Debt, bargaining, and credibility in firm–supplier relationships

ARTICLE IN PRESS Journal of Financial Economics 93 (2009) 382–399

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Journal of Financial Economics journal homepage: www.elsevier.com/locate/jfec

Debt, bargaining, and credibility in firm–supplier relationships$ Christopher A. Hennessy , Dmitry Livdan 1 Haas School of Business, University of California, Berkeley, CA 94720, USA

a r t i c l e i n f o

abstract

Article history: Received 8 December 2005 Received in revised form 23 January 2008 Accepted 15 May 2008 Available online 5 May 2009

We examine optimal leverage for a downstream firm relying on implicit (self-enforcing) contracts with a supplier. Performing a leveraged recapitalization prior to bargaining increases the firm’s share of total surplus. However, the resulting debt overhang limits the range of credible bonuses, resulting in low input quality. Optimal financial structure trades off bargaining benefits of debt with inefficiency resulting from overhang. Consistent with empirical evidence, the model predicts that leverage increases with supplier bargaining power (e.g., unionization rates) and decreases with utilization of non-verifiable inputs (e.g., human capital). & 2009 Elsevier B.V. All rights reserved.

JEL classification: G32 D21 J50 Keywords: Leverage Debt overhang Bargaining Implicit contracts

1. Introduction Why are firms with high taxable incomes reluctant to lever-up despite apparent tax benefits? Bankruptcy costs offer a potential explanation. However, direct costs of bankruptcy are relatively small. In a seminal paper, Titman (1984) argues that financial distress may entail large indirect costs. His model shows that high leverage potentially reduces sales of long-lived goods since customers anticipating a bankruptcy liquidation expect higher costs of parts and servicing.

$ We are grateful to Antonio Bernardo, Sugato Bhattacharyya, Patrick Bolton, Jonathan Levin, Christine Parlour, and Steven Tadelis for feedback. We thank an anonymous referee for suggesting the finite horizon model. We also thank seminar participants at Texas Finance Festival, London School of Economics, Tanaka Business School, and London Business School.  Corresponding author. Tel.: +1 510 643 1900. E-mail addresses: [email protected] (C.A. Hennessy), [email protected] (D. Livdan). 1 Tel.: +1 510 642 4733.

0304-405X/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jfineco.2008.05.006

Although Titman’s model offers a partial resolution of the capital structure puzzle, it is incomplete. First, many defaulting firms are reorganized rather than liquidated. Second, costs of distress are often quite large on the supply side. For example, United Airlines suffered losses of $700 million during the summer of 2001 due to pilot work stoppages.2 Not coincidentally, United filed for Chapter 11 bankruptcy protection shortly thereafter. Third, Titman’s model fails to explain why firms take on debt in the first place. Of course, one may appeal to tax benefits of debt outside his model. However, many firms assume high debt burdens despite having low taxable income. Again, commercial airlines provide a case in point. Finally, his model fails to explain the empirically observed positive relationship between leverage and worker unionization rates shown by Bronars and Deere (1991) and Matsa (2006). This paper offers a unified model explaining why financial distress entails large indirect supply side costs, even if defaulting firms are costlessly reorganized rather 2

See Lowenstein (2002) for an account.

ARTICLE IN PRESS C.A. Hennessy, D. Livdan / Journal of Financial Economics 93 (2009) 382–399

than liquidated; why firms with little or no taxable income assume high debt burdens; and why leverage is positively related to supplier bargaining power. The basic causal mechanisms are simple. We first show there is a bargaining benefit associated with creating debt overhang. To see this, consider a bargaining game with equally strong parties dividing eight slices of pie, with failure to reach agreement resulting in no pie for either. Each party receives four slices. Now suppose one party has the ability to sell two slices prior to bargaining over the remaining six slices. Under this strategy, the seller captures the value of five (¼ 2 þ 12  6) slices. A similar argument shows that the sale of debt also creates a bargaining benefit provided that cooperation between the firm and its supplier increases the value of the lenders’ claim. That is, there is a bargaining benefit to debt overhang in the sense of Myers (1977). We next show that strategic debt overhang creates agency costs for firms relying upon (implicit) relational contracts for the provision of incentives. This is because relational contracts rely upon the bilateral surplus shared by the firm and the agent to reward the payment of discretionary bonuses and rebates. The sale of surplus to a lender reduces bilateral surplus and necessarily reduces the range of credible (self-enforcing) discretionary payments. This compression of bonuses reduces incentives, efficiency, and profits. In fact, benefits and costs of debt are shown to represent two sides of the same coin: optimal leverage entails a tradeoff between bargaining benefits of debt overhang and efficiency costs. Firms with high (ex ante) bargaining power are most concerned about preserving efficiency while those with low bargaining power are most concerned about extracting surplus. Thus, optimal leverage is decreasing in firm bargaining power. To illustrate these effects, we consider a setting with repeated trade in which an agent (e.g., upstream firm or employee) privately observes his production costs.3 We depart from the traditional screening model (e.g., Laffont and Tirole, 1993) by assuming the quality of the input supplied by the agent cannot be verified by a court, necessitating reliance upon relational contracts. Although tradeoffs between rent extraction and efficiency are a feature of traditional screening models with verifiable quality, the tradeoffs in our model differ fundamentally. The traditional screening model endows the principal with all bargaining power ex ante. Inefficiency then arises from the need to pay informational rents to low-cost agents. In our model, the principal does not necessarily have full bargaining power ex ante. Rather, she performs a leveraged recapitalization prior to bargaining in order to increase her share of total surplus given limited bargaining power. Inefficiency then arises from the fact that debt overhang compresses the set of credible bonuses. The key difference between our model and existing relational contracting models, e.g., MacLeod and Malcomson (1989) and Levin (2003), is that we analyze optimal leverage.

3 The insights of the model carry over if one considers hidden actions rather than hidden information.

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The tradeoffs described are most similar to those derived by Dasgupta and Sengupta (1993) in a model featuring static moral hazard and verifiable output.4 Both models posit a bargaining benefit to debt. However, the costs arising from debt differ. As in Brander and Spencer (1989) and Dasgupta and Sengupta (1993) demonstrate a negative incentive effect arising from placing a principal and agent junior to a lender. In these models, incentives become muted because the agent’s output accrues to the lender in the event of default. In our relational contracting model, the distorting effect of debt persists despite the principal and agent having a senior claim to joint output each period. Further, we show that even non-defaultable debt can diminish the power of incentives. This is because an overhang problem exists whenever cooperation between the principal and agent causes an otherwise defaultable bond to become risk-free. Although the setting is different, the cause of the decline in cooperative behavior can be linked to the duopoly model of Maksimovic (1989). Both models incorporate debt into repeated games where failure to cooperate is punished by reversion to the worst possible subgame perfect equilibrium. In both models, debt inhibits cooperation if the lender captures some of the benefit from cooperation. The most important difference between the models can be found in the effect coming from debt. Our model illustrates that debt overhang limits a firm’s ability to provide incentives to agents. Maksimovic shows that debt overhang limits the stability of collusion. A second important difference between the models is that Maksimovic predicts that zero debt is optimal, whereas our model can generate interior optimum leverage ratios in the absence of tax shield benefits to debt or direct bankruptcy costs. We turn next to the empirical relevance of the model. A wide range of studies show the prevalence of implicit contracts. For example, Banerjee and Duflo (2000) present evidence that implicit contracts are frequently utilized in the customized software industry, with proxies for reputation (e.g., firm age) having significant predictive power in determining which party pays for overruns. Good-faith agreements are also pervasive in labor markets. Gillian, Hartzell, and Parrino (2005) find that less than half the firms in the ‘‘S&P’’ 500 had a comprehensive explicit employment agreement with their CEO. Relatedly, Hayes and Schaefer (2000) present evidence suggesting that implicit contracting explains a large portion of top executive pay. Implicit contracts are also used for rankand-file compensation. For example, the up-or-out promotion system is a widely used implicit incentive contract for young associates in law firms (see Gilson and Mnookin, 1990). Similarly, investment banks, consulting firms, and advertising agencies provide incentives through discretionary bonus payments that are based upon subjective measures of performance.

4 Bronars and Deere (1991) derive a bargaining benefit from debt relying on exogenous costs of default. Perotti and Spier (1993) illustrate a bargaining benefit to issuing debt ex post, in wage renegotiations, which is costly to the firm ex ante as workers demand risk premiums.

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Fig. 1. Timeline of basic model. The principal (P) is the manager of a public corporation. At the start of Period 1, P discovers a business opportunity requiring the input of an agent (A). At this time, and prior to contracting with A, P can issue a bond and distribute the proceeds as a dividend to shareholders. The bond face value c is due in Period 2. The debt market is perfectly competitive and the bond sells for DðcÞ. In Period 0, P contacts A and the two bargain over the signing bonus (w0 ) to be paid to A in exchange for his agreeing to become an employee. The signing bonus is determined in an alternating offers bargaining game with perfect information and constant costs of delay. Period 1 is the first round of potential bilateral trade. At the start of Period 1 P offers her employee a compensation package sufficient to satisfy A’s participation constraint. The compensation package for Period 1 consists of a fixed wage (w1 ) and a quality-contingent bonus b. Next, A privately observes his unit cost of increasing input quality, y. With cost information inhand, A chooses quality q. Next, P receives Period 1 cash flow equal to aq  bq2 . At the end of Period 1, P pays a discretionary bonus. At the start of the last period, P and A each choose between one of two strategies, ‘‘bargain’’ or ‘‘boycott.’’ Both P and A must bargain if bilateral trade is to occur in Period 2. If bargaining takes place, A will receive a wage equal to his outside option payoff of zero in Period 2. On the equilibrium path P pays A the promised bonus bðqÞ, both parties choose to bargain, and trade occurs in Period 2. However, if P fails to deliver the promised bonus, A punishes her by boycotting.

Consistent with our predictions, Bronars and Deere (1991) find that leverage is positively correlated with industry unionization rates. Matsa (2006) uses changes to state labor laws as a source of exogenous variation and finds that leverage increases in labor bargaining power. Finally, Kale and Shahrur (2006) find a positive relationship between leverage and concentration in supplier industries. This suggests the bargaining channel central to the model is operative. The particular agency cost of debt implied by the model is likely to be important in high-tech supply chains since issues of quality control are central. This is consistent with the evidence in Titman and Wessels (1984) that high-tech firms eschew debt. Further, since judicial verifiability is difficult when inputs are customized and/or complex, the model predicts that firms using specialized inputs will choose low debt. Consistent with this prediction, Banerjee, Dasgupta, and Kim (2008) show a negative relationship between leverage and reliance on specialized inputs.5 The model also predicts agency costs of debt are particularly high for humancapital intensive firms, since the performance of skilled workers is often subjective and output intangible. Consistent with this prediction, Qian (2003) reports a negative relation between leverage and human-capital intensity.6 Another prediction of the model is that highly levered firms will produce lower quality products. Rose (1988) finds that financial distress is associated with declining safety records at airlines. Maksimovic and Titman (1991) present additional evidence suggesting that financial distress causes lower product quality. A similar prediction is generated by the model developed by Maksimovic and Titman (1991) where debt creates a moral hazard problem

5

This evidence is also consistent with the model of Titman (1984). A recent paper by Berk, Stanton, and Zechner (2006) posits a complementary cost of debt. In their model, leverage prevents the firm from credibly insuring agents against human-capital risk. 6

in that a levered seller has less to lose from misleading consumers about product quality prior to purchase. In order to abstract from the theory of Titman (1984), we consider a downstream firm selling a non-durable good. In order to abstract from the theory of Maksimovic and Titman (1991), we assume that the quality of the final good is directly observed by the consumer prior to purchase. In our model, the decline in quality is not due to seller moral hazard. Rather, the decline in quality stems from the inability of the seller to provide incentives to suppliers. Thus, the model presented here offers a complementary causal mechanism explaining the observed negative relationship between leverage and product quality. The remainder of the paper is as follows. Section 2 presents the main arguments using a simple four-period model. Section 2.3 extends the basic model to an infinite horizon setting. Section 3 concludes. 2. Basic model This section illustrates the basic causal mechanisms using a stylized four-period model with a reduced-form endgame. Section 2.3 models the continuation-game explicitly and relaxes other simplifying assumptions. 2.1. Economic setting A timeline is provided in Fig. 1. The principal (P) is the manager of a public corporation. Her payoff is equal to that of shareholders. The corporation enters the model with zero debt, zero cash on hand, and enjoys frictionless access to equity and debt financing. At the start of Period 1, P discovers a business opportunity requiring the input of an agent (A). At this time, and prior to contracting with A, P can issue a bond and distribute the proceeds as a dividend to shareholders. The bond face value c is due in Period 2. This assumption

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regarding debt maturity ensures the lender has no claim to Period 1 cash flow.7 Despite this assumption, it will be shown that the long-term debt obligation has a negative effect on efficiency in Period 1. In contrast to our model, Brander and Spencer (1989) and Dasgupta and Sengupta (1993) consider settings with verifiable output where the lender has a senior claim to the output. They show that a senior debt obligation interferes with incentive provision by truncating the agent’s payoff in bad states of nature. Our maturity assumption rules out this effect. The debt market is perfectly competitive and the bond sells for D: In the event of default, lenders (L) have a senior claim to Period 2 cash flow, with no direct costs of default. The bond is public and cannot be renegotiated nor called, and contains a covenant prohibiting additional debt. Since public debt can be held by numerous bondholders, communication, and coordination costs are high. Further, as argued by Smith and Warner (1979), it is difficult to renegotiate public debt since unanimity is required to change any core provision of a public bond.8 In Period 0, P contacts A and the two bargain over the signing bonus (w0 Þ to be paid to A in exchange for his agreeing to become an employee. Equivalently, one can think of A as being an upstream supplier being asked to sign an exclusivity arrangement in exchange for a fee. The signing bonus is determined in an alternating offers bargaining game with perfect information and constant costs of delay.9 Rubinstein (1982) shows that under technical conditions, the unique subgame perfect equilibrium of such a game entails immediate agreement with P receiving her impasse payoff plus a share L 2 ½0; 1 of the total surplus that P and A stand to gain from reaching agreement.10 The parameter L depends on relative costs of delay, with L being high if P has relatively low bargaining costs. Finally, it is worth noting that although L stands to benefit from cooperation between P and A, this benefit does not enter the pool of bilateral surplus available to be divided between P and A at the time they bargain. For simplicity, A’s impasse payoff is normalized to zero. Period 1 is the first round of potential bilateral trade. Since there is no slavery, at the start of Period 1 P must offer her employee a compensation package sufficient to satisfy A’s participation constraint. The compensation package for Period 1 consists of a fixed wage (w1 ) and a qualitycontingent bonus b  0. The non-negativity constraint on b is relaxed in the next section. Since the fixed wage is independent of quality, payment of w1 can be enforced by a court. The bonus is discretionary. Since P is the only party called upon to make discretionary payments, it is optimal for her to have all bargaining power ex post, as we 7 Since profits from relational trade in Period 1 are not verifiable, there can be no covenant requiring retention of those profits. 8 Empirically, Gilson, John, and Lang (1990) and Asquith, Gertner, and Scharfstein (1994) show that public debt is the best predictor of failed private workouts. 9 The bargaining costs are direct legal costs and do not stem from time value of money. 10 The impasse payoff is defined to be the payoff from perpetual disagreement. The technical conditions require that costs of delay are sufficiently small and unequal.

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have assumed here. However, the assumption that P can actually be given full ex post bargaining power is not necessary for our results. Rather, P must simply hold some bargaining power ex post in order for cooperation between P and A to create positive spillovers for L. Next, A privately observes his unit cost of increasing input quality. Unit costs are drawn from Y  fyL ; yH g; with 0oyL oyH and pi 2 ð0; 1Þ denoting the probability of yi : With cost information in-hand, A chooses q  0: Quality is observed by all parties, but is not verifiable by a court. Next, P receives Period 1 cash flow equal to aq  bq2 ; where a4yH and b40: Under these assumptions, firstbest quality entails qFB ðyÞ  ða  yÞ=2b.

(1)

At the end of Period 1, P pays a discretionary bonus. Consistent with the assumption that quality is not verifiable, the cash flow attributable to the quality of the agent’s input is not verifiable by a court. If this cash flow stream were verifiable, the court could deduce q and a quality-contingent explicit contract could be enforced. In reality, however, it is impossible to compute the cash flow attributable to the quality of each particular input. At the start of the last period, P and A each choose between one of two strategies, ‘‘bargain’’ or ‘‘boycott.’’ Both P and A must bargain if bilateral trade is to occur in Period 2. If bargaining takes place, A will receive a wage equal to his outside option payoff of zero in Period 2. The density function for the firm’s cash flow with trade is g whereas the density function under no-trade is h: The minimum cash flow in Period 2 is zero and the maximum is P. The corresponding cumulative density functions are smooth and satisfy the first-order stochastic dominance relationship GðpÞoHðpÞ for all cash flows p 2 ð0; PÞ: The expected value of Period 2 cash flow under trade and no-trade are denoted EðpjTÞ and EðpjNTÞ, respectively. In this simple coordination game, trade and no-trade are both Nash equilibrium outcomes. On the equilibrium path P pays A the promised bonus bðqÞ; both parties choose to bargain, and trade occurs in Period 2. However, if P fails to deliver the promised bonus, A punishes her by boycotting.11

2.2. The fundamental tradeoff We compute first the values received by P and A at date zero, when they bargain over the signing bonus w0 . A’s outside option has value zero. If bargaining were to break down, P would have a continuation value equal to the value of levered equity at the start of Period 2 under notrade. This value is denoted as V 2 ðcÞ and is computed as V 2 ðcÞ ¼

Z

P

ðp  cÞhðpÞ dp.

(2)

c

Correspondingly, we let V 2 ðcÞ denote the value of levered equity at the start of Period 2 with cooperative trade: 11 The equilibrium concept is perfect public equilibrium which demands that play following each history be a Nash equilibrium.

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V 2 ðcÞ ¼

Z

P

ðp  cÞgðpÞ dp.

(3)

c

Therefore, if they can reach agreement in Period 0, P and A anticipate total bilateral surplus (S) equal to their combined continuation values on the cooperative equilibrium path less the value of their no-trade payoffs. Letting the subscript i index the agent’s costs, we have SðcÞ ¼ sðcÞ þ ½V 2 ðcÞ  V 2 ðcÞ, X pi ½ða  yi Þqi  bq2i . sðcÞ ¼

(4)

i2fL;Hg

The first term s entering the equation for total bilateral surplus is the expected surplus from trade in Period 1. The second term is the gain captured by levered equity from cooperative trade in Period 2. Using the Rubinstein (1982) bargaining model, the payoffs to P and A at date zero are equal to their impasse payoffs plus a share of total bilateral surplus. The date zero payoffs to P and A are, respectively, denoted as V 0 ðcÞ ¼ V 2 ðcÞ þ LSðcÞ, U 0 ðcÞ ¼ ð1  LÞSðcÞ.

(5)

This particular division of total bilateral surplus is achieved by setting w0 ðcÞ ¼ U 0 ðcÞ: To see this, recall that as an employee of the firm A receives his outside option payoff of zero in Periods 1 and 2. Anticipating his weak bargaining position ex post, A demands a high signing bonus. When choosing the face value of debt, P maximizes the cum-dividend value of equity in Period 1. This is equal to

(6)

Eq. (6) explains why the downstream firm would be willing to create overhang despite the efficiency costs. In particular, note that P only captures a fraction L of any efficiency gain. However, P captures the entire value of the debt issuance. In other words, debt issuance entails a concentrated benefit to P and an efficiency cost that is shared with A. We now rewrite P’s objective function in terms of debt overhang. Since there are no direct costs of default, the respective debt values under trade and no-trade are DðcÞ ¼ EðpjTÞ  V 2 ðcÞ, DðcÞ ¼ EðpjNTÞ  V 2 ðcÞ.

(7)

Formally, debt overhang, denoted D, is equal to the increase in debt value attributable to cooperative trade between P and A:

DðcÞ  DðcÞ  DðcÞ.

(8)

It follows that D is increasing in the face value of debt, with

D0 ðcÞ ¼ HðcÞ  GðcÞ40 8c 2 ð0; PÞ.

SE : b  V 2 ðcÞ  V 2 ðcÞ ¼ EðpjTÞ  EðpjNTÞ  DðcÞ.

(9)

Substituting Eqs. (7) and (8) into P’s ex ante objective function one obtains V 1 ðcÞ ¼ ð1  LÞDðcÞ þ LsðcÞ þ ½ð1  LÞEðpjNTÞ þ LEðpjTÞ. (10)

(11)

From the SE constraint it follows that overhang diminishes credibility by depleting the pool of surplus available to reward fulfillment of implicit contracts. This overhang effect is indirect. By construction, P has a senior claim on the cash flows generated from trade in Period 1. Nevertheless, the efficiency of trade in Period 1 is diminished by debt overhang. The next subsection provides a complete characterization of the effect of debt on Period 1 surplus. However, in order to characterize the optimal debt level it is sufficient to note that s is decreasing in c: Differentiating (10) with respect to c it follows that at an interior optimum c : ð1  LÞD0 ðc Þ þ Ls0 ðc Þ ¼ 0, ð1  LÞD00 ðc Þ þ Ls00 ðc Þo0.

V 1 ðcÞ  DðcÞ þ V 0 ðcÞ ¼ DðcÞ þ V 2 ðcÞ þ L½sðcÞ þ V 2 ðcÞ  V 2 ðcÞ.

Eq. (10) highlights the fundamental tradeoff involved in choosing the debt level. The first term captures the bargaining benefit coming from debt overhang, which is increasing in c. Further, this term is most important for a firm that is in a weak bargaining position ex ante. On the other hand, there is an efficiency cost to debt overhang in that bilateral surplus ðsÞ from trade in Period 1 is decreasing in c. Concern over efficiency is most important for a firm that is in a strong bargaining position ex ante. To see why debt overhang induces inefficiency, note that P will only pay the promised bonus if it is selfenforcing. A contract is self-enforcing if all parties prefer delivering promised discretionary payments to reneging. Self-enforcement (SE) demands that

(12)

Applying the implicit function theorem to the first-order condition, we find that optimal debt is decreasing in ex ante bargaining power, with @c D0 ðc Þ  s0 ðc Þ ¼ o0. @L ð1  LÞD00 ðc Þ þ Ls00 ðc Þ

(13)

Proposition 1 summarizes this analysis. Proposition 1. If the firm has all bargaining power ex ante (L ¼ 1), zero debt is optimal. If the firm has no bargaining power ex ante (L ¼ 0), optimal debt face value is c ¼ P. At an interior optimum, optimal debt face value is decreasing in ex ante bargaining power. 2.3. The optimal self-enforcing contract This subsection characterizes the optimal self-enforcing contract, confining attention to the case of interest where the self-enforcement constraint is binding. To this end, we adopt Assumption 1:

yL



a  yL 2b



  a  yH þ ðyH  yL Þ 2b

¼ EðpjTÞ  EðpjNTÞ.

(14)

Assumption 1 allows us to treat the unlevered firm as a convenient yardstick since the condition ensures FB that such a firm is just able to implement ðqFB L ; qH Þ with

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a self-enforcing contract. To see this, note that incentive compatibility demands the low-cost type be paid his costs plus the informational rent he could capture if he were to deviate and produce qH . Thus, the left side of Eq. (14) measures the required bonus to the low-cost type if the firm were to implement first-best. Under the stated condition, such a bonus is only credible for a firm with zero debt. We turn next to contract details. At the start of Period 1, P designs a contract that maximizes the Period 1 surplus, since he holds all bargaining power at this point in time. In order to push A down to his outside option payoff of zero, P offers the following fixed wage: X  pi ½bi  yi qi . (15) w1 ¼  i2fL;Hg

Effectively, this fixed payment allows P to recoup the expected informational rent received by A.12 The principal chooses a surplus-maximizing quality schedule ðqL ; qH Þ, with corresponding bonus payments   ðbL ; bH Þ; subject to incentive compatibility conditions and a self-enforcement constraint. Without loss of generality,  it is assumed that b ¼ 0 for all qefqL ; qH g. P solves the following program:13 max

fqL ;qH ;bL ;bH g

s.t.

sðqL ; qH Þ IC i : bi  yi qi  bj  yi qj IC 0i : bi  yi qi  0

8iaj,

8i,

SEi : bi  EðpjTÞ  EðpjNTÞ  DðcÞ

8i.

(16)

The first constraint is a standard incentive compatibility (IC) condition. The second constraint, analogous to an interim participation constraint, ensures A does not choose some qefqL ; qH g, e.g., q ¼ 0: The self-enforcement constraint ensures promised bonus payments are credible. Adding the constraints IC L and IC H and canceling terms one obtains ðyH  yL ÞðqL  qH Þ  0 ) qL  qH .

(17)

Thus, any incentive compatible contract must entail (weakly) higher quality by the low-cost type. From this result and the IC L constraint it follows that bL  bH þ yL ðqL  qH Þ  bH .

(18)

Thus, in solving for the optimal contract we can replace the SEH constraint with qL  qH . Next, we note that an optimal contract gives zero rent to the high-cost type,  with bH ¼ yH qH : To see this, note that the IC L constraint demands bL  yL qL  bH  yL qH  bH  yH qH .

(19)

IC 0H

is slack, so too is the Therefore, if the constraint constraint IC 0L : In this case it would be possible to reduce bL and bH by the same infinitesimal amount and satisfy all constraints. This contradicts the working premise that self-enforcement is a binding constraint. 12 The fact that the fixed wage is negative is an artifact of normalizing the agent’s outside payoff to zero. 13 We assume the probability of high cost is sufficiently high such that P wants the high-cost type to produce.

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Finally, it must be the case that IC L is binding in an optimal contract. If not, the first inequality in Eq. (19) would be strict and the constraint IC 0L would also be slack. It would then be possible to lower bL by an infinitesimal amount and satisfy all constraints. This contradicts the working premise that self-enforcement is a binding constraint. To summarize the analysis thus far, an optimal contract entails the following bonus scheme: 

bH ¼ yH qH , 

bL ¼ yL qL þ ðyH  yL ÞqH .

(20)

This bonus scheme respects all incentive constraints provided that qL  qH : Further, the SEH constraint is redundant provided that qL  qH and SEL are satisfied. Thus, we can restate the program as max

sðqL ; qH Þ

fqL ;qH g

s.t.

SEL : yL qL þ ðyH  yL ÞqH  EðpjTÞ  EðpjNTÞ  DðcÞ qL  qH .

(21)

Proposition 2 shows there is a transparent relationship between debt overhang and quality. Proposition 2. If c is sufficiently small or if yL =yH  pL ; the optimal contract is fully separating with " # pH yL  FB DðcÞ, qL ¼ qL  2 pH yL þ pL ðyH  yL Þ2 " # pL ðyH  yL Þ DðcÞ. (22) qH ¼ qFB H  2 pH yL þ pL ðyH  yL Þ2 If c is sufficiently large and yL =yH 4pL ; the optimal contract entails pooling both types at q ¼

EðpjTÞ  EðpjNTÞ  DðcÞ

yH

.

(23)

Proof. See Appendix A. In a standard screening model, where q is verifiable in a court, the output of the low-cost type would be set equal to first-best.14 However, as argued by Levin (2003), selfenforcing contracts entail a different set of tradeoffs. In a standard screening model, the principal trades efficiency against extraction of informational rents. In the present model, the principal attempts to maximize efficiency ex post subject to the constraint that discretionary payments must be credible. Appendix A shows that when the contract entails separation we have 0  @s 2bpH ðqFB H  qH ÞD ðcÞ ¼ o0. @c ðyH  yL Þ

(24)

When the contract entails pooling we have 0 FB  @s 2b½pH qFB H þ pL qL  q D ðcÞ ¼ o0. @c yH

14

See Laffont and Tirole (1993) for a discussion.

(25)

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Fig. 2. Timeline of extended model. In the extended model, the principal (P) has multiple product lines. For those product lines where A is not needed to supply inputs, cash flows (xt ) are i.i.d. random variables drawn from an exponential distribution with mean one. The other source of profits for P comes from selling the output of A. In Period 0, prior to bargaining with an agent (A), P has the option to issue a consol bond with coupon c. The bond cannot be renegotiated or called, and a covenant prohibits additional debt. The proceeds raised from the debt flotation are used to finance a dividend payment to shareholders prior to bargaining over the signing bonus (w0 ). Next, P makes contact with A and they bargain over the discounted value of the pool of bilateral surplus that will be generated by virtue of reaching agreement. The quality of the output produced by A in Period t is denoted qt . Quality is observable but non-verifiable. Cash flow from relational trade accrues directly to P and is equal to aqt  bq2t . This cash flow is non-verifiable. The cost of production incurred by A is yt qt . The cost yt is an i.i.d. random variable drawn from a uniform distribution on ½y; y. After privately observing yt , A chooses qt . At the start of each period, P first observes xt and decides whether to pay c or default. If P continues, then P and A play a coordination game in which each chooses ‘‘bargain’’ or ‘‘boycott.’’ After bargaining takes place, A privately observes yt and chooses qt : Upon observing qt ; the party with discretion chooses whether to deliver bonus payment bt . In the event of default, lender (L) becomes the new owner of the firm. There are no costs of default except for a one-period suspension of relational trade. Post-default, L also has the ability to issue debt in order to increase his share of total surplus relative to A. Due to the stationarity of the economic environment, L will choose the same coupon as did P when he reorganizes the firm.

3. Extended model This section extends that of the previous section along five dimensions. First, we consider an infinite horizon setting and model the continuation games explicitly. Second, we allow for alternative assumptions regarding ex post bargaining power. Third, the lender is allowed to recontract with the agent in the event of default. Fourth, we consider a continuum of cost types. Finally, we do not restrict the sign of discretionary payments. A positive value of b is interpreted as a bonus and a negative value is interpreted as a rebate.

3.1. Economic setting To examine the link between debt overhang and selfenforcing contracts in an infinite horizon setting, we extend the models of MacLeod and Malcomson (1989) and Levin (2003) who analyze relational contracts for unlevered firms. An essential difference is that their papers treat outside options as exogenous. In the present model, P’s outside option value depends upon leverage. Further, their models are silent on optimal leverage and the use of debt as a bargaining tool. A timeline for the extended model is provided in Fig. 2. Time is discrete and all parties share the discount factor d 2 ð0; 1Þ: In the extended model, P has multiple product lines. For those product lines where A is not needed to

supply inputs, cash flows (xt ) are i.i.d. random variables drawn from an exponential distribution with mean one.15 The other source of profits for P comes from selling the output of A. Prior to bargaining with A, P has the option to issue a consol bond with coupon c: The bond cannot be renegotiated or called, and a covenant prohibits additional debt. In the event of default, L becomes the new owner of the firm. There are no costs of default except for a oneperiod suspension of relational trade. Post-default, L also has the ability to issue debt in order to increase his share of total surplus relative to A.16 Due to the stationarity of the economic environment, L will choose the same coupon as did P when he reorganizes the firm.17 The proceeds raised from the debt flotation are used to finance a dividend payment to shareholders prior to bargaining over the signing bonus (w0 ). Next, P makes contact with A and they bargain over the discounted value of the pool of bilateral surplus that will be generated by

15

An exponential distribution is assumed for the sake of tractability

only. 16 If the agent was also a public company, it would also have an incentive to issue debt during the reorganization period. This would generate an interesting tragedy-of-the-commons as both firms lever-up with the goal of capturing surplus. 17 The one-period suspension of trade is needed to ensure stationarity of the coupon. Without this assumption, L would be choosing a coupon knowing this period’s x value is particularly low.

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virtue of reaching agreement. Again, L denotes the bargaining power of P at the time A is hired. The quality of the output produced by A in Period t is denoted qt : Quality is observable but non-verifiable. Cash flow from relational trade accrues directly to P and is equal to aqt  bq2t : Again, this cash flow is non-verifiable. The cost of production incurred by A is yt qt : The cost yt is an i.i.d. random variable drawn from a uniform distribution on Y  ½y; y where y 40 and y  1 þ y oa:18 Since the monotone hazard rate property is satisfied, there would be full separation of types in the traditional screening model which assumes q is verifiable. After privately observing yt ; A chooses qt 2 Q : The periodic surplus ðsÞ from relational trade is equal to expected cash flow less costs incurred by A: s¼

Z

y

½ða  yÞqðyÞ  bq2 ðyÞ dy.

(26)

y

If the first-best quality schedule (1) were implemented, periodic surplus would be #  " 3 1 y  y3 sFB  . (27) a2  aðy þ yÞ þ 3 4b The bonus payment is a function b : Q ! R: If the implicit contract calls for b  0; P has discretion whether to pay the bonus. If the contract calls for bo0; then A has discretion regarding whether to pay the rebate. Due to the stationarity of the economic environment, there is no loss in generality in confining attention to stationary agreements. In particular, for all t prior to default, a stationary agreement calls for bt ¼ b for t  0 and wt ¼ w for t  1. The signing bonus w0 need not equal w; however. At the start of each period, P first observes xt and decides whether to pay c or default. If P continues, then P and A play a coordination game in which each chooses ‘‘bargain’’ or ‘‘boycott.’’ If either chooses boycott, no trade takes place in the period. If P and A both choose bargain, P receives a fraction l 2 ½0; 1 of the periodic surplus.19 The parameter l is assumed to be exogenously fixed by technology. After bargaining takes place, A privately observes yt and chooses qt : Upon observing qt ; the party with discretion chooses whether to deliver bt. At this point we note that ex ante bargaining power (L) and ex post bargaining power (l) need not be equal, although the model accommodates this possibility. In seminal work, Williamson (1985) argues that the move from spot market transactions to enduring relationships is often accompanied by a ‘‘fundamental transformation’’ in bargaining power.20 For example, Hart (1995) argues that shifts in residual control rights ex post alter bargaining power. Relatedly, Masten (1988) argues that employers, as 18 If the cost shocks of A were not independent, the analysis would become considerably more complicated. See the discussion of the ratchet-effect in Laffont and Tirole (1993). 19 Levin (2003) assumes that P and A can set the ex post sharing convention in the original implicit contract. However, a verbal commitment to be weak ex post may be vulnerable to opportunism. 20 For example, an academic is much more likely to successfully negotiate a high research budget before he/she has signed on the dotted line, rather than after.

389

such, enjoy the privilege of authority, which translates into bargaining power. Our objective is to characterize the maximum degree of cooperation feasible under self-enforcing contracts and the effect of debt on the feasible set. To this end, we rely on a result established by Abreu (1988) for infinitely repeated games with discounting. Abreu shows the maximum degree of cooperation feasible is that which emerges when deviations are punished by reversion to the worst possible subgame perfect equilibrium. In other words, harsh punishments of deviations, which only occur off the equilibrium path, induce greater cooperation on the equilibrium path.21 Here the worst possible subgame perfect equilibrium is for P and A to play boycott in each period following any party reneging on b. Further, in the worst possible subgame perfect equilibrium, the punishment phase continues after a default by P. In particular, off the equilibrium path, L and A are expected to play boycott in each period following a default if any party has ever reneged on a bonus.22 In the models of Brander and Spencer (1989) and Dasgupta and Sengupta (1993), senior debt interferes with incentive provision since all cash flow accrues to the lender in the event of default. The stated timing assumptions deliberately preclude this effect. In an arbitrary period t; P pays periodic debt service before A produces anything. Once the periodic debt payment is made, P has a senior claim on the corresponding period’s cash flow. Conventional wisdom holds that debt interferes with supplier relationships in a direct manner: ‘‘Suppliers do not want to do business with a highly levered firm fearing they will not be paid if default occurs.’’ This is equivalent to arguing that suppliers are reluctant to accept a junior debt claim. Since there is nothing new in claiming that senior debt crowds out junior debt, the present model deliberately rules out this story as well. In particular, the discretionary payment bðqt Þ is to be paid in period t, prior to the next coupon which comes due at the start of period t þ 1. Therefore, when P and A trade in period t, they recognize that bðqt Þ is senior to the next debt payment. Nevertheless, it will be shown that the future debt obligation crowds out the bonus payment, despite the latter enjoying seniority. 3.2. The fundamental tradeoff revisited Let V  denote the cum-dividend value attained by equity accounting for the dividend financed by the debt flotation. Let V 0 and U 0 denote the values attained by P and A after bargaining over the signing bonus. Let V and U denote the value of the claims held by P and A at the start of future periods (t  1) on the equilibrium path, prior to a default. Finally, let V, D, and U denote the value of the 21 This reasoning is also the basis for the topsy-turvy principle in industrial organization which states that the credible threat of intense competition can sustain collusion. See Shapiro (1989). 22 To the extent that one views L as being a less credible punisher, the case against debt finance would be even stronger since A would anticipate relief post-default. This would diminish A’s incentive to fulfill implicit contracts and thus reduce efficiency on the equilibrium path.

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claims held by P, L, and A, respectively, in the event of a permanent suspension of trade. Without loss of generality, it is assumed that the only source of profits for A is supplying inputs to P, which implies U ¼ 0. The total pool of bilateral surplus available to P and A at the time they bargain over the signing bonus is S  V þ U  V: The signing bonus is set such that each player gets his impasse payoff plus a share of bilateral surplus. Thus, V 0 ¼ V þ LS, (28)

U 0 ¼ ð1  LÞS.

In order to achieve the correct splitting of surplus ex ante, the signing bonus is determined by w0 ¼ w þ U 0  U.

(29)

For example, if the agent will be in a weak position ex post, with l high, then U will be low relative to U 0 and A demands a large signing bonus. Let R denote the total discounted value of all future surplus created by relational trade including the discounted value of surplus from trade between P and A (prior to default) and between L and A after default. It follows that R  sFB =ð1  dÞ: The following identity states that the value of the claims held by P, A, and L sum up to the value of cash flow generated by the stand-alone production line plus the value created by relational trade VðcÞ þ UðcÞ þ DðcÞ 

1 þ RðcÞ. 1d

(30)

We now rewrite P’s ex ante maximand (V  ) in terms of debt overhang. To this end, the value of debt off the equilibrium path is computed as a residual, with DðcÞ ¼

1  VðcÞ. 1d

(31)

Using identities (30) and (31), P’s maximand can be expressed as V  ðcÞ  DðcÞ þ V 0 ðcÞ ¼ ð1  LÞDðcÞ þ LRðcÞ þ

1 . 1d

(32)

Eq. (32) is the infinite horizon analog of the objective function in the basic model (10). Once again, optimal debt trades off the bargaining benefit from debt overhang against distortions of relational trade. Firms in a weak bargaining position are more concerned about generating overhang, while those in a strong bargaining position are more concerned about maintaining efficient trade. This hints at the possibility, confirmed numerically, that the optimal debt coupon is decreasing in ex ante bargaining power. 3.3. Valuation of contingent-claims We begin by computing payoffs to all parties off the equilibrium path, in the event that relational trade is permanently suspended. We have established that U ¼ 0; while D can be computed as a residual. To compute V; note that if P and A break off trade, P only receives gross cash flow of x each period. Since x has the positive real line as a support, there exists a critical value of the coupon e c

(to be determined) such that debt becomes defaultable if and only if c4e c. Thus, ce c)V ¼

1c . 1d

(33)

Next we compute P’s reservation value V assuming that default occurs at some xd 40, where xd is defined implicitly by a limited liability condition: xd  c þ dV ¼ 0.

(34)

From the limited liability condition it follows that Z 1 V¼ ½x  c þ dVex dx ¼ ½dV  c þ 1 þ xd exd ¼ exd . xd

(35) Since lnðVÞ ¼ xd ; we can rewrite the limited liability condition, arriving at an equation defining V implicitly as c4e c ) dV  ln V ¼ c.

(36)

Since levered equity value is continuous in the coupon, e c can be determined by substituting the equity value from Eq. (33), with zero default risk, into Eq. (36). It follows that off the equilibrium path debt becomes risky at e c ¼ d: Recall that ex post, P captures ls in expected value each period from relational trade, with A capturing the remainder. In order to achieve this split, the fixed wage must satisfy

ls ¼

Z

y

½aqðyÞ  bq2 ðyÞ  bðqðyÞÞ dy  w.

(37)

y

Note that the first term on the right side of Eq. (37) is the expected cash flow accruing to P net of the bonus. If this value exceeds ls; then P and A set w40 in order to arrive at the appropriate division of periodic surplus ex post. On the equilibrium path, P takes into account the value of relational trade in making her default decision. When ls40; default is discouraged. Following the same reasoning as that applied for computing claim values off the equilibrium path, it follows that c  ls  d ) V ¼

1  c þ ls ; 1d

U¼

ð1  lÞs ; 1d

D¼

c . 1d (38)

If c  ls4d, there exists an xd 40 such that P would find it optimal to default if xt oxd . Using the same reasoning as that applied when computing V, levered equity value on the equilibrium path is defined implicitly as c  ls4d ) dV  ln V ¼ c.

(39)

Conveniently, for defaultable debt the probability of no-default, denoted r; is just equal to V: The value of A’s claim ex post consists of the value he receives in the event of no-default this period, plus the value of his claim in the event of default: c  ls4d ) U ¼ r½ð1  lÞs þ dU þ ð1  rÞdU 0 )U¼

rð1  lÞs þ ð1  rÞdU 0 . 1  rd

(40)

The value of debt consists of the value L receives in the event of no-default this period, plus the value of his claim in the event of default. In the event of default, L receives

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the operating cash flows of the firm in the current period plus the same ex ante payoff as attained by A, with the latter quantity being discounted. Thus, c  ls4d ) D ¼ r½c þ dD þ ð1  rÞ½Eðxjx  xd Þ þ dV   )D¼

rc þ ð1  rÞ½Eðxjx  xd Þ þ dV   . 1  rd

(41)

This analysis allows us to identify conditions such that debt overhang is zero, summarized in Lemma 1.

with high values of S being necessary to sustain high quality. Finally, Lemma 2 indicates that any implementable quality schedule must be weakly decreasing in A’s cost. Lemma 1 describes the bonus schedule that can be used to elicit the agent’s private information. Lemma 3. If q is weakly decreasing in the agent’s cost, then  the schedule b is sufficient to ensure incentive compatibility (42), where

Lemma 1. If c  d or l ¼ L ¼ 0; then D ¼ D: 

Proof. Under the first condition, there is no default risk and D ¼ D ¼ c=ð1  dÞ: Under the second condition, reversion to no-trade has no effect on the default probability. Further, lender recoveries in default are unaffected by reversion to no-trade. & Lemma 1 tells us that a necessary condition for generating some debt overhang, and with it a bargaining benefit, is that the firm must have some bargaining power ex ante or ex post. If l ¼ L ¼ 0; attempts to capture surplus via debt issuance are futile.

391



b ðqðyÞÞ  b ð0Þ þ yqðyÞ þ

Z

y

qðtÞ dt y





b ðqÞ  b ð0Þ

8qeQ m .

Proof. See Appendix B. Lemma 1 states that the bonus consists of a constant  b ð0Þ, plus A’s cost, plus an informational rent that is decreasing in the revealed y. It is easy to verify that the lowest bonus is at q ¼ 0: 



inf b ðqÞ ¼ b ð0Þ.

(46)

q

It may also be verified that for an arbitrary type y23: 3.4. The set of credible agreements 

In order for a particular quality schedule q to be implementable by the relational contract ðw; bÞ, the quality schedule must satisfy the following incentive compatibility condition:



b ðqðyÞÞ ¼ b ðqðyÞÞ þ

qðyÞ 2 arg max bðqÞ  yq q2Q

8y 2 Y .

(42)

In a standard screening model, the agent is constrained to choose qt from a menu Q m , where Q m  fe q 2 Q : 9y 2 Y s.t. e q ¼ qðyÞg.

(43)

In the current model, A is also free to choose any level of quality in the complement of Q m denoted Q cm : Finally, the agreement must be self-enforcing, with neither party being called upon to make a discretionary payment exceeding the discounted value they retain by avoiding permanent reversion to no-trade. The respective self-enforcement conditions for P and A are SEP :

sup bðqÞ  dðV  VÞ.

SEA :

 inf bðqÞ  dU.

q2Q q2Q

(44)

Lemma 2 shows bilateral surplus plays a critical role in maintaining good-faith agreements.

y

y qðyÞ þ

Z

y

qðtÞ dt  dS,

y

q0 ðyÞ  0

8y 2 Y.

(45)

Proof. See Appendix B. The first necessary condition in Lemma 2 provides a critical insight. When good-faith agreements are used to provide incentives, bilateral surplus is a valuable resource,

(47) 

From the fact that q0 ðtÞ  0 it follows that b is highest for the low-cost type: 

sup b ðqÞ ¼ b ðqðyÞÞ.

(48)

q

In order to isolate the effect of debt overhang, the analytical results utilize Assumption 2 :

y qFB ðyÞ þ

Z

y y

qFB ðyÞ dy ¼



d

 sFB .

1d

(49) Assumption 2 is the direct analog of Assumption 1 from the basic model, ensuring there is just enough surplus such that the first-best schedule ðqFB Þ could be implemented using a self-enforcing contract if c ¼ 0. In fact, Proposition 3 uses this equality to show that if the conditions of Lemma 1 are indeed satisfied, and there is zero debt overhang, then first-best can be implemented. Proposition 3. If c  d or l ¼ L ¼ 0; implying D ¼ D; then condition (49) ensures the first-best quality schedule qFB can  be implemented using the bonus schedule b with 

Lemma 2. A quality schedule q : Y ! Q generating bilateral surplus S can be implemented only if

tq0 ðtÞ dt.

y



IC :

Z

b ð0Þ ¼ ð1  lÞdsFB =ð1  dÞ.

(50)

Proof. See Appendix B. There is one noteworthy detail regarding the relational contract described in Proposition 3. In particular, discretion over b must be shifted towards the party who will suffer most from reversion to no-trade. For example, if l ¼ 1; then only P stands to lose from reversion to 23 Here we have used the first-order condition for incentivecompatibility. See Eq. (64).

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0.7 First−best Pooling Partial pooling

0.6

Quality

0.5 0.4 0.3 0.2 0.1 0 2

2.1

2.2

2.3

2.4

2.5 2.6 Cost

2.7

2.8

2.9

3

Fig. 3. Agent’s cost and quality. This figure illustrates Proposition 5, plotting quality, q, as a function of the cost parameter, y. The solid line is the first-best schedule. The dotted line represents the q schedule that is implemented for intermediate levels of debt overhang which result in partial pooling. The dashed line represents the q schedule that is implemented for high levels of debt overhang which result in full pooling.

no-trade. Consequently, discretion for the bonus would  then reside with P, with b  0 and b ð0Þ ¼ 0: Proposition 4 establishes a transparent causal relationship between debt overhang, in the mathematical sense of Myers (1977), and inefficiently low input quality.24 Proposition 4. If condition (49) is satisfied, first-best quality can be implemented only if there is zero debt overhang ðD ¼ DÞ. Proof. Identities (30) and (31) imply S  V þ U  V ¼ R  ðD  DÞ 

sFB  ðD  DÞ. 1d

If D4D; then condition (49) implies condition (45) cannot be satisfied for the function q ¼ qFB . & Given that only the principal is levered, it is tempting to conclude that debt overhang can be avoided by structuring the agreement such that only the agent is called upon to make discretionary payments. However, good-faith agreements rely upon the bilateral surplus available to the principal and agent to support cooperation. If D4D, Proposition 4 shows that the credibility of both the principal and agent is diminished. There are a number of parallels with Myers’s (1977) analysis of the investment distortions arising from debt overhang. For example, it is not default risk that is responsible for distortions. Even default-free debt can be distorting. Rather, the distortion is due to externalities captured by outstanding debt. In Myers’ model, the action generating a positive externality is investment by levered equity. In the present model, the action generating a positive externality is fulfillment of the relational contract by the principal and agent. Essentially, the two parties are investing in an intangible asset, what Zingales (2000) 24

See Section 3.2 of Myers (1977), which discusses the effect of lender externalities on investment incentives.

labels ‘‘organizational capital.’’ This organizational capital is particularly fragile relative to physical capital since the party with discretion must pay the promised amount bðqt Þ or the asset vanishes. Proposition 5, which is the analog of Proposition 2 in the basic model, determines the nature of the distortion caused by debt overhang. Proposition 5. If condition (49) is satisfied and debt overhang is positive then there is partial pooling for D  D sufficiently low. There exists a type yp 2 ðy; yÞ such that quality is set at a constant level qðyÞ ¼ qðyp Þ for all y 2 ½y; yp : Higher cost types produce qðyÞ ¼ qFB ðyÞ 

ðyp  y Þ2 . 4b y

(51)

If D  D is sufficiently high, there is full pooling with quality fixed at qoqFB ðyÞ: Proof. See Appendix B. Fig. 3 illustrates Proposition 5, plotting q as a function of

y: The solid line is the first-best schedule. The dotted line represents the q schedule that is implemented for intermediate levels of debt overhang which result in partial pooling. The dashed line represents the q schedule that is implemented for high levels of debt overhang which result in full pooling. It is worth recalling that since costs are drawn from the uniform distribution, the standard screening model with verifiable q predicts full separation of types and qðyÞ ¼ qFB ðyÞ: In contrast, debt overhang induces pooling and suboptimal quality for all types. 3.5. Numerical solution of extended model Having characterized the effect of debt on efficiency (Proposition 5), we next analyze the optimal debt coupon. Due to the complexity of the infinite horizon model, a

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closed-form solution is not feasible. This subsection presents numerical solutions of the model, pinning down the optimal coupon as a function of the firm’s ex ante (L) and ex post (l) bargaining power. The numerical algorithm is described in Appendix C. Before discussing particular cases, we recall the optimal coupon maximizes the cum-dividend value of equity, given in Eq. (32). This equation tells us that the optimal coupon trades off the surplus extraction created by debt against the distortions arising from debt overhang.

Results are presented in Table 1. The first column shows the optimal debt coupon is zero if the firm has full ex ante bargaining power. The second column (l ¼ L ¼ 0:25) illustrates an interesting case. At the optimal coupon, debt is risk-free on the equilibrium path since c  ls ¼ 0:7968  d ¼ 0:8; while debt is risky off the equilibrium path since c ¼ 0:82434d: Intuitively, the firm is in a weak bargaining position ex ante and thus finds it optimal to generate some debt overhang despite the distortions that result. Note that relative to the case with no debt, quality is lower when there is debt overhang. The last column illustrates a case where the firm has no bargaining power ex ante. However, the fact that the firm will enjoy some bargaining power ex post allows it to extract surplus by creating debt overhang. The optimal debt coupon increases relative to the previous case with debt being risky both on and off the equilibrium path. Fig. 4 plots the cum-dividend value of equity as the coupon is changed for this case. Initially, equity value is equal to 5 ¼ ð1  dÞ1 ; reflecting the value of the firm with no-trade. Equity value then spikes upwards when the coupon is sufficiently large to generate debt overhang and a bargaining benefit. As shown in Fig. 5, periodic surplus from trade declines as the coupon is increased, resulting in an interior optimum. To summarize, the numerical results in the infinite horizon model confirm the intuition provided by the basic model. Consistent with Proposition 1, optimal leverage is declining in ex ante bargaining power.

Table 1 This table reports optimal coupon for different pairs of ðL; lÞ. The model is solved numerically using solution algorithm provided in Appendix C. The parameter values are chosen as follows: b ¼ 1; yL ¼ 2; yH ¼ 3; a ¼ 3:33; d ¼ 0:8. The first column shows the optimal debt coupon is zero if the firm has full ex ante bargaining power. The second column (l ¼ L ¼ 0:25) illustrates an interesting case. At the optimal coupon, debt is risk-free on the equilibrium path since c  ls ¼ 0:7968  d ¼ 0:8; while debt is risky off the equilibrium path since c ¼ 0:82434d. Intuitively, the firm is in a weak bargaining position ex ante and thus finds it optimal to generate some debt overhang despite the distortions that result. Note that relative to the case with no debt, quality is lower when there is debt overhang. The last column illustrates a case where the firm has no bargaining power ex ante. However, the fact that the firm will enjoy some bargaining power ex post allows it to extract surplus by creating debt overhang. The optimal debt coupon increases relative to the previous case with debt being risky both on and off the equilibrium path. Parameter 

c D V  DD s qðyp Þ qðyÞ c  ls

L ¼ 1; l ¼ 1

L ¼ 0:25; l ¼ 0:25

L ¼ 0; l ¼ 0:5

0.0000 0.0000 5.5872 0.0000

0.8243 4.1214 5.1563 0.0249

0.9057 4.3016 5.0195 0.0195

0.1174 0.1816 0.0852

0.1101 0.1663 0.0808

0.0798 0.1120 0.0644

0.1174

0.7968

0.8658

393

4. Conclusion In his seminal paper, Myers (1977) shows that levered equity has an incentive to underinvest relative to first-best whenever outstanding debt profits from capital accumulation. The influence of Myers’ model on the practice of corporate finance is well illustrated by the common inclusion of dividend and asset sale restrictions in bond

5.03

Principal Payoff

5.025 5.02 5.015 5.01 5.005 5 0

0.5

1

1.5

2 2.5 Coupon

3

3.5

4

Fig. 4. Cum-dividend equity value. This figure plots the cum-dividend value of equity, V , as a function of the coupon, c. The model is solved numerically using solution algorithm provided in Appendix C. The parameter values are chosen as follows: b ¼ 1; yL ¼ 2; yH ¼ 3; a ¼ 3:33; d ¼ 0:8; L ¼ 0; l ¼ 0:5. In this case the firm has no bargaining power ex ante. Initially, equity value is equal to 5 ¼ ð1  dÞ1 ; reflecting the value of the firm with no-trade. Equity value then spikes upwards when the coupon is sufficiently large to generate debt overhang and a bargaining benefit.

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0.12 0.1

Periodic surplus Debt overhang

Value

0.08 0.06 0.04 0.02 0 −0.02 0

0.5

1

1.5

2 2.5 Coupon

3

3.5

4

Fig. 5. Periodic surplus and debt overhang. This figure plots the periodic surplus, s, and the debt overhang, D  D, as functions of the coupon, c. The model is solved numerically using solution algorithm provided in Appendix C. The parameter values are chosen as follows: b ¼ 1; yL ¼ 2; yH ¼ 3; a ¼ 3:33; d ¼ 0:8; L ¼ 0; l ¼ 0:5. In this case the firm has no bargaining power ex ante. It shows that the sufficiently large coupon generates debt overhang, shown by the solid line, and a bargaining benefit. The periodic surplus from trade, shown by the dashed line, declines as the coupon is increased, resulting in an interior optimum.

covenants. This paper shows that the overhang problem is more general, having an adverse impact on operational efficiency if the firm relies upon implicit contracts to provide incentives. When there is debt overhang, incentives become low-powered, quality declines, and joint profits in a supply chain are diminished. Despite the fact that debt overhang can distort incentives, it is shown that overhang can be an optimal response for firms facing imperfectly competitive agents, with debt overhang helping firms extract a larger fraction of total surplus. The optimal degree of debt overhang balances surplus extraction against efficiency, implying that weak firms will choose higher debt levels. Taken together, the model can account for the cycle of leverage, mistrust, and low quality that plagues many unionized industries. The import of the theory offered here is heightened by recent trends in the way companies operate. As argued by Che (2008), the trend toward outsourcing increases the importance of constructing efficient procurement arrangements. Although procurement and labor contracts are typically the province of the chief operating officer, the theory offered here suggests the desirability of integrating operating and financing policies.

Surplus can be rewritten as X 2 pi ð2qFB i qi  qi Þ.

sðqL ; qH Þ ¼ b

(52)

i2fL;Hg

Since SEL binds, we can use it to express qH in terms of qL to obtain qH ðqL Þ ¼

KðcÞ  yL qL yH  yL

,

(53)

where we have introduced the following notation:

KðcÞ  EðpjTÞ  EðpjNTÞ  DðcÞ.

(54)

Next, we substitute (53) back into (52) to obtain ( " # 2b KðcÞ2 FB s½qL ; qH ðqL Þ ¼ pH ðyH  yL ÞqH KðcÞ  2 ðyH  yL Þ2 2 FB þ ½pL qFB L ðyH  yL Þ  yL ðyH  yL ÞpH qH

þ KðcÞpH yL qL 2

½yL pH þ ðyH  yL Þ2 pL 

 q2L . 2

(55)

From the first-order condition we have qL ¼

2 FB pL qFB L ðyH  yL Þ  yL ðyH  yL ÞpH qH þ KðcÞpH yL

y2L pH þ ðyH  yL Þ2 pL

.

(56)

Rearranging terms yields qL ¼ qFB L  Appendix A. Proof of Proposition 2

pH yL FB ½yL qFB L þ ðyH  yL ÞqH  KðcÞ. y2L pH þ ðyH  yL Þ2 pL (57)

The second part of Proposition 2 characterizes the optimal contract when the constraint binds. In that particular case, q follows directly from substituting qL ¼ qH ¼ q into the SEL constraint. This appendix solves a relaxed program ignoring the constraint qL  qH : We then verify that this condition is slack under the conditions stated in the first part of the proposition.

And using the SEL constraint one obtains KðcÞ  yL qL qH ¼ yH  yL pL ðyH  yL Þ FB ¼ qFB ½yL qFB H  2 L þ ðyH  yL ÞqH  KðcÞ. yL pH þ ðyH  yL Þ2 pL (58)

ARTICLE IN PRESS C.A. Hennessy, D. Livdan / Journal of Financial Economics 93 (2009) 382–399

Next we consider comparative static properties. Substitution of qL and qH into Eq. (55) yields ( " # 2b KðcÞ2    FB s  sðqL ; qH Þ ¼ pH ðyH  yL ÞqH KðcÞ  2 ðyH  yL Þ2 )  2 ðq Þ 2 . (59) þ½yL pH þ ðyH  yL Þ2 pL  L 2 Note that

For an arbitrary type y: eðyÞ ¼ u eðyÞ þ u

Z y

y

e0 ðtÞdt. u

(69)

e one obtains Differentiating u e0 ðtÞ ¼ ½b0 ðqðtÞÞ  tq0 ðtÞ  qðtÞ. u

(70)

In order for the first-order (64) to be met, it must be that

K0 ðcÞ ¼ D0 ðcÞ

e0 ðtÞ ¼ qðtÞ. u

and @qL @qL 0 pH yL K ðcÞ ¼  2 ¼ D0 ðcÞ. @c @K yL pH þ ðyH  yL Þ2 pL

(60)

We can now calculate @s =@c as follows: @s 2bpH 0  ¼  fðyH  yL ÞqFB H  KðcÞ þ yL qL gD ðcÞ @c ðyH  yL Þ2 2bpH ¼  fqFB  qH gD0 ðcÞ, yH  yL H

Z

y

qðtÞ dt.

(72)

y

(61)

Now, note that A is free to choose q ¼ 0 and get bð0Þ: In order for type y to stay on the menu it must be the case that bðqðyÞÞ  yqðyÞ  bð0Þ.

(73)

Substituting (73) into (72) and rearranging terms yields

s ¼ ½a  EðyÞq ðcÞ  b½q ðcÞ2 @s D0 ðcÞ ¼ ½a  EðyÞ  2bq : @c yH

(71)

Substituting (71) into (69) and rearranging terms, it follows that any IC contract must satisfy bðqðyÞÞ ¼ bðqðyÞÞ  yqðyÞ þ yqðyÞ þ

where we have used SEL . When there is complete pooling of types

)

395

(62)

&

yqðyÞ þ

Z

y

qðtÞ dt  bðqðyÞÞ  bð0Þ.

(74)

y

Appendix B. Proofs for extended model

Since the type y was arbitrary, the stated condition must hold for type y:

B.1. Proof of Lemma 2

y qðyÞ þ

Z

y

qðtÞ dt  bðqðyÞÞ  bð0Þ  sup bðqÞ  inf bðqÞ  dS. q

y

In analyzing necessary conditions for satisfaction of IC, break A’s decision into two parts. First consider the constrained problem where A must choose from Q m . IC demands

y 2 arg max Jðy; b yÞ  b½qðb yÞ  yqðb yÞ.

(63)

by2Y

The first-order necessary condition for truth-telling is 3

J 2 ðy; yÞ ¼ 0

0

½b ðqðyÞÞ  yq0 ðyÞ ¼ 0

8y 2 Y .

(64)

0

00

00

0

2

8y 2 Y. (65)

Since (64) must hold point-wise in y; the partial derivative of the left side of the stated equality must be zero. This implies 00

0

8y 2 Y . (66)

Substituting (66) into (65), the second-order necessary condition for truth-telling demands J 22 ðy; yÞ ¼ q0 ðyÞ  0

8y 2 Y.

(67)

This establishes the necessity of the stated monotonicity condition. Next, define A’s realized period-payoff under the agreement as eðyÞ  w þ bðqðyÞÞ  yqðyÞ. u

The last inequality follows from adding the SEP and SEA constraints. & B.2. Proof of Lemma 3 

To establish that the proposed contract (b ) satisfies the first- and second-order conditions for truth-telling, let 

J 22 ðy; yÞ ¼ ½b ðqðyÞÞ  yq ðyÞ þ b ðqðyÞÞ½q ðyÞ  0

½b ðqðyÞÞq0 ðyÞ  1q0 ðyÞ þ ½b ðqðyÞÞ  yq00 ðyÞ ¼ 0

(75)

J  ðy; b yÞ  b ½qðb yÞ  yqðb yÞ.

and the second-order necessary condition is

(68)

q

(76)

Using Leibniz’ formula, it follows that J 2 ðy; b yÞ ¼ ðb y  yÞq0 ðb yÞ,  00 b b b J ðy; yÞ ¼ ðy  yÞq ðyÞ þ q0 ðb yÞ. 22

(77)

From the hypothesis that q is weakly decreasing, it follows that J 2 ðy; yÞ ¼ 0 and J22 ðy; yÞ  0: Next, we must verify that no type is better off choosing  qeQ m : Any qeQ m pays weakly less than w þ b ð0Þ net of production costs. However, we know that for an arbitrary  type yoy; the contract b induces eðyÞ ¼ w þ b ð0Þ eðyÞ4u u

(78)

with the 4 sign following from the fact that a type yoy masquerading as type y would get a payoff strictly greater eðyÞ: The first- and second-order conditions above than u ensure that truthful reporting yields an even higher payoff. &

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B.3. Proof of Proposition 3

change in the state variable q

Assume first that c  d; implying P never defaults.  From Lemma 1 it follows that b ensures satisfaction of IC. We must verify satisfaction of SEP and SEA. Choose an  arbitrary l 2 ½0; 1: Then set b ð0Þ ¼ ð1  lÞdsFB =ð1  dÞ and set w such that P captures ls in expectation. The SEP constraint is satisfied, with

max



FB

FB

b ½q ðyÞ  y q ðyÞ þ

Z

y y

ð1  lÞdsFB q ðyÞ dy  ð1  dÞ (79)

where the second equality uses Assumption 2 and the last equality follows from the fact that P is allocated lsFB out of the bilateral surplus each period. The SEA constraint is also satisfied, with

dð1  lÞsFB ¼ dU. b ð0Þ  ð1  dÞ 

(80)

Assume next that c4d and l ¼ L ¼ 0: In this case default occurs with positive probability. We need only   check that b satisfies SEA, since b  0. In the present FB case, l ¼ 0 implies A captures s each period prior to default, while D ¼ L ¼ 0 implies A captures sFB =ð1  dÞ in capitalized value upon default. Thus, U ¼ sFB =ð1  dÞ and SEA is satisfied. & B.4. Proof of Proposition 5 This proposition characterizes the quality schedule implemented under optimal agreements. By construction,  the scheme b ensures IC. The objective is to find the schedule q that maximizes s; subject to the remaining constraints: monotonicity, SEP, and SEA. In order to simplify the problem, note that SEP and SEA can be replaced with a single SE constraint SE : y qðyÞ þ

Z





sup b ðqÞ  inf b ðqÞ ¼ y qðyÞ þ

Z

q

(81)

y

qðtÞ dt.

(82)

y

The condition SE (81) implies that 



½dðV  VÞ  sup b ðqÞ þ ½dU þ inf b ðqÞ  0. q

(84)

subject to the SE constraint above and monotonicity, q0 ðyÞ  gðyÞ,

(85)

gðyÞ  0.

(86)

V þU ¼

r½Eðxjx  xd Þ  c þ s ð1  rÞdU 0 þ . 1  rd 1  rd

Substituting this sum into (81) allows us to rewrite the SE constraint as Z y  y

þ





rd ½ða  tÞqðtÞ  bq2 ðtÞ  qðtÞ dt  y qðyÞ  dV 1  rd

rd½Eðxjx  xd Þ  c d2 ð1  rÞU 0 þ  0. 1  rd 1  rd

(87)

The revised SE constraint can be converted into an endpoint condition, since it is essentially an integral constraint. Define a second state variable K:  Z y rd ½ða  tÞqðtÞ  bq2 ðtÞ  qðtÞ dt. (88) KðyÞ  y 1  rd The equation of motion for K is   rd ½ða  yÞqðyÞ  bq2 ðyÞ  qðyÞ. K 0 ðyÞ ¼ 1  rd

(89)

And we have the following constraints, with the second representing SE: KðyÞ ¼ 0, KðyÞ  y qðyÞ  dV þ

(90)

rd½Eðxjx  xd Þ  c d2 ð1  rÞU 0 þ  0. 1  rd 1  rd (91)

qðtÞ dt  dðV þ U  VÞ.

To see this, note that



½ða  yÞqðyÞ  bq2 ðyÞ dy

y

y y

q

y

Next we rewrite the sum of V and U:

FB

dlsFB ¼ ¼ dðV  VÞ, ð1  dÞ

Z

q

q

(83)

If b ð0Þ is such that both bracketed terms are positive, then SEP and SEA are satisfied. Now note that lowering w and  raising b ð0Þ by equal amounts keeps V and U constant. Therefore, if the first bracketed term is positive and the second negative, SEP and SEA can be satisfied by lowering  w and raising b ð0Þ by equal amounts until SEA is just satisfied. A similar argument would apply if the first bracketed term were negative and the second positive. Finally, note that the constraint (81) tightens as D  D increases. The optimal schedule q solves the following program, where g represents the control policy regulating the

The objective is to maximize the objective function (84) subject to: (85), (86), (89), (90), and (91). The solution and notation follows Leonard and van Long (1992), who present sufficient conditions on pages 212 and 250. Let pq and pK denote the costate variables for the two state variables q and K: Let x denote the multiplier on the control constraint (86). Let m denote the multiplier on the new SE constraint (91). Necessary conditions include the following transversality conditions:

pK ðyÞ ¼ m,

(92)

pq ðyÞ ¼ 0,

(93)

pq ðyÞ ¼ m y

(94)

plus complementary slackness for the monotonicity and SE constraints

xðyÞ  0,

(95)

xðyÞgðyÞ ¼ 0,

(96)

ARTICLE IN PRESS C.A. Hennessy, D. Livdan / Journal of Financial Economics 93 (2009) 382–399

m  0,

(97)

"

#

m KðyÞ  y qðyÞ  dV þ

rd½Eðxjx  xd Þ  c d2 ð1  rÞU 0 þ ¼ 0. 1  rd 1  rd (98)

Next, form the Lagrangian d ¼ ða  yÞqðyÞ  bq2 ðyÞ þ pq ðyÞgðyÞ    rd ½ða  yÞqðyÞ  bq2 ðyÞ  qðyÞ  xðyÞgðyÞ. þ pK ðyÞ 1  rd

(99) The costate variable for K must satisfy: p0K ðyÞ ¼ dK ¼ 0

8y 2 Y.

(100)

The costate variable for q must satisfy:    dr p0q ðyÞ ¼ dq ¼ 1 þ pK ðyÞ ½ða  yÞ  2bqðyÞ 1  dr  pK ðyÞ

8y 2 Y.

(101)

The optimality condition is dg ¼ pq ðyÞ  xðyÞ ¼ 0

8y 2 Y.

(102)

Attention is confined to cases where there is a debt overhang and first-best is not feasible. Then m40. Eq. (100) tells us that pK is constant. From (92) it must be the case 8y that pK ðyÞ ¼ m: Substituting this condition, plus (102) into (101) yields 3 2 6 ða  yÞ  2bqðyÞ ¼ 6 4

m

7 7

0

5½1  x ðyÞ=m. dr 1þm 1  dr 

(103)

From (103), on any interval where the monotonicity constraint does not bind (x ¼ 0): qðyÞ ¼ qFB ðyÞ 

m=2b

 . dr 1þm 1  dr

(104)

Lemma 5 will prove useful in characterizing the solution. & e; y. y s.t. q0 ðe yÞo0; then q0 ðyÞo0 8y 2 ðy Lemma 5. If 9 e Proof of Lemma 5. Suppose to the contrary 9 y s.t.  þ q0 ðy Þo0 and q0 ðy Þ ¼ 0: From complementary slackness  þ on the control, we know xðy Þ ¼ 0 and xðy Þ40; which 0 implies x ðyÞ40: From (103) we know that when q is constant on some interval, then 8t on that interval:

x00 ðtÞ ¼ 1 þ

m



1þm

 40.

dr 1  dr

(105)

0

Thus, x is positive and increasing above y. This contradicts the transversality condition pq ðyÞ ¼ 0; since (102) demands xðyÞ ¼ pq ðyÞ: & 8 > < dVðc0 ; cÞ þ lsðc0 ; cÞ  c0  ln Vðc0 ; cÞ ¼ 0 Vðc0 ; cÞ ¼ 1  c0 þ lsðc0 ; cÞ > :¼ 1d

rðc0 ; cÞ ¼ Vðc0 ; cÞ,

397

Using the boundary condition pq ðyÞ ¼ xðyÞ ¼ m y 40; the complementary slackness condition demands that there is some region of pooling over the lowest cost types. Taken in conjunction with Lemma 5 it follows that there is either complete or partial pooling of types. To establish the conditions for partial pooling of types in, say, ½y; yp , integrate the condition (103) from y to yp : Using the boundary condition pq ðyÞ ¼ xðyÞ ¼ m y and the complementary slackness condition xðyp Þ ¼ 0; we have the following condition pinning down the cutoff type for pooling: ðyp  y Þ2 ¼ 2y

m

1þm



.

(106)

dr 1  dr

This equation has at most one solution in ðy; yÞ: When the solution falls outside Y; complete pooling must result. In the event of complete pooling of types, the quality produced can be determined by integrating the condition (103) over all types. Quality under complete pooling is given by: 0  1 B B q ¼ qFB ðyÞ  2b @

1



my



1C  C oqFB ðyÞ: 2A

dr 1þm 1  dr

&

(107) Appendix C. Numerical algorithm In order to compute the optimal coupon for the initial manager, we must recognize that the initial manager does not choose the coupon for future owners, post-default. Therefore, the numerical algorithm computes values and equilibria assuming c0 is chosen by the original manager who anticipates that some coupon c will be chosen by all future owners in a stationary equilibrium. As described below, we look for an equilibrium where the optimal initial coupon satisfies c0 ðce Þ ¼ ce : The steps are as follows: max  and Step 1: Discretize the initial coupon c0 2 ½cmin 0 ; c0 min max . post-default coupons c 2 ½c ; c Step 2: Solve for Vðc0 Þ and Dðc0 Þ using 8 > < dVðc0 Þ  c0  ln Vðc0 Þ ¼ 0 if c0 4d; (108) Vðc0 Þ : 1  c0 > if c0  d; :¼ 1  d Dðc0 Þ ¼ 1=ð1  dÞ  Vðc0 Þ. Step 3: Compute values and equilibria induced by a given initial coupon c0 assuming c is chosen by all future owners.

if c0  lsðc0 ; cÞ4d; if c0  lsðc0 ; cÞ  d;

(109) (110)

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Uðc0 ; cÞ ¼

8 rðc0 ; cÞð1  lÞsðc0 ; cÞ þ ½1  rðc0 ; cÞdU 0 ðc; cÞ > > > < 1  drðc0 ; cÞ

if c0  lsðc0 ; cÞ4d;

> ð1  lÞsðc0 ; cÞ > > : if c0  lsðc0 ; cÞ  d; 1d 8   rðc0 ; cÞc0 þ ½1  rðc0 ; cÞ dV  ðc; cÞ þ Eðxjx  xd Þ > > > if c0  lsðc0 ; cÞ4d; < 1  drðc0 ; cÞ Dðc0 ; cÞ ¼ > c0 > > if c0  lsðc0 ; cÞ  d; : 1d

(113)

U 0 ðc0 ; cÞ ¼ ð1  LÞ½Vðc0 ; cÞ þ Uðc0 ; cÞ  Vðc0 Þ.

(114)

Eðxjx  xd Þ ¼ 1 þ

Vðc0 ; cÞ ln Vðc0 ; cÞ . 1  rðc0 ; cÞ

(115)

Then find the pooling type and induced surplus using the following three equations derived in Appendix B:

yp qp þ

aðy  yp Þ 2b

2



y  y2p ðyp  y Þ2 ðy  yÞ  4b 4b y

¼ d½Vðc0 ; cÞ þ Uðc0 ; cÞ  Vðc0 Þ,

a  yp 2b



ðyp  y Þ2 , 4b y

(116)

(117)

1 2 2 sðc0 ; cÞ ¼ ½aqp  bðqp Þ2 ðyp  yÞ  qp ðyp  y Þ 2    2 1 1 3 þ a2 ðy  yp Þ  aðy  y2p Þ þ ðyH  y3p Þ 4b 3 ! ! 4 y  yp ðyp  y Þ . (118)  16b y2 Step 4: Compute optimal initial coupon for each possible value of the post-default coupon c: c0 ðcÞ 2 arg max c0

V  ðc0 ; cÞ.

(119)

Step 5: An equilibrium ce satisfies c0 ðce Þ

(112)

V  ðc0 ; cÞ ¼ Dðc0 ; cÞ þ Vðc0 Þ þ L½Vðc0 ; cÞ þ Uðc0 ; cÞ  Vðc0 Þ,

The conditional expectation is given by

qp ¼

(111)

¼ ce .

(120)

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