Chapter 4 Agency Problems in Corporate Finance 4.1 Introduction As we discussed in the Chapters 1 and 2 when we covered Modigliani-Miller the standard theory of capital structure that has been the mainstay of text- books is the trade-o? theory. This argues that the benefitofdebtisthe tax shield and the cost is the deadweight costs of bankruptcy. The tradi- tional view was that these deadweight costs were bankruptcy and liquidation costs. In the 1970’s this theory was criticized because it didn’t seem it could satisfactorily explain observed capital structures. For long periods of time corporations in the US have on average had long term debt worth about 30-40% of their total value (see, e.g., Rajan and Zingales (1995)). They have also paid corporate taxes most of the time. Evidence on bankruptcy costs provided by Warner (1977) and others suggested that the direct costs of bankruptcy such as lawyers’ fees were low. Haugen and Senbet (1978) pointed out that bankruptcy and liquidation costs should not be confused. If liquidation costs were high they could be avoided by renegotiation with debtholders in bankruptcy. Given bankruptcy costs are low and corporate tax rates in the US at that time were 46% the standard theory seemed to suggest that if corporations increased their debt slightly they could increase their value. The fact that they did not do this suggested that the theory was incorrect. The di?culty in explaining firms’ payout policy in the Modigliani- Miller framework extended to include taxes (the so-called ”dividend puzzle”) 1 2 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE also contributed to the dissatisfaction with traditional approach. All of this lead to a number of other approaches. These included personal taxes (Miller (1977)), and approaches based on asymmetric information. There were two main strands based on asymmetric information, signalling models and agency theory. We will consider the role of signalling in a subsequent chapter. Here we will focus on agency theory. In a seminal paper Jensen and Meckling (1976) suggested that we should think of the firm as consisting of groups of securityholders with di?ering interests rather than as a single agent as traditional theory had done. They emphasized two conflicts. The first is between shareholders or entrepreneurs and bondholders. The second is between shareholders and managers. These conflicts lead to two agency problems. Toillustratethefirst agencyproblemconsider the shareholder-bondholder conflict. Given that shareholders obtain any payo? in excess of the debt repayment they (or managers acting in their interest) have an incentive to take risks so that the average payment they receive is increased. They showed that firms acting in the interest of shareholders may be willing to accept negative net present value projects if the shareholders’ average payment is increased at the expense of the bondholders. This is the risk shifting (also sometimes called asset substitution) problem. The problem is not restricted to the shareholder-bondholder conflict. It can also arise in the context of the shareholder-manager problem. The second agency problem that Jensen and Meckling (1976) stressed was the e?ort problem. This can be illustrated in the context of the between shareholder-manager problem but also arises in the bondholder-entrepreneur problem. If managers have a disutility of e?ort and are paid a wage then they will have an incentive to shirk rather than act in shareholders’ interests. It is therefore important that managers’ incentives are aligned with those of shareholders. Myers (1977) pointed to another crucial agency problem, debt overhang. If a firm has a large amount of debt outstanding then the proceeds to any new safe project that it undertakes will flow to the existing bondholders. As a result if the firm acts in the interests of shareholders it will be unwilling to accept even safe projects even if they have a positive net present value. The papers by Jensen and Meckling (1976) and Myers (1977) had a huge impact. At one point the Jensen and Meckling paper was the most cited paper in Economics. A large literature focused on the conflict between share- holders and managers. Grossman and Hart (1982) pointed to the incentive 4.2. THE RISK SHIFTING PROBLEM 3 e?ects of debt. If a firm takes on a lot of debt the managers will be forced to work hard. Jensen (1986) also emphasized the incentive aspects of debt in his famous “free cash flow” theory. If managers have access to large amounts of funds, i.e. free cash flow, they may use it to pursue their own interests rather than the shareholders’. One way the shareholders can prevent this is for the firm to take on a lot of debt. Easterbrook (1984) pointed to the incentive e?ects of dividends. If managers pay out a large amount in dividends they will be unable to waste the funds pursuing their own interests. The Jensen and Meckling article also lead to a consideration of how the managers’ incentives could be aligned with those of the shareholders through executive compensation. There is a large literature on executive compensa- tion which is summarized in Murphy (1998). Finally, there is also a large literature justifying debt as an optimal con- tract which uses an agency approach. The three pioneering papers in this lit- erature are Townsend (1979), Diamond (1984) and Gale and Hellwig (1985). In this chapter we will cover the following applications of agency theory to corporate finance. ? The risk shifting problem. ? Debt overhang. ? Debt and equity as incentive devices. ? Executive compensation. ? Debt as an optimal contract. 4.2 The Risk Shifting Problem As discussed in the Introduction one of the most important conflicts of inter- est between equityholders and bondholders is that if managers act in equity- holders’ interest they may accept negative NPV investments at the expense of bondholders. The basic idea is the following. Suppose a firm has $1,000 in cash the day before its debt, which has a face value of $5,000, comes due. If the equityholders (or the managers acting on their behalf) do nothing then the firm will go bankrupt and they will get nothing. What should they do? Suppose the equityholders took the cash and went to Atlantic City. If they 4 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE win they might get $20,000 say. In that case they can pay o? the $5,000 debt and still have $15,000 left over. If they lose they get nothing but they would have got nothing anyway so they are no worse o? from gambling. The bondholders are of course worse o?if they lose, they get nothing whereas they would have got $1,000 if the equityholders hadn’t gambled. The problem is that when the firm is near bankruptcy the equityholders are gambling with the bondholders money. They will therefore be prepared to invest in risky projects even though they are negative NPV. Although this example may seem rather extreme something rather like it happened early on in Federal Express’s history. Fortunately in that case the managers won but they could have easily lost. Letusgothroughthisexampleinalittlemoredetailbeforewedevelop aformalmodel. 4.2.1 A Simple Example of Risk Shifting Firmhas $1,000 in cash. It has bonds outstanding on which the next payment is $5,000. Firm does nothing: Value of bonds $1,000 Value of equity 0 Firm invests in project costing $1000 (payo?s occur immediately so ignore discounting): Probability = 0.02 Payo? =20,000 Probability = 0.98 Payo? =0 Expected payo? = -1,000 + 0.02x20,000 = -1,000 + 400 = -600 This is a very bad project. Firm does project: If it’s successful, Value of bonds = 5,000 Value of equity = 15,000 If it’s unsuccessful, Value of bonds = 0 Value of equity = 0 Therefore, Expected value of bonds = 0.02 x 5,000 = 100 4.2. THE RISK SHIFTING PROBLEM 5 Expected Value of equity = 0.02 x 15,000 = 300 Notice that the bondholders are worse o?by 900 and the equityholders are better o? by 300. The NPV of the project was -600 so this is the majority of the drop in value with the other 300 coming fromthe transfer to equity. Thus even though its a lousy project, it’s worth doing as far as the equityholders are concerned. The conclusion is that the stockholders of levered firms gain when business risk increases and this leads to an incentive to take risks. 4.2.2 A Formal Model of Risk Shifting Let A denote the set of actions available to the manager with generic element a. Typically, A is either a finite set or an interval of real numbers. Let S denote a set of states with generic element s. For simplicity, we assume that the set S is finite. The probability of the state s conditional on the action a is denoted by p(a,s). The revenue in state s is denoted by R(s) ≥ 0. The manager’s utility depends on both the action chosen and the con- sumption he derives from his share of the revenue. The shareholder’s utility depends only on his consumption. We maintain the following assumptions about preferences: ? The agent’s utility function u : A×R + → R is additively separable: u(a,c)=U(c)?ψ(a). Further, the function U : R + → R is C 2 and satisfies U 0 (c) > 0 and U 00 (c) ≤ 0. ? The principal’s utility function V : R→ Ris C 2 and satisfies V 0 (c) > 0 and V 00 (c) ≤ 0. Notice that the manager’s consumption is assumed to be non-negative. This is interpreted as a liquidity constraint or limited liability. Risk shifting occurs when the manager has a convex reward schedule and prefers riskier projects, other things being equal. We can think of this as a case where the principal is a bondholder and the agent is the managers of the firm acting in the shareholders’ interest who have issued debt to finance the risky venture. 6 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE There is a fixed cost of financing a project which we normalize to zero and a finite number of projects a =1,...,A identified with the probability distributions p(a,s). The contract between the shareholder and the manager requires the shareholders to pay the cost of the investment and pay the manager w(s) contingent on the outcome R(s). The manager has a utility function U(c) and chooses the project a to maximize his expected utility P s p(a,s)U(w(s)). Because the manager has limitedliabilityandnopersonal resources, w(s) ≥ 0. We assume that the principal and agent both know all the parameters of the model, the cost function ψ(a), the possible outcomes R(s),theagent’s utility function U(·), etc. There is asymmetric information about the choice of project, which gives rise to an incentive problem. Both the principal and the agent observe the contract (a,w(·)) that specifies the manager’s remuneration and the project that should be chosen and they both observe the realization s. However, only the manager observes the actual choice of project. Casting this in the form of a principal-agent problem, the principal is assumed to choose the contract (a,w(·)) to maximize his expected return P s p(a,s)V (R(s) ? w(s)), subject to an incentive constraint (IC) and an individual rationality or participation constraint (IR): max (a,w(·)) P s p(a,s)V (R(s)?w(s)) (IC) P s p(a,s)U(w(s)) ≥ P s p(b,s)U(w(s)),?b (IR) P s p(a,s)U(w(s)) ≥ ˉu Of course, there is a participation constraint for the principal as well. If the solution to this problem does not give the principal a return greater than his opportunity cost, it may not be optimal for him to invest in the project at all. Supposethattheprincipal is riskneutral andtheagentstrictlyriskaverse. Then the obvious solution is to o?er the agent a fixed wage w(s)= ˉw such that u(ˉw)=ˉu. The agent will be indi?erent between all projects so it will be optimal for him to choose the project that maximizes the principal’s payo?, namely, the project a that maximizes expected revenue. But note that it is also optimal for him to choose any other project so we have not found a very robust method of implementing the e?cient project. Suppose that the agent is risk neutral andthe principal strictlyriskaverse. Then optimal risk sharing would require that the agent bear all the risk, assuming that this is consistent with the budget constraint. Recall that we 4.2. THE RISK SHIFTING PROBLEM 7 assume the agent’s consumption is non-negative (limited liability). In the first best, we have seen that when the manager is risk neutral there is a number r>0 such that w(s)=max{R(s)?r,0},?s, and the return to the principal is R(s)?w(s)=min{R(s),r},?s. With this payment structure, the entrepreneur chooses a to maximize his expected return X s p(a,s)w(s)= X s p(a,s)max{R(s)?r,0}. Suppose that the principal is restricted to o?ering an incentive scheme of this form. Then the (constrained) principal-agent problem is max (a,r) P s p(a,s)V (min{r,R(s)}) s.t. r ≥ 0 (IC) P s p(a,s)max{R(s)?r,0} ≥ P s p(a,s)max{R(s)?r,0},?s (IR) P s p(a,s)max{R(s)?r,0} ≥ ˉu For any probability vector p =(p 1 ,...,p S ) let P(s)= s X σ=0 p σ and A s = s X σ=0 P σ (R(σ +1)?R(σ)). A distribution p 0 is a mean-preserving spread of p if it satisfies one of the following equivalent conditions: Proposition 1 Suppose that P s p s R(s)= P s p 0 s R(s). The following condi- tions are equivalent: (i) P s σ=0 A σ ≤ P s σ=0 A 0 σ ; (ii) for any non-decreasing function f : S → R with non-increasing di?erences P s p 0 s f (s) ≤ P s p s f (s); (iii) p 0 is obtained from p in a finite sequence of transformations at each step of which the probability of one outcome is reduced and the probability mass is redistributed to a higher and lower outcome in a mean-preserving way. 8 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE Suppose that p(a,·) is a mean-preserving spread of p(b,·). Then, for any number r, X s p(a,s)max{R(s)?r,0} ≥ X s p(b,s)max{R(s)?r,0}. This follows immediately from the proposition and the fact that the function f(s)=max{R(s) ? r,0} has non-decreasing di?erences. In other words, the entrepreneur has a preference for risk (a preference for mean-preserving spreads). Theprincipalontheotherhandwantstomaximize P s p(a,s)V (min{r,R(s)}). At any solution of the principal-agent problem, the participation constraint should be satisfied with equality: P s p(a,s)w(s)= P s p(a,s)max{R(s) ? r,0} =ˉu. Thus, in the absence of the incentive problem the principal seeks to maximize X s p(a,s)V (min{r,R(s)}) subject to X s p(a,s)max{R(s)?r,0} =ˉu. For example, if the principal is risk neutral he would always prefer a project with a higher expected value. But once the incentive constraint is imposed, the risk shifting preferences of the agent have to be taken into account. 4.3 Debt Overhang The risk taking or asset substitution problem is not the only one. Myers (1977) pointed out that firms rather than accepting negative NPV projects have an incentive to forego positive NPV projects. This incentive results from a debt overhang problem. The reason this arises is that equityholders with existing debt have to share the rewards of new projects with bondholders. To see how this works consider another simple example. 4.3.1 A Simple Example of Debt Overhang The firm has no cash and has debt of $10,000. The firm does nothing: 4.3. DEBT OVERHANG 9 The firm will go bankrupt. The firm’s investment opportunity: Invest $2,000 and receive return $11,000 with certainty (ignore discount- ing). Expected return = -2,000 + 11,000 = +$9,000 This is clearly a very attractive project. Is it worth the firm doing it? The firm does the project: Value of bonds = $10,000. Payo? to Equityholders = -2,000 + 1,000 = -$1,000. The will not be prepared to put up the money for investment since even though it’s a very good project they lose money from doing it. Even if the firm has $2,000 cash on hand they would not do the project since the shareholders would be better o? to pay the money as a dividend. This example illustrates the conclusion that if business risk is held con- stant, any increase in firm value is shared among bondholders and stockhold- ers. Thus, only if bondholders are willing to put up most of the money will the firmundertake the investment. However, bondholders mayget veryimperfect information. They may not be able to tell whether its this type of project or thetypethatwehadinthepreviousexample.Asaresultofthisasymmetric information the project will not be undertaken. 4.3.2 A Formal Model of Debt Overhang The manager in this example chooses a level of e?ort a that results in a probability distribution p(a,s) over the outcomes s. There is no investment required. Themanager’sutilityfunctionisU(c)?ψ(a). Thecontractbetween the shareholder and the manager specifies a reward w(s) as a function of the state s. Limited liability implies that w(s) ≥ 0. The manager will choose the e?ort that maximizes his expected utility P s p(a,s)U(w(s)?ψ(a).The shareholder chooses the incentive scheme w(·) to provide the manager with an incentive to pursue his (the shareholder’s) interests. The interaction of the manager and shareholder can be written as a principal-agent problem in which the shareholder chooses the e?ort level to 10 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE maximize his expected return subject to (IC) and (IR): max (a,w(·)) P s p(a,s)[R(s)?w(s)] s.t. w(s) ≥ 0,a≥ 0 (IC) P s p(a,s)U(w(s))?ψ(a) ≥ P s p(b,s)U(w(s))?ψ(b),?b (IR) P s p(a,s)U(w(s))?ψ(a) ≥ ˉu. We can use this model of e?ort to illustrate the so-called debt overhang problem, if an entrepreneur has a pre-existing debt he may not wish to un- dertake a project with positive net present value. It is easiest to fitthisinto our present framework by representing the investment as e?ortthatmustbe undertaken by the entrepreneur. Suppose that r is the face value of the debt. The status quo is represented by a probability distribution p, which has zero cost of e?ort. The new project will result in a probability distribution p 0 , which has a positive cost c 0 . We assume that p 0 dominates p in the sense of first-order stochastic dominance and X s p 0 (s)R(s)?c 0 > X s p(s)R(s). (4.1) However, the entrepreneur will undertake the new project only if X s p 0 (s)max{R(s)?r,0}?c 0 ≥ X s p(s)max{R(s)?r,0} (4.2) and condition (4.1) does not necessarily entail (4.2). In fact, it is easy to find examples in which the new project will not be undertaken. We can even find conditions under which it might be optimal for the bondholder’s to forgive the debt in order to encourage greater e?ort(investment)onthepartofthe entrepreneur. 4.4 Debt and Equity as Incentive Devices Grossman and Hart (1982) emphasizes the incentive e?ects of debt: a man- ager whose firm is loaded with debt knows that shirking may result in an inability to service the debt. Insolvency or liquidation will be costly for the manager: he loses perquisites of his present job, is forced to search for an- other, and once he finds another job he may earn less because his reputation has been damaged. This is equivalent to adding a non-pecuniary benefit 4.5. EXECUTIVE COMPENSATION 11 to success or a non-pecuniary penalty to failure. With this change in the problem, debt-like incentive schemes may be approximately optimal. In a famous paper, Jensen (1986) made a closely related point. He argued that if firms have a lot of spare resources available they will have an incentive to use these resources, or“free cash flow”ashecalledit,topursuetheirown interests. He suggested that in order to prevent these agency problems the firms should take on a lot of debt. This would mean that the free cash flow was paid out and could not be wasted. He made this argument at a time when Leveraged Buy Outs (LBOs) were becoming common. Takeovers by outsiders or management groups would mostly be financed by debt. Often the debt was issued in the junk bond markets. Jensen’s theory provided one explanation for these LBO’s. Typically the leveraged debt structures did not last for long. Firms would sell o? assets to pay down debt or reduce debt in some other way. Another explanation for LBOs is that the purchasers had superior information and as a result debt finance was superior. An important aspect of using large amounts of debt that Grossman and Hart (1982) and Jensen ignored was that large amounts of debt would also create a risk shifting problem and a debt overhang problems. Easterbrook (1984) argued that agency problems could provide an expla- nation for dividend policy. The argument was related to that in Grossman and Hart (1982) and Jensen (1982). He suggested that firms could provide incentives for e?ort by committing to paying out large sums as dividends. This has the same kind of advantageous features as debt but without creating incentives to take risks or a debt overhang problem. Agency problems have received relatively little attention in the payout policy literature. This is an interesting topic for future research. 4.5 Executive Compensation One of the most obvious practical applications of principal-agent problems is to executive compensation. Jensen and Meckling’s (1976) emphasis on the shareholder-manager problem points directly to a need to use compensation to align managers’ and shareholders’ interests. An excellent survey of this topic is contained in Murphy (1999). He argues that although the agencyparadigmhas been an extremelyinflu- ential one on the executive compensation literature, the standard principal- 12 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE agent literature has relatively few implications. For example, one of the main results in this literature is Holmstrom’s (1979) informativeness princi- ple. This states that all information that is available on the performance of the agent should be used in the contract between the principal and agent. In the context of the shareholder-manager problem this means that all corre- lated variables should be used to determine executive compensation. In fact it turns out that the use of other firm’s performance information is rarely used. To the extent that it is, it is usually accounting information rather than stock price information. Murphy (1999) provides a good description of the way that executive compensation operates in practice. There has been an explosion in academic research on this topic in recent years so that we know much more than we used to. This increase in interest was caused by a rapid increase in executive compensation in the US and also the development of the agency paradigm. In recent years there has been a significant change in the way in which US CEOs are compensated. Base salary and bonuses based on accounting information have always been important. In recent years stock options have become much more important. The compensation varies significantly across countries with compensation being the highest in financial services and the lowest in regulated utilities. Comparing CEO pay internationally, there is considerable variation. However, the US has the highest paid executives with the average being about twice as high as the average in other countries. The form of payment is quite di?erent too. In the US stock options play a much larger role than in other countries. Moreover the form of pay in other countriesisdi?erent. Much more is in the form of bonus and stock options in the US than in other countries. The typical compensation package for a CEO consists of a base salary, an annual bonus and stock options. The base salary is usually set with the help of compensation consultants. They survey what other CEOs are receiving in comparable companies and make a recommendation to the company. Annual bonus plans depend on accounting information such as earnings or earnings before interest and taxes (EBIT). There is usually some target that the firm must reach. Typical plans would pay a bonus when the chosen measure was 80% of the target and the bonus would go on increasing up to 120% of the target. Stock options are the other important component. These are more long term in nature and as a result are often changed if circumstances change considerably. There are important tax advantages of options. Overall, a careful examination of the executive compensation literature 4.6. DEBT AS AN OPTIMAL CONTRACT 13 shows that the problem is much richer than the standard principal-agent model is able to capture. Much work remains to be done in this area. 4.6 Debt as an Optimal Contract Another important application of the principal-agent approach has been to the literature on why debt might be an optimal contract. In contrast to most of the literature which takes the contract form as given this literature attempts to derive everything from first principles. There are three standard references, Townsend (1979), Diamond (1984) and Gale and Hellwig (1985). We develop the latter model as an illustration. Suppose an entrepreneur has an indivisible risky project and limited re- sources. He undertakes the project jointly with a wealthy investor. The contracting problem between the entrepreneur and the investor can be rep- resented as a principal-agent problem in which the investor takes the role of the principal and the entrepreneur takes the role of the agent. The contract is chosen to maximize the investor’s payo? subject to an incentive constraint and a constraint on the entrepreneur’s payo?. There is a single consumption good that serves as the numeraire. The project requires an input of K>0 units of the good at the first date and produces a random revenue of R(s) units of the good at the second date in state s =0,1,...,S. The probability of state s is denoted by p(s) > 0. Without loss of generality, assume that R(0) = 0 <R(1) < ... < R(S). The entrepreneur has initial wealth of ω>0 andisassumedtoberisk neutral, subject to a non-negativity constraint on consumption and limited liability. The investor is risk neutral and has “unlimited” wealth. The opportunity cost of funds is assumed to be 1. The investor and the entrepreneur have the alternative of investing in a safe asset that earns a gross return of 1 unit per unit invested. The entrepreneur observes the state s and hence the revenue R(s) without cost. The investor can observe the output and enforce the contract by paying acostc>0. A contract specifies an investment in the venture 0 ≤ e ≤ ω made by the entrepreneur, the set of states B in which the investor observes the state 14 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE s after paying the cost c,andapaymentr(s) by the entrepreneur to the investor in each state s. Note that we are implicitly assuming that ? the investor puts up K ?e of the investment in the project; ? the probability of the investor observing the state is either 0 or 1; ? and that there is complete commitment, that is, we treat this as a standard mechanism design problem. A contract is characterized by the triple (e,r(·),B) which determines the entrepreneur’s consumption in state s w(s) ≡ R(s)?r(s)+(ω?e), that is, the output of the project minus the payment to the principal plus his investment in the safe asset. A feasible contract must satisfy w(s) ≥ 0 or r(s) ≤ R(s)+ ω?e for all s. The principal’s objective function is X s p(s)r(s)? X s∈B p(s)c?(K ?e) since he receives r(s) units in state s, he observes the state if and only if s ∈ B, and he contributes K ?e at the first date. The agent’s payo? is P s p(s)w(s). The reservation utility of the en- trepreneur ˉu takes into account any opportunity cost of managing the ven- ture (e?ort required, alternative occupations) together with the value of the wealth ω. The entrepreneur will participate in the contract if and only if it satisfies the individual rationality constraint X s p(s)w(s) ≥ ˉu. If the principal observes the true state, there is no need for an incentive constraint; but in states s/∈ B the contract must give the agent an incentive to reveal the state truthfully. Suppose that the true state is s and the agent reports ?s/∈ B. The agent will be better o? only if r(?s) <r(s).Thecontract is feasible only if r(s) ≤ R(s)+ω ?e,foralls,soifr(?s) <r(s) it follows that r(?s) ≤ R(s)+ω?e and it is feasible for the agent to misreport ?s when the true state is s. Thus, the incentive to misreport is removed if and only if r(s) ≤ r(?s). This gives the following simple result. 4.6. DEBT AS AN OPTIMAL CONTRACT 15 Proposition 2 The contract is incentive-compatible if and only if r(s) ≤ r(?s),??s/∈ B. The problem can now be defined formally as follows: max P s p(s)r(s)? P s∈B p(s)c?(K ?e) s.t (IR) P s p(s)w(s) ≥ ˉu (IC) r(s) ≤ r(?s),??s/∈ B. We now proceed to show that, if the principal-agent problem has a solu- tion, it has one in the form of a standard debt contract. In a standard debt contract the repayment schedule r(·) has the form r(s)=min{R(s), ˉr} for some constant ˉr. There may be a multiplicity of solutions, in which case not every solution may have these properties, but the standard debt contract is at least optimal and is sometimes the unique optimum. Suppose that (e,r(·),B) is a solution to this principal-agent problem. Then we can transform (e,r(·),B) by stages into a standard debt contract without losing the optimality property. The first step is to show that without loss of generality e = ω.Calthispropertymaximum equity participation (MEP). To see this, replace (e,r(·),B) with (e 0 ,r 0 (·),B) where e 0 = ω and r 0 (s)=r(s)?(e?ω) for every s. By inspection we can see that the value of the objective function has not changed and the constraints are still satisfied. Proposition 3 (Maximum equity participation) Without loss of generality, if (e,r(·),B) is a solution of the principal-agent problem then we can assume that e = ω. Henceforth, we represent the optimal solution by (r(·),B), where it is under- stood that e = ω. The next property is called uniform repayment when the entrepreneur is solvent, that is, r(s)=r(s 0 ),?s,s 0 /∈ B. This follows immediately from the incentive constraint. Proposition 4 (Uniform repayment) If (z,B) is a solution of the principal- agent problem then r(s)=r(s 0 ) for all s,s 0 /∈ B. 16 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE We have shown that there is a constant repayment r(s)=ˉr whenever thetrueoutcomeisnotverified. The next step is to show that bankruptcy only occurs when the revenue is not large enough to allow the entrepreneur to make the fixed payment ˉr. Proposition 5 (Bankruptcy rule) If (z,B) is a solution of the principal- agent problem then B = {s : R(s) < ˉr},whereˉr = r(s) for some s/∈ B. Proof. Let ˉr = r(s) for s/∈ B. Obviously, R(s) < ˉr implies that r(s) < ˉr so s ∈ B; what we need to show is that the converse holds. Suppose then that r(s) ≥ ˉr for some s ∈ B. Then (IC) implies that r(s) ≤ ˉr.Therearetwo cases to consider. Case (a) If r(s)=ˉr then we can define B 0 = B\{s} and clearly (r(·),B 0 ) is an improvement on (r(·),B), contradicting the definition of an optimum. Case (b) If r(s) < ˉr then we can define a new contract (r 0 (·),B 0 ) as follows. Let B 0 = B\{s} and define r 0 (·) by putting r 0 (s 0 )= ? ˉr?ds 0 = s r(s 0 )?ds 0 6= s where d = p(s)(ˉr?r(s)). By construction, (IR) and (IC) are satisfied and the objective function is increased. Again, we have a contradiction of optimality. Finally, we can show that it is optimal to have maximum recovery in bankruptcy. Proposition 6 (Maximum recovery) If (r(·),B) is an optimal contract then, without loss of generality, we can assume that r(s)=R(s) when s ∈ B. Proof. If (r(·),B) is an optimal contract, define ˉr 0 implicitly by X s p(s)max{R(s)? ˉr 0 ,0} =ˉu andthendefine a contract (r 0 (·),B 0 ) by B 0 = {s : R(s) < ˉr 0 } and r(s)= min{R(s), ˉr 0 }. Clearly, ˉr 0 ≤ ˉr,soB 0 ? B. On the other hand, (IR) holds exactly so that P s p(s)w 0 (s) ≤ P s p(s)w(s).Thus, X s p(s)r(s)? X i∈B p(s)c?(K ?ω) ≤ X s p(s)r 0 (s)? X s∈B 0 p(s)c?(K ?ω). This completes the proof that the standard debt contract is an optimal solution to the principal-agent problem. 4.6. DEBT AS AN OPTIMAL CONTRACT 17 Proposition 7 If (r(·),B) is an optimal solution of the principal-agent prob- lem then there exists a number ˉr such that r(s)=min{R(s), ˉr} and B = {s : R(s) < ˉr}. The optimal contract is completely characterized by the choice of repayment ˉr and the principal-agent problem can be equivalently stated as follows: max P s p(s)min{R(s), ˉr}? P {R(s)<ˉr} p(s)c?(K ?ω) s.t P s p(s)max{R(s)? ˉr,0} ≥ ˉu (IR) and the unique solution to the problem is given by the value of ˉr that satisfies (IR) as an equation. 4.6.1 Randomization Randomization is not allowed in the characterization of the standard debt contract. To see that randomization might lead to better payo?s, con- sider a simple example with two outcomes (R(1),R(2)) with R(1) = 0 and R(2) = R>0. Suppose that the optimal contract (without randomization) is characterized by 0 < ˉr<R, which requires the principal to observe the true state with probability one if s =1. However, this is not necessary for incentive compatibility. There is only one incentive-compatibility constraint, corresponding to misrepresenting the true state as s =1when s =2.The equilibrium payo? for the agent is R? ˉr>0. If the principal observes the state with probability π when the agent reports s =1then the agent’s payo? ifthetruestateiss =2will be at least (1?π)R.Thisassumesthatifthe agentiscaughtlyingtheentireoutputisseized.Anyotherrulewillmakethe incentive constraint “tighter”. To discourage the agent from misrepresenting the truth, π must satisfy (1?π)R ≤ R? ˉr,or π ≥ ˉr R . By choosing π<1 the principal saves the cost of observing the state and thus increases the objective function by (1?π)c. Randomization is not something that we see in practice, although it is of- ten argued that random monitoring occurs but is disguised by “purification”, that is, dependence on irrelevant random variables. 18 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE Another reason why randomization does not occur is that the principal cannot commit to use the random strategy and ex post will often have an incentive to avoid the cost of observing the state. This leads us to study the optimal contract in the absence of commitment. Mookherjee and Png (1989) have studied the use of random monitoring in a contracting problem. What follows is based on their analysis. Let B(s) denote the probability of monitoring (verification) if state s is reported by the agent, let r 0 (s) denote the repayment if s is reported and the state is not verified and let r 1 (s) denote the payment if s is reported and the state is verified to be s. The Revelation Principle allows us to restrict attention to mechanisms with truthful equilibria. Since the state is revealed truthfully in equilibrium, there is no loss of generality in assuming that the agent’s consumption is zero if the state is verified and it turns out that he reported untruthfully. Thus, the contracting problem can be written as follows: max P s p(s)[R(s)?B(s)r 1 (s)?(1?B(s))r 0 (s)] P s p(s)[B(s)r 1 (s)+(1?B(s))r 0 (s)?B(s)c]?K ≥ ˉv B(s)r 1 (s)+(1?B(s))r 0 (s) ≤ B(?s)R(s)+(1?B(?s))r 0 (s),??s ? r 0 (s) ≤ R(s) r 1 (s),r 0 (s) ≤ R(s),0 ≤ B(s) ≤ 1. The following properties are easily established. ? Optimal schemes exist. ? Any incentive scheme in which the participation constraint is not bind- ing is not optimal. (Assume that ˉv ≥ 0). ? The agent should never be punished for telling the truth: r 1 (s) ≤ r 0 (s). ? If verification is random, i.e., 0 <B(s) < 1, then the truth is rewarded: r 1 (s) <r 0 (s). ? If a state s is verified with positive probability, then there must exist a state ?s such that the agent is indi?erent between reporting ?s truthfully and reporting s. ? In any optimal incentive scheme: (a) reports corresponding to the high- est payment r 0 (s) will not be verified and all other reports will be verified with positive probability; (b) reports corresponding to higher values of r 0 (s) will be audited with equal or lower probability; further if r 0 (s) >r 0 (?s) and B(?s) > 0 then B(s) <B(?s). 4.6. DEBT AS AN OPTIMAL CONTRACT 19 In general, the incentive scheme does not have to satisfy monotonicity. The most we can guarantee are the following properties: ? Suppose there are only two possible states, s and ?s with R(s) <R(?s). Then in any optimal incentive scheme, B(?s)=0and r 0 (?s) ≥ r 0 (s). ? There is an optimal incentive scheme in which the highest revenue report R(s) is not verified and is associated with the highest value of r 0 (s) and the highest consumption R(s)?r 0 (s). 4.6.2 Contracts without commitment Consider the two-state example again. If the agent announces that the state is s =1, the principal will have no incentive to observe the state unless he believes that the true state is s =2with positive probability. In fact, there will be a probability that makes him indi?erent. Suppose that when the true state is s =2the agent reports s =1with probability γ. Then the probability of s =2given the report of s =0is γ 0 = p(2)γ p(2)γ + p(1) and if we choose γ so that γ 0 R = c then it will be optimal to observe the state with probability π =ˉr/R,which in turn makes it optimal for the agent to randomize between s =1and s =2 when the true state is s =2. However, if there are many states s and correspondingly many values R(s),thenitwillnotbepossibletomaketheinvestorindi?erent between verifying and not verifying the true state in each case. Krasa and Villamil (2000) have studied a general problem of borrowing and lending without commitment. Analyzing contracting without commitment is complicated if there is asymmetric information because a signaling game arises at the second period and signaling games typically have multiple equilibria. A simpler approach is to assume that the outcome y i is observable but not verifiable. That is, both the principal and agent know what the outcome is (without cost) but 20 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE a third party, such as the court, does not observe the outcome and so can- not enforce the contract. The cost c of verifying the outcome is literally the cost of providing proof to the third party. Since the principal knows the true outcome, he knows when it is optimal to pay the cost and obtain the promised payment. It will be optimal to enforce the contract if and only if R(s) ≥ c. The analysis of the optimal contract will be much the same as in the case with commitment except that nothing will be collected in states where R(s) <c. If we allow for renegotiation, nothing will be paid in states where R(s) < c.IfR(s) >cand the creditor can make a take-it-or-leave-it o?er, i.e., has all the bargaining power, he will demand min{R(s), ˉr} and the borrower will give it to him. If the borrower can make a take-it-or-leave-it o?er, he will o?er min{ˉr,R(s)}?c and the creditor will accept. 4.6.3 Contracts with non-pecuniary penalties The Diamond model di?ers from the costly state verification model by allow- ing for non-pecuniary punishments on the entrepreneur in the event that the loan is not fully repaid. The entrepreneur makes a payment r(s) contingent on the outcome R(s) and receives a non-pecuniary punishment φ(s).The principal-agent problem is stated as follows, with the entrepreneur’s payo? in the objective function: max P s p(s)[R(s)?r(s)?φ(s)] s.t s ∈ argmax r(?s)≤R(s) R(s)?r(?s)?φ(?s) P s p(s)r(s) ≥ K. where K is the opportunity cost of the investor’s contribution. Diamond suggests the following repayment scheme: put φ ? (s)=max{ˉr?r ? (s),0} and r ? (s)=min{R(s), ˉr}. Then R(s)?r ? (?s)?φ ? (?s)=R(s)?r ? (?s)?max{ˉr?r ? (?s),0} = R(s)? ˉr = R(s)?r ? (s)?φ ? (s) 4.6. DEBT AS AN OPTIMAL CONTRACT 21 since r ? (?s)?φ ? (?s)=ˉr.Soforalls the incentive constraint is automatically satisfied. However, the penalties also enter into the participation constraint, so it is not clear that this is an optimal contract. To show that the contract (r ? ,φ ? ) is optimal, let ˉr be the smallest value that satisfies the constraint X s p(s)min{R(s), ˉr} ≥ K. Now suppose that there exists another (r,φ) that yields a higher value to the problem above. To satisfy the lender’s participation constraint, there must be a payment r(s) ≥ ˉr that is incentive compatible for some value R(s). Then R(s)?r(s)?φ(s) ≥ R(s)?r(?s)?φ(?s),?r(?s) ≤ r(s). This implies that for all r(?s) ≤ ˉr ≤ r(s), φ(?s) ≥ r(s)+φ(s)?r(?s) ≥ ˉr + φ(s)?r(?s) ≥ ˉr?r(?s) ≥ ˉr?R(?s) = φ ? (?s). Since φ ? (?s)=0for all r(?s) > ˉr,thisimpliesthatφ ? gives the smallest penal- ties consistent with the lenders’ participation constraint. This completes the proof that (r ? ,φ ? ) is the optimal contract. Risk choices in the Diamond model There are N risk neutral entrepreneurs and NM risk neutral investors. Each entrepreneur i =1,...,N has an investment project yielding an uncertain return y i = θ i f(k) when he makes an investment k. The random variables {θ i } are positive, with expected value 1, and are i.i.d. with distribution function F strictly increasing on the support [0, ˉ θ]. The production function f(·) is C 1 with f(0) = 0,f 0 (0) > 1 and f 0 (k) > 0. Each investor has funds ω/M. The opportunity cost of funds is 1. 22 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE Direct Finance Under the assumption that the investors cannot observe the return to the project, the optimal contract takes the form (k,ˉr) where k is the investment and ˉr the promised repayment. The entrepreneur’s payo? is Ey i ? ˉr = f(k)? ˉr and the investor’s payo? is E min{y i , ˉr}?k. The problem is to choose {(k i , ˉr i )} to maximize X i f(k i )? ˉr i subject to the constraints E min{θ i f(k i ), ˉr i } ≥ k i ,?i, and X i k i ≤ ωN. Proposition 8 (a) If the function f is strictly concave, the solution of the direct investment problem requires k i = k ? ≤ ω and ˉr i = r(k ? )k ? where r(k) is defined by E min{θ i f(k)/k,r(k)} =1. and k ? > 0 if and only if lim k→0 r(k) <f 0 (0).(b)Iff is strictly convex, the solution requires k i =ˉr i =0for all but one i and the remaining contract (k j , ˉr j ) satisfies k j = ωN, ˉr j = r( ωN) ωN if r( ωN) <f( ωN) and k j = ˉr j =0if r( ωN) >f( ωN).(c)Iff is linear, then ˉr i =ˉrk i .Iff(k)=ck and ˉr<cthen P i k i = ωN and the aggregate payo? to entrepreneurs is equal to (c?ˉr) ωN;ifˉr>cthen k i =0for all i and the aggregate payo? to entrepreneurs is 0. 4.6. DEBT AS AN OPTIMAL CONTRACT 23 Intermediated Finance Suppose the investors have provided K units of finance to the bank and demanded a repayment of R. The intermediary provides k i units to each entrepreneur and can enforce any repayment 0 ≤ g i (y i ) ≤ y i by monitoring at a cost c per firm. If an entrepreneur is not monitored, g i (y i )=0. The entrepreneur’s payo? is Ey i ?Eg(y i )=f(k i )?Eg(θ i f(k i )) and the intermediary’s is X i Eg i (θ i f(k i )) + K ? X i k i ?N 0 A?R where N 0 is the number of entrepreneurs who are monitored. The investors payo? is E min ( X i g i (θ i f(k i ),R ) ?K. It is assumed that (K,R) is chosen before the contracts between the interme- diary and the entrepreneurs and that the contracts are chosen to maximize a weighted sum of the payo?s to the intermediary and the entrepreneurs subject to P i k i ≤ K and Eg i (θ i f(k i ))?k i ?A ≥ 0. Proposition 9 Assume that f(k) ? kf 0 (k) <Afor all k ≥ 0.Forgiven K and R the maximization of a weighted sum of the entrepreneurs’ and intermediary’s payo?s requires setting k i =0forallbutatmostonei.If f(k) ? k>Afor some k ≤ K the remaining entrepreneur j is monitored and receives funds k j such that f 0 (k j ) ≥ 1 with equality unless k j = K,with repayment function g j satisfying g j (y j )=y j if α<1/2 and Eg j (θ j f(k j )) = k j +A if α>1/2.Iff(k)?k<Afor all k ≤ K then entrepreneur j receives no funds either. References Berle, A. and G. Means (1932). The Modern Corporation and Private Property. Chicago: Commerce Clearing House, Inc. Diamond, D. “Financial Intermediation and Delegated Monitoring,” Re- view of Economic Studies 51 (1984) 393-414. 24 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE Easterbrook, F. (1984). “Two Agency-Cost Explanations of Dividends,” American Economic Review 74,650-659. Gale, D. and M. Hellwig. “Incentive-Compatible Debt Contracts: The One-Period Problem,” Review of Economic Studies 52 (1985) 647-663. Grossman, S. and O. Hart (1982). “Corporate Financial Structure and Managerial Incentives,” in J. McCall, (ed.), The Economics of Information and Uncertainty, Chicago: University of Chicago Press. Grossman, S. and O. Hart (1983). “An Analysis of the Principal-Agent Problem,” Econometrica 51,7-45. Haugen, R. and L. Senbet (1978). “The Insignificance of Bankruptcy Costs to the Theory of Optimal Capital Structure,” Journal of Finance 34, 383-393. Hellwig, M. “Allowing for Risk Choices in Diamond’s ‘Financial Interme- diationas DelegatedMonitoring’,”MannheimUniversity(1998)unpublished. Holmstrom, B. (1979). “Moral Hazard and Observability,” The Bell Jour- nal of Economics 10, 74-91. Jensen, M. (1986). “Agency Costs of Free Cash Flow, Corporate Finance, and Takeovers,” American Economic Review 76, 323-29. Jensen, Michael and William Meckling (1976). “Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure,” Journal of Financial Economics 3, 305-60. Krasa, S. and A. Villamil, “Optimal Contracts when Enforcement is a Decision Variable,” Econometrica (2000). Mookherjee, D. and I. Png, “Optimal Auditing, Insurance, and Redistri- bution,” Quarterly Journal of Economics 104 (1989) 399-415. Miller, M. (1977). “Debt and Taxes,” Journal of Finance 32,261-275. Murphy, Kevin J. (1999). “Executive Compensation,” in O. Ashenfelter and D. Card (eds.), Handbook of Labor Economics, Volume 3B,NewYork and Oxford: Elsevier Science, North-Holland, 2485-2563. Myers, S. (1977). “Determinants of Corporate Borrowing,” Journal of Financial Economics 5, 147-75. Rajan, R. and L. Zingales (1995). ”What do we know about Capital Structure? Evidence from International Data,” Journal of Finance 50, 1421- 1460. Townsend, R. (1979). “Optimal Contracts and Competitive Markets with Costly State Verification,” Journal of Economic Theory 22,265-293. Warner, J. (1977). “Bankruptcy Costs: Some Evidence,” Journal of Fi- nance 32, 337-347.