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EC908: Corporate Finance
(Lecture 5: Adverse selection (end), Moral Hazard)
João Miguel Ejarque
jejarque@essex.ac.uk
January, 2004
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 1
Recap Lecture 4. Adverse Selection. Hidden Information.
• Signaling with debt.
— Ross (1977). In this model we saw:
∗ A costly action is needed to achieve a separating equilibrium.
∗ The informed agent (the manager) will signal his type using debt.
∗ He accepts the possibility of a punishment later. This future loss is compensated
by a gain in his current payoff which is a positive function of the current value of
the firm. This value increases due to efficient signalling.
∗ The bad agent will have no incentive to lie since the choice of debt by the good
agent will imply too high a probability of being punished in the future.
∗ The contract achieves truthtelling as it aligns the goals of manager and sharehold-
ers.
— Leland and Pyle (1977).
∗ The manager is risk averse. We can use his risk aversion against him.
∗ The cost he suffers is the suboptimal risk diversification. The "contract" is similar
to the previous model because it also involves a "payment" proportional to the
value of the firm.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 2
Today
• Signaling with equity.
— Myers and Majluf (1984)
∗ In this case we study a negative signal.
∗ Stock repurchases send the opposite signal.
— Akerlof’s Lemons Problem
• Moral hazard (Hidden Action)
• These things matter.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 3
Myers and Majluf (1984)
• Main idea:
— A firm wants to raise money for a project.
— If it issues new equity for this project, it invites outsiders to share not only the project
but also all of its exhisting assets.
— Thus, outside investors will infer that exhisting assets are not very valuable.
— So, not knowing for sure what the firm is worth, outside investors will not be willing
to pay much for this new equity.
— Afterwards, if the firm is actually good, then its equity will have been underpriced.
— In addition, because outside finance is costly, a good firm should always rely on
retained earnings to finance new projects.
— This is a pecking order idea.
• Keywords: negative signaling, underpricing.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 4
• Model Preliminaries
— Two periods. The firm will operate only once in period 2 and then be liquidated.
— The firm has assets X in period 1 and needs to raise I for a project which will pay
V > I.
— There is no discounting. The two periods are very close in time (two days).
— The cash flow of the firm in period 2 is X + V if the investment is made, and X if
it is not.
— If the entrepreneur had enough money to pay I he would have done so.
— He could issue debt. Since V > I the debt would be risk free. Outside investors
would have no problem buying the debt and nothing would be learned about X, but
it would not matter. So, we must assume that issuing debt is impossible.
• These are the preliminaries.
— Using equity will be problematic if there is asymetric information about X.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 5
• But first lets look at full information.
— Outside investors know X.
— When they buy equity, if they get a fraction α of the firm, their wealth in period 2 is
α [X + V ]
and of course in a competitive market (remember no discounting) this will equal the
cost I. Thus:
I
α∗ =
X +V
— The inside equity (the entrepreneur) is worth the fraction (1 − α) of the firm:
W = (1 − α∗) [X + V ] = X + V − I
and since V > I he clearly will issue the new equity because...
— ...he extracts the entire rent from this new project.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 6
• Now lets look at asymetric information
— Assume X can take two values, L and H. The true value of X is only known by the
entrepreneur (inside equity).
— Outside investors have a prior probability that the firm is type H equal to p.
— This defines the expected intrinsic value as
¯
X = pH + (1 − p)L
— If the project is not undertaken, the inside equity retains its value X = H, L, and
the entrepreneur’s wealth is
W NI = X
— Suppose now that equity is issued. Competitive capital market implies
£ ¤
I=α X ¯ +V
where investors now break even only in expectation.
— The necessary equity fraction required by outsiders is then
I
¯
α≡ ¯
X +V
and note that α is decreasing in p: the better the prior that the firm is good, the
¯
less outside investors require.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 7
— The wealth of the entrepreneur when he invests is now given by
W I = (1 − α) [X + V ]
¯
and notice that it is X, and not X bar in this expression.1
— His optimal choice depends on
∙ ¸
X +V
W I − W NI = (1 − α) [X + V ] − X = V − I ¯
¯ = V − IU
X +V
— Now, if X = L he will surely invest as V > I anyway. In addition, the U factor will
be less than one.
∗ So, a low type firm is overpriced in the sense that its cost of capital is too low.
∗ Investors think the firm is better than it really is, and so require a smaller share in
the firm (thus lower returns) than they should.
— Now, if X = H he may not invest even though V > I. This is because the U factor
is now bigger than 1.
∗ A high type firm is underpriced in the sense that its cost of capital is too high.
∗ Investors think the firm is worse than it really is, and so require a bigger share in
the firm (thus higher returns) than they need to.
1
There is an issue about when information is disclosed and when the market values these assets. Because if you sold these shares what would be their price? Should
it be a function of the true X as here, or of X bar?
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 8
• What happens with debt?
— To have a more complete pecking order we need to make the payoff V of the project
random, so that debt is risky and bankruptcy can happen.
— In this context, the higher the debt (relative to equity), the higher the risk of bank-
ruptcy, but the lower the underpricing effect from the negative signal from new equity.
— Now, any new equity will imply negative signalling, but the first unit of debt will not
imply bankruptcy.
— So a pecking order emerges: retained earnings, debt (pays interest), then equity.
— Debt is better than equity if there is a faster drop in the share price when new equity
is issued, than a rise in bankruptcy probability when new debt is issued.
— These ideas are the opposite characteristics to the Free Cash Flow idea
∗ In FCF, too much retained earnings is bad because managers will steal more.
∗ Here retained earnings are good because they save on costly external finance.
∗ Costly: new equity carries a signaling penalty, and new debt pays interest.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 9
Myers and Majluf Bottomline:
• Bottomline
• This is a version of Akerlof’s lemons problem.
• In the limit (as p gets small) bad firms drive good firms out of the market as the
underpricing gets too severe.
• Here we are not in a signalling equilibrium.
• As the model is written, debt cannot really be used to signal, because debt is a senior
claim, and here is riskless as V > I.
• But this could perhaps be fixed by making V random.
£ ¤
• It is infact a good exercise for you to try, using a uniform distribution V ∈ 0, V ¯
and see if debt can be used as a signal. Suppose that there is an exogenous debt limit,
so that debt can still make the firm bankrupt, but is not enough to finance the whole
project financing needs.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 10
The market for Lemons
George Akerlof
The market for Lemons
A fundamental contribution to the Economics of Information
George Akerlof is 2001 Nobel Laureate
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 11
The market for Lemons
• In a market for used cars, there are cars of many qualities, extremely bad, very bad,
quite bad, just bad, so so, etc etc, until very good.
• Bad cars are bad. They are lemons. You bite them, and you find out they are not sweet.
• Sellers know the quality of their cars.
• Buyers don’t know the quality. The quality is not observable.
• The only thing buyers can judge, is the chance of getting a good car (fraction of good
cars on the market).
• Buyers and sellers meet only once.
• All deals are final.
• What happens?
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 12
The market for Lemons
• Buyers are only willing to pay an average price for the car.
P BUY ER = q GoodP Good + qAverageP Average + q BadP Bad...
• Otherwise they lose money in expectation.
• However...
• Sellers of good cars take their cars out of the market at such a price.
• So, the average quality drops.
• But then the average price buyers are willing to pay also drops.
• And then, the next best cars are taken off the market,
• and then...
• and then...
• and then...the market collapses!
• Why exactly did this happen?
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 13
The market for Lemons
• The root of the problem is the asymetric information. Given the heterogeneity of the
product, asymetric information implies bad products are a negative externality on good
products.
• They key to solve the problem is to break the asymetric information.
— Either through costly signaling.and/or incentive contracts.
— Or via repeated games and reputation (with punishment strategies).
— Or via regulation (legal monitoring).
• Examples of Lemons markets
— Health Insurance. Mississipi Farming Insurance.
∗ Why doesn’t the price just rise?
— Education. What affects the value of your degree?
∗ What should schools do? Improve the quality of the best students? Improve the
quality of the average student? Of the worst students?
• Again, in the Myers and Majluf example, can we use debt to solve the problem?
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 14
A pecking order dilemma2
• Consider a firm that is priced on the stock market.
• This firm has an R&D department that is secretly developing a new technology.
• In order to finish developing the project the firm needs a large injection of cash.
• This technology may be successful in which case the firm will see a huge increase in
shareprices.
• But it may also fail, resulting in a loss of all the R&D effort put into the project, the
loss of the new cash injection, and a drop in shareprices.
• The new tecnhology cannot be revealed to the public because competitors can steal
the idea and patent the product first. This implies the firm cannot convince outside
investors of the quality of its project.
• But the firm’s management has announced to the media that "new R&D projects in the
pipeline are very promising".
• How, can this firm raise the cash it needs?
2
Taken from Grinblatt and Titman, page 647, example 18.6.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 15
Simple model of Moral Hazard3
• An agent (entrepreneur or firm) wants to raise money for a project.
— The project costs I and implies a random return given by
½
R w.p. p
I⇒
0 w.p. 1 − p
— The agent has initial wealth (assets) worth w0 < I. He must borrow the difference.
— The agent will take an action that will affect the outcome of the project. The action
cannot be observed. He decides to put in effort e. This will affect the probability of
success of the project, but also higher effort will lower his utility of leisure from U to
zero: ½
1 ⇒ p = pH ⇒ 0
e= L , pH > pL
0 ⇒ p=p ⇒ U
— The agent faces no punishment for failure. He has limited liability.
— The return R will be divided between the agent and a lender:
R = R a + Rb
3
Taken from Flavio Toxvaerd’s notes.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 16
• The lender, acts in a competitive market so he will break even.
— Assuming that in equilibrium the agent puts in effort we have for the lender a break
even condition:
pH Rb = I − w0
— Now assume that the total (expected) surplus is positive only if the agent puts in
high effort:
pH R − I > 0
pLR − I + U < 0
— We can rewrite the bottom condition to get
L
¡ a b
¢
p R + R − I + U + w0 − w0 < 0
£ L a ¤ £ L b ¤
p R + U + w0 + p R − (I − w0) < 0
where the first term is the gain for the agent, and the second is the gain for the
lender.
— So, if there is no effort, at least one of them will lose money (and/or utility).
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 17
• Incentive compatibility
— In order for high effort to be an equilibrium the agent must not want to deviate:
pH Ra > pLRa + U
⇒
a U
Rmin = H
p − pL
which defines the minimum partition the agent will accept that is incentive compat-
ible. Remember that everyone is risk neutral.
— Of course, the other side of the coin is that the maximum we can offer outside
financiers is
b a U
Rmax = R − Rmin ≡ R − H
p − pL
— Now the break even condition implies the project goes ahead only if
∙
b
pH Rmax ≥ I − w0
¸
U
pH R − H L
≥ I − w0
p −p
and we can rewrite this as
H U £ H ¤
w0 ≥ p H L
− p R−I
p −p
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 18
• Conclusions
— This last condition implicitly defines a minimum collateral requirement:
H U £ H ¤
¯
w0 = p H L
− p R−I
p −p
— If the agent does not have enough assets (w0 < w0) there is no project, even though
¯
it may have a positive NPV. This is called credit rationing.
— If the agent has enough assets (w0 > w0) his payoff gain is:
¯
pH Ra − w0 = pH R − pH Rb − w0 = pH R − I
— He captures the entire surplus of the project.
— Because of competition the lender cannot do better than break even.
• So:
— The Moral Hazard problem implies credit rationing and underinvestment.
— This underinvestment implies that ex-ante the value of the firm is lower.
— It also implies there is a limit to what you can offer lenders because you need to
guarantee a payoff to the insider.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 19
• Debt overhang
— Suppose the agent now has a debt with face value D which has to be paid next
period.
— This is equivalent to a reduction in net assets.
— The minimum collateral requirement is altered:
H U £ H ¤
w0 = p H
˜ − p (R − D) − I
p − pL
— Now, if his initial assets were enough before:
¯
w0 > w0
— That may not be the case anymore if
˜
w0 < w0
— This is the debt overhang we saw before.
— Carrying a debt makes profitable investments that would have been viable otherwise,
no longer possible.
— Exercise: see if it makes any difference whether old debts have first claim or not.4
4
Hint: if old debts are paid last, the amount D is extracted from the agent’s payoff, Ra . If old debts are paid first, the amount D is extracted from total assets ex
post, R, leaving R-D. Note, the minimum collateral condition in Toxvaerd’s notes for the debt overhang case is wrong.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 20
• Renegociation (see also lecture 3)
— The agent has a debt with face value D which has to be paid next period.
— To make it simple he has no assets.
— The debt obligation is senior.
— Suppose that it was the case that for the lender
∙ ¸
H U
p R− H >I
p − pL
— But also that now ∙ ¸
H U
p R− H −D <I
p − pL
— That is, if there was not debt, the project would have gone ahead, just after satisfying
the agent’s Moral Hazard rents. But the debt spoils it all, since there is not enough
to satisfy everyone.
— Note that the agent has limited liability, so at worst he gets zero if there is no project,
or his leisure benefit if the project goes ahead.
— So, unless old debt holders renegociate, everyone loses.
— Only old debtors can take any action, because new investors will only
join voluntarily, and for that they must break even.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 21
— They will accept a reduction in their payments just until the project goes ahead:
∙ ¸
U
pH R − H L
−d =I
p −p
— Therefore, renegociation ensures that everyone gets some rent.
— Old Brazilian proverb: "Old debts are not meant to be paid."
— New Brazilian proverb:
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 22
More General Version: Grossman and Hart (1982)
• Main Idea
— Shareholders (the principal) need to have control of a manager (the agent).
— The manager will take an unobserved action (waste some company money) which
will hurt shareholders.
— They cannot control this directly so they must provide him with an incentive contract
so that he behaves. The incentive contract will have both a carrot and a stick.
— Crucial difference with respect to signalling problems. There is no uncertainty re-
garding the type of the manager. There is a problem of lack of direct control over
his actions. But because the type is not uncertain, there is no need for the manager
to signal his type.
— In the signalling problem, the manager is a good guy and does nothing to hurt the
firm. It is in the interest of good managers to send a voluntary costly signal to the
market, and this also benefits the firm as the market correctly prices its shares.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 23
• Model
— There are two periods. In the first period the firm issues debt and equity B + E to
raise R funds to invest in a project. The debt is paid out in period two and has face
value D.
— The firm has a manager who likes his perks. But he is also the one who decides how
much of the R money will be invested in the project (I) and how much he will spend
on himself afterwards (R-I).
— The project pays a return
zg(I)
∗ where z is a random variable over the interval [0, z ], with distribution f (z). Also
¯
g(0) = 0, g 0(I) > 0, g 00(I) < 0.
— The realization of the shock z is not known when making the investment decision.
— And, more importantly, the separate components of (z, I) are not observable even
ex post. Only the total output zg(I) is observable.5
5
Except in the case of bankruptcy.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 24
• Ex post payoffs
• So, ex post equity holders, bond holders, and managers get a payoff:6
π E = max [zg(I) − D, 0]
1
B
π 1 = min [zg(I), D]
∙ ¸
R − I if zg(I) > D
πM =
1 0 if zg(I) < D
• Now, given the investment decision (I ∗ (D)), bankruptcy occurs if the shock is:
D ∗
z<z =
g (I ∗)
which happens with probability F (z ∗).
— Now, ∂z ∗/∂D > 0, and ∂z ∗/∂I = −Dg 0/g 2 < 0.
— This is the key. Shareholders will issue debt even though that raises the probability
of bankruptcy, because the manager also has a loss in case of bankruptcy, and so he
will invest more.
6
Manager gets zero if the firm goes bankrupt because of bankruptcy procedures: after auditing it will be possible to find out separately what z and I were. In this
case courts simply take R − I away from the manager.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 25
• All equity firm
— In this case
D 0
= =0 z∗ =
g (I) g (I)
— Therefore the manager never gets caught because there never is bankruptcy.
— Therefore the manager invests zero and eats R.
— But, more importantly, the market knows this, and the value of the firm is zero.
— The moral hazard problem is so strong that it destroys the value of the firm.
— Thus, issuing debt will provide discipline on the manager and alleviate the problem.
— Debt here is chosen by equity holders, so this is not a signalling problem.
— It can actually be shown that the debt contract is an optimal contract (if we were to
choose the type of contract to offer).7
7
Williamson, S.D. (1987), “Costly monitoring, loan contracts, and equilibrium credit rationing,” Quarterly Journal of Economics 102 (1), pp. 135-145.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 26
Debt and Equity. Summary of moves.
• Manager’s decision
— Given the debt level D, he maximizes his payoff πM by choosing I, which yields
1
I(D).
• Firm’s decision
— Choose D to maximize equity value πE given optimal reaction I(D) from the man-
1
ager, and a requirement that bondholders will participate voluntarily:
B
¡ b
¢
π 1 (D) ≥ 1 + r B˜
where rb is exogenous.
˜
• Key issues
— Is the investment effort chosen by the manager positive given D?
∗ Yes because if I=0 there is certain bankruptcy and the manager gets zero.
— Is the debt level D positive?
∗ Yes. If D=0, then the manager chooses I=0, and the firm has no value.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 27
• Debt and Equity
— First, what does the manager do?
— Given D, he chooses I to maximize his payoff
Z z
¯
M
π1 = (R − I)f (z) = (R − I) (1 − F (z ∗))
z∗
— The first order condition is ∙ ¸
∗
∂F ∂z
− (1 − F (z ∗)) − (R − I)
∗ ∂I
=0
∂z
— Is there an interior solution for investment?
— Yes: note that if investment is zero then there is certain bankrputcy as g(0) = 0,
and so the manager gets zero. If I = R, then the manager gets zero also. He is
certainly better off somewhere in the middle.
— Now, this first order condition determines a solution
I ∗ (D)
— So, differentiate this first order condition to find the sign of ∂I ∗/∂D, (it is positive).
∗ This positive derivative implies the manager raises his effort if the firm issues more
debt.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 28
• What does the firm do?8
— Shareholders choose debt to maximize their payoff, conditional on participation by
bondholders, and on the optimal action from the manager, I ∗ (D):
Z z
¯
E
max π 1 (D) = max [zg (I ∗ (D)) − D] f (z) dz
D D z ∗ (I ∗ (D))
subject to
Z ¯
z Z z ∗ (D)
∗
¡ ¢
s.t. πB
1 (D) = Df (z) dz + ˜b
zg (I ) f (z) dz ≥ 1 + r B
z ∗ (D) 0
where rb, is a required return on bonds in the market and here is exogenous. But
˜
this condition does not affect the problem since it just implicitly defines B.
— The first order condition is
∂ ¡ E ¢
π 1 (D) = 0
∂D
• Is there an interior solution for Debt?
— When D = 0, there is no bankruptcy and the value of the firm is zero.
— So, D>0 is not first best because of costly bankruptcy, but due to Moral Hazard,
D > 0.
8
Different from the lecture notes.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 29
• Conclusions
— There is a solution to the moral hazard problem.
— The solution involves a trade-off between accepting bankruptcy with some probability,
and getting some more value for the firm.
— This is exactly in the same spirit as in the signalling problems we have studied.
— However, here there is no signaling.
— The type of the agents in known for sure.
— But his actions are hidden, and they can harm the firm. The firm must accept a
costly solution to the incentive problem.
— The solution carries a cost for both the firm and the manager.
— There is an efficiency cost of too much bankruptcy.
— On the methodological aspect, this is a more complex problem to solve than the pre-
vious signaling problems we saw. The reason for that is that there are two optimizing
agents in the problem. Whereas before we were not looking at an optimal contract,
since it was in the interest of the manager to find his own optimal signaling in a
credible way, here a fundamental part of the problem is the optimal decision of the
shareholder.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 30
What Now?
These things matter!
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 31
Manager and Board Compensation
• Managers have power to affect the outcome of the firm.
— Therefore their compensation must be an incentive scheme.
— It must be tied to the value of the firm. A flat fee carries little incentive.
— "Firms show the greatest tendency to artificially inflate accounting earnings when
managers have the most to gain from an increase in share prices."9
— Hall and Liebman (QJE, 1998) look at CEO compensation between 1980 and 1994.
— They look at 478 of the largest publicly traded companies in the US.
∗ The median CEO was 58 years old, had been with the company for 22 years, and
earned about 1 million dollars plus 30% of that in stock options.
Age T W C w s.o.
58 22 1.050.000$ 324.000$
— They find that CEO compensation does change with the value of the firm.
9
Grinblatt and Titman, page 637. In 1987 "General Motors increased the estimated useful life of its plant and equipment, thereby reducing depreciation charges, and
increasing reported earnings by 1.2 billion." Note that nothing intrinisic changed. It is true however, that firms often "sit" on suboptimally used real estate, particularly
their office spaces. If they sold their offices, and rented them back, their shareprices should rise.
EC908 - Corporate Finance - Lecture 5: Adverse Selection (end), Moral Hazard 32
• Boards.
— Why do firms have boards? (Bennedsen, 2002)? This is for later.
— How much do board members earn and is their pay related to their performance?
— How liable are they?
— Data
∗ CEO’s with less active boards receive more money.
∗ CEO’s get sacked more often if board member compensation is related to the
performance of the company.
∗ Share prices drop if CEO’s appoint a board member.
∗ But are board members really there for the money, or are they there for the status?
Some people think it is the status, but the data seem to indicate that in generally
they perform better given the right incentives.
∗ Bennedsen finds little effect of boards on performance which is line with the idea
that board members are too close to CEO’s. But it could also simply reflect that
CEO’s have an incentive contract that is working well.
