FINANCIAL MARKETS AND DECISIONS II

David KelseyDepartment of Economics

University of Exeter

January 2010

TOPICS THIS TERM

1. The Modigliani-Miller Theorems.

2. The Market for Lemons.

3. Adverse Selection and the Debt-Equity Ratio.

4. Moral Hazard and Incentives.

5. Incentive Effects of Debt and Equity.

6. Takeovers and Auctions.

COURSE ORGANISATION

THE COURSE CONSISTS OF 20 LECTURES IN SPRING AND SUMMER TERMS.

Assessment 100% EXAMINATION

Web-site http://people.exeter.ac.uk/dk210/fmd-II-09.html

No lectures 18th and 19th March.

1 THE MODIGLIANI - MILLER THEOREMS

1.1 TYPES OF SECURITIES

Tirole, pp. 75-80.

Debt and Equity Assume that a firm has issued debt, which requires it to make repay-

ments of value D next period.

The only other security issued is equity. Equity-holders have limited liability.

Returns to debt are concave in earnings.

Returns to equity are a convex function of earnings.

45o����������������������

LendersEarnings

.......................................................Firm’s EarningsD

D Firm’s Earnings

EquityEarnings

����������������������

45o

There is a conflict of interest.

• Shareholders will be risk loving.

— Their profits are a convex function of the firms returns.

— Limited liability means that they receive all the rewards of risky investments but

their losses are limited.

• However bondholders will be risk-averse since their returns are a concave function of

firm earnings.

Junior Debt

• In the case of default senior debtholders are paid first,

— once senior debt is paid, junior debt receives any remaining funds;

• junior debt is more risky than senior debt and therefore pays a higher rate of return.

Consider a firm which has promised to pay $D on senior debt.

It subsequently issue junior debt, which has contractual payments of $d next period.

Returnsto Debt

��������������������������������

����������������.................................

D + dD

45o

Preferred Stock

• Preferred stock receives a fixed payment.

• If the payment is not repaid there is no default.

• No dividends can be paid on equity if the payment on preferred stock is not made.

Convertible Debt

• Is debt, which can be exchanged for equity at a predetermined conversion rate.

1.2 THE DEBT-EQUITY RATIO

1.2.1 REFERENCES

Modigliani and Miller, “The Cost of Capital and the Theory of Investment”, American

Economic Review 1958

MILLER Journal of Economic Perspectives 1988 + COMMENTS.

In 1958:

• Returns on debt: 3-5%;

• Returns on equity 15-20%.

The conventional wisdom was that a levered firm was worth more.

In contrast Modigliani and Miller showed that the debt-equity ratio cannot affect the value

of the firm.

FRAMEWORK

Modigliani and Miller study an economy with no market distortions.

Assume that the only securities which firms issue are debt and equity.

Consider two firms, F = 1, 2. Let:

TF =total value of F ,

SF =market value of equity in firm F ,

BF =market value of bonds in firm F .

TF = SF +BF .

Theorem 1.1 1st Modigliani-Miller Theorem. SUPPOSE THAT:

• A FIRM’S TOTAL RETURNS X, ARE UNAFFECTED BY THE FIRM’S FINANCIAL

DECISIONS;

• INVESTORS CAN BORROW AND LEND ON THE SAME TERMS AS FIRMS;

THEN IN EQUILIBRIUM, THE FIRM’S DEBT-EQUITY RATIO CANNOT AFFECT ITS

VALUE.

Proof. CONSIDER TWO FIRMS, FIRM 1 AND FIRM 2, BOTH OF WHOSE

EARNINGS MAY BE DESCRIBED BY THE SAME RANDOM VARIABLE X.

FIRM 1 IS 100% EQUITY FINANCED, T1 = S1.

FIRM 2 IS LEVERED, T2 = B2 + S2.

THE TOTAL PAYMENT TO SHAREHOLDERS IN FIRM 2 IS X −B2r.

r = INTEREST RATE.

SUPPOSE, IF POSSIBLE, THE LEVERED FIRM HAS HIGHER VALUE T2 > T1.

CONSIDER AN INVESTOR WHO INITIALLY OWNS FRACTION α OF THE EQUITY

OF FIRM 2.

THIS PORTFOLIO GIVES RETURNS α (X −B2r) .

SUPPOSE (S)HE SOLD THIS PORTFOLIO AND BORROWED $αB2.

• (S)HE COULD BUY FRACTION αS2+αB2S1

OF THE EQUITY IN FIRM 1.

• THIS GIVES RETURNSαS2 + αB2

S1X − αB2r

= α

(T2T1

X −B2r

)

> α (X −B2r) .

This sequence of trades will give the investor a riskless profit.

This cannot happen in equilibrium.

Thus we may conclude T1 � T2.

NOW SUPPOSE THAT T2 < T1.

CONSIDER AN INVESTOR WHO INITIALLY OWNS FRACTION α OF THE EQUITY

OF FIRM 1.

RETURNS = αX, VALUE = αT1.

SUPPOSE INSTEAD THE INDIVIDUAL PURCHASED FRACTION αT1T2

SHARES IN

FIRM 2 AND αT1T2B2 BONDS.

COST = αT1T2S2 + αT1

T2B2 = αT1

T2(S2 +B2) = αT1

T2T2 = αT1.

RETURNS = αT1T2(X −B2r) + αT1

T2B2r = αT1

T2X > αX.

THUS THE INVESTOR HAS BEEN ABLE TO GET HIGHER RETURNS AT THE SAME

COST.

THERE IS COMPLETE SEPARATION BETWEEN THE REAL AND FINANCIAL SIDES

OF THE ECONOMY.

ALL INDIVIDUALS HAVE THE SAME CONSUMPTION BEFORE AND AFTER A

CHANGE IN THE FIRM’S DEBT EQUITY RATIO.

THUS ALL ARE INDIFFERENT.

TODAY

1. Tax and Modigliani-Miller

2. Dividend Policy

1.3 TAX AND DEBT

DEBT INTEREST CAN BE DEDUCTED FROM CORPORATE TAX, BUT DIVIDENDS

CANNOT.

ASSUME:

• THE RETURNS OF FIRMS 1 AND 2 ARE GIVEN BY THE SAME RANDOM VARI-

ABLE X.

• FIRM 1 100% EQUITY. FIRM 2 ISSUES B2 BONDS.

UNDER THE SAME CONDITIONS AS THE MODIGLIANI-MILLER THEOREM.

Proposition 1.1 IF THERE IS A CORPORATE INCOME TAX LEVIED AT RATE t THE

LEVERED FIRM HAS GREATER TOTAL VALUE BY AMOUNT tB2.

Proof. AS BEFORE, FIRM 1 IS 100% EQUITY FINANCED, FIRM 2 IS LEVERED.

PORTFOLIO 1: α SHARES IN FIRM 1,

• COST = αS1,

• RETURNS = α(1− t)X.

PORTFOLIO 2: α SHARES IN FIRM 2 AND α(1− t)B2 BONDS.

• COST = αS2 + α(1− t)B2,

• RETURNS = α(1− t)(X − rB2) + α(1− t)rB2 = α(1− t)X.

SINCE THESE TWO PORTFOLIOS YIELD THE SAME RETURNS THEY MUST HAVE

THE SAME PRICE.

HENCE αS1 = αS2 + α(1− t)B2,

S1 = S2 +B2 − tB2,

T1 + tB2 = T2.

THE LEVERED FIRM HAS GREATER TOTAL VALUE BY AMOUNT tB2.

Remark 1.1 tB2 = CAPITALISED VALUE OF THE TAX DEDUCTION.

THE OPTIMAL FINANCIAL STRUCTURE OF THE FIRM IS 100% DEBT.

1.4 DIVIDEND POLICY

Modigliani and Miller’s second result concerns how the value of the firm is affected by

dividend policy.

Pay-outs from firms to shareholders include:

• Dividends;

• Share repurchases by the firm;

• Terminal dividends at takeovers or mergers;

— In 1999 pay-out from mergers and acquisitions was greater than pay-outs from

dividends and repurchases combined.

Shareholders do not receive the returns of the firm, just the dividends the management

decide to pay.

MM show that firm value is independent of dividend policy.

• If capital markets are perfect, by borrowing and lending consumers can undo the

effect of any change in a firm’s dividend policy.

MM refer to a ceteris paribus change in dividend policy. A dividend cut forced by a adverse

shock to the business is not ceteris paribus.

1.4.1 MODEL

There are two time periods: t = 1, 2;

Dt = Dividend in period t;

Bt = Borrowing of the firm in period t;

I = investment in period 1;

X1 = returns in period 1;

X2 (I) =returns in period 2.

Consider a typical shareholder who owns fraction α of the firm:

ct = consumption in period t;

et = other income in period t.

1.4.2 SECOND MODIGLIANI-MILLER THEOREM

Theorem 1.2 2nd Modigliani-Miller Theorem. ASSUME:

• THE TOTAL RETURNS X OF A FIRM ARE UNAFFECTED BY FINANCIAL DECI-

SIONS;

• INVESTORS CAN BUY AND SELL SECURITIES ON THE SAME TERMS AS THE

FIRM;

THEN THE FIRM’S DIVIDEND POLICY CANNOT AFFECT ITS VALUE.

Proof. In period 1 the firm’s budget constraint is:

X1 +B1 = D1 + I,

or B1 = D1 + I −X1.

In period 2 the budget constraint is:

X2 (I) = D2 +B1 (1 + r) .

Hence D2 = X2 (I)−B1 (1 + r) = X2 (I)− (D1 + I −X1) (1 + r) .

Consider a shareholder who owns fraction α of the equity. His/her budget constraint is:

c1 +c21+r = e1 + αD1 +

e21+r + α D2

1+r

= e1 + αD1 +e21+r + α

X2(I)−(D1+I−X1)(1+r)1+r

= e1 + αD1 +e21+r + α

X2(I)1+r − α

D1(1+r)1+r − α

(I−X1)(1+r)1+r

c1 +c21+r = e1 +

e21+r + α

X2(I)1+r + αX1 − αI.

The budget constraint is independent of D1 and D2.

Thus consumption will not depend on the firm’s dividend policy.

Consequently no other real variables will be changed in the new equilibrium. Hence the

value of the firm must be the same in the new equilibrium.

Remark 1.2 From the shareholder’s budget constraint

c1 +c21 + r

= e1 +e21 + r

+ αX2 (I)

1 + r+ αX1 − αI

we can see that the optimal level of investment is given by αX ′2(I)1+r − α or

X′2 (I) = 1 + r.

Note this does not depend on the preferences of the shareholder, i.e. all shareholders are

unanimous.

• IF THE FIRM’S DIVIDEND POLICY CHANGES ALL MEMBERS OF THE ECON-

OMY WILL BE INDIFFERENT BETWEEN THE SITUATIONS BEFORE AND AF-

TER THE CHANGE.

• DIVIDEND POLICY CANNOT AFFECT THE VALUE OF THE FIRM.

• INVESTMENT DECISIONS CAN BEMADE SEPARATELY FROMDIVIDEND POL-

ICY.

1.4.3 TAX EFFECTS

IN MOST COUNTRIES CAPITAL GAINS ARE TAXED AT A LOWER RATE THAN

DIVIDEND INCOME.

SHAREHOLDERS’ INCOME WOULD BE MAXIMISED BY PAYING NO DIVIDEND

AND INSTEAD REPURCHASING SHARES. THIS WOULD GIVE THE SHAREHOLD-

ERS A CAPITAL GAIN.

1.4.4 EVIDENCE ON PAY-OUTS

MM implies that if a firm cuts dividends and uses the saving to retire debt this has no

effect on its value.

Under similar assumptions we may show that if a firm cuts dividends and uses the savings

to retire equity this has no effect on its value.

Taking into account tax saving replacing dividends by share repurchases should increase

the value of the firm.

Over time dividends have been reduced and share repurchases have increased.

In the United States

• Before 1980 dividends were the most important form of pay-out to shareholders

• Since 1980 dividends have decreased over time.

— Share repurchases are the dominant form of cash pay-out.

— In 1974 27% used only share repurchases,

— In 1998 81% used only share repurchases.

• Corporations tend to smooth dividends over time.

— Repurchases are much more variable.

• Share price reacts positively to dividend increases and announcements of share repur-

chases.

Figure 4:

Figure 5:

Figure 6:

TODAY

• Finish MODIGLIANI - MILLER

• Lemons (Adverse Selection)

LAST WEEK

MODIGLIANI - MILLER THEOREMS The value of the firm does not depend

on the debt equity ratio or on dividend policy.

Allowing for tax effects, replacing dividends by share repurchases should increase the value

of the firm by the amount of tax saved.

Figure 7:

EXPLANATIONS

• Repurchases are replacing dividends because they are taxed at a lower rate.

• Repurchases tend to increase the amount paid out to management under stock option

schemes.

1.4.5 ASSUMPTIONS REQUIRED FOR MODIGLIANI -MILLER THEOREMS

1. CONTROL ASPECTS OF SHARES IGNORED.

2. SHAREHOLDERS CAN LEND AND BORROW AT THE SAME INTEREST RATE

AS FIRMS.

NOT CRUCIAL SINCE ARBITRAGE. COULD BE PERFORMED BY HOLDING

COMPANIES.

3. NO BANKRUPTCY.

4. TAX IGNORED.

1.4.6 BANKRUPTCY

Increasing debt levels will increase the probability of bankruptcy.

Increasing bankruptcy costs will reduce the value of the firm, (contrary to Modigliani

Miller).

Bankruptcy is different from liquidation:

• Liquidation is where the firm can no longer be operated profitably;

— assets are sold off on secondary markets.

• In bankruptcy a firm is no longer able to make the contracted payments on its debt;

— Bankruptcy does not imply that production ceases;

— instead bankruptcy is a financial reorganisation of the firm.

In the absence of other market distortions, bankruptcy costs need not be high.

• Existing equity could be cancelled

• Existing debt is then converted into the new equity in a reorganised firm.

In practice bankruptcy costs arise from market distortions, e.g. agency costs are higher

in over-leveraged firms.

Gambling for resurrection .

1.5 CONCLUSION

Modigliani and Miller say that how the value of the firm does not depend on how it is

financed.

Many find this paradoxical.

The rest of the course studies how asymmetric information can explain this apparent

paradox.

Moral hazard explanations. The choice of financing can change incentives.

Adverse selection explanations: More profitable firms choose a particular form of fi-

nance.

2 THE MARKET FOR LEMONS

See separate file.

3 ADVERSE SELECTION AND THE DEBT-EQUITY

RATIO

3.1 INTRODUCTION

3.1.1 BACKGROUND

The Modigliani-Miller analysis assumes a perfect capital market.

Both firms and individuals may borrow and lend as much as they wish at the market

interest rate.

In fact there is often credit rationing, limits are placed on how much an agent can borrow

and some agents are denied loans altogether.

Credit rationing can be explained by asymmetric information in credit markets.

3.2 LEMONS PROBLEMS IN THE CREDIT MARKET

Reference Tirole, Ch. 6.

3.2.1 MODEL

An entrepreneur needs $I to finance an investment project.

• The borrower has limited liability.

• He/she has no funds to invest.

• The project is either a success in which case it yields income R or it fails yielding

no income.

• There are two types of borrowers.

— A good borrower succeeds with probability p.

— A bad borrower succeeds with probability q < p.

The entrepreneur cannot influence the probability of success.

There are two cases;

1. pR > I > qR only the good type is creditworthy.

2. pR > qR > I both types are creditworthy.

Fraction α of the borrowers are good.

Let m = αp+ (1− α) q denote the average success rate.

3.2.2 SYMMETRIC INFORMATION

The good type always receives funding. He/she is paid RGb if successful, where RG

bsatisfies:

p(R−RG

b

)= I.

The bad borrower receives funding if and only if qR > I.

His/her reward for success is RBb if successful, where RB

b satisfies:

q(R−RB

b

)= I.

RBb < RG

b .

Define rG, rB by R−RGb = I (1 + rG) , R−RB

b = I (1 + rB) .

The good type gets a better interest rate, rG < rB.

These contracts are not viable if the lender cannot identify the types.

The bad borrower can always pretend to be good to get the lower interest rate.

3.2.3 ASYMMETRIC INFORMATION

Assume that the borrower knows whether his/her project is good or bad but the lender

does not.

Since the lender cannot tell the two types apart, the contract pays Rb in event of success

and 0 otherwise.

No Lending mR < I.

Let α∗ denote the minimal number of good borrowers needed to make a loan profitable

i.e.

α∗ (pR− I) + (1− α∗) (qR− I) = 0

Then there will be an equilibrium with no lending if there are too few good borrowers i.e.

α � α∗

The presence of bad borrowers prevents good borrowers from obtaining funding.

This is inefficient as the good entrepreneur does not get a loan.

Adverse selection causes under-investment.

Lending mR � I.

Either the bad borrower is creditworthy or α � α∗.

The borrower’s reward for success is Rb, defined by

m (R−Rb) = I. (1)

There is cross-subsidisation.

• Lenders make money on the good type.

• Lenders lose money on the bad type.

Rb < RGb

The presence of the bad type reduces the profits of the good type.

Define r by R−Rb = I (1 + r) .

The good type has to pay a higher interest rate because of the presence of the bad types.

If the bad project is not creditworthy.

• It will be financed under asymmetric information even though it is not efficient.

• Adverse selection causes over-investment.

3.2.4 MARKET TIMING

Firms tend to issue shares when stockmarket prices are high.

One explanation is that adverse selection has less influence during a boom.

Suppose now that the probability of success of a good (resp. bad) type is p + τ (resp.

q + τ).

The parameter τ ≷ 0 represents market conditions.

The condition for financing becomes (m+ τ)R � I.

If market conditions are better (i.e. τ is larger) then it is more likely that firms can obtain

funding.

In a boom the intrinsic value of the project becomes large compared to the lemons problem.

3.2.5 COLLATERAL

The presence of bad types means that good types can borrow on less favourable terms.

Suppose now that the borrow is able to pledge collateral. If the project fails the lender

seizes the collateral.

This is costs less to the good borrower, since (s)he loses the collateral with lower proba-

bility.

Thus it is possible to get a signalling equilibrium, where the bad borrower offers no

collateral and gets a loan at a high interest rate.

The good borrower signals that (s)he is good by offering collateral and gets a loan at a

lower interest rate.

For this to be an equilibrium it must be the case that the cost of posting collateral for

the bad borrower is greater than any gain (s)he would get from a low interest rate.

Such a signalling equilibrium is inefficient since the collateral is lost with positive proba-

bility. (Assuming the collateral is worth more to the lender than to the borrower.)

3.2.6 INITIAL PUBLIC OFFERINGS (IPO)

Shares are usually under priced at initial public offerings

The average price of shares on secondary markets is 15-20% above the offer price.

Explanations

• Collusion between underwriters and institutional investors.

• Adverse Selection

3.2.7 MODEL

An entrepreneur needs $I to finance an investment project.

• The project is either a success in which case it yields income R or it fails yielding

no income.

• There are two types of borrowers.

— A good borrower succeeds with probability p.

— A bad borrower succeeds with probability q < p.

The entrepreneur has an initial cash endowment A < I.

Assumption 3.1 Only the good borrower is creditworthy:

qR < I −A < pR.

With symmetric information the good borrower’s reward for success would be RGb , defined

by

p(R−RG

b

)= I −A. (2)

Assumption 3.2 A < qRGb .

If the borrower receives reward RGb for success then both good and bad borrowers will

apply for loans. As a result the lender will make losses.

By reducing the reward for success it is possible to get a separating equilibrium where

only the good borrower applies for a loan.

The highest reward, R∗b, which is unappealing to a bad borrower is given by

qR∗b = A.

Suppose the good borrower signals that (s)he is good by pledging his/her entire wealth

and accepts a reward R∗b in event of success.

The lender’s profit will be

p (R−R∗b)− (I −A)

Using equation (2)

p (R−R∗b)− (I −A) = p (R−R∗b)− p(R−RG

b

)

= p(RGb −R∗b

)> 0.

Thus the issue is under-priced in the sense that lenders make a positive profit.

The under-pricing signals a good quality loan.

In relative terms under-pricing is given by

p(R−R∗b

)

p(R−RG

b

) =p(R−R∗b

)

I −A

=pR− I − [(p− q) /q]A

I −A.

The closer p is to q the more the issue needs to be under priced to deter the bad borrower.

3.2.8 SUMMARY

Adverse selection can explain why credit markets are different.

Adverse selection can give rise to under-investment.

It can also give rise to over-investment.

Good borrowers will wish to signal they are good

• Collateral

• Under pricing of IPO’s

3.2.9 Collateral MODEL (not 2010)

The presence of bad types means that good types can borrow on less favourable terms.

Borrowers may signal that they have a good project by pledging collateral.

If the project fails the lender seizes the collateral.

This is costs less to the good borrower, since (s)he loses the collateral with lower proba-

bility.

Assumption 3.3 Under symmetric information even the bad borrower does not need to

pledge collateral,

0 < V ≡ qR− I < V ≡ pR− I.

SYMMETRIC INFORMATION

Assume the lender can identify the borrower’s type.

The good borrower receives a reward RGb defined by

p(R−RG

b

)= I

His/her utility is equal to:

pRGb = pR− I = V.

Similarly the bad borrower receives a reward RBb defined by

q(R−RB

b

)= I

His/her utility is equal to:

qRBb = qpR− I = V .

Note that

RGb =

V

pand RB

b =V

q

ASYMMETRIC INFORMATION

Suppose the good borrower pledges collateral worth C to him/her.

• The collateral will be seized by the lender in case of failure.

• The collateral is worth βC to the lender, 0 � β < 1.

Is there a combination of a reward Rb and a pledge of collateral C, which will convince

a lender that the borrower has a good project?

To be profitable to the lender such a contract must not be attractive to the bad borrower.

This contract offers the bad borrower:

qRb − (1− q)C.

If the lender knew the borrower were bad, (s)he would get utility V .

Thus for the contract with collateral to be unattractive to the bad we require:

qRb − (1− q)C � V . (3)

In addition we must satisfy the lender’s individual rationality constraint:

p (R−Rb) + (1− p)βC � I. (4)

Since lenders are assumed to be competitive, the equilibrium contract will maximise the

good borrower’s utility:

pRb − (1− p)C,

subject to (3) and (4).

SOLUTION

Both constraints are binding. The solution⟨R∗b, C

∗⟩can be found by solving the con-

straints as simultaneous equations.

R∗b = R−

[(1− q)− β (1− p)

p (1− q)− βq (1− p)

]

I > RGb ,

C∗ =I

1 + q (1− p) (1− β) / (p− q).

The good borrower prefers to offer collateral to being taken for the bad borrower.

pR∗b − (1− p)C > pRBb .

The good borrower needs to pledge more collateral:

• The larger is β.

• The greater the asymmetry of information, i.e. the smaller is q.

The bad borrower gets an undistorted contract.

The equilibrium is inefficient since the collateral is lost with positive probability.

3.3 ADVERSE SELECTION AND INVESTMENT

Reference Myers, S.C. and N.S. Majluf, (1984), “Corporate Financing and Investment

Decisions when Firms have Information that Investors do not have”, Journal of Financial

Economics, 13, 187-221.

Assume that management is better informed than outside investors about the true value

of the firm.

The firm needs to sell equity to fund an investment opportunity.

There is an adverse selection problem.

Those firms which sell equity will on average be less valuable.

Under rational expectations the shares will sell for less than their expected value.

As a result some firms will not be able to fund some profitable investment opportunities.

The decision to issue stock can convey bad news to the market.

Example 3.1 Suppose that the true value V of the firm is uniformly distributed between

$100 and $200.

The true value of the firm is known to the management but not to outside investors. (It

is private information.)

Management acts in the interest of existing stockholders

Suppose that management decides to issue new stock at price $P.

Then outside investors know P � V.

The expected value of the firm (to outside investors) is : 50 + 12P.

If P > 100, 50 + 12P < P.

Thus the only price at which outside investors will buy is $100.

There is adverse selection.

• The firms which are most keen to issue new stock are those whose share price is most

over-valued.

• These are precisely the firms whose stock outside investors least wish to buy.

Since equity can never be sold at a profit the firm will not issue new stock.

YESTERDAY

Myers, S.C. and N.S. Majluf, (1984), “Corporate Financing and Investment Decisions

when Firms have Information that Investors do not have”, Journal of Financial Economics,

13, 187-221.

Due to lemons problems an existing firm may find it difficult to sell new equity.

TODAY

Assume a firm need to sell equity to fund a new investment.

Adverse selection will depress the price at which equity can be sold, thus reducing invest-

ment.

Problem sheet 1, questions 1-3,.

3.3.1 MODEL

Now assume that the firm has a profitable investment opportunity.

It may be worth selling stock to fund the investment even though the sale of stock will

make a loss.

A firm has an asset in place which has value A (random).

There is an investment opportunity whose net present value is B, (random).

Let a (resp. b) denote the realisation of A, (resp. B).

It is efficient to invest if and only if its net present value (NPV) is positive.

Management has private information.

• Management knows the true value of the existing stock a and the investment oppor-

tunity b.

• The market only knows the distributions of A and B.

Let P ′ be the value of old shareholders stock if new stock is issued.

There are two equally probable states of nature, s1, s2.

Asset values are:

s1 s2Asset in place a 150 50Investment b 20 10

The investment costs E = $100.

Suppose first that the firm issues stock and makes the investment in both states of nature.

Then P ′ = 115 = 12 (150 + 50 + 20 + 10) = A+ B.

In s1 the true value of the firm is V = V o + V n = $270 = 170 + 100

The market value at t = 0 is:

V o = P ′

P ′+E.V = 115

215.270 = 144.42,

V n = EP ′+E

.V = 100215.270 = 125.58.

In s2 the true value of the firm is $160 = V o + V n = 60 + 100

The market value at t = 0 is:

V o = 115215.160 = 85.58,

V n = 100215.160 = 74.42.

Both old and new shares are correctly priced to investors,

P ′ = 12 (144.42 + 85.58) = 115

E = 12 (125.58 + 74.42) = 100.

Pay-offs to the old shareholders from the two possible investment policies are:

Issue & invest do nothingV o in s1 144.42 150V o in s2 85.58 50

It is not profitable to issue new stock when the existing asset has high value.

The cost of issuing new stock below the true value is greater than the benefit of being

able to make the investment.

Suppose that the firm only invests in s2.

Then if the firm issues stock, the market knows the state is s2.

Issue & invest do nothingV o in s1 – 150V o in s2 60 –

The average payoff to old stockholders is 12 (150 + 60) = 105 < 115, (the first best

solution).

Suppose at t = 0 the firm holds cash of £100.

Invest do nothingV o in s1 170 150V o in s2 60 50

The firm invests in both states which increases its NPV by $10.

The investment is profitable if it is made from retained funds but not if it is funded by a

new equity issue.

This illustrates the value of a cash reserve.

The higher the NPV of the new investment the more likely is investment to take place.

s1 s2Asset in place a 150 50Investment b 100 10

Suppose that the firm issues stock and makes the investment in both states of nature.

Then P ′ = 155 = 12 (150 + 50 + 100 + 10) = A+ B.

In s1 the true value of the firm is $350 = V o + V n = 250 + 100

The market value at t = 0 is

V o = P ′

P ′+E.V = 155

255.350 = 212.75

V n = EP ′+E

.V = 100255.350 = 137.25.

Thus it is desirable to sell shares and invest in s1.

3.3.2 DEBT FINANCE

Risk-free debt is equivalent to cash.

Suppose that the firm finances the project with risky debt.

By similar reasoning management is more likely to issue debt when their private informa-

tion suggests the firm is more likely to default.

Hence the market will treat the decision to issue debt as a bad signal about the riskiness

of debt.

The distortion is smaller if the project is financed by debt, since debt always has the first

call on the firm’s funds.

3.3.3 PECKING ORDER

As far as possible projects should be financed with securities least subject to adverse

selection.

• first with retained funds, (no distortion)

• second with debt, (small distortion)

• third with junior debt convertibles etc.(larger distortion).

• fourth equity, (greatest distortion).

The Modigliani-Miller theorem does not hold. The value of the firm is not independent

on how it finances investments.

3.3.4 CONCLUSIONS

Adverse selection can reduce investment.

• Need asymmetric information about both assets in place and new investment oppor-

tunities.

This explains why stock issues lower the share price. The market interprets a stock issue

as a signal the stock is overvalued.

These problems will be less severe for a conglomerate firm.

• If a firm has a diversified set of investments in different industries then the variance

of the manager’s inside information is reduced.

• This reduces the lemons problem associated with new equity issues.

TODAY

• Financial Signalling

• Problem sheet 1, question 3,.(if time permits)

TOMORROW

• Moral Hazard

3.4 DEBT AS A SIGNAL OF PROFITABILITY

UNDER ASYMMETRIC INFORMATION TOTAL RETURNS MAY DEPEND ON THE

FINANCIAL STRUCTURE OF THE FIRM.

MANGERS MAY BE BETTER INFORMED THAN MARKETS ABOUT THE FUTURE

PROSPECTS OF THE FIRM.

THIS CREATES AN ADVERSE SELECTION PROBLEM.

Reference Ross, S. (1977), “The Determination of Financial Structure: The Incentive

Signalling Approach,” Bell Journal of Economics, 8, 23-40.

OUTLINE

1. INCREASING DEBT RAISES THE PROBABILITY OF BANKRUPTCY.

2. BANKRUPTCY IS COSTLY TO MANAGERS.

3. MANAGERS ARE BETTER INFORMED ABOUT FUTURE EARNINGS THAN THE

MARKET.

4. FIRMS WITH HIGHER CASH FLOW FACE LOWER PROBABILITY OF BANK-

RUPTCY.

A SIGNALLING EQUILIBRIUM IS POSSIBLE WHERE FIRMS WITH HIGHER ANTICI-

PATED FUTURE EARNINGS TAKE ON MORE DEBT. THE MARKET TREATS THIS

AS A POSITIVE SIGNAL AND THE SHARE PRICE RISES.

3.4.1 MODEL

Assumption 3.4 FINANCIAL MARKETS ARE COMPETITIVE WITH NO TRANSAC-

TIONS COSTS OR TAXES.

2 TIME PERIODS t = 0, 1.

2 TYPES OF FIRMS A (GOOD) AND B (BAD).

a =TOTAL RETURN OF TYPE A FIRMS (IN PERIOD 1).

b = TOTAL RETURN OF TYPE B FIRMS (IN PERIOD 1). a > b.

ASSUME THAT PRICING IN THE ASSET MARKET IS RISK NEUTRAL.

FIRMS ARE CONTROLLED BY MANAGERS.

Assumption 3.5 THE FIRM’S TYPE IS THE MANAGER’S PRIVATE INFORMATION

(AT t = 0).

Assumption 3.6 MANAGER’S PAY IS DETERMINED BY A KNOWN INCENTIVE

SCHEDULE.

M = (1 + r)γoVo + γ1V1, IF V1 � F ;M = (1 + r)γoVo + γ1(V1 − L), IF V1 < F ;

M = MANAGER’S PAY;

r = INTEREST RATE;

Vo, V1 =VALUE OF THE FIRM AT t = 0, 1;

L = BANKRUPTCY PENALTY, IMPOSED ON THE MANAGER;

F = FACE VALUE OF THE DEBT ISSUED BY THE FIRM AT t = 0.

THE MANAGER CHOOSES F TO MAXIMISE M .

3.4.2 A SIGNALLING EQUILIBRIUM

Investor’s Beliefs

LET F ∗ BE SUCH THAT b � F ∗ � a.

IF F > F ∗ INVESTORS PERCEIVE THE FIRM TO BE OF TYPE A.

IF F � F ∗ INVESTORS PERCEIVE THE FIRM TO BE OF TYPE B.

THE INITIAL VALUE OF THE FIRM IS PERCEIVED TO BE THE FOLLOWING FUNC-

TION OF THE DEBT LEVEL:

Vo(F ) =a1+r IF F > F ∗; Vo(F ) =

b1+r IF F � F ∗.

TYPE A FIRM

THE MANAGER OF A TYPE A FIRM RECEIVES:

• MA(FA) = (γo + γ1)a, IF F ∗ < FA ≤ a;

• MA(FA) = γob+ γ1a, IF FA � F ∗.

THE MANAGER’S INCOME WILL BE MAXIMISED BY CHOOSING A DEBT LEVEL

IN THE RANGE,

F ∗ < FA � a.

TYPE B FIRM

THE MANAGER OF A TYPE B FIRM RECEIVES:

MB(FB) = (γo + γ1)b, IF FB � b � F ∗;

MB(FB) = γoa+ γ1(b− L), IF FB > F ∗.

IN EQUILIBRIUM THE MANGER OF A TYPE B FIRM SHOULD NOT WISH TO

FALSELY SIGNAL THAT HIS/HER FIRM IS OF TYPE A.

THIS IMPLIES THAT FOR F ′ > F ∗,

MB(F ′) = γoa+ γ1(b− L) < MB(FB) = (γo + γ1)b,

WHICH HOLDS IF AND ONLY IF γo(a− b) < γ1L.

THE MANAGER’S SHARE OF THE GAINS FROM A FALSE SIGNAL MUST BE LESS

THAN HIS/HER SHARE OF THE BANKRUPTCY COST.

IF γ1 = 0 A SIGNALLING EQUILIBRIUM IS NOT POSSIBLE SINCE MANAGERS

WOULD NOT BEAR ANY FRACTION OF THE BANKRUPTCY COST.

IF γo = 0 A SIGNALLING EQUILIBRIUM IS NOT POSSIBLE SINCE MANAGERS

WOULD NOT RECEIVE ANY BENEFIT FROM RAISING THE VALUE OF THE FIRM

IN PERIOD 0.

Remark 3.1 THE EQUILIBRIUM IS EFFICIENT.

3.4.3 OTHER FINANCIAL SIGNALLING MODELS

LELAND AND PYLE

• Leland, H. and D. Pyle (1977), “Informational Asymmetries, Financial Structure and

Financial Intermediation”, Journal of Finance, 32, 371-387.

SHOW THAT THE FRACTION OF A PROJECT OWNED BY THE ENTREPRENEUR

CAN BE SIGNAL OF PROFITABILITY OF THE PROJECT.

• MANAGERS ARE RISK AVERSE.

• MANAGERS ARE PRIVATELY INFORMED ABOUT THE PROFITABILITY OF

THE PROJECT.

• THE MORE EQUITY A MANAGER HOLDS THE MORE RISK (S)HE IS EXPOSED

TO. THIS COST IS ROUGHLY INDEPENDENT OF EXPECTED RETURNS.

• THE BENEFITS OF HOLDING EQUITY ARE HIGHER IN A FIRM WITH HIGHER

EXPECTED RETURNS.

IN EQUILIBRIUM, MANAGERSWILL HOLDMORE EQUITY IN A FIRMWITH HIGHER

EXPECTED RETURNS.

INVESTORS CAN MAKE DEDUCTIONS ABOUT THE VALUE OF THE FIRM FROM

THE FRACTION OF EQUITY OWNED BY THE MANAGER.

EVIDENCE EQUITY ISSUES (LOWERING THE DEBT-EQUITY RATIO) TENDS TO

LOWER THE VALUE OF FIRMS. THIS IS CONSISTENT WITH SIGNALLING MODELS

OF DEBT.

BHATTACHARYA SHOWS THAT DIVIDENDS CAN BE A SIGNAL OF FUTURE

PROFITABILITY. THIS EXPLAINS WHY FIRMS PAY DIVIDENDS DESPITE THE TAX

DISADVANTAGE.

Reference Bhattacharya, S. “Imperfect Information, Dividend Policy and the ‘Bird in

the Hand’ Fallacy”, Bell Journal of Economics, 10, 259-270

3.4.4 CONCLUSION

WHY DO FIRMS USE FINANCIAL SIGNALLING RATHER THAN DIRECTLY TRANS-

MITTING INFORMATION TO SHAREHOLDERS?

1. DIRECT TRANSMISSION OF INFORMATION MAY VIOLATE INSIDER TRADING

RULES.

2. DIRECT TRANSMISSION OF INFORMATION MAY GIVE VALUABLE INFORMA-

TION TO COMPETITORS.

THIS WEEK

MANAGERS MAY HAVE PRIVATE INFORMATION ABOUT THE FIRM WHICH IS

NOT KNOWN TO FINANCIAL MARKETS.

IN GENERAL THIS WILL CREATE A BIAS IN FAVOUR OF DEBT FINANCING.

1. LEMONS PROBLEMS IN THE CREDIT MARKET.

2. ADVERSE SELECTION AND INVESTMENT.

3. DEBT AS A SIGNAL OF PROFITABILITY.

TOMORROW

Problem sheet 1, questions 1-3,.

LAST WEEK

An entrepreneur needs $I to finance an investment project.

• The project is either a success in which case it yields income R or it fails yielding

no income.

• There are two types of borrowers.

— A good borrower succeeds with probability p.

— A bad borrower succeeds with probability q < p.

The entrepreneur cannot influence the probability of success.

There are two cases;

1. pR > I > qR only the good type is creditworthy.

2. pR > qR > I both types are creditworthy.

Fraction α of the borrowers are good.

Let m = αp+ (1− α) q denotes the average success rate.

With symmetric information the good type would get a lower interest rate.

This will not be possible when the lender cannot identify the types as the bad borrower

could always (falsely) claim to be good.

TODAY

• Moral Hazard (theory)

NEXT WEEK

Friday 19th February Finish Problem sheet 1 and Problem sheet 2.

4 MORAL HAZARD AND INCENTIVES

4.1 INTRODUCTION

In a typical moral hazard problem there are two individuals, the principal (she) and the

agent (he).

The agent can choose an action which influences the principal’s profit.

The principal cannot observe the action directly but can observe the level of profit.

The relationship between that action and the level of profit is random.

The principal must control the agent indirectly by offering an incentive contract.

Examples

Principal Agent ActionInsurance Company Purchaser of Insurance Preventing loss

Shareholders CEO Raising profitLandlord Farm labourer Producing a good harvestRegulator Utility Cost reduction

References

• *McMillan, J. Games Strategies and Managers, Oxford University Press, Chs. 8,9.

• *Milgrom and Roberts Ch.7.

4.2 MODEL

2 INDIVIDUALS A PRINCIPAL (SHE) AND AN AGENT (HE).

e = EFFORT EXPENDED BY AGENT. NOT OBSERVABLE BY THE PRINCIPAL.

z = OUTPUT OBSERVABLE BY THE PRINCIPAL.

z = e+ x.

x = RANDOM VARIABLE, Ex = 0.

y = SIGNAL OBSERVED BY THE PRINCIPAL. Ey = 0.

w = WAGE PAID TO THE AGENT BY THE PRINCIPAL.

4.2.1 THE PRINCIPAL

The principal uses a linear incentive scheme:

w = α+ β(z + γy) = α+ β(e+ x+ γy).

P (e) denotes the principal’s gross profit, e.g. P (e) = q.z, where q denotes the price of

output.

The principal is risk neutral and maximises expected net profit:

π = P (e)−Ew = P (e)− (α+ βe).

4.2.2 THE AGENT

The agent has utility

U = Ew −C(e)−1

2r var(w)

= α+ βe− C(e)−1

2rβ2 var(x+ γy).

C(e) = cost of effort

r = parameter measuring risk aversion

• r = 0, corresponds to risk neutrality.

u = reservation utility of the agent, i.e. he will not work for the principal unless he

receives at least utility u by doing so.

4.3 EFFORT OBSERVABLE

(FIRST BEST, SYMMETRIC INFORMATION)

THE PRINCIPAL WILL OFFER THE AGENT A CONTRACT WHICH SPECIFIES THE

AMOUNT OF EFFORT TO BE SUPPLIED AND PAYS A FIXED WAGE.

THE PRINCIPAL WILL PAY THE LOWEST WAGE WHICH WILL INDUCE THE AGENT

TO WORK.

HENCE: w −C(e) = u OR w = u+C(e).

π = P (e)−w = P (e)− u−C(e).

THE 1st ORDER CONDITION FOR PROFIT MAXIMISATION IS:

P ′(e∗) = C′(e∗).

THIS EQUATION DETERMINES THE FIRST BEST LEVEL OF EFFORT.

THE FIRST BEST PROFIT LEVEL IS: π = P (e∗)− u−C(e∗).

4.4 RISK NEUTRAL AGENT

IF THE AGENT IS RISK NEUTRAL THE PRINCIPAL MAY ATTAIN THE FIRST BEST

PROFIT LEVEL EVEN IF EFFORT IS UNOBSERVABLE.

THE PRINCIPAL SHOULD HAND THE PROFITS OVER TO THE AGENT LESS A

LUMP-SUM K.

THEN Ew = P (e)−K.

THE AGENT’S EXPECTED UTILITY IS:

P (e)−K −C(e).

THE 1st ORDER CONDITION FOR CHOICE OF EFFORT IS:

P ′(e∗) = C′(e∗).

HENCE THE AGENT WILL PERFORM THE FIRST-BEST EFFORT LEVEL.

THE PRINCIPAL WILL PAY THE AGENT THE MINIMAL AMOUNT TO INDUCE HIM

TO ACCEPT THE JOB HENCE:

P (e∗)−K − C(e∗) = u.

THE PRINCIPAL RECEIVES:

K = P (e∗)− C(e∗)− u,

WHICH IS THE FIRST BEST PROFIT LEVEL.

FRANCHISE CONTRACT

• THE FRANCHISE OPERATOR PAYS THE PARENT COMPANY A FIXED FEE

TO RUN AN OUTLET. THE OPERATOR KEEPS THE PROFITS FROM THE

OUTLET.

MANAGEMENT BUY-OUTS (MBO)

• THE EQUITY OF OUTSIDE SHAREHOLDERS IS PURCHASED BY CURRENT

MANAGEMENT.

• THE PURCHASE IS FUNDED BY ISSUING DEBT.

4.5 RISK AVERSE AGENT

FRANCHISING THE BUSINESS TO THE AGENT IS NOT POSSIBLE. SINCE THE

AGENT WOULD BEAR ALL THE RISK.

THE AGENT IS RISK AVERSE AND THEREFORE WOULD NOT WORK FOR THE

PRINCIPAL WITHOUT A HIGHER EXPECTED WAGE TO COMPENSATE.

ON THE OTHER HAND IF THE AGENT WAS COMPLETELY PROTECTED FROM

RISK HE WOULD HAVE NO INCENTIVE TO PUT IN EFFORT.

THE PRINCIPAL FACES A TRADE-OFF. AS SHE RAISES INCENTIVES SHE GETS

MORE EFFORT FROM THE AGENT BUT HAS TO PAY HIGHER EXPECTED WAGES

TO COMPENSATE FOR THE RISK.

4.5.1 THE INFORMATIVENESS PRINCIPLE

ANY VARIABLEWHICH INCREASES THE ACCURACYWITHWHICH PERFORMANCE

CAN BE MEASURED SHOULD BE USED IN DETERMINING THE AGENT’S PAY.

Proposition 4.1 THE OPTIMAL VALUE OF γ IS GIVEN BY: γ = − cov(x, y)/ var(y).

Proof. THE PRINCIPAL SHOULD CHOOSE THE CONTRACT SO THAT

α+ βe− C(e)− 12rβ

2 var(x+ γy) = u.

HENCE EXPECTED PROFITS ARE GIVEN BY:

π = P (e)− α− βe

= P (e)− C(e)−1

2rβ2 var(x+ γy)− u.

IN PARTICULAR γ SHOULD BE CHOSEN TO MINIMISE var(x+ γy).

RECALL,

var(x+ γy) = var(x) + γ2 var(y) + 2γ cov(x, y).

THE VALUE OF γ WHICH MINIMISES THIS IS DETERMINED BY:

2γ var(y) + 2 cov(x, y) = 0.

HENCE γ = − cov(x, y)/ var(y).

EXAMPLES PERFORMANCE OF OTHERWORKERS DOING SIMILAR TASKS, THE

STATE OF THE NATIONAL/REGIONAL ECONOMY.

γ = − cov(x, y)/ var(y)

• If cov(x, y) > 0 (resp. < 0) then x and y tend to move in the same (resp. opposite)

directions.

• If cov(x, y) = 0 the signal y should not be used.

— If x and y are independent then basing the agent’s pay on y simply exposes him

to more risk.

• All signals y such that cov(x, y) �= 0 should be used in performance evaluation.

• The more inaccurate the signal the less weight it receives.

The Informativeness Principle ANY VARIABLE WHICH INCREASES THE ACCU-

RACY WITH WHICH PERFORMANCE CAN BE MEASURED SHOULD BE USED IN

DETERMINING THE AGENT’S PAY

THIS WEEK

1. OPTIMAL LEVEL OF INCENTIVES. (THE INCENTIVE INTENSITY PRINCIPLE.)

2. OPTIMAL MEASUREMENT OF PERFORMANCE. (THE MONITORING INTEN-

SITY PRINCIPLE.)

3. Problem sheets 1 and 2.

Recall

w = α+ β(z + γy)

γ = − cov(x, y)/ var(y)

• If cov(x, y) > 0 (resp. < 0) then x and y tend to move in the same (resp. opposite)

directions.

• If cov(x, y) = 0 the signal y should not be used.

— If x and y are independent then basing the agent’s pay on y simply exposes him

to more risk.

• All signals y such that cov(x, y) �= 0 should be used in performance evaluation.

4.5.2 APPLICATION: DEDUCTIBLES AND CO-PAYMENTS

Car Insurance TYPICALLY HAS A DEDUCTIBLE. i.e. THE CUSTOMER PAYS A

FIXED AMOUNT PER ACCIDENT.

THIS IS BECAUSE EFFORT BY THE DRIVER CAN REDUCE THE CHANCE OF AN

ACCIDENT BUT WILL NOT TYPICALLY AFFECT THE COST OF AN ACCIDENT.

Medical Insurance THE CUSTOMER TYPICALLY HAS TO PAY A FIXED FRAC-

TION OF ANY BILL.

IN THIS CASE, THE CUSTOMER HAS MUCH GREATER INFLUENCE OVER THE

SIZE OF THE LOSS.

4.5.3 THE INCENTIVE-INTENSITY PRINCIPLE

INCENTIVES ARE HIGHER

1. THE LOWER THE AGENT’S RISK AVERSION.

2. THE MORE ACCURATELY PERFORMANCE CAN BE MEASURED.

3. THE HIGHER THE MARGINAL PROFITABILITY OF EFFORT.

4. THE GREATER THE RESPONSIVENESS OF EFFORT TO INCENTIVES, (WHICH

IS MEASURED BY C′′(e).)

Proposition 4.2 OPTIMAL INCENTIVE INTENSITY IS GIVEN BY:

β = P ′(e)/[1 + rV C′′(e)],

WHERE V = var(x).

Proof. THE AGENT WILL CHOOSE THE LEVEL OF EFFORT e TO MAXIMISE HIS

UTILITY:

U = α+ βe−C(e)−1

2rβ2 var(x).

THE FIRST ORDER CONDITION FOR THIS IS: β −C′(e) = 0 OR

β = C′(e). (5)

THE PRINCIPAL PAYS THE AGENT JUST ENOUGH TO ACHIEVE HIS RESERVATION

UTILITY:

α+ βe− C(e)− 12rβ

2V = u, =⇒ α+ βe = u+ C(e) + 12rβ

2V.

THE PRINCIPAL’S NET PROFITS ARE GIVEN BY:

π = P (e)− α− βe = P (e)− u− C(e)−1

2rβ2V.

SINCE β = C′(e) BY (5), WE FIND:

π = P (e)− u− C(e)−1

2rV C′(e)2.

THE 1st ORDER CONDITION FOR OPTIMAL CHOICE OF e IS:

dπ

de= P ′(e)−C′(e)−

1

2rV 2C′(e)C′′(e) = 0.

HENCE C′(e)[1 + rV C′′(e)] = P ′(e).

SOLVING

β = C′(e) = P ′(e)/[1 + rV C′′ (e)].

SUMMARY

THE PRINCIPAL’S PROFIT DEPENDED ON THE LEVEL OF EFFORT EXPENDEDBY THE AGENT. THE EFFORT WAS NOT OBSERVABLE..

THE PRINCIPAL WANTS TO GIVE THE AGENT INCENTIVE TO EXPEND EFFORTBY LINKING HIS PAY TO OUTPUT (OR PROFIT).

IF EFFORT IS UNOBSERVABLE AND THE AGENT IS RISK AVERSE THE PRINCIPALFACES A TRADE OFF.

• AS INCENTIVES ARE RAISED THE AGENT WILL EXERT MORE EFFORT.

• HOWEVER THE AGENT WILL BE EXPOSED TO MORE RISK AND WILL NEEDHIGHER WAGES TO COMPENSATE.

TAKING ACCOUNT OF BOTH THESE EFFECTS THE PROFIT MAXIMISING LEVELOF INCENTIVES IS GIVEN BY:

β =P ′(e)

1 + rV C′′(e).

4.5.4 THE MONITORING INTENSITY PRINCIPLE

NOW ASSUME THE PRINCIPAL MAY INCREASE THE ACCURACY WITH WHICH

THE AGENT’S PERFORMANCE IS MEASURED BY SPENDING MORE ON MONI-

TORING.

M(V ) = COST OF REDUCING THE VARIANCE TO V .

M ′(V ) < 0, IT COSTS MORE TO ACHIEVE A LOWER VARIANCE.

M ′(V ) IS INCREASING. HENCE THE MARGINAL COST OF VARIANCE REDUCTION

IS GREATER THE LOWER THE CURRENT VARIANCE.

THE PRINCIPAL’S EXPECTED PROFITS ARE THEN GIVEN BY:

π = P (e)−C(e)−1

2rV β2 −M(V ).

THE 1st ORDER CONDITION FOR OPTIMAL CHOICE OF V IS:

M ′(V ) = −1

2rβ2.

SINCE M ′(V ) IS INCREASING THIS IMPLIES THAT THE HIGHER β THE LOWER

WILL BE THE VARIANCE OF THE PERFORMANCE MEASURE, V .

Proposition 4.3 The Monitoring Intensity Principle IF AN AGENT HAS HIGHER

INCENTIVES THEN HIS/HER PERFORMANCE WILL BE MONITORED MORE CARE-

FULLY.

...............................................................................................

................................................................................................................................

...................

−M ′ (V )

12rβ

2

12rβ

2

V V variance

cost

Monitoring allows the principal to pay the agent in a less risky way. Hence either:

• the principal can obtain a given level of effort from the agent while imposing less risk

on him. This reduces the risk premium and hence the principal’s wage bill;

• monitoring lowers the cost of increasing incentives, which allows the principal to put

the agent on a more high powered incentive scheme.

In Japan firms are typically monitored by banks. Management pay is lower in Japan then

the USA.

After an MBO management is much more closely monitored and given much stronger

incentives which improves performance.

4.6 CONCLUSION

In the absence of market distrsions a risk averese person will be fully insured, (see FMD

I).

With moral hazard a risk averse agent will bear some risk.

5 INCENTIVE EFFECTS OF DEBT AND EQUITY

5.1 INTRODUCTION

5.1.1 BACKGROUND

Recall, capital Markets are different. In particular quantity constraints and credit rationing

are common.

Moral Hazard explanations:

• high payments to outside suppliers may reduce the incentives for effort.

• debt may give a perverse incentive for the firm to take on too much risk.

• preexisting debt may distort the incentive for new investment.

References

• Tirole Ch. 3.

• Myers, S.C., ‘Financing of Corporations’ in Handbook of the Economics of Finance,

Elsevier.

• *Milgrom and Roberts, Ch.15.

5.2 MORAL HAZARD AND BANKRUPTCY

Recall from section 1.1

Shareholders are protected by limited liability.

They do not care about earnings in the event that the firm is bankrupt.

Returns to equity are a convex function of earnings.

D Firm’s Earnings

EquityEarnings

����������������������

45o

Bondholders only care about earnings in the event of bankruptcy and the probability of

bankruptcy.

Returns to debt are concave in earnings.

45o����������������������

LendersEarnings

.......................................................Firm’s EarningsD

IF A FIRM HAS ISSUED DEBT THERE IS THE POSSIBILITY OF MORAL HAZARD.

BY MAKING RISKY INVESTMENTS THE FIRM CAN TRANSFER WEALTH FROM

STATES IN WHICH IT IS BANKRUPT TO STATES IN WHICH IT IS NOT BANKRUPT.

THIS HAS THE EFFECT OF TRANSFERRING WEALTH FROM BONDHOLDERS TO

SHAREHOLDERS.

SUPPOSE THE FIRM CAN CHOOSE FROM TWO PROJECTS, PROJECT A AND

PROJECT B. THESE PROJECTS HAVE THE SAME EXPECTED RETURNS.

• HOWEVER PROJECT B HAS HIGHER VARIANCE.

• A 100% EQUITY FINANCED FIRM OWNED BY DIVERSIFIED SHAREHOLDERS

WILL BE INDIFFERENT BETWEEN THE TWO PROJECTS.

• A LEVERED FIRM WILL PREFER PROJECT B i.e. THE PROJECT WITH THE

HIGHER VARIANCE.

• THIS REMAINS TRUE IF THE RISKY PROJECT B HAS SLIGHTLY LOWER RE-

TURNS.

Example 5.1 THERE ARE TWO POSSIBLE STATES OF NATURE s1, s2 EACH WITH

PROBABILITY 12.

A FIRM HAS DEBT OF $2m.

IT HAS A CHOICE OF TWO PROJECTS

• PROJECT A PAYS $3m FOR CERTAIN.

• PROJECT B PAYS $6m IN s1, £0 IN s2.

s1 s2 Expected ReturnA 1 1 1B 4 0 2

RETURNS TO EQUITY

s1 s2 Expected ReturnA 2 2 2B 2 0 1

RETURNS TO DEBT

5.2.1 GAMBLES FOR RESURRECTION

The moral hazard problem is worse at higher levels of debt.

• The higher the debt level the greater the number of states in which the firm is

bankrupt.

• Shareholders do not care about returns in these states.

• Thus they have a greater incentive to make risky investments.

— If successful the firm will be saved

— Debtholders bear the losses

• This is similar to problems arising from excessive bonuses for traders.

— An extreme example is Nick Leeson who took increasing large risks to cover

previous losses at Barings Bank.

— The savings and loans crisis in the US was made worse by banks taking on large

risks in attempts to avoid bankruptcy.

For this reason, LBO’s, which involve high levels of debt are monitored closely.

5.2.2 OPTION PRICING

Suppose that a firm has issued debt with face value D.

Effectively the shareholders have an option to purchase the firm at price D.

The value of an option increases with the variance of the underlying asset.

Thus shareholders have an incentive to make risky investments, which will increase the

value of the levered firm.

5.2.3 INTEREST RATES

THEMORAL HAZARD PROBLEMBECOMESWORSE AT HIGHER INTEREST RATES.

SUPPOSE THERE ARE TWO POSSIBLE PROJECTS a AND b.

EACH IS EITHER A SUCCESS OR A FAILURE. FAILURES YIELD ZERO RETURNS.

Ra (RESP. Rb) DENOTES THE RETURNS ON PROJECT a (RESP. b) IF SUCCESS-

FUL.

pa (RESP. pb) DENOTES THE PROBABILITY OF SUCCESS ON PROJECT a, (RESP.

b).

ASSUME

• pa < pb, Ra > Rb. HENCE a IS THE MORE RISKY PROJECT.

• pbRb > paRa i.e. THE RISKY PROJECT HAS LOWER EXPECTED RETURN.

πa = (Ra − (1 + r)B)pa PROFIT ON PROJECT a,

πb = (Rb − (1 + r)B)pb PROFIT ON PROJECT b.

Proposition 5.1 IF AT INTEREST RATE r0, A FIRM IS INDIFFERENT BETWEEN

TWO PROJECTS, AN INCREASE IN THE INTEREST RATE, RESULTS IN THE FIRM

PREFERRING THE MORE RISKY PROJECT.

Proof. SINCE THE FIRM IS INDIFFERENT BETWEEN THE TWO PROJECTS AT

INTEREST RATE ro :

(Ra − (1 + ro)B)pa = (Rb − (1 + ro)B)pb.

DEFINE,

f(r) = πa − πb = Rapa −Rbpb − (1 + r)B(pa − pb),

dfdr = −B(pa − pb) > 0.

THUS THE FIRM PREFERS THE RISKY PROJECT, a, IF AND ONLY IF r > ro.

.............................ro

Profits

r

πb

πa

�����������������������������������

������������������������������������������������������

Figure 11: Moral hazard is worse at higher interest rates

�������������������������������������������������������

.............................ro

Profits

r

πb

πa

�

�

��

�

..............

..............

..............

....

..............................................

Figure 12: Relation between profit and interest rates

5.2.4 SUMMARY

Moral Hazard can result in leveraged firms choosing unduly risky projects.

• The moral hazard problem is more severe at higher debts levels.

• The moral hazard problem is worse at higher interest rates.

Bondholders will anticipate the moral hazard problem and demand a high return to com-

pensate.

• Ultimately the cost of moral hazard falls on the firm.

Implication: We should see higher debt levels in industries where it is harder to make risky

investments e.g. regulated industries.

5.2.5 SOLUTIONS

Covenants to debt

• investments should be diversified and risks should be hedged where possible.

Convertible debt.

• This blocks any scheme which has the effect of transferring wealth from debtholdersto equity holders.

• In particular it prevents shareholders from exploiting limited liability by taking onexcessive risk.

• Strip financing

— If debt and equity are sold in equal proportions to all investors then there is noincentive to adopt policies which transfer resources from debt to equity.

5.3 OUTSIDE FINANCING AND INCENTIVES

Tirole Ch. 3.

5.3.1 INTRODUCTION

Credit rationing may be due to moral hazard.

A borrower will bear the full cost of working hard to ensure the investment succeeds.

However (s)he must share the benefits of success with the lender.

An increase in the interest rate reduces the borrower’s share of the returns.

Hence (s)he has a lower incentive to supply effort.

There are two individuals an entrepreneur and a lender.

The Entrepreneur An entrepreneur has initial assets A.

He/she needs I > A to invest in a project.

The borrower has limited liability.

Lenders Lenders make zero expected profit (due to competition).

The entrepreneur and the lenders are risk neutral.

The Project The project is either a success in which case it yields income R or it fails

yielding no income.

• The probability of success depends on whether the entrepreneur exerts effort.

• Effort is discrete.

• Effort may be time but can also measure the extent to which the manager works in

the lender’s interests rather than his/her own.

— not over-investing in pet projects

— not avoiding difficult decisions such as sackings or closing poorly performing di-

visions

— not consuming excessive perks, executive jets, luxury apartments etc.

There is a moral hazard problem.

• Effort cannot be observed.

• Success or failure can be observed.

No effort gives success with probability pL and private benefit B for the entrepreneur.

Effort yields success with probability pH > pL and no private benefit.

∆p = pH − pL.

The Loan Contract Rℓ = lender’s share of the returns.

Rb = borrower’s share of the returns.

Both receive 0 returns in the event of failure.

Assumption 5.1 The project is only viable if the entrepreneur supplies effort i.e.,

pHR− I > 0 and

pLR+B − I < 0. (6)

Equation (6) implies any loan acceptable to the lender must give the entrepreneur an

incentive to supply effort.

Equation (6) can be written as [pLRℓ − (I −A)] + [pLRb +B −A] < 0.

With no effort, either the lender makes a loss or the borrower would be better off using

his/her money for consumption.

5.3.2 THE LENDER’S CREDIT ANALYSIS

For the borrower to have an incentive to supply effort, the following inequality must hold:

pHRb � pLRb +B or

∆pRb � B. (7)

This is known as the incentive compatibility constraint.

The highest income, which can be pledged to lenders while maintaining incentives is:

R−B

∆p.

The expected pledgable income is

P = pH

(

R−B

∆p

)

.

For lenders to break even we need:

P = pH

(

R−B

∆p

)

� I −A.

This is referred to as the individual rationality constraint.

A necessary condition for a loan to be possible is:

A � A = I +BpH∆p

− pHR. (8)

Assumption 5.2 An entrepreneur with no initial wealth will not obtain a loan, i.e.

A > 0⇔ pHR− I < BpH∆p

. (9)

Equation (9) says that the NPV is less than BpH∆p which is the rent which must be left

to the borrower to give him/her an incentive to supply effort.

BpH∆p will be referred to as the agency rent.

∆ppH= pH−pL

pHmeasures the extent to which success is a signal of effort.

There is credit rationing since if A < A, the entrepreneur will not get a loan despite the

fact that the project has positive NPV.

Credit rationing is more likely if:

• The entrepreneur has insufficient assets A.

• The agency cost i.e. BpH∆p is high.

Since there is credit rationing, the entrepreneur’s utility is not continuous in wealth but

instead jumps up at A = A.

More generally, if there is asymmetric information, generally one unit of wealth may be

worth more than 1 to the borrower.

5.3.3 REPUTATION

Suppose that the private benefit from no effort were b < B.

This reduces the asset threshold to A (b) = pHb∆p − (pHR− I) < A (B) .

From equation (8)

A (B)− A (b) =pH∆p

(B − b) .

A more reliable borrower is more likely to obtain an loan.

Now suppose that the true value of the private benefit is uncertain.

It may be B with probability ν and b with probability 1− ν.

Suppose an entrepreneur seeks repeated loans from the same lender.

Over time the lender may be able to get an estimate of the private benefit.

Thus a borrower with a good reputation is more likely to get a loan.

TODAY

• INCENTIVE EFFECTS OF CORPORATE FINANCE

— Efficient use of Information

— Diversification

• PROBLEM SHEET 3

Correction

The reduction in A due to a good reputation i.e. lower private benefit

A (B)− A (b) =pH∆p

(B − b)− (pHR− I) .

should be

A (B)− A (b) =pH∆p

(B − b) .

5.3.4 EFFICIENT USE OF INFORMATION

Recall the informativeness principle (see section 4.5.1) says that all relevant information

should be used.

The model can be reinterpreted as having 3 states of nature.

1. Favourable state, probability pL. The market is sufficiently favourable that the project

will succeed even without effort.

2. Unfavourable state, probability (1− pH). The market is so bad that the project will

fail even if the entrepreneur supplies effort.

3. Intermediate state probability ∆p = pH − pL. The project will succeed if and only

if the entrepreneur supplies effort.

Now assume that the lender will learn ex-post whether the state was favourable or not.

Consider the following incentive scheme

• the entrepreneur receives 0 if the state is favourable;

• otherwise (s)he receives Rb in the case of success and 0 in the case of failure.

The incentive constraint is still:

∆pRb � B. (10)

Pledgable income is maximised by setting Rb =B∆p.

Since the entrepreneur is no longer paid just for being lucky, the pledgable income has

increased to:

pHR−B.

Recall previously we found that pledgable income was

P = pHR− pHB

∆p.

Efficient use of information can increase pledgable income.

5.4 DIVERSIFICATION

If a firm invests in two or more independent projects this can increase its ability to borrow.

Income from one project can be pledged against the loan for the other.

This increases the pledgable income and hence reduces the moral hazard problem.

In the limit the law of large numbers would tell the borrower precisely how much effort

the borrower was exerting.

5.4.1 TWO PROJECTS

A risk-neutral entrepreneur has two projects. His/her initial wealth is 2A.

Each project requires an initial investment of $I > A.

Each yields R if successful and $0 otherwise.

The probability of success depends on whether the entrepreneur supplies effort.

No effort gives success with probability pL and private benefit B.

Effort yields success with probability pH > pL and no private benefit.

The returns of the two projects are independent.

Total returns are either 2R,R or 0.

Let R2, R1and Ro denote the borrower’s reward when the number of successful projects

is 2, 1, 0 respectively.

The expected reward of the borrower is:

p2HR2 + 2pH (1− pH)R1 + (1− pH)2Ro.

To provide the entrepreneur with maximal incentives (s)he should only be rewarded when

both projects are successful,

i.e. R1 = Ro = 0, R2 > 0.

Thus (s)he receives R2 if both projects are successful and 0 otherwise.

Note R1 = 0 can be interpreted as cross-pledging. Returns from the successful project

are used to repay the loan on the other project.

The condition for effort to be supplied on both projects is:

p2HR2 � p2LR2 + 2B

or

(pH + pL)R2 �2B

∆p. (11)

Using equation (11), the expected payment to the borrower is:

p2HR2 =2p2HB

(pH+pL)∆p= 2 (1− d2)

pHB∆p , where d2 =

pLpH+pL

, 0 � d2 �12.

Two projects can be funded if:

2pHR− 2 (1− d2)pHB

∆p� 2 (I −A) .

The condition for a single project to be financed was:

pHR−pHB

∆p� I −A.

Diversification facilitates financing.

5.4.2 MANY PROJECTS

With n projects the condition for funding is,

pHR− (1− dn)pHB

∆p� I −A,

where

dn =pL

(pn−1H + pn−1L

)

pnH + pnL.

Since dn is increasing in n, funding becomes easier the more independent projects the

firm has.

As n→∞, dn →pLpH

and the condition for funding converges to

pHR−B � I −A.

With a very large number of projects the lender will detect shirking with high probability

due to the law of large numbers.

Diversification increases borrowing capacity.

There are also costs of adding new projects, which have to be taken into account.

The optimal size of the firm is determined by the trade off between the benefits of

diversification and the costs of a larger organisation.

Limited Attention As more projects are added the entrepreneur

Hiring subordinates to handle new projects creates new agency problems

Non-Core Business Diversification may not be desirable if the new projects are in areas

in which the entrepreneur is less competent.

5.4.3 PRODUCT MARKETS (not 2010)

Brander and Lewis, (1986), Oligopoly and Financial Structure, American Economic Re-view.

A firm’s choice between debt and equity financing can affect the product market equilib-rium.

Consider two firms in a Cournot oligopoly firm A and firm B.

Suppose that demand is uncertain. Assume that marginal profit is higher in states wheretotal profit is higher.

A leveraged firm will only be interested in profit in the more favourable states of nature.

Then the leveraged firm will produce higher output. This will induce its rival to reduceoutput.

Hence the leveraged firm may make higher profit.

Thus the Modigliani-Miller Theorem may not hold if there is imperfect competition in theproduct market.

PLAN FOR REST OF COURSE

Today Behavioural FinanceTomorrow Problem sheets 3 and 418th & 19th March no lecture25th & 26th March. Takeovers and AuctionsApril 1st RevisionApril 2nd Bank HolidayMay 3rd Revision

5.5 INCENTIVE EFFECTS OF DEBT: UNDER INVESTMENT

Reference MYERS, S. “DETERMINANTS OF CORPORATE BORROWING” Journal

of Financial Economics, 1977.

Suppose a firm has issued risky debt.

Since debt is senior to equity, bondholders will have first call on any earnings the firm

makes.

This reduces shareholders incentives to invest.

This can be a barrier to new investment and hence reduces the value of the firm.

A similar problem arises with sovereign debt.

Assumption 5.3 THERE IS ONE FIRM WHICH HAS NO FIXED ASSETS. ITS VALUE

DERIVES FROM A FUTURE INVESTMENT OPPORTUNITY.

MODEL

S = FINITE SET OF n STATES OF NATURE.

ALL STATES HAVE EQUAL PROBABILITY 1n.

I = INVESTMENT REQUIRED AT t = 1 TO INITIATE THE PROJECT.

V (s) = value of the firm if investment is made in state s.

5.5.1 THE INVESTMENT DECISION

• THE DECISION IS MADE AFTER THE STATE OF NATURE, s IS KNOWN.

• THE INVESTMENT IS MADE IF IT IS PROFITABLE FOR THE SHAREHOLDERS.

• IF NO INVESTMENT IS MADE THE VALUE OF THE FIRM IS ZERO.

THE EFFICIENT SOLUTION

• THE FIRM SHOULD INVEST IF AND ONLY IF V (s) > I.

5.5.2 CASE 1: THE FIRM IS ALL EQUITY FINANCED

INVESTMENT OCCURS IF AND ONLY IF

V (s) > I.

ASSUME V (s1) < V (s2) < ... < V (sn).

LET sa BE THE LOWEST STATE IN WHICH IT IS WORTH INVESTING

V (sa−1) < I < V (sa).

THE EXPECTED VALUE OF THE FIRM IS

1

n

n∑

i=a

V (si)− I

.

.........................................................................................................

s

I

V (s)$

.........................................sa

Figure 13: The firm with no debt

.........................................................................................................

s

I

V (s)$

.........................................sa

Cost of Investment

Figure 14: The firm with no debt

.........................................................................................................

s

I

V (s)$

.........................................sa

Cost of Investment

Profit

Figure 15: The firm with no debt

5.5.3 CASE 2: THE FIRM IS PARTLY DEBT FINANCED

SUPPOSE THE FIRM HAS ISSUED RISKY DEBT:

• DEBT REQUIRES PAYMENT P ;

• PAYMENT IS DUE AFTER RETURNS ON THE INVESTMENT ARE REALISED;

• DEBT IS SENIOR TO EQUITY.

SHAREHOLDERS WILL INVEST IF AND ONLY IF

V (s) > I + P.

SHAREHOLDERS WILL INVEST IF AND ONLY IF

V (s) > I + P.

LET sb BE THE LOWEST STATE IN WHICH IT IS WORTH INVESTING,

V (sb−1) < I + P < V (sb).

THE EXPECTED VALUE OF THE FIRM IS

1

n

n∑

i=b

V (si)− I

.

THIS IS A MORAL HAZARD PROBLEM. BONDHOLDERS WOULD PREFER THE

FIRM TO INVEST IF

I < V (s) < I + P.

.........................................................................................................

s

I

V (s)$

.......................................................................................................I + P ...........................................................

���

����

�����

����

���

��

��

.........................................sa sb

COMMENTS

• The Modigliani-Miller theorem does not hold. A levered firm is worth less than a

100% equity firm.

• In the extreme case where V (s) < I + P in all states the firm is worthless.

• If bondholders anticipate the moral hazard problem when the bonds are originally

sold they will demand higher returns. Thus the cost of moral hazard falls on equity

holders.

The diagram on the next slide shows firm and debt values as a function of payment

promised to creditors.

$

V

P

V = total value of the firm;

$

V

P

VD

VD = value of debt.

$

V

P

VD

.................................................................................................V ∗

Thus the firm can never borrow more than V ∗.

This is a possible explanation of credit rationing.

5.5.4 APPLICATIONS AND EXTENSIONS

THE PAYOFF OFMOST ASSETS DEPENDS ON FUTURE DISCRETIONARY INVEST-

MENTS BY THE FIRM,

e.g. MAINTENANCE, ADVERTISING, RAW MATERIALS OR LABOUR.

HENCE THE UNDER-INVESTMENT PROBLEM MAY APPLY TO A LARGE CLASS

OF ASSETS.

DEBT CAPACITY

BOOK VALUES RATHER THAN MARKET VALUES ARE USED TO DETERMINE A

FIRM’S DEBT CAPACITY.

BOOK VALUES REFER TO ASSETS ALREADY IN PLACE.

5.5.5 RENEGOTIATION

In states where, I + P > V (s) > I, the firm is bankrupt.

However it will be less bankrupt if the investment is made.

There is scope to renegotiate the debt.

Bondholders can offer to reduce the repayments if shareholders make the investment.

5.5.6 SECONDARY MARKETS FOR ASSETS

SUPPOSE THAT THE FIRM CAN SELL ITS CAPITAL FOR $Q.

IT IS SOCIALLY DESIRABLE FOR THE FIRM TO SELL ITS CAPITAL IF

Q > V (s) .

THE SHAREHOLDERS WISH TO SELL IF:

P +Q > V (s) .

THUS THERE IS A DANGER THAT THE FIRM MIGHT BE LIQUIDATED WHEN IT

IS NOT EFFICIENT TO DO SO.

FOR THIS REASON DEBT HAS RESTRICTIVE COVENANTS PROHIBITING THE

SALE OF THE FIRM’S ASSETS.

5.6 CONCLUSION

The Modigliani-Miller results imply that firms should be indifferent about their debt-equity

ratios.

Tax considerations imply that the optimal financial structure is 100% debt.

Asymmetric Information implies that the optimal debt-equity ratio is less than 100% debt.

...........................................................D/E0 1

Total Costof capital

Cost ofequity

Cost ofdebt

Figure 20:

NEXT WEEK

• Auctions and Takeovers

• Problem Sheet 3.

No Lectures 18th and 19th March

6 AUCTIONS AND TAKEOVERS

6.1 INTRODUCTION

6.1.1 WHY ARE AUCTIONS IMPORTANT?

1. AUCTIONS PLAY A LARGE PART IN THE ECONOMY.

2. MANY ITEMS ARE SOLD BY AUCTION

(a) ART

(b) CATTLE

(c) HOUSES

3. MANY ITEMS ARE BOUGHT BY AUCTION.

(a) THE GOVERNMENT MAKES MAJOR PURCHASES BY A

TENDERING PROCESS.

(b) THE PRIVATE SECTOR ALSO USES AUCTIONS FOR PURCHASES.

4. TAKEOVERS.

5. SPECTRUM AUCTIONS.

6. AUCTIONS PROVIDE A THEORY OF HOW PRICES ARE DETERMINED.

• J. McMillan, Games, Strategies, Managers, OUP., 1992. Chapter 11, and p. 208-209.

• McAfee, R.P. and J. McMillan, (1987) "Auctions and Bidding" Journal of Economic

Literature, 25, 699-738.

• Milgrom, (1989), ‘Auctions and Bidding: A Primer’, Journal of Economic Perspec-

tives, 3, 3-22.

6.1.2 TYPES OF AUCTIONS

First-Price Sealed-Bid Auction A SINGLE OBJECT IS FOR SALE.

BIDDERS SUBMIT THEIR BIDS IN SEALED ENVELOPES TO THE AUCTIONEER.

THE OBJECT IS SOLD TO THE HIGHEST BIDDER AT A PRICE EQUAL TO HIS/HER

BID.

English (Open) Auction THE BIDDERS ARE ALL IN THE SAME ROOM.

BIDDERS CALL OUT BIDS PUBLICLY.

THE OBJECT IS SOLD TO THE HIGHEST BIDDER AT A PRICE EQUAL TO HIS/HER

BID.

6.1.3 PRIVATE VALUE AUCTIONS

THE OBJECT FOR SALE HAS A DIFFERENT VALUE TO EACH BIDDER e.g. ART

AUCTION, HOUSE AUCTION.

6.1.4 COMMON VALUE AUCTION

THE OBJECT FOR SALE HAS THE SAME VALUE $X TO ALL BIDDERS. AT THE

TIME OF THE AUCTION BIDDERS DO NOT KNOW X BUT ONLY HAVE AN ESTI-

MATE OF X.

e.g. AUCTION FOR MINERAL RIGHTS.

6.2 COMMON VALUE AUCTIONS

6.2.1 MINERAL RIGHTS GAME

• There are 21 bidders for an object (e.g. mineral rights).

• The object will have value X to the successful bidder.

• At the time of the auction none of the bidders know the true value X. They do have

estimates of the true value.

• Specifically there are 21 estimates which take values,X−10,X−9, ...,X−1,X,X+

1, ...,X + 10. These estimates are randomly distributed among the bidders.

• The object will be sold to the highest bidder at a price equal to the bid. i.e. this is

a first price sealed bid auction.

THIS EXAMPLE IS DRAWN FROM McMillan p. 139.

LET Ei = ESTIMATE OF BIDDER i.

Bi = BID OF BIDDER i

IF YOU LOSE THE AUCTION YOU RECEIVE NOTHING. HENCE YOU ARE ONLY

INTERESTED IN WHAT HAPPENS IF YOU WIN THE AUCTION.

ASSUME THAT BIDS ARE INCREASING IN THE ESTIMATE.

IF i WINS THE AUCTION Ei = X + 10.

HENCE X = Ei − 10.

THIS ILLUSTRATES THE WINNER’S CURSE. WINNING IS BAD NEWS.

THE EQUILIBRIUM BID IS Ei−11, WHICH CORRECTS FOR THE WINNER’S CURSE

AND ALLOWS A SMALL MARGIN FOR PROFIT.

NOTE THIS CONFIRMS THE CONJECTURE THAT THE BID IS AN INCREASING

FUNCTION OF THE ESTIMATE.

AT WHAT PRICE WILL THE OBJECT BE SOLD?

THE OBJECT WILL BE SOLD AT PRICE X − 1.

THIS ILLUSTRATES THE WAY THE MARKET CAN AGGREGATE INFORMATION.

THE SELLER GETS THE BULK OF THE SURPLUS.

6.3 THE WINNER’S CURSE

A common-value auction will be won by the bidder with the highest estimate.

• Thus if you win the auction you know that all other bidders have a lower estimate.

• The highest estimate is the least accurate and it overvalues the object by the greatest

amount.

• If the winning bidder has not corrected for this he/she will pay more for the object

than it is worth.

The winner’s curse is increased when there are more bidders.

• i.e. having the highest estimate of 50 bidders is worse news than having the highest

estimate of 4 bidders.

Reference Capen, Clapp and Campbell, (1971), “Competitive Bidding in High Risk

Situations”, Journal of Petroleum Technology.

The following statement is from a painting contractor:

I do most of my work for a few builders that I’ve known for years. My estimates

of what it will cost to do a job for one of them come out about right. Sometimes

a little high and sometimes low, but about right overall. Occasionally when

business is slow, I bid on a big job for another builder, but those jobs are different.

They always run more than I expect.

6.3.1 BUYERS’ STRATEGIES FOR COMMON VALUE AUCTIONS

• Presume that your own estimate is the highest.

• On this assumption calculate your valuation of the object.

• Assume other bidders behave similarly.

• Make a bid equal to the expected value of the second highest valuation.

6.3.2 SELLERS’ STRATEGIES FOR COMMON VALUE AUCTIONS

THE SELLER SHOULD TRY TO REDUCE THE WINNER’S CURSE AND HENCE EN-

COURAGE HIGHER BIDS.

1. HOLD AN OPEN (ENGLISH) AUCTION

IN AN OPEN AUCTION (AS OPPOSED TO A SEALED BID AUCTION) YOU CAN

SEE RIVALS’ BIDS. THIS REVEALS INFORMATION ABOUT OTHER BIDDERS’

ESTIMATES AND TENDS TO REDUCE THE WINNER’S CURSE.

2. RELEASE AN INDEPENDENT VALUATION.

ALSO ACTS TO REDUCE THE WINNER’S CURSE

Remark 6.1 CHRISTIES AND SOTHERBY’S RELEASE EXPERTS ESTIMATES OF

THE AUCTION PRICE.

6.3.3 PUBLIC PROJECTS

PUBLIC PROJECTS FREQUENTLY COME IN OVER BUDGET.

• ESTIMATES ARE OBTAINED

• THOSE PROJECTS WITH THE LOWEST ESTIMATES ARE CHOSEN

• THESE PROJECTS HAVE ESTIMATES WHICH ARE BIASED DOWNWARDS.

• PROJECTS CHOSEN ARE TYPICALLY OVER BUDGET

6.3.4 TAKEOVERS

Roll, R. (1986) “The Hubris Hypothesis of Corporate Takeovers”, Journal of Business,

59, 197-216.

Recall:

• In a takeover, shareholders in the target make gains of 30-50%.

• In contrast the raider makes losses or barely breaks even.

Roll argues that the large premia paid by raiders are due to the winner’s curse.

THE HUBRIS HYPOTHESIS

1. The raider appraises the value of the target.

2. If the raider’s valuation of the target exceeds the current market value the raider

makes a bid.

3. Those valuations which are greater than the market value on average overestimate

the value of the firm.

• The winner’s curse.

4. The raider fails to correct for this. (Hubris)

5. The raider pays too much for the target.

TODAY

• AUCTIONS AND TAKEOVERS (CONCLUSION),

Common Value Auctions

RECALL THE KEY IDEA IN COMMON VALUE AUCTIONS WAS THE WINNER’S

CURSE.

Examination, Saturday 15th May, 9:30-11:30.

Common Value Auction

64

69

74

79

84

89

94

74 78 82 86 90 94

Value

Bid

Figure 21:

6.3.5 RADIO SPECTRUM AUCTIONS

• McAfee, R.P. and McMillan, J. “Analyzing the Airwaves Auction”, Journal of Eco-

nomic Perspectives 1996, 10, 159-175.

• Klemperer, P. 2004 Auctions: Theory and Practice, Princeton University Press. $35.

— http://www.paulklemperer.org/index.htm

New Zealand 1990, Australia 1993, USA 1994,

UK 2000, Europe 2000-2001.

European 3G Spectrum Auctions

2000 2001Austria €100 Belgium €45Germany €615 Denmark €95Italy €240 Greece €45Netherlands €170Switzerland €20UK €650

All figures euros per capita

• 2000 was the peak of the dotcom boom.

• A major reason for the different outcomes is the amount of competition in the auction.

6.4 AUCTIONS WITH ALMOST COMMON VALUES

IN MOST AUCTIONS BIDDERS ARE NOT IDENTICAL.

e.g. IN A TAKEOVER BATTLE, ONE BIDDER MAY HAVE A LARGER STAKE IN THE

TARGET THAN THE OTHER.

SMALL DIFFERENCES CAN HAVE A LARGE EFFECT.

1. • Klemperer, P., (1998), “Auctions with Almost Common Values: The ‘Wallet

Game’ and its Applications” European Economic Review, 42, 757-69.

www.nuff.ox.ac.uk/economics/people

/klemperer.htm

6.4.1 THE WALLET GAME

• AN OBJECT IS FOR SALE IN AN ENGLISH AUCTION.

• THERE ARE TWO BIDDERS i = 1, 2.

• THE VALUE OF THE OBJECT IS V = X1 +X2.

• X1 AND X2 ARE RANDOM INTEGERS BETWEEN 0 AND X.

• BIDDER i OBSERVES Xi.

Proposition 6.1 In the symmetric equilibrium of the wallet game bidder i continues

bidding until the price reaches 2Xi.

Proof. CONSIDER PLAYER 1.

ASSUME THAT PLAYER 2 CONTINUES BIDDING UNTIL THE CURRENT PRICE p,

IS EQUAL TO 2X2.

IF THE CURRENT PRICE IS p BIDDER 1 KNOWS X2 �p2.

HENCE IF HE WINS AT PRICE p HIS RETURNS ARE X1 +p2. THIS IS GREATER

THAN p PROVIDED p � 2X1.

DOES NOT DEPEND ON THE DISTRIBUTION OF X1 AND X2.

PLAYERS TAKE ACCOUNT OF THE WINNER’S CURSE.

ASSUME THAT X1,X2 ARE UNIFORMLY DISTRIBUTED ON[0, X

].

IF THE PRICE IS 2X1, THEN X2 �p2 = X1. HENCE THE (UNCONDITIONAL)

EXPECTED VALUE OF X2 IS 12

(X +X1

)> X1.

THE UNCONDITIONAL EXPECTED VALUE OF THE OBJECT IS

V = X1 +12

(X +X1

)> 2X1.

Example 6.1 X1 = 30.

IF 1 WINS AT PRICE 61 V = 30 + 612 = 60

12

IF 1 WINS AT PRICE 59 V = 30 + 592 = 59

12,

WHERE V DENOTES THE EXPECTED VALUE OF THE OBJECT.

THE WALLET GAME ALSO HAS ASYMMETRIC EQUILIBRIA:

b1 (X1) = 4X1, b2 (X2) =43X2,

e.g. IF X2 = 30, 2 BIDS UP TO 40.

IF 2 WINS AT 60, X1 = 15⇒ V = 45.

• IF PLAYER 1 BIDS MORE AGGRESSIVELY THIS INCREASES THE WINNER’S

CURSE FOR PLAYER 2.

• THIS CAUSES PLAYER 2 TO BID LESS AGGRESSIVELY

• THIS DECREASES THE WINNERS CURSE FOR PLAYER 1 HENCE PLAYER 1

CAN BID STILL MORE AGGRESSIVELY.

...etc.

6.4.2 THE ASYMMETRIC WALLET GAME

• AN OBJECT IS FOR SALE IN AN ENGLISH AUCTION.

• THERE ARE TWO BIDDERS i = 1, 2.

• THE VALUE OF THE OBJECT TO BIDDER 1 IS, X1 +X2 + 1.

• THE VALUE OF THE OBJECT TO BIDDER 2 IS, X1 +X2.

• X1 AND X2 ARE RANDOM INTEGERS BETWEEN 0 AND X.

• BIDDER i OBSERVES Xi.

Proposition 6.2 IN EQUILIBRIUM OF THE ASYMMETRIC WALLET GAME BIDDER

1 ALWAYS WINS THE AUCTION AT PRICE p = X2.

Proof. In equilibrium bidder 2 quits the auction when the price reaches X2. Bidder 1

never quits.

Bidder 2 should never bid more than X +X2.

If X1 � X − 1,

X1 +X2 + 1 � X − 1 +X2 + 1 = X +X2.

Hence the value to 1 is always greater than the price.

If X1 � X − 1 player 1 should never quit bidding.

Thus if 2 wins the auction (s)he knows X1 � X − 1.

So 2 should never bid more than X − 1 +X2.

1 knows the price will always be less than X +X2 − 1.

If X1 = X − 2 the value to 1 is

X1 +X2 + 1 = X − 2 +X2 + 1 = X +X2 − 1

Thus when X1 = X − 2, 1 should stay in the auction forever.

If we continue reasoning in this way, we find 2 should never bid more than

X2 + X − 3,X2 + X − 4, ...,X2

and 1 should never quit if

X1 = X − 3, X − 4, ..., 0

THE ASYMMETRIC WALLET GAME IS AN ALMOST COMMON VALUE AUCTION

IN WHICH ONE PLAYER HAS A SMALL ADVANTAGE.

THE PLAYER WHO HAS AN ADVANTAGE ALWAYS WINS THE AUCTION.

SELLERS’ STRATEGIES FOR ALMOST COMMON VALUES

• USE A FIRST SEALED BID AUCTION.

— This prevents the bidder with an advantage from always outbidding the rival.

6.4.3 LOS ANGELES SPECTRUM AUCTION

IN THIS AUCTION, PACIFIC TELEPHONE HAD A SMALL ADVANTAGE.

• ITS BRAND NAME WAS ALREADY KNOWN

• IT HAD A DATABASE ON POTENTIAL CUSTOMERS

PACIFIC TELEPHONE BOUGHT THE LOS ANGELES LICENCE AT A LOW PRICE

Chicago $31 No Bidder had an advantage

LOS ANGELES $26Pacific Telephonehad an advantage

New York $17 Sprint had an advantage

6.4.4 TAKEOVERS AND TOEHOLDS

A SITUATION IN WHICH 2 OR MORE FIRMS ARE TRYING TO TAKE-OVER A TAR-

GET IS EFFECTIVELY AN ENGLISH AUCTION.

IF ONE OF THE BIDDERS HAS A SHAREHOLDING. OF SIZE θ IN THE TARGET

THEN A TAKEOVER IS LIKE THE ASYMMETRIC WALLET GAME.

BY SIMILAR REASONING TO THE ASYMMETRIC WALLET GAME IF ONE BIDDER

HAS A TOEHOLD (S)HE WILL ALWAYS WIN THE AUCTION.

IF BOTH BIDDERS HAVE A TOEHOLD THE PLAYERWITH THE LARGER TOEHOLD

HAS A VERY SUBSTANTIAL ADVANTAGE. HOWEVER (S)HE DOES NOT ALWAYS

WIN THE AUCTION.

• LARGER TOE-HOLDERS WIN MORE OFTEN

• AT LOWER PRICES.

TOEHOLD MODEL

• AN OBJECT IS FOR SALE IN AN ENGLISH AUCTION.

• THERE ARE TWO BIDDERS i = 1, 2.

• THE VALUE OF THE OBJECT TO BIDDER 1 IS, X1 +X2 + θp.

• THE VALUE OF THE OBJECT TO BIDDER 2 IS, X1 +X2.

• X1 AND X2 ARE RANDOM INTEGERS BETWEEN 0 AND X.

• BIDDER i OBSERVES Xi.

Proposition 6.3 IN EQUILIBRIUM BIDDER 1 ALWAYS WINS THE AUCTION.

FOOTBALL IN 1999 BSkyB A SATELLITE TELEVISION COMPANY TRIED TO AC-

QUIRE MANCHESTER UNITED

THIS WAS BLOCKED BY THE UK GOVERNMENT

• BSkyB WOULD HAVE A TOEHOLD AND HENCE A SIGNIFICANT ADVANTAGE

IN THE AUCTION FOR THE TELEVISION RIGHTS TO THE PREMIER LEAGUE

FOOTBALL.

MANCHESTER UNITED’S SHARE OF THE PREMIER LEAGUE REVENUES WOULD

GIVE BSkyB A TOEHOLD OF 7% IN THE AUCTION FOR TELEVISION RIGHTS.

BIDDING COSTS IF THERE ARE TOEHOLDS AND SMALL ENTRY OR BIDDINGCOSTS THE SMALLER FIRM WILL NOT ENTER THE BIDDING.

THIS WILL RESULT IN THE LARGER FIRM WINNING THE AUCTION AT A LOWPRICE.

AN OWNERSHIP STAKE OF SUFFICIENTLY LESS THAN 50%MAY GIVE EFFECTIVECONTROL OF A COMPANY.

WELLCOME TAKEOVER GLAXO OFFERED £9bn.

GLAXO’S BIDDING FEE WAS £30m.

ZENECA WILLING TO PAY £10bn.

ROCHE ALSO WILLING TO PAY MORE.

BUT REFUSED TO COMPETE WITH GLAXO IN AN AUCTION.

• SEALED BID AUCTIONS ARE BETTER THAN ENGLISH AUCTIONS FOR WAL-LET GAMES.

An object is for sale by auction. The object will have value X to the successful bidder.At the time of the auction none of the bidders know the true value X. They do haveestimates of the true value. Specifically there are 21 estimates which take values,

X − 10,X − 9, ...,X − 1,X,X + 1, ...,X + 10.

These estimates are randomly distributed among the bidders.

This is a first price sealed bid auction. The object will be sold to the highest bidder at aprice equal to the bid.

• Do not talk or look at other peoples cards

• Your estimate is the red number on the card,

• Write how much you are prepared to bid in black or blue on the card.

• Make an independent note of your estimate and how much you bid.

• X was chosen by a random number generator.

Common Value Auction

64

69

74

79

84

89

94

74 78 82 86 90 94

Value

Bid

Figure 22:

Do not read any further.

maxAEru′ (w −A+A (1 + r)) = 0 (12)

Differentiating (12) with respect to w we obtain: