![Page 1: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/1.jpg)
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.
![Page 2: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/2.jpg)
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.
![Page 3: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/3.jpg)
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).
![Page 4: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/4.jpg)
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.
![Page 5: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/5.jpg)
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 .
![Page 6: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/6.jpg)
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.
![Page 7: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/7.jpg)
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).
![Page 8: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/8.jpg)
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
![Page 9: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/9.jpg)
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.
![Page 10: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/10.jpg)
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!
![Page 11: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/11.jpg)
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.
![Page 12: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/12.jpg)
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.
![Page 13: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/13.jpg)
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.
![Page 14: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/14.jpg)
• 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.
![Page 15: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/15.jpg)
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?
![Page 16: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/16.jpg)
Another Argument........
Dividends are safer than future payments. ⇒ Don’t they
increase firm value?
• MM show that this theory is flawed
![Page 17: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/17.jpg)
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.
![Page 18: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/18.jpg)
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
![Page 19: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/19.jpg)
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).
![Page 20: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/20.jpg)
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
![Page 21: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/21.jpg)
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.
![Page 22: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/22.jpg)
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.
![Page 23: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/23.jpg)
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.
![Page 24: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/24.jpg)
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).
![Page 25: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/25.jpg)
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.
![Page 26: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/26.jpg)
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
![Page 27: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/27.jpg)
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.
![Page 28: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/28.jpg)
• 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
![Page 29: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/29.jpg)
Proposition (MM with corporate and personal
taxes):
V (D) = V (0) +
1− (1− τ ) (1− τE)
(1− τD)
D.
![Page 30: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/30.jpg)
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.
![Page 31: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/31.jpg)
• ⇒ 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.
![Page 32: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/32.jpg)
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.
![Page 33: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/33.jpg)
• Additional assumptions:
– Firms’ cashflow is certain (debt is riskfree).
– No short sales.
• Yield on tax-exempt (e.g., municipal) bonds: r0.
![Page 34: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/34.jpg)
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).
![Page 35: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/35.jpg)
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.
![Page 36: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/36.jpg)
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.
![Page 37: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/37.jpg)
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.
![Page 38: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/38.jpg)
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.
![Page 39: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/39.jpg)
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.
![Page 40: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/40.jpg)
MODELS BASED ON INCENTIVE
PROBLEMS
• Moral hazard.
• Moral hazard and credit rationing.
• Jensen and Meckling (1976).
– Effort problem.
– Risk-shifting problem.
![Page 41: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/41.jpg)
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.
![Page 42: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/42.jpg)
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.
![Page 43: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/43.jpg)
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.
![Page 44: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/44.jpg)
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
![Page 45: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/45.jpg)
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.
![Page 46: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/46.jpg)
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.
![Page 47: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/47.jpg)
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.
![Page 48: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/48.jpg)
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.
![Page 49: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/49.jpg)
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.
![Page 50: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/50.jpg)
• 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).
![Page 51: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/51.jpg)
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.
![Page 52: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/52.jpg)
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.
![Page 53: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/53.jpg)
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.
![Page 54: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/54.jpg)
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.
![Page 55: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/55.jpg)
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.
![Page 56: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/56.jpg)
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.
![Page 57: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/57.jpg)
Model
Same as before except:
• XL > 0, to be able to discuss financing choices.
• I > XL, for simplicity.
• W = 0, for simplicity.
![Page 58: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/58.jpg)
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.
![Page 59: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/59.jpg)
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.
![Page 60: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/60.jpg)
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.
![Page 61: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/61.jpg)
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.
![Page 62: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/62.jpg)
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.
![Page 63: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/63.jpg)
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.
![Page 64: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/64.jpg)
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.
![Page 65: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/65.jpg)
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).
![Page 66: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/66.jpg)
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.
![Page 67: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/67.jpg)
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:
![Page 68: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/68.jpg)
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?
![Page 69: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/69.jpg)
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.
![Page 70: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/70.jpg)
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).
![Page 71: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/71.jpg)
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.
![Page 72: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/72.jpg)
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.
![Page 73: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/73.jpg)
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.
![Page 74: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/74.jpg)
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.
![Page 75: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/75.jpg)
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.
![Page 76: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/76.jpg)
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.
![Page 77: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/77.jpg)
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 ]
.
![Page 78: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/78.jpg)
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}.
![Page 79: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/79.jpg)
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.
![Page 80: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/80.jpg)
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.
![Page 81: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/81.jpg)
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.
![Page 82: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/82.jpg)
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.
![Page 83: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/83.jpg)
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
.
![Page 84: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/84.jpg)
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.
![Page 85: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/85.jpg)
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)
![Page 86: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/86.jpg)
• 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)
.
![Page 87: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/87.jpg)
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).
![Page 88: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/88.jpg)
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.
![Page 89: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/89.jpg)
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.
![Page 90: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/90.jpg)
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).
![Page 91: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/91.jpg)
(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.
![Page 92: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/92.jpg)
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.
![Page 93: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/93.jpg)
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.
![Page 94: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/94.jpg)
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.
![Page 95: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/95.jpg)
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.
![Page 96: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/96.jpg)
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.
![Page 97: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/97.jpg)
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.
![Page 98: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/98.jpg)
• ⇒ 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.
![Page 99: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/99.jpg)
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)
![Page 100: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/100.jpg)
• 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.
![Page 101: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/101.jpg)
Pooling Equilibria?
• Under Assumption (**):
∀α < 1, UθG(1, P ) > UθG
(α, θ̂XH
).
• ⇒ No pooling equilibrium.
![Page 102: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/102.jpg)
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.
![Page 103: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/103.jpg)
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.
![Page 104: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/104.jpg)
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.
![Page 105: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/105.jpg)
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.
![Page 106: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/106.jpg)
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.
![Page 107: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/107.jpg)
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.
![Page 108: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/108.jpg)
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.
![Page 109: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/109.jpg)
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).
![Page 110: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/110.jpg)
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 .
![Page 111: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/111.jpg)
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.
![Page 112: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/112.jpg)
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.
![Page 113: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/113.jpg)
• 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.
![Page 114: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/114.jpg)
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).
![Page 115: Modigliani-Miller Theorem Under some assumptions, corporate](https://reader033.vdocuments.net/reader033/viewer/2022052706/5868cba31a28ab7f7d8b6f6a/html5/thumbnails/115.jpg)
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).