Resolution of Financial Distress under Chapter 11

Transcription

1 Resolution of Financial Distress under Chapter 11 Amira Annabi, Michèle Breton and Pascal François HEC Montreal December 1, 2008 Abstract This paper examines the reorganization process under Chapter 11 of the U.S. bankruptcy code. Our model considers two classes of creditors and accommodates several features of Chapter 11, including the intervention of the bankruptcy judge. We model the strategic interaction between claimants under Chapter 11 as a costly multiple-stage bargaining process, and solve it in a game theory setting. Using a structural framework, we extend the existing literature by generating reorganization and liquidation outcomes. We nd that these outcomes are a ected by the characteristics of the rm and of the negotiation game: the likelihood of liquidation increases with the probability of the bankruptcy judge intervention, asset volatility, length of negotiation process, and nancial distress costs. JEL classi cation: C61, C7, G33, G34. Keywords: Credit risk, capital structure, bankruptcy costs, Chapter 11, game theory, dynamic programming. Preliminary, comments welcome. Annabi was supported by a grant from IFM 2 and CREF. Breton was supported by a grant from IFM 2 and NSERC. François was supported by a grant from IFM 2 and FQRSC. We would like to thank participants at the 2007 EFMA annual meeting in Vienna, 2007 FMA annual meeting in Orlando as well as Hatem Ben Ameur, Jan Ericsson and Jean Helwege for their useful comments. Correspondence to: Amira Annabi, HEC Montreal, 3000 chemin de la Côte-Sainte-Catherine, Montreal, Quebec, Canada, H3T 2A7; Tel: (514) ext. 2697; Fax: (514) ; amira.annabi@hec.ca. 1

2 1 Introduction The beginning of the 21 st century was marked by the most spectacular nancial bankruptcies in the last decades and raised the awareness of both academic and professional communities of the importance of credit risk events for the valuation of corporate risky debt. In the U.S., Chapter 11 of the bankruptcy Code, thereafter called the Code, presents an alternative to the liquidation of a bankrupt rm by de ning a judicial context in which the rm can reorganize its activities in order to emerge as a viable entity. For example, Enron (31; 237:00$MM. liabilities) and WorldCom (45; 984:00$MM. liabilities), 1 considered as the most important recent defaults, did use this provision of the Code in their attempt to survive and avoid liquidation. The aim of this paper is to account for the characteristics of Chapter 11 negotiation in the speci cation of the outcomes of the reorganization. Chapter 11 de nes the following main reorganization s features: The reorganization plan ling and timing, the automatic stay of assets during negotiation, and the con rmation of the plan. The Code gives the debtor the right to propose the rst plan within a period of 120 days of the initial bankruptcy time. If the plan is not led within this period, or accepted by the creditors within 60 additional days, then any claimant class can propose its own plan. A reorganization plan speci es a new capital structure of the rm, describing how the creditors are paid in terms of cash or new securities. To con rm the plan, the claimants are rst regrouped into di erent classes, where claimants have almost the same characteristics. For instance, senior and junior unsecured creditors are regrouped into di erent classes. As detailed in White (1989), implementation of a reorganization plan is made through either a "unanimous consent 1 Source: Altman and Hotchkiss (2006). 2

3 procedure" or "cram-down". The rst procedure requires a majority in value (two-thirds) and number (half) of the claimants of each impaired class. The second one occurs when the unanimous consent procedure fails, and the court unilaterally imposes, or crams-down, the plan on a dissenting class, as long as it is considered as fair and equitable. This paper models the strategic interaction between claimants in Chapter 11 as a multiple-stage bargaining process, and solves it in a non-cooperative game theory setting. Our paper adds to earlier literature by modeling a complex and realistic negotiation process, incorporating di erent features of Chapter 11 negotiation described in the Code, and by considering two classes of creditors with di erent seniorities. The claimants are allowed to sequentially propose reorganization plans, one of which can be con rmed by the bankruptcy judge if all claimants agree on its implementation. We also account for Chapter 11 s cramdown provision that allows the judge to impose a reorganization plan, thereby putting an end to a lengthy and costly negotiation. Moreover, the bankruptcy judge can stop negotiation by converting reorganization under Chapter 11 into Chapter 7 liquidation. We characterize the conditions under which various outcomes of the negotiation process under Chapter 11 (liquidation and reorganization) are obtained. We also relate these conditions to the bankruptcy judge s strategy and behavior (equity-favoring versus creditor-favoring), the volatility of the underlying assets and the default barrier at which the rm enters Chapter 11 reorganization. A key feature of our model is that it can generate liquidation as an equilibrium outcome. This is possible because of the non-cooperative behavior of the players, and because a portion of nancial distress costs is proportional to the length of the negotiation process. We nd that the likelihood of a liquidation 3

4 outcome increases with the probability of the bankruptcy judge intervention, asset volatility, length of negotiation process, and nancial distress costs. The remainder of the paper is organized as follows: After a brief review of the related literature in Section 2, we de ne the main ingredients of our model of the negotiation process under Chapter 11 in Section 3. In Section 4, we solve the game by backward induction and characterize the possible equilibrium outcomes of the default event. Section 5 presents numerical illustrations and sensitivity analyses, and Section 6 is a conclusion. 2 Related literature Our paper is related to the literature that focuses on the resolution of - nancial distress in the context of structural models of default. This literature considers mainly three cases: In the rst case, default leads to an immediate liquidation of the rm under Chapter 7 of the Code (see Merton (1974), Black and Cox (1976), Brennan and Schwartz (1984)). In the second case, the rm enters out-of-court, or private negotiation. For instance, in a binomial model, Anderson and Sundaresan (1996) model negotiation as a take-it-or-leave-it offer made by the manager to creditors. Anderson et al. (1996) generalize the preceding model to continuous time. Mella-Barral and Perraudin (1997) and Mella-Barral (1999) study, in a continuous time private negotiation, the impact of bargaining power on the bilateral o er made by equityholders or creditors. Hege and Mella-Barral (2000) generalize Mella-Barral (1999) by introducing the tax advantage of debt and allowing for multiple negotiations rounds. The third case considers public negotiation, mainly under Chapter 11 of the U.S. Bankruptcy Code. 2 Earlier literature focuses on the description of the mechanisms 2 See Altman and Hotchkiss (2006) for a detailed description of the Code amendment. 4

5 of Chapter 11 s reorganization (e.g. White (1989), Gilson et al. (1990)). The empirical literature on Chapter 11 is extensive, and we focus here on the papers that consider the default event as given, and then analyze and describe the subsequent negotiation procedure and the rm valuation after emergence from Chapter 11. Two key features of Chapter 11 negotiation process have been empirically investigated. The rst one is the importance of the bankruptcy judge characteristics on the outcome of the negotiation process. Bris et al. (2006) and Chang and Schoar (2007) show that the judges di er in their behavior towards claimants, where some of them are debtor-favoring and others creditor-favoring. Chang and Schoar (2007) show that this judge s speci city has an impact on post-bankruptcy credit ratings and rates of re- ling in Chapter 11. The second feature is the duration of Chapter 11 negotiation. Carapeto (2005) documents that two-thirds of Chapter 11 rms require more than one reorganization plan before an agreement can be attained. Empirical studies indicate that the average duration of negotiation is somewhat over two years; observed durations range from essentially zero (Franks and Torous (1989) report one case that lasted only 37 days) to more than seven years (Warner (1977)). The outcome of Chapter 11 reorganization is also widely discussed in the literature. For example, in their study of a sample of 1; 770 public companies that led for Chapter 11 between 1979 and 2002, Hotchkiss and Mooradian (2004) are able to determine some resolution of the case by June 2004, for 79% of the rms studied. They nd that almost 21:5% of the rms are liquidated under Chapter 7, while the remaining emerge as publicly or non publicly-registered companies, or merge with another operating company. However, Chapter 11 is not always a successful reorganization, even if the rm emerges as an entire entity. In fact, Altman and Hotchkiss (2006) show that, between 1984 and 2004, some rms that already 5

6 led and emerged from Chapter 11 once, led for a second (Chapter 22), and even a third (Chapter 33) time in Chapter 11. The reported numbers show that these events are rather rare. For example, in 2003, Altman and Hotchkiss (2006) reports only 17 Chapter 22 cases, and 1 Chapter 33 case over 9; 404 Chapter 11 cases. While signi cant progress has been done in empirical exploration of Chapter 11, less has been done regarding rigorous theoretical modeling of negotiation. Brown (1989) proposes a description of the agenda policies, and the cram-down rules that determine the outcome of a public negotiation. Baird and Morrison (2001) highlight the impacts of a formal bankruptcy process involving a bankruptcy judge. In a theoretical set-up, they argue that the judge controls the liquidation decision, which is compared to the exercise of a real option. They point out that some factors can prevent the judge to act optimally, such as the lack of information and expertise. Theoretical structural models on public negotiation include recent papers that are built on the concept of assets excursion beyond some endogenous barrier (e.g. Fan and Sundaresan (2000), François and Morellec (2004), Moraux (2004), Ericsson and Renault (2006), Chernov, Broadie and Sundaresan (2007) and Galai, Raviv and Wiener (2007)). Fan and Sundaresan (2000) consider that the default event is triggered endogenously, and that the rm emerges once the asset values cross again the default barrier. In a contingent valuation framework, they propose a game-theory setting to model the strategic interactions between debtor and creditor. They study two reorganization approaches: debt-equity swap and strategic debt reductions, which are di erentiated by the existence of corporate taxes. In the absence of taxes, claimants resort to a debt-equity swap, where they bargain over the value of the assets. However, the existence of taxes lead to a strategic debt service 6

7 case, where the claimants bargain over the whole value of the rm. In both cases, the negotiation game is modeled as a Nash Bargaining Game, where the bargaining powers are exogenous. Moraux (2004) de ne the bankruptcy as an excursion of assets values under an endogenous default barrier, without considering a reorganization procedure. François and Morellec (2004) build on the negotiation model of Fan and Sundaresan (2000). They consider that claimants negotiate the strategic debt service at the beginning of the reorganization period, which length depends on the assets excursion below some endogenous default boundary. The rm is liquidated if this excursion lasts more than a speci ed exclusivity period. Ericsson and Renault (2006) generalize the preceding models by allowing the rm to be reorganized out-of-court (Fan and Sundaresan (2000) bargaining model) prior entering formal reorganization under Chapter 11 (François and Morellec (2004) excursion model). Assuming the same reorganization set-up as François and Morellec (2004), Chernov, Broadie and Sundaresan (2007) expand the liquidation events by considering an endogenous liquidation barrier. They also assume that the claimants negotiate the distribution of the dividends that were suspended and accumulated during renegotiation, and that are used to pay the accumulated suspended coupons. Galai, Raviv and Wiener (2007) allow for multiple public reorganizations, where the emergence of the rm from each bankruptcy event depends mainly on the accumulated information about the rm s past bankruptcies. An important issue, only recently addressed in the literature, is that negotiation involves often more than one class of creditors. In a discrete time framework, Noe and Wang (2000) study the optimal negotiation sequence when the rm is indebted to many creditors. The public negotiation involves some of Chapter 11 s features, such that the possibility of the Absolute Priority Rule 7

8 (APR) violations and costly negotiation. By having the rst move advantage, debtors choose the optimal sequence of bilateral negotiation that maximizes their own payo, and capture most of the negotiation surplus. However, Noe and Wang (2000) assume that negotiation is not time consuming, and the outcomes of the negotiation game ultimately depend on the debtor s e ort to generate cash own. Hackbarth et al. (2007) examine a rm nanced with a mix of bank and market debt, where only the bank has the ability to renegotiate. Breccia (2004) extends Mella-Barral and Perraudin (1997) technique and studies two-stage sequential restructuring of two debt classes, senior unsecured and subordinated debt. Taking into account impairment strategy allows the negotiation to occur, in the rst round, between equityholders and only one class of creditors. However, if the game reaches the second stage, all the claimants are involved in negotiation which is modeled as a Nash Bargaining Game, as in Fan and Sundaresan (2000). Financial distress costs play an important role in the reorganization under Chapter 11. Considered as frictions, nancial distress costs are one of the reasons why claimants negotiate, especially in small rms. These costs are opportunity costs such as the lost sales and pro ts caused by customers choosing not to deal with a rm that may enter bankruptcy. 3 They are more di cult to measure, and there is less evidence in the literature on how they are estimated. Franks and Torous (1989) argue that the time in bankruptcy is a proxy for indirect bankruptcy costs, while Bris et al. (2006) propose the retention of asset value during negotiation. 3 See Altman and Hotchkiss (2006), p

9 3 The negotiation process model under Chapter 11 In this paper, we adopt a non-cooperative paradigm to model the public negotiation process between the claimants. Moreover, we assume that the process is costly and time-consuming, and that the Judge plays an important role in its outcome. We model the negotiation between the claimants as a mix of sequential and simultaneous non-cooperative games, which are played in successive bargaining rounds, assumed of equal length d for simplicity. The next sections describe the rm, the strategic and non-strategic players, the possible outcomes, and the bankruptcy cost structure that we consider in our negotiation model. 3.1 The rm The rm is owned by the equityholders and nanced initially by a mix of perpetual senior (unsecured) and subordinated debt, receiving constant and continuous coupons until default. We adopt the structural approach to default, assuming that the default event is triggered by the movement of the rm s asset value relative to some barrier. In our economy, the value of the assets of the rm follows a log-normal process under the risk neutral measure: dv t = (r ) V t dt + V t dw t (1) where r denotes the risk-free rate, the payout rate, the volatility of the assets, and W t is a Q Brownian motion de ned on a probability space (; F; F; Q). The default event, at t = 0, starts the negotiation process under Chapter Strategic players When the negotiation process starts, we assume that the rm is managed by the same board of directors as prior to ling. Then, we can characterize the 9

10 debtor as being in possession of its own a airs, and as stipulated in the Code, label him debtor-in-possession or DIP. We assume that during the negotiation process the interests of equityholders are represented by the DIP, denoted by e. Moreover, abstracting from hold-out problems among creditor s classes, we assume that each class is represented by a single representative player, and we denote the representative senior creditor by s and junior creditor by j. The claimants are thus represented by three strategic players, labeled e, s and j. During the negotiation process, each player in turn has the opportunity to propose a reorganization plan, while the two remaining players can decide to approve it or reject it. 4 Players take their decisions individually and independently, by taking into account their best individual interest. 3.3 Non-strategic player Recent empirical papers (e.g. Chang and Schoar (2007), Bris et al. (2006)) show that behavioral di erence among the bankruptcy judges is an important characteristic of the supervising bankruptcy Court, which has an impact on the outcome of the process. Bris et al. (2006) empirically document three factors that statistically di erentiate judges: the fraction paid out to creditors in case of cram-down, the duration of Chapter 11 negotiation, and the violation of the APR. In that spirit, we allow the bankruptcy judge to have an important role in the negotiation process. Thus, the judge has the opportunity to decide on the maximum number of negotiation rounds, denoted K, and to interfere and stop the process at each round k K with a known probability, denoted q k. This probability re ects the impatience of the judge, which can increase with each 4 Under the Code, the requirements for the approval are two-thirds in value and a majority in number for each class of creditors, and two-thirds in value for shareholders. 10

11 bargaining round and the length of the negotiation process. The judge can interfere to impose, or cram-down, a reorganization plan; this plan may be the last plan proposed, or the judge may decide to impose her own reorganization plan, where z 2 [0; 1] de nes the probability that the judge will impose her own plan. The judge s plan can be related to a bargaining solution where she decides on the bargaining powers of the claimants. We assume that these bargaining powers, denoted ; describe the judge s attitude towards the claimants. Finally, the judge can also stop the process by converting Chapter 11 negotiation into Chapter 7 liquidation. 5 The judge is thus characterized by the parameters K, q k, z, and, which we assume known by all the claimants at the beginning of the negotiation process. 3.4 Outcomes In each successive negotiation round, one of the player proposes a reorganization plan, and the other two vote to accept or reject it. We consider three possible outcomes. In the rst case, the rm is reorganized and emerges as a new entity. This new rm may be shared between the claimants according to the plan proposed at that round (if the players agreed on it, or if the judge imposed it), or according to the judge s plan. In the second case, the rm is liquidated. This happens if the plan is unanimously rejected and if the judge decides to stop the negotiation process. Finally, in the third case, the game moves to the next negotiation round, where another player is selected to propose a new reorganization plan. This happens if the players do not agree to implement the plan, and the judge does not interfere in the bargaining process. 5 To liquidate the rm, the bankruptcy judge can invoke one of the causes described in section 1112(b)(4) of the Bankruptcy Code. For example, showing that there is substantial or continuing loss to the estate and the absence of a reasonable likelihood of rehabilitation. Other causes can include some negotiation technicalities. 11

12 Empirical ndings (see Carapeto, 2005) show that successfully reorganized rms may need more than one reorganization plan. This cannot be explained in a perfect and complete information setting, since negotiation is costly and time-consuming. In our model, the possibility of reaching an agreement in more than one negotiation round is explained by the uncertainty about the judge s intervention in the negotiation process. 3.5 Bankruptcy costs Financial distress costs Here, we model the nancial distress costs to be borne by the claimants as a sum of a xed costs and a proportional cost to the time spent in the negotiation process. 6 Thus, if the process duration is of k bargaining rounds of length d, the proportional nancial distress costs are given by kd. These costs a ect directly the value to be shared by the claimants; if the rm is reorganized, then these costs reduce the total value of the assets to be shared, while if the rm is liquidated, they are deemed in priority from the remaining assets value. This is equivalent to assuming that proportional nancial distress costs reduce the assets value of the rm during the negotiation process. Moreover, the xed part is assumed to be proprtional to the value of the assets at the entry in Chapter 11 and is given by. These costs do not a ect the negotiation process once the rm enters Chapter LoPucki and Doherty (2004) nd that the amount of legal fees depend primarily on the rm s size, measured by assets, and the total time elapsed from ling to con rming reorganization plan. Bris et al. (2006) approximate indirect nancial distress costs by the reported asset value changes during bankruptcy and the time spent in reorganization. François and Morellec (2004) model nancial distress costs as a continuous proportion of the remaining asset values, paid while the rm is under reorganization. 12

13 3.5.2 Liquidation costs Liquidation costs are assumed to be proportional to the rm s remaining asset value, net of nancial distress costs. The proportion of the asset recovered in a liquidation is denoted by 1. 4 Solving the negotiation game In this section, we solve for the equilibrium strategies of the three strategic players, and obtain, for each player, the expected outcome value of the negotiation game, at the moment the default event is triggered. The entry in Chapter 11 negotiation is characterized by the initial (contractual) coupon and by the rm s asset value at the default occurrence, which are taken here as parameters. We rst de ne precisely the timing of events from the default occurrence, over an in nite horizon. The game is then solved by backward induction. 4.1 Time sequence of events The rm s asset process is denoted V t, and the initial contractual coupon is denoted c 0 = c 0 s + c 0 j, where c0 s is the senior debt coupon and c 0 j is the subordinated debt coupon. The rm enters Chapter 11 negotiation at time t = 0 and asset value V 0. We model the evolution of the rm from t = 0 over an in nite horizon (see Figure 1). At t = 0, coupon and dividend payments are suspended. The DIP then has d units of time to prepare a rst reorganization plan to be submitted to the creditors. At t = d, the rst plan is proposed to the creditors. If both creditors approve the plan, or if the judge intervenes and imposes a plan, a new reorganized rm emerges; this rm distributes dividends and new reorganized coupons, and 13

14 continues its operations until a default barrier is reached at T. If the judge intervenes and imposes liquidation, the rm is liquidated according to the APR and the process terminates. Otherwise, the junior creditor has d units of time to prepare a second reorganization plan to be submitted to the two other players. At t = 2d, the second plan is proposed to the equity holder and to the senior creditor. Again, the rm may emerge if both players approve the plan, or if the judge cram-downs a plan, or may be liquidated if the judge so decides. Otherwise, the senior creditor has d units of time to prepare a third reorganization plan to be submitted to the two other players. At t = 3d, the third plan is proposed, with the three same possible outcomes. If the process continues, the claimants alternate in proposing reorganization plans following the same sequence (i.e. equityholder, then junior creditor, then senior creditor), until either the rm is reorganized or liquidated. Finally, we assume that any further nancial distress after the rm emerges from Chapter 11 leads to the liquidation of the rm. 4.2 Liquidation values If the rm is liquidated after k negotiation rounds at time t = kd and asset value v = V t, the senior, junior and equityholders liquidation payo s, according to APR, are given respectively by and! L j (v) = min! L s (v) = min " max (1 ) v; c0 s ; (2) r # (1 ) v! L e (v) = max (1 ) v c 0 s r ; 0 ; c0 j r ; (3) c 0 r ; 0 : (4) We denote by! L (v) =! L s (v);! L j (v);!l e (v) the vector of liquidation values at v: 14

15 4.3 Emergence values If the rm emerges from nancial distress after k negotiation rounds at time t = kd and asset value v = V t, then the reorganized rm continues its operations by distributing new coupons c = c s + c j to the senior and junior creditors respectively, until further default at T > t. At default time T, the rm is liquidated following APR and incurs proportional liquidation costs. The value at (t; v) of the reorganized rm depends on the reorganized coupon and is given by: " Z T E vt (c + V u ) e r(u t t) du # i + (1 )E vt he r(t t) D (5) where E vt () denotes the expectation E Q (jt; V t = v) under the risk-neutral measure Q, represents the tax rate and D is the default barrier. Firm speci c values are indexed by F. Under our assumption that further default leads to immediate liquidation, the value of the rm after emergence, which is the object of bargaining between claimants, is given by (see Leland, 1994):! R F (v; c) = v + c! =(1 ) =(1 ) D D 1 D (6) r v v where = + ++, = r 2 2 and = p 2r + 2 : The rst term in (6) is the value of the assets at the emergence time, the second term is the present value of tax bene ts of the operating rm, and the third term is the present value of liquidation costs. Moreover, under the APR, the value of senior debt is given by! =(1 ) D h 1 + min (1 ) D; c s v r! R s (v; c) = c s r i =(1 ) D (7) v 15

16 and the value of junior debt is given by = c j r! R j (v; c) 1! =(1 ) D h h + min max (1 ) D c i s v r ; 0 ; c j r i =(1 ) D (8): v Following Leland (1994), we assume that default is decided by equityholders, and that D is determined so as to maximize equity value, given the limited liability of equityholders. The optimal liquidation barrier for equityholders is then: D = (1 ) c: (9) r Notice that the reorganized coupon c has a direct impact on the liquidation barrier. Using (9) and rearranging, the total value of the rm and the payo s of the claimants at (t; v) when the reorganized coupon is c are given by:! R F (v; c) = v (1 + rv c 1 +! R s (v; c) +! R j (v; c) = v rv c 1 1 (1 (1 )! 1=(1 ) ) c ; (10) rv! 1=(1 ) ) c rv (11) and! R e (v; c) = v (1 ) (1 c + (1 ) rv! 1=(1 ) ) c : (12) rv Notice that, at a given (t; v), both the value of the reorganized rm and of the reorganized debt are concave in c, while the value of equity is decreasing in c. We denote by! R (v; c) =! R s (v; c);! R j (v; c);!r e (v; c) the vector of reorganization values at v when the reorganized coupon is c. 4.4 Bankruptcy judge s plan A reorganized rm may emerge from nancial distress after k negotiation rounds at time t = kd and asset value v = V t under the bankruptcy judge s 16

17 plan. Our de nition of the judge s plan is consistent with the Code, which stipulates that the cram-down plan must be fair and equitable. To model the fairness condition, we assume that the judge s plan gives to each player at least his liquidation payo, thus ruling out APR violation, and shares the residual value among the claimants according to some sharing vector, denoted by = s ; j ; e ; satisfying: 0 i 1; i 2 fs; j; eg X i2fs;j;eg i = 1: Thus, if the judge imposes her reorganization plan, corresponding to a reorganized coupon c; at v = V t, we assume that each claimant s payo satis es! R i (v; c) = i! R F (v; c) (1 )v +! L (v), i {z } i 2 fs; j; eg (13) Residual value where! R F (v; c) is de ned in (10) and the!l (v) are de ned in (2) i (4). The sharing vector de nes the proportion of the bene ts of cooperation that each player gets from the judge s plan, which can be assimilated to the solution of a Nash bargaining game, where represents the vector of the claimant s bargaining powers, and where the liquidation payo s represent the non-cooperation threat. For a given v, the reorganized coupon satisfying (13) is denoted by c (v) and is obtained by solving! R e (v; c ) e! R F (v; c ) (1 )v =! L e (v): (14) which has a unique solution (see Appendix A.3). 4.5 Continuation values If the rm is neither reorganized, nor liquidated after k negotiation rounds, then we de ne continuation values at time t = kd and asset value v = V t, which 17

18 are the expected values of the players payo s at the next negotiation round, taking into account the dynamics of the rm s asset value and the nancial distress costs. Denote! (v; k) =! s (v; k) ;! j (v; k) ;! e (v; k) the vector of equilibrium outcomes of negotiation round k, at t = kd, k 2 [1; K], that is, for i 2 fs; j; eg : 8! L i (v) if rm is liquidated at k ><! i (v; k) = (v; c) if rm is reorganized at k with new coupon c >:! R i! C i (v; k) otherwise. The continuation value for each player at t = kd, k 2 [0; K], v = V t is then de ned by:! C i (v; k) = e rd E vt! V (k+1)d ; k + 1, i 2 fs; j; eg, k < K (15)! C i (v; Kd) = 0, i 2 fs; j; eg We denote! C (v; k) =! C s (v; k) ;! C j (v; k) ;!C e (v; k) the vector of continuation outcomes at (v; kd) and! C F (v; k) =!C s (v; k) +! C j (v; k) +!C e (v; k) the continuation value of the rm at (v; kd), k 2 [0; K] : 4.6 Equilibrium solution of a negotiation round game Table 1 presents the normal form representation of the game at a given round k, between the claimant who proposes a reorganization plan, labelled 0 for "Leader", and the other two claimants, labelled 1 and 2 for "Follower 1 and Follower 2", who vote on it. Figure 2 is a game-tree representation of the rst round game. The outcome of a given negotiation round depends on the pair of binary decisions made by Followers 1 and 2, on the plan proposed by the Leader, on the continuation values, and on the judge s characteristics. We use a Stackelberg/Nash equilibrium solution concept to solve this three-player game, where the outcomes are vectors in R 3. Thus, when the Leader proposes his 18

19 reorganization plan, he takes into account the reactions of the two Followers, where neither player has a unilateral incentive to change his strategy. Notice that a reorganization plan is completely de ned by a proposal c = (c s ; c j ) for the reorganized coupon, which is su cient to compute the share of each player in the reorganized rm, according to (7), (8) and (12). We rst solve for the best proposal of the leader leading to the four pair of binary decisions by the followers, denoted (D 1 ; D 2 ) ; where D i 2 fa; Rg is the decision of Follower i, A stands for Accepting the leader s plan and R stands for Rejecting the leader s plan". This proposal is a plan c = (c s ; c j ) which is the solution, at a given t = kd; v = V t, of the following optimization problem 7 : max! 0(v; k) (16) c s.t.! i (v; k) Q b ik, i 2 f1; 2g (17) where b ik represents what Follower i can achieve by unilaterally deviating from his decision. 1. If both followers accept the plan, or the decision pair is (A; A), the outcome vector is! R (v; c). In that case, the leader s best proposal is the solution of max! R 0 (v; c) :! R i (v; c) b ik, i 2 f1; 2 (18) c where b ik is obtained by comparing the reorganization payo with the expected outcome when one of the followers accept the plan, while the other rejects it,! R i (v; c) q k z! R i v; c + (1 z)! R i (v; c) + (1 q k )! C i (v; k) 7 The detailed algorithm is presented in Appendix B. 19

20 or, equivalently: 8 >< b ik = >: q k z! R i (v;c )+(1 q k )! C i (v;k) 1 q k (1 z) if q k (1 z) < 1 1 otherwise., i 2 f1; 2g. (19) Denote c AA (v; k) the solution of (18) and! AA i (v; k) the outcome for Player i, i 2 f0; 1; 2g when the leader proposes plan c AA (v; k) so that the equilibrium reaction of the followers is (A; A) : 2. If Follower 1 accepts the plan while Follower 2 rejects it, or the decision pair is (A; R), then the outcome vector is q k z! R v; c + (1 z)! R (v; c) + (1 q k )! C (v; k). The leader s best proposal is the solution of max! R 0 (v; c) :! R 1 (v; c) b 1k,! R 2 (v; c) b 2k (20) c where b 1k ; b 2k are obtained by requiring q k z! R 1 v; c + (1 z)! R 1 (v; c) + (1 q k )! C 1 (v; k) q k! 0 1(v) + (1 q k )! C 1 (v; k) q k z! R 2 v; c + (1 z)! R 2 (v; c) + (1 q k )! C 2 (v; k)! R 2 (v; c) or, equivalently: b 1k = b 2k = 8 >< >: 8 >< >:! L 1 (v) z!r 1 (v;c ) 1 z if z < 1 and q k > 0 q k z! R 2 (v;c )+(1 1 otherwise, q k )! C 2 (v;k) (1 q k (1 z)) if q k (1 z) < 1 q k! R 2 v; c + (1 q k )! C 2 (v; k) otherwise. (21) (22) 3. The leader s best proposal corresponding to the decision pair (R; A) is obtained by changing the identity of the Followers. Denote c AR (v; k) and c RA (v; k) the solution of (20) ; and! AR i (v; k) (resp.! RA i (v; k)) the outcome for Player i, i 2 f0; 1; 2g when the leader proposes plan c AR (v; k) (resp. c AR (v; k)) so that the equilibrium reaction of the followers is (A; R) (resp. (R; A)): 20

21 4. If both followers reject the plan, the outcome vector is q k! L (v) + (1 q k )! C (v; k), which does not depend on c. It su ces that the leader proposes nothing to both followers to achieve this outcome. Denote this plan c RR (v; k) and! RR i (v; k) the outcome for Player i, i 2 f0; 1; 2g when the leader proposes plan c RR (v; k) so that the equilibrium reaction of the followers is (R; R) : The solution of optimization problems (18) and (20) depends on the identity of the leader, and can be obtained analytically (see Appendices A.1 and A.2). The equilibrium strategy vector of the negotiation round, denoted (v; k) = f i (v; k)g, i 2 f0; 1; 2g, is obtained by comparing the leader s outcome corresponding to the four possible decision pairs. The leader s equilibrium strategy is the one that maximizes his share, so that the equilibrium outcome vector and strategies at t = kd, v = V t are given by: D (v; k) = arg max D 1D 2 f! D1D2 0 (v; k)g 0 (v; k) = c D (v;k) (v; k) i (v; k) = D i (v; k), i 2 f1; 2g! i (v; k) =! D (v;k) i (v; k), i 2 f0; 1; 2g: (23) 4.7 Equilibrium solution at rst default time Starting from the last negotiation round, the equilibrium outcome vector is obtained by backward induction as a function of t = kd and v = V t. Notice that the equilibrium outcome vector at a given k cannot be obtained in closed form as a function of v, and we use a numerical algorithm to compute, at a given negotiation round, the outcomes of claimants on a grid of discretized asset values. Each claimant s outcome function at a given k is then approximated by a piecewise linear interpolation function, which is used in (15) to obtain the 21

22 continuation value. Finally, the expected outcome of the negotiation process for each claimant at the default event (t = 0), as a function of the default barrier V 0 for a given contractual coupon c 0 is given by! C i (V 0; 0). 5 Numerical illustration This section provides a detailed analysis of the equilibrium probabilities and their sensitivity to the di erent parameters and variables of the model. 5.1 Data Data sources and sample selection Our sample consists in public US rms that led for Chap 11 from 1997 to In this sample, we include rms which default time is maintained by New Generation Research, Inc. ( Our initial sample contains 1811 rms that were either liquidated, reorganized or merged after ling for Chap 11. We then apply the following lters:. First, we select large companies with total asset value of more than $1 Billion. This rst lter leads to 190 rms. Second, we exclude nancial rms, insurance, real estate and public administration rms since they have a di erent treatment under Chapter 11. The second lter leads to 163 rms. Because we use rm characteristics recorded in COMPUSTAT, we exclude 25 rms not covered by this database. Among the rms left, one was registered twice 8 and two rms led for Chapter 11 twice 9 during our sample period. Our nal sample consists of 135 rms and 137 Chapter 11 cases. Two rms in our sample have led for Chapter 11 twice. 8 US Airways was reported as Passenger Airline that entered into Chap 11 in 08/11/2002 and as Holding company for Passengers Airlines that defaulted in 09/12/2004. We keep only the rst observation. 9 Montgomery Wald Holding led for Chapter 11 in 07/07/1997 and then in 12/28/2000. McLeod USA INC defaulted in 1/30/2002, emerged and then defaulted again in We keep both Chapter 11 events. 22

23 Table 2 provides information on ling dates as well as the sector distribution. Unsurprisingly and as shown by Panel A, the majority of the rms in our sample led for Chapter 11 during the recession. Moreover, Panel B shows that the transportation and utilities sector had the highest default rate Data description Our goal is to characterize a typical rm initiating a Chapter 11 reorganization. Table 3 provides information on rm characteristics including the drift of the assets value, the volatility parameter, the payout ratio, the coupon rate c 0 V 0, the initial assets value V 0 and the share of senior debt in total debt denoted. The parameters are computed using a sample of rms over the three years prior to their lings for Chapter 11. The payout rate is calculated from the quarterly balance sheet as a weighted average of the rms revenue rate on the 12 quarters preceding Chapter 11 ling, such that = Coupon Rate Leverage + Dividend Yield (1-Leverage) (24) where the Coupon Rate is approximated by 0 X the Leverage by Leverage = Coupon Rate = X n=1:n 0 X i=1:12 X n=1:n i=1:12 X i=1:12 X i=1:12 I n t e r e s t P a i d n;i 12 T o t a l L ia b ilit i e s n;i N 12 T o t a l L ia b ilit i e s n;i 12 T o t a l L ia b ilit i e s n;i i=1: N X 1 C A n T o t a l E q u i ty n;i 12, (25) 1 C A n, (26) 23

24 and nally the Dividend Yield by Dividend Yield= X n=1:n 0 X i=1:12 X i=1:12 C a s h D i v i d e n d s n;i 12 T o t a l E q u i ty n;i N 12 1 C A n. (27) Finally, the share of senior debt is computed from the annual balance sheet over the three years preceding Chapter 11 ling as 10 = 1 0 X n=1:n X i=1:3 X i=1:3 D e b t S u b o r d in a t e d n;i 3 T o t a l L ia b ilit i e s n;i N 3 1 C A n (28) The drift and volatility parameters are computed using the following relationships: E s ln Vt V s = 2 (t s), for s < t (29) 2 and V ar s ln Vt V s = 2 (t s), for s < t: (30) Therefore, we estimate the asset s volatility by computing the standard deviation of the quarterly logarithmic distribution of the returns, as described in (30). The risky return is estimated by replacing the payout rate and the volatility by their values in the expression of the drift (29). Regarding the estimation of the tax rate, we assume a constant rate of 35%. 11 Finally, we approximate the risk-free interest rate r by the average 10 years Constant Maturity Treasury (CMT), which is 3:83% The quarterly amout of Debt Subordinated is not reported by COMPUSTAT. 11 We conduct an estimation of the tax rate using quarterly and annual COMPUSTAT data, as the ratio of Taxes paid over the income before taxes of the preceding scal year. We nd out that rms in the years preceding the entry in Chapter 11 have on average negative income before tax, and therefore we obtain negative taxes. 12 Source: 24

25 Table 4 summarizes the base case values of the parameters that we use in our numerical illustration to describe Chapter 11 negotiation. Regarding the bankruptcy costs, the literature o ers di erent estimation methods and a wide range of values. 13 In this paper, we use the estimation provided by Bris et al. (2006) for the following reasons: First, they treat simultaneously the estimation of the nancial distress costs and the liquidation costs. Second, they have the largest Chapter 11 sample used to calculate costs. 14 Finally, their sample data range ( ) is close to ours. Therefore, we x the liquidation costs at 8:1% of the assets value at liquidation, and the xed nancial distress costs at 16:9% of the pre-bankruptcy assets value V 0. The proportional nancial distress costs can be arbitrarily set to any value in [0; KV 0 ], where K is the maximum number of negotiation rounds. The maximum value is set such that the value of the assets is destroyed at the end of the baragaining process. There is less empirical evidence on the bankruptcy judge s parameters. Following the Bankruptcy Code (s 1121), the debtor must le a reorganization plan within 120 days of the bankruptcy ling. This period can be and usually is extended upon the debtor s requests. We assume that the length of a bargaining round is 6 months, i.e. d = 0:5. Moreover, we assume a total number of negotiation rounds of K = 3, thus allowing each claimant to present its reorganization plan. 15 Moreover, we assume that the judge s impatience is an 13 These costs can be estimated as a percentage of rm value prior to bankruptcy (Warner (1977), Altman (1984), Weiss (1990), (Almeida and Philippon (2007)), total liquidating value of assets (Ang, Chua and McConnell (1982)), pre-bankruptcy assets (Bris et al. (2006)), assets at beginning of case (Luben (2000), LoPucki and Doherty (2004)). Financial distress costs values are very heterogenous, and range from an average of 1:4% of assets at beginning of Chapter 11 case (LoPucki and Doherty (2004)) to 16:9% of pre-bankruptcy assets (Bris et al. (2006)) 14 For example, Altman (1984) use a sample of 19 Chapter 11 cases, Weiss (1990) 37 Chapter 11 cases, Betker (1997) 75 traditional Chapter 11 cases and LoPucki and Doherty (2004) 48 cases. 15 Carapeto (2005) shows that on a sample of 144 Chapter 11 rms that reorganized successfully over the period , the average number of reorganization plans of rms with more than one plan is 3:2. Moreover, she shows that about two-thirds of Chapter 11 rms 25

26 increasing function of the elapsed time in the reorganization process, i.e. q k = k K for 1 k K, and that the judge is equally likely to impose her own plan as the last proposed plan, such that z = 0: Bargaining powers Building on the ndings of Bris et al. (2006) and Chang and Schoar (2007), we assume that the judges are grouped into three classes: equity-favouring, neutral and creditor-favouring judges. 16 In our model, a neutral judge does not change the distribution of bargaining powers in the distressed rm in case of immediate liquidation which results in the following claimants bargaining powers n n i (v) =!L i (v)! L, i 2 fs; j; eg, (31) (v) and X n i (v) = 1 (32) i=fs;j;eg Equity or creditor favouring judge have relatively important deviations (in our numerical illustrations, we use = 40%) from the neutral bargaining power vector. Hence, for an equity-favouring judge, the bargaining powers become: e e (v) = min ( n e (v) + ; 1), 0 1 e s (v) = (1 e e) c0 s c 0, (33) whereas a creditor-favouring judge uses the following: c e (v) = max ( n e (v) ; 0), 0 1 c s (v) = (1 c e (v)) c0 s c 0 : (34) require more than one plan of reorganization before an agreement can be attained. Moreover, on average, the one-plan rm spent 100 days in chapter 11 and the multi-plan rm almost a year. 16 In this study, we are not looking for the motivations beyond judge s behavior, but rather for its impact on the equilibrium strategies and the value of claims in the reorganized rm. 26

27 As discussed in section 4:4, the judge does not decide directly on the di erent shares to be o ered to the claimants but rather on the allocation of the residual value which is proportional to the claimant s bargaining powers. Figure 4 shows the resulting claimants shares as a function of the assets value. Notice that, except for very high values of the assets, the impact of judge s behavior on cram-down shares is not very important, which re ects the fairness assumption. The judge grants to each claimant a liquidation payo that respects the Absolute Priority Rule, and then distributes the residual value. However, for nancially distressed rms with low assets values, once the nancial distress costs are redeemed, the residual value is very low which makes the impact of the judge s behavior in these cases relatively minor. Figure 3 shows how each claimant s bargaining powers evolve as a function of the asset value for three scenarios of bankruptcy judge s behaviors: equityfavouring, neutral and creditor-favouring. The top panel shows that when the bankruptcy judge is neutral, the creditors hold the total control of the rm for moderate states of the assets which is the case of the pre-bankrupt rm. In fact, the senior creditor controls the rm as long as the liquidation value does not exceed his coupon. When the assets value increases but not high enough to redeem both senior and junior coupons, the junior creditor starts gaining power while the residual claimant is left with nothing. Finally, when the rm becomes able to repay both coupons, the equityholder s bargaining power increases at the expense of creditors bargaining powers (for V t > 119:06). Compared to the neutral behavior case, a creditor-favouring judge is more concerned by favoring both creditors overs the equityholders. Indeed, the junior creditor bargaining powers is higher while the senior bargaining powers is lower for moderate asset values. Finally, the bottom panel shows that the impact of an equity-favouring 27

28 judge on the claimant s bargaining powers is more important when the threat of liquidation fades, which allows equityholders to control the rm. 5.3 Outcomes of Chapter 11 reorganization In this section, we analyze the determinants of the equilibrium outcomes at the end of each bargaining round. These outcomes are: liquidation of the rm under Chapter 7, reorganization of the rm and its emergence as a viable entity, or continuation of the negotiation process to the following round. Our numerical algorithm computes, at each negotiation round, the intervals for the value of the assets v over which the equilibrium strategy pairs of the followers are constant. In the overwhelming majority of cases, we nd three distinct equilibrium regions in the assets space: for bad states of the assets (where v 2 R k ), at equilibrium both followers reject the plan, and the rm is liquidated with probability q k while the negotiation continues to the next round with probability (1 q k ); for states where the rm is recovering (where v 2 A k ), at equilibrium both followers accept the plan, and the rm is reorganized under the leader s plan. for good states of the assets (where v 2 M k ), at equilibrium one of the followers accepts the plan, while the other rejects it, and the rm is reorganized with probability q k while the negotiation continues to the next round with probability (1 q k ). In some few cases however, we nd di erent behaviors. For instance, an unreported analysis shows that when the probability that the judge imposes her own plan is high (for example z = 0:9) and the game lasts at most three 28

29 bargaining rounds (K = 3), the A k set is formed of two disjoint intervals at k = f1; 2g. In this case, the weight on the judge s plan in each claimant s continuation payo is high, and the shape of the cram-down shares as reported in Figures 4 a ects what the leader has to o er to the other claimants. Once the equilibrium regions are de ned, we compute at the end of each negotiation round the probability that the asset value be in each of these regions, conditional on the outcome of the preceding round, from which the probability of liquidation and emergence at each negotiation round is obtained (see Appendix C for details). Table 5 reports on the liquidation and reorganization probabilities at the end of each round when the time-proportional nancial distress costs are high, moderate and null. The choice of the cost range is based on the ndings of Bris et al. (2006) where nancial distress costs are considered high if all existing assets are used to cover these costs, and moderate if they are lower than the total value of existing asset. Our base case moderate nancial distress costs imply equilibrium liquidation probabilities that are consistent with the empirical frequencies reported in Altman and Hotchkiss (2006) (21:5%) and Denis and Rodgers (2007) (18%). Comparing the equilibrium probabilities in Table 5, we observe that the total liquidation probability is a non-decreasing function of the time-proportionnal nancial distress costs and a decreasing function of the remaining time in negotiation. Panel A shows that the rm is not liquidated if there is no timeproportionnal nancial distress costs. Moreover, unreported results shows that in that case, the leader has no interest in reorganizing the rm, and rather prefers the continuation of the negotiation until the last round. 29

30 Another related issue is the relationship between the equilibrium outcomes and the length of negotiation. At the rst round, the perspective of continuation leads the equityholder to propose a plan that is rejected by both creditors for low assets values, and accepted by them for moderate values. This allows all the claimants to avoid paying heavy nancial distress costs because the perspective of recovering from nancial distress in the next round is unlikely. For higher assets values, the equityholder proposes a plan that is accepted only by the senior creditor, granting the possibility of continuation if the judge does not interfere in the negotiation. At the second round, the equilibrium outcome depends on the number of remaining negotiation rounds. If the second round also happens to be the last one, then the junior creditor proposes a plan that is rejected by one of the remaining claimants for moderate to high asset values. However, when one negotiation round is remaining, the junior creditor proposes a plan that is rejected by both claimants for lower assets values, and accepted for moderate ones. For high values of the assets, the plan is accepted by only one claimant and the negotiation is likely to move to the next round. 5.4 Sensitivity analysis In this section, we analyze the sensitivity of the equilibrium strategies to the assets volatility, which captures the depth of nancial distress, and the negotiation speci c factors. 17 Table 6 provides some insights on the relationship between assets volatility and the equilibrium probability. It shows that, at the end of the rst bargaining round, the liquidation probability increases with the volatility at the expense of the reorganization probability. This result is to be related to the convex relationship between the equityholder s claim and the 17 We also conducted further analysis to measure the sensitivity of the results to the priority of senior debt, the arbitrary default barrier V 0 and the contractual coupons. None of these tests are conclusive. 30