Chapter 4 Agency Problems in Corporate Finance 4.1 Introduction the standard theory of co.apters 1 and 2 when we covered Modigliani-Miller As we discussed in the Ch apital structure that has been the mainstay of text- books is the trade-off theory This argues that the benefit of debt is the 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 didnt 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 difficulty in explaining firms'payout policy in the Modigliani- Miller framework extended to include taxes(the so-called"dividend puzzle")
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 textbooks is the trade-off theory. This argues that the benefit of debt is the tax shield and the cost is the deadweight costs of bankruptcy. The traditional 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 difficulty in explaining firms’ payout policy in the ModiglianiMiller 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 theor In a seminal paper Jensen and Meckling(1976) suggested that we should think of the firm as consisting of groups of securityholders with differing 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 To illustrate the first agency problem consider the shareholder-bondholder conflict. Given that shareholders obtain any payoff in excess of the debt repayment they (or managers acting in their interest) have an incentive te 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 confict. It can also arise in the context of the shareholder-manager problem The second agency problem that Jensen and Meckling(1976) stressed was the effort 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 effort 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 How 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 hu 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
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 differing 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. To illustrate the first agency problem consider the shareholder-bondholder conflict. Given that shareholders obtain any payoff 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 effort 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 effort 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 shareholders and managers. Grossman and Hart (1982) pointed to the incentive
4.2. THE RISK SHIFTING PROBLEM effects 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 Hlow "theory. If managers have access to large amounts of funds, i.e. free cash How, 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 effects 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 nanagers' 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 the 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
4.2. THE RISK SHIFTING PROBLEM 3 effects 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 effects 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 compensation which is summarized in Murphy (1998). Finally, there is also a large literature justifying debt as an optimal contract which uses an agency approach. The three pioneering papers in this literature 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 interest between equityholders and bondholders is that if managers act in equityholders’ 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
CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE win they might get $20,000 say. In that case they can pay off the S5, 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 off from gambling. The bondholders are of course worse off 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 risk 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 Let us go through this example in a little more detail before we develop a formal model 4.2.1 A Simple Example of Risk Shifting Firm has $1,000 in cash. It has bonds outstanding on which the next payment isS5.000 Firm does nothing Value of bonds s1. 000 Value of equity 0 Firm invests in project costing $1000(payoffs occur immediately so ignore Probability =0.02 Payoff= 20,000 Probability=0.98 Payoff= 0 Expected payoff=-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 Value of bonds =0 Value of equity =0 Therefore Expected value of bonds = 0.02 x 5,000= 100
4 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE win they might get $20,000 say. In that case they can pay off 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 off from gambling. The bondholders are of course worse off 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. Let us go through this example in a little more detail before we develop a formal model. 4.2.1 A Simple Example of Risk Shifting Firm has $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 (payoffs occur immediately so ignore discounting): Probability = 0.02 Payoff = 20,000 Probability = 0.98 Payoff = 0 Expected payoff = -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 Expected Value of equity =0.02 x 15,000= 300 otice that the bondholders are worse off by 900 and the equityholders are better off by 300. The NPV of the project was -600 so this is the majority of the drop in value with the other 300 coming from the 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 risk 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)20 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 (a,c)=U(c)-v(a) Further, the function U: R+- R is C and satisfies U(c>0 and U"(c)≤0. The principal's utility function V: R-R is C and satisfies V(c>0 nd"(c)≤0 Notice that the manager's consumption is assumed to be non-negative This is interpreted as a liquidity constraint or limited liability. Pcr Risk shifting iects, other things being equal. We can think of this as a ccurs when the manager has a convex reward schedule and fers riskier proj 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
4.2. THE RISK SHIFTING PROBLEM 5 Expected Value of equity = 0.02 x 15,000 = 300 Notice that the bondholders are worse off by 900 and the equityholders are better off by 300. The NPV of the project was -600 so this is the majority of the drop in value with the other 300 coming from the 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 consumption 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 C2 and satisfies U0 (c) > 0 and U00(c) ≤ 0. • The principal’s utility function V : R → R is C2 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
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 probabilit 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 Spla, sU(w(s)). Because the manager has limited liability and no personal resources,(s)≥0 We assume that the principal and agent both know all the parameters of the model, the cost function v(a), the possible outcomes R(s), the agent'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 p roject 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 SpLa, s)V(R(s-w(s), subject to an incentive constraint(IC) and an individual rationality or participation constraint (IR) pla, S (IC)∑。p(a,s)U((s)≥∑,P(b,s)U((s),b p(a,s)U((s)≥ 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 Suppose that the principal is risk neutral and the agent strictly risk averse Then the obvious solution is to offer the agent a fixed wage w(s)=w such that u(w)=i. The agent will be indifferent between all projects so it will be optimal for him to choose the project that maximizes the principals payoff, 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 efficient project Suppose that the agent is risk neutral and the principal strictly risk averse 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
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 P function U(c) and chooses the project a to maximize his expected utility s p(a, s)U(w(s)). Because the manager has limited liability and no personal 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), the agent’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 P (a, w(·)) to maximize his expected return 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)) ≥ u¯ 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. Suppose that the principal is risk neutral and the agent strictly risk averse. Then the obvious solution is to offer the agent a fixed wage w(s)= ¯w such that u( ¯w)=¯u. The agent will be indifferent between all projects so it will be optimal for him to choose the project that maximizes the principal’s payoff, 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 efficient project. Suppose that the agent is risk neutral and the principal strictly risk averse. 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 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)= maxR(s-T, 01, s, and the return to the principal is R(s)-(s)=min(R(s), r1,Vs With this payment structure, the entrepreneur chooses a to maximize his expected return ∑pa,s)m(s)=∑p(,)max{(s)-r,0 Suppose that the principal is restricted to offering an incentive scheme of this form. Then the(constrained) principal-agent problem max(a,r(a, s)V(minT, R(s))) r≥0 ∑、p(a,s)max{f(s)-r,0}≥∑,p(a,s)max{(s)-r,0},vs max R(s)-r,0} For any probability vector p=(p1, .,ps)let P()=∑ d A=∑P(R(a+1)-Ra) A distribution p is a mean-preserving spread of p if it satisfies one of the following equivalent conditions Proposition1 Suppose that∑、p,R(s)=∑。p,R(s). The following cona tion ≤∑。=04 (ii) for any non-decreasing function f: S-R with non-increasing difference∑spf(s)≤∑。Psf(s) (iii) p 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
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 offering 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} ≥ u¯ For any probability vector p = (p1, ..., pS) let P(s) = Xs σ=0 pσ and As = Xs σ=0 Pσ(R(σ + 1) − R(σ)). A distribution p0 is a mean-preserving spread of p if it satisfies one of the following equivalent conditions: Proposition 1 Suppose that P s psR(s) = P s p0 sR(s). The following conditions are equivalent: (i) Ps σ=0 Aσ ≤ Ps σ=0 A0 σ; (ii) for any non-decreasing function f : S → R with non-increasing differences P s p0 sf (s) ≤ P s psf (s) ; (iii) p0 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(, ) is a mean-preserving spread of P(b, ) Then, for any number r ∑p(a,s)max{R()-r,0≥∑p(,smax{B(s)-r,0 This follows immediately from the proposition and the fact that the functi f(s)= max(R(s)-r, 0 has non-decreasing differences. In other words the entrepreneur has a preference for risk(a preference for mean-preserving The principal on the other hand wants to maximize > pla, s)V(min(, R(s))) At any solution of the principal-agent problem, the participation constraint should be satisfied with equality: s P(a, s)w(s)= sp( a snax r,0=i. Thus, in the absence of the incentive problem the principal seeks to maximize ∑pa,sV(min{,R(s)) subject to p(a, s)max(R(s)-r,Of 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 S10.000 The firm does nothing
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 differences. In other words, the entrepreneur has a preference for risk (a preference for mean-preserving spreads). The principal on the other hand wants to maximize 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} = ¯u. 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} = ¯u. 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 The firm will go bankrupt The firms investment opportunity Invest $2,000 and receive return $11,000 with certainty(ignore discount- xpected return=-2,000+11,000=+89,000 E This is clearly a very attractive project. Is it worth the firm doing it? The firm does the project Value of bonds=$10000 Payoff 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 off 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- Thus, only if bondholders are willing to put up most of the money will the firm undertake the investment. However, bondholders may get very imperfect information. They may not be able to tell whether its this type of project or the type that we had in the previous example. As a result of this asymmetric 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 effort a that results in a probability distribution p(a, s)over the outcomes s. There is no investment required. The manager's utility function is U(c-v(a). The contract between the shareholder and the manager specifies a reward w(s) as a function of the state s. Limited liability implies that w(s)20. The manager will choose the effort that maximizes his expected utility >spla, s)U(w(s)-v(a).The shareholder chooses the incentive scheme w( to provide the manager with an incentive to pursue his(the shareholders)interests The interaction of the n and shareholder can be written principal-agent problem in which the shareholder chooses the effort level to
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 discounting). 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. Payoff 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 off to pay the money as a dividend. This example illustrates the conclusion that if business risk is held constant, any increase in firm value is shared among bondholders and stockholders. Thus, only if bondholders are willing to put up most of the money will the firm undertake the investment. However, bondholders may get very imperfect information. They may not be able to tell whether its this type of project or the type that we had in the previous example. As a result of this asymmetric 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 effort a that results in a probability distribution p(a, s) over the outcomes s. There is no investment required. The manager’s utility function is U(c)−ψ(a). The contract between 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 effort 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 effort level to
10 CHAPTER 4. AGENCY PROBLEMS IN CORPORATE FINANCE maximize his expected return subject to(IC) and(Ir) maxa()∑。p(a,s)[B(s)-u(s) (s)≥0,a≥0 p(a,s)U((s)-v(a)≥∑p(b,s)U((s)-v(b),vb (IR) sp(a,s)U((s)-v(a)≥元 We can use this model of effort 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 fit this into our present framework by representing the investment as effort that must be 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 effort. The new project will result in a probability distribution p which has a positive cost c. We assume that p dominates p in the sense of first-order stochastic dominance and ∑p(s)(s)->∑叭(s)B(s) (4.1) However, the entrepreneur will undertake the new project only if ∑p()max{(s)-r,0-c≥∑s)max{(s)-r,0(42) 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 effort(investment)on the part of the 4.4 Debt and Equity as Incentive Devices Grossman and Hart(1982) emphasizes the incentive effects 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 reputatio has been damaged. This is equivalent to adding a non-pecuniary benefit
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) ≥ u. ¯ We can use this model of effort to illustrate the so-called debt overhang problem, if an entrepreneur has a pre-existing debt he may not wish to undertake a project with positive net present value. It is easiest to fit this into our present framework by representing the investment as effort that must be 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 effort. The new project will result in a probability distribution p0 , which has a positive cost c0 . We assume that p0 dominates p in the sense of first-order stochastic dominance and X s p0 (s)R(s) − c0 > X s p(s)R(s). (4.1) However, the entrepreneur will undertake the new project only if X s p0 (s) max{R(s) − r, 0} − c0 ≥ 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 effort (investment) on the part of the entrepreneur. 4.4 Debt and Equity as Incentive Devices Grossman and Hart (1982) emphasizes the incentive effects of debt: a manager 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 another, 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
