity dominates debt but also all other con-

tracts. This holds in more general models (see Green

1984).

Extension to Managerial Firms?

• The model fits entrepreneurial firms.

• Can we extend it to large firms in which many key de-

cisions are taken by employed professional managers?

• Does it provide a theory of capital structure for such

firms?

No:

• The effort model is useful for managerial firms only

if managers are not a priori indifferent to the firm’s

operating decisions.

• At best, a theory of managerial compensation, not

capital structure.

Extension to Managerial Firms?

• The literature happily applies the theory also (and in

fact primarily) to managerial firms.

• That is, it presents all firms as being entrepreneurial

but derives implications for managerial firms.

• This requires a non-standard assumption about man-

agerial behavior:

Assumption: Managers act in the interest of share-

holders.

• Otherwise, the problem could be solved by a con-

tract linking managerial compensation to the entire

firm value rather than, e.g., the value of the existing

equity (Dybvig and Zender 1991).

• “Coherent” interpretation: Only existing shareholders

can sign secret contracts with managers, i.e., undo

the optimal contract (Persons 1994).

• But why?

• With these caveats in mind, the analysis goes through

unchanged. (In fact, there is no scope for risk-shifting

with equity finance, i.e., the problem does not even

arise since managers serve all shareholders).

• In fact, in entrepreneurial firms, risk-neutrality may

not be a compelling assumption. The entrepreneur

may be bearing a lot of idiosyncratic risk. Hence, he

might take too little risk?

Risk-Shifting Model’s Implications

• More debt when there is less risk-shifting potential:

e.g.,

– Regulated public utilities with less managerial dis-

cretion (Bradley, Jarrell and Kim 1984).

– Firms in mature industries with few growth oppor-

tunities (Barclay, Smith and Watts 1992).

• Risk shifting incentives are higher in financial distress

because limited liability kicks in (“Gambling for Res-

urrection”).

• For instance, managers may delay filing for bankruptcy

to keep equity’s option value alive.

• Or they may file for Chapter 11 rather than Chapter

7.

Mitigating asset substitution:

• Covenants to debt contract, e.g., interest coverage

requirements or prohibition of investments into new,

unrelated lines of business (Smith and Warner 1979).

• Convertible debt alleviates existing shareholders’

risk-taking incentives by allowing debtholders to share

in the upside, making shareholders’ payoff partly con-

cave (Green 1984).

New Perspective on Capital Structure

• The optimal capital structure minimizes the sum of all

agency costs.

• Hence, the optimal capital structure is likely to be a

mix of debt and equity.

• Note: Jensen and Meckling (1976) study both prob-

lems separately. They conjecture that a debt-equity

mix is optimal. In a model including both problems,

new issues arise, e.g., the entrepreneur may try to con-

ceal low effort with high risk choices. Hellwig (1994)

finds that a debt-equity mix is indeed optimal (though

not uniquely so).

• Agency costs include monitoring and bonding costs.

INFORMATION ASYMMETRIES

• Under-diversification (Leland and Pyle 1977).

• Debt as a managerial signal (Ross 1977).

Main ideas:

(1) Information asymmetries between:

• (Some of) the firm’s existing claimholders.

• New investors.

(2) Outside finance is costly due to asymmet-

ric information:

• Misallocation of funds.

• Credit rationing: Some valuable projects

cannot be financed.

• Costs incurred to prevent the above such

as:

– Monitoring.

– Signalling.

– Etc.

Model

Two dates (t = 1, 2), no discounting

An entrepreneur has the following project:

• At t = 1:

– Need I > 0.

– Entrepreneur’s resources available W < I.

• At t = 2:

– Cash flow X ∈{XL, XH

}.

– Pr[X = XH

]≡ θ ∈ {θB, θG}.

– ∆θ ≡ θG − θB > 0.

Notation:

• Investors’ prior ν ≡ Pr [θ = θG] .

• Average θ̂ ≡ θB + ν∆θ.

• The project’s value is: V (θ) = XL + θ∆X − I.

Assumption: The good type’s project is valuable,

i.e., V (θG) > 0.

Assumption (for now): XL = 0.

First Best

• If V (θ) > 0, the entrepreneur should raise funds by

selling claims:

RL = 0 and RH ≤ XH such that θRH ≥ I −W.

• For instance,

RL = 0 and RH =I −W

θ.

Information Asymmetry

Assumption:Only the entrepreneur knows the actual

θ.

• Absent further information, the investors pay θ̂RH .

• ⇒ Investors would:

– Make money on good firms.

– Lose money on bad firms.

• In other words:

– Good firms would sell underpriced claims.

– Bad ones would sell overpriced claims.

– Good firms would subsidize bad firms.

Remark (Milgrom 1981):

• Soft information: The entrepreneur knows but cannot

prove θ.

• Hard information: He can decide whether to prove θ.

• Only soft information leads to problems:

– Investors assume the worst case given their infor-

mation.

– ⇒ The entrepreneur always reveals all hard infor-

mation.

Perfect Bayesian Equilibrium (PBE)

A Perfect Bayesian Equilibrium of this game is defined

as:

• Strategies: RHB and RH

G for the bad and good type

respectively (Convention: RH = 0 means that the

project is not undertaken).

• Beliefs: Investors beliefs following any observed ac-

tion RH :

ν(RH) ≡ Pr[θ = θG | RH

].

• Incentive Compatibility Constraints: RHB and

RHG are optimal for the bad and good type respectively

given the investors’ beliefs.

• Bayes Rule: Investors’ beliefs are obtained from a

priori distribution and observed actions using Bayes’

Rule, i.e., for RH ∈ {RHB , RH

G} :

ν(RH) =Pr

[(θ = θG) ∩RH

]Pr [RH ]

.

Remarks:

• Beliefs are also defined for off-equilibrium moves, i.e.,

ν(RH) is defined ∀RH , not only for RHG and RH

B .

• Beliefs following an off-equilibrium move are not pinned

down by Bayes Rule, i.e., for RH /∈ {RHB , RH

G}, ν(RH)

can take any value.

• To construct equilibria, take ν(RH) = θB for RH /∈{RH

B , RHG}.

Payoffs

• θ̂(RH) ≡ Investors’ expectation about θ following ac-

tion RH :

θ̂(RH) = θB + ν(RH)∆θ.

• If the project is financed, the entrepreneur’s expected

payoff is:

W︸ ︷︷ ︸Available Wealth

+ V (θ)︸ ︷︷ ︸Firms Actual Value

+ θ̂(RH) ·RH︸ ︷︷ ︸Raised from Investors

− θRH︸ ︷︷ ︸Claims actual value

• This can be rewritten as:

W + V (θ)︸ ︷︷ ︸Ents true worth

−(θ − θ̂(RH)

)RH

︸ ︷︷ ︸IA discount

Note: The discount can be negative.

Separating Equilibria with Both Types

Investing

• If RHG 6= RH

B , Bayes Rule pins down the investors’

beliefs:

θ̂(RHG ) = θG and θ̂(RH

B ) = θB.

• The bad entrepreneur’s payoff from playing RHB is:

W + V (θB)︸ ︷︷ ︸true worth

− (θB − θB) RHB︸ ︷︷ ︸

=0

• By deviating to RHG , he would get:

W + V (θB)︸ ︷︷ ︸true worth

− (θB − θG) RHG︸ ︷︷ ︸

<0

• ⇒ No such equilibrium.

Separating Equilibria with Only Bad Types

Investing?

• The bad entrepreneur prefers to invest iff:

W + V (θB) ≥ W or V (θB) ≥ 0.

• By deviating to RHB , the good entrepreneur would get:

V (θG)− (θG − θB) RHB = V (θB) + (θG − θB)(XH −RH

B ) ≥ 0.

• ⇒ No such equilibrium.

Separating Equilibria with Only Good Types

Investing

• The bad entrepreneur prefers not to invest iff:

V (θB) + (θG − θB) RHG ≤ 0.

• Moreover, the good entrepreneur needs to raise at

least (I −W ):

θGRHG ≥ I −W.

• Such a separating equilibrium exists iff:

V (θB) +∆θ

θG(I −W ) ≤ 0.

Stuff

• A necessary but not sufficient condition is V (θB) < 0.

Otherwise, bad entrepreneurs prefer investing.

• The condition is more likely to be satisfied when bad

entrepreneurs then have to bear a larger fraction of

their project’s negative value, i.e.,

– for smaller (I −W ),

– for more negative V (θB).

• Under this condition, a continuum of separating PBE

exist:

RHG ∈

I −W

θG;−V (θB)

∆θ

.

Pooling Equilibria with No Type Investing

• The bad entrepreneur prefers not to invest iff:

V (θB) ≤ 0.

• The good entrepreneur prefers not to invest iff:

V (θG) ≤ ∆θ

θB(I −W ).

• This can be rewritten as:

V (θB) ≤ −∆θ

θGW.

• This is stronger than the previous condition.

Pooling Equilibria with Both Types Investing

• If RHB = RH

G = RH0 , Bayes Rule pins down the in-

vestors’ beliefs:

θ(RH0 ) = θ̂.

• Feasibility constraint:

RH0 ≤ XH . (1)

• The good entrepreneur prefers to invest if his project’s

value exceeds the discount:

V (θG) ≥ (θG − θ̂)RH0 . (2)

• He is better off not deviating to any another RH ≥I−WθB

(i.e., allowing him to raise at least (I − W )) if

the discount is minimum for RH0 :

(θG − θ̂)RH0 ≤ (θG − θB)

I −W

θB. (3)

• The bad entrepreneur prefers to invest if:

−V (θB) ≤ (θ̂ − θB)RH0 . (4)

• He is always better off not deviating to any another

RH .

• The entrepreneur is able to raise (I −W ) iff

RH0 ≥ I −W

θ̂. (5)

• Such an equilibrium exists iff:

V (θB) ≥ max

−ν∆θI

θ̂; − ν∆θ (I −W )

θB(1− ν)

.

Proof:

• Conditions (1) and (4) are compatible iff V (θ̂) ≥ 0.

V (θB) ≥ −ν∆θI

θ̂

• V (θ̂) ≥ 0 ⇒ Conditions (1) and (5) are compatible.

• V (θ̂) ≥ 0 ⇒ Conditions (2) and (4) are compatible.

• V (θ̂) ≥ 0 ⇒ Conditions (2) and (5) are compatible.

• Conditions (3) and (5) are always compatible.

• Conditions (3) and (4) are compatible iff:

V (θB) ≥ −ν∆θ (I −W )

θB(1− ν).

To Summarize

• Recall: V (θG) > 0.

• Separating equilibrium with only good types investing:

V (θB) ≤ −∆θ

θG(I −W ).

• Pooling equilibrium with no investment:

V (θB) ≤ −∆θ

θGW.

• Pooling equilibrium with both types investing:

V (θB) ≥ max

−ν∆θI

θ̂; − ν∆θ (I −W )

θB(1− ν)

.

• When a separating equilibrium exists, the Intuitive Cri-

terion eliminates pooling equilibria but not the sepa-

rating equilibria.

Cho-Kreps Intuitive Criterion

A given PBE violates the Intuitive Criterion if there is

an out-of-equilibrium move RH /∈ {RHB , RH

G} and a subset

of types T ⊆ {θB, θG} such that:

i) Any type θ /∈ T prefers not to deviate to RH , for all ν

such positive weights are put only on elements of T .

ii) Any type θ ∈ T prefers to deviate to RH , for all ν

such that positive weights are put only on elements of

T .

Intuition: Following a move that type θ would make

under no circumstance, investors’ beliefs should put no

weight on type θ.

An Example

Assumption: W = 0, hence only pooling equilibria

exist.

• Suppose that the good type could choose the equilib-

rium to be played he would chose RH = 0 or RH = Iθ̂.

min RH

s.t.

θ̂RH ≥ I (F) Feasibility

RH ≤ XH (LL) Limited Liability

(1) Under-investment.

• Suppose that the average value is negative, i.e.,

V (θ̂) < 0.

• Credit rationing: Neither type of project is

undertaken. Indeed, there is no feasible repayment

(i.e., RH ≤ XH) such that investors expect to break

even (Lemon’s Problem).

(2) Over-investment.

• Suppose that the bad project’s value is negative, but

the average value is positive, i.e.,

V (θ̂) > 0 > V (θB).

• Both types of projects are financed. Indeed,

good entrepreneurs make a profit despite the discount

on claims:

θG(XH −RH) = θG(XH − I

θ̂) =

θG

θ̂V (θ̂) > 0.

• ⇒ Bad firms “pool” with good firms and get financed.

Mitigating Information Asymmetry Problems

Internal funds:

• Suppose that the entrepreneur has W > I.

• No credit rationing: Good projects that would not be

financed externally can be undertaken.

• No bad projects financed: Good entrepreneurs prefer

to self-finance because external finance is more expen-

sive (i.e., claims are sold at a discount) due to pooling

by bad entrepreneurs.

Information-insensitive assets:

• Suppose that the entrepreneur has an asset worth

W > I about which there is no information asym-

metry.

• Claims on this asset are sold at their fair price, i.e., no

discount.

• ⇒ The entrepreneur can finance the project.

Reducing the informational gap:

• To convey his type to investors, a good entrepreneur

is willing to pay up to:

min

(θG − θ̂)I

θ̂; V (θG)

.

• Monitoring/Certification: By a bank, venture

capitalist, auditor, etc.

• Signalling: Many Corporate Finance models in spe-

cific contexts such as collateral, debt maturity, divi-

dends, IPO underpricing, etc.

– General idea: Good types prove themselves by un-

dertaking an action costly enough to deter mim-

icking by bad types.

– ⇒ The cost needs to be greater for bad than for

good types.

RISK-BEARING AS A SIGNAL

Leland and Pyle (1977).

Main idea:

• By retaining a large equity stake in their

firms, good entrepreneurs can signal their

type to investors because:

– A large stake is costly (under-diversification).

– It is more costly for worse entrepreneurs,

because of their greater downside risk.

Model

• A risk-averse entrepreneur considers selling part of his

firm’s cash flow claims to risk neutral investors so as

to reduce his risk exposure.

Same model as before except that the entrepreneur:

• already undertook the project at t = 0.

• considers selling some shares at t = 1.

• is risk averse with respect to wealth at t = 2:

– VNM utility function u(X), with u′ > 0 and u′′ <

0.

– Normalization: u(0) = 0.

First Best

• By selling a fraction (1− α) at price P , type θ gets

Uθ(α, P ) ≡ θu(αXH + (1− α)P

)+ (1− θ)u ((1− α)P ) .

• Absent information asymmetry, the price is P = θXH .

• The entrepreneur’s expected utility is maximized for

α = 0 since:

∂Uθ(α, θXH)

∂α= θ(1− θ)XH

u′(αXH + (1− α)θXH

)−u′

((1− α)θXH

)

< 0 because u′′ < 0.

First best:

• The entrepreneur sells his entire stake.

• The investors bear all the risk.

• The entrepreneur is fully insured.

Asymmetric Information

• Absent further information, investors are willing to pay

θ̂XH .

• ⇒ An entrepreneur’s utility for selling claims on all

cash flows is

u(θ̂XH

)rather than u

(θXH

).

• ⇒ “Bad” entrepreneurs are even more eager to sell

claims.

Assumption (**):

θG(1− θ̂)

θ̂ (1− θG)>

u′ (0)

u′ (XH).

• That is,

∂UθG(α, θ̂XH)

∂α> 0 at α = 1.

• This implies

∂UθG(α, θ̂XH)

∂α> 0 for all α.

• ⇒ Good entrepreneurs prefer to retain their claims

and be exposed to risk rather than selling underpriced

claims.

• ⇒ Investors’ rational expectations should reflect that

good types are not selling claims on all cash flows.

• ⇒ This affects the price.

• ⇒ We need to analyze equilibria.

Example:

No Perfect Bayesian Equilibrium with αG = 0

Proof by contradiction. Suppose that αG = 0.

• Given the investors’ beliefs ν (α), they will pay (1− α) P (α)

for claims on a fraction (1− α) of the cash flows with:

P (α) = (θB + ν (α) ∆θ) ·XH .

• Good entrepreneurs prefer αG = 0 to α if:

u(P (0)) ≥ UθG(α, P (α)) . (6)

• Bad entrepreneurs prefer αB to α if:

UθB(αB, P (αB)) ≥ UθB

(α, P (α)) . (7)

• Suppose that αB = 0:

– ⇒ By Bayes’ Rule, ν (0) = ν.

– ⇒ The (ICG) constraint is violated (by Assump-

tion (**)).

• Suppose that αB 6= 0:

– ⇒ By Bayes’ Rule, ν (0) = 1 and ν (αB) = 0.

– ⇒ By the (ICB) constraint, UθB(αB, P (αB)) ≥

u(θGXH

).

– ⇒ P (αB) ≥ θGXH > θBXH .

– ⇒ ν (αB) > 0, a contradiction.

Pooling Equilibria?

• Under Assumption (**):

∀α < 1, UθG(1, P ) > UθG

(α, θ̂XH

).

• ⇒ No pooling equilibrium.

A Separating Equilibrium

αG = 1.

• αG = 1.

• αB = 0.

• ∀α 6= 1, ν (α) = 0.

• ν (1) = 1.

• Indeed, under Assumption (**)

∂UθG

(α, θBXH

)∂α

> 0 ∀α.

• Intuition: Retaining shares is a signal of confidence

success.

Other Separating Equilibria

• Suppose that investors view “selling a tiny fraction”

as a signal of good quality.

• The good type will “sell a tiny fraction” since he would

then get:

(1− α)

−∂UθG

(α, θGXH

)∂α

> 0.

• By mimicking, the bad type would get (almost):

θBu(XH

).

• ⇒ He is better off selling the entire firm and getting:

u(θBXH) > θBu(XH).

• ⇒ Expectations are correct, this is a PBE.

How large can (1− α) be?

• Bad types must prefer to sell the entire firm. Hence,

α must satisfy

UθB(0, θBXH) ≥ UθB

(α, θGXH

).

• The RHS is strictly decreasing in α.

• The inequality is satisfied for α = 1 and violated for

α = 0.

• ⇒ There exists a unique α∗ ∈ (0, 1) such that LHS=RHS.

• Hence, separation can be sustained for all

αG ≥ α∗ and αB = 0.

Selection with Cho-Kreps

• Puts some constraints on the possible beliefs following

an off-equilibrium move.

• Consider a PBE with α̂ > α∗.

• Suppose the investors observe off-equilibrium move

α = α∗ + ε < α̂.

• Can they “reasonably” believe that the firm is bad?

• The criterion imposes a posterior belief 0 for types

which would never be strictly better off deviating.

• For all ν, the bad type is better-off with αB = 0 than

with any αB > α∗.

• ⇒ The criterion imposes ∀α > α∗, ν(α) = 1.

• But then the good type can always improve on α̂.

• Hence, all equilibria with αG > α∗ are eliminated.

Comments

• Investors require entrepreneurs to invest their own wealth.

• This is inefficient as the entrepreneur bears diversifi-

able risk.

• Alternative signals that are less costly?

• Retrading? Holding a large stake is a signal only

if one is committed to keeping it. What if the en-

trepreneur can retrade after the issue? (See Admati,

Pfleiderer and Zechner 1995).

• Model of an entrepreneur going to the market for first

time. However, less readily applied to seasoned offer-

ings.

• (Seasoned) block sale may have quite different moti-

vation and hence informational content.

DEBT AS SIGNAL BY MANAGERS

Ross (1977).

Main idea:

(1) Managerial model:

• Financial distress imposes costs on man-

agers.

• Managers care about market values, not

only fundamentals.

(2) For a given debt level, better firms are less

likely to enter financial distress.

(3) ⇒ Debt is less costly for managers of bet-

ter firms. ⇒ Can be used as a signal.

Model

Firm run by a manager who:

• Privately knows θ ∈ {θB, θG} .

• Chooses the face value of debt K at t = 0.

• Maximizes (by assumption):

λV0 + (1− λ)[V1 − (K −X)+

],

where

• λ ∈ (0, 1).

• Vt : Firm’s market value at t.

• (K −X)+: Cost incurred by the manager in financial

distress.

• Note: No uncertainty after t = 1. ⇒ V1 = X.

Debt as a Signal

• Managers of good firms want, to some extent, to con-

vey this type to the market. Since K > XL is costly,

debt might be a signal.

Pooling Equilibria

• Example: K = 0, supported by ν (K) = 0 ∀K 6=0.

• Clearly, K = 0 is the most efficient pooling PBE.

• Good type gets λV (θ̂) + (1− λ)V (θG).

Separating Equilibria: KG > 0 KB = 0.

• Good type gets V (θG)− (1− λ) (1− θG) KG, rather

than λV (θB) + (1− λ)V (θG).

• Bad type gets V (θB), rather than λV (θG) + (1 −λ)V (θB)− (1− λ) (1− θB) KG.

• ⇒ Separation requires:

λ∆V

(1− λ) (1− θG)≥ KG ≥

λ∆V

(1− λ) (1− θB).

• Cho-Kreps kills all separating equilibria but the “best”

one(K∗

G = λ∆V(1−λ)(1−θB)

), in which the good type gets:

V (θG)− λ∆V

1− θG

1− θB

.

• If the good type is better off in the “best” separating

than in any pooling PBE, Cho-Kreps selects that PBE,

i.e.,

λ(V (θG)− V̂

)> λ

1− θG

1− θB

∆V .

Comments

• Ross’ model is for large firms run by managers who

are not necessarily major shareholders (unlike LP)

• To sustain a separating equilibrium, managers must be

interested in both current (market) value and actual

performance.

– If λ = 1, there is no cost, hence no way to sepa-

rate.

– If λ = 0, there is no need to separate.

• K∗G is increasing in λ.

• λ may be interpreted as the intensity of the takeover

threat:

– Benevolent manager: Prevents existing sharehold-

ers from selling under-valued stocks (Stein 1988).

– Self-interested manager: Dislikes takeovers.

– Implication: More takeover pressure. ⇒ More

leverage.

• The cost may also be a loss in reputation for the man-

ager.

Note: In Ross (1977), the cost of default is fixed (i.e.,

independent of the shortfall) but cash flows can take more

than two values.

• Profitability and leverage are positively related. Coun-

terfactual.

• Implicit assumption: Managers cannot trade se-

cretly on their own accounts. Otherwise:

– Good types do not signal and buy the stock.

– Bad types signal falsely and short the stock.

• Why use capital structure as a signal? Alternatively,

managers could promise to take a pay cut if perfor-

mance is poor.

Manager’s objective:

• The manager’s objective is exogenous. However, it

can be motivated as follows. Suppose initially all man-

agers are offered a fixed wage.

λE[V0] + (1− λ)E[V1] = w.

• After being hired, managers at good firms will want

to signal. They can alter their incentive scheme to

λV0 + (1− λ)[V1 − (K −X)+

]+ C

and issue debt XH > K > XL. (Note this is also

in the interest of shareholders of good firm provided

that the constant C is such that total compensation

is not increased).

THE CURSE OF MM

Diversity of Outside Claims?

• MM applies to the claims held by outside investors.

• ⇒ The structure of outside claims is irrelevant.

• Conflicts between insiders and outsiders generate op-

timal split of cash flows between insiders and outsiders

(e.g. inside equity and outside debt), but not among

outsiders.

• ⇒ Diversity of outside claims cannot be explained:

a mix of diverse outside claims could be merged and

repackaged into identical claims.

• To obtain a theory of the structure of outside claims,

we must (?) take the same way: Consider incentive

and information problems of outside investors (e.g.

incentives to monitor).