Chapter 9 Bankruptcy procedures 9.1 Critique of existing procedures (i) Auctions. The problem with auctions is that assets sold o? piecemeal may be sold at a substantial discount. ? The financing problem. It takes too long to raise money from a large number of investors. A small number of investors may be risk averse and unwilling to pay the expected value of the assets. ? Lack-of-competition problem. The costs of participating in an auction keeps the numbers small. (ii) Structured Bargaining. (E.g., Chapter 11). Chapter 11 mixes two kinds of problems, who should get what (whose debt forgiven and by how much) and what should be done with the firm (liquidated, re-organized, and if re-organized under what financial structure). Conflicts of interest and asymmetric information are likely to lead to breakdown. Placing decisions in the hands of representatives and supervising judges creates agency problems. Problems with Chapter 11: (a) takes a great deal of time; (b) serious loss of value during Chapter 11; (c) significant legal and administrative costs; (d) soft on management; (e) judges abuse discretionary power. Incentives to delay: ability to delay resolution gives bargaining power to junior creditors (c.f. alternating o?ers bargaining); option value of delay in case value of assets increases. (iii) Administration. (E.g., the French system). Saves costs and unlikely to be soft on management. However, judge may not have required expertise. 1 2 CHAPTER 9. BANKRUPTCY PROCEDURES (iv) Automatic Financial Restructuring. Bankruptcy automatically trig- gers conversion of all debt to equity. The problem is there is no punishment for management and hence no bonding role for debt. 9.2 The AHM-Bebchuk procedure The goal of a good procedure is (i) it maximizes ex post value of the firm(with appropriate distribution across claimants) and (ii) it preserves the (ex ante) bonding role of debt by penalizing management adequately in bankruptcy states. When bankruptcy occurs, all debt is immediately cancelled. The new firm is all equity. A judge is appointed to supervise the process. He has two taskes: (A) solicit cash and non-cash bids for new all-equity firm; (B) allocate rights to the shares in the firm. Task A: Soliciting Bids. There is no di?erence between soliciting bids for the assets of the firm and a proposal to run the firm as a going concern, once non-cash bids are allowed. E.g., the management could o?er to buy the firm by o?ering one share in the new (identical) firm for each share in the old firm. Task B: Allocating Rights. Assume that the value of the claims is settled as under existing procedure (Chapter 11 or Chapter 7). Then there are n classes of creditors (i =1,...,n)whoareowedD 1 ,...,D n ,where1 is most senior, 2 next most senior, etc. Shareholders are class n +1. Suppose that V is the publicly known value of the firm. Then class i receives S i ,where S 1 =min{V,D 1 } and S i is determined recursively by the formula S i =min{V ? X j<i S j ,D i },i=2,...,n and the shareholders receive what is left over S n+1 = V ? n X i=1 S i . Since V is not known, Bebchuk has constructed the following scheme. 9.2. THE AHM-BEBCHUK PROCEDURE 3 ? The most senior class (class 1) is allocated 100% of firm’s equity (a creditor owed d 1 receives a fraction d 1 /D 1 of shares). The firm has the right to redeem the claim at a price of D 1 . ? The next most senior class (class 2), is given the option to buy equity at a price of P 2 = D 1 ;however,thefirm can redeem this claim at a price of D 2 . ? Class i investors (3 ≤ i ≤ n) have the option to buy equity at P i = P j<i D j , but the firm can redeem the claim at D i . ? Shareholders (i = n+1)can buy equity at a price of P n+1 = P n i=1 D i . ? After the options have been exercised, there is a vote by the new equity holders on which of the cash and non-cash bids to accept. Suppose that various bids have been received but that di?erent classes of creditors believe the bids are worth di?erent amounts (recall that there are non-cash bids). Let class i’s valuation of the best bid be V i . How will the Bebchuk scheme work? Class i>1 will want to buy equity if V i >P i .What if this is true for more than one class? Presumably the firm’s right to redeem the claim takes precedence over the right to buy and the most junior creditor for whom V i >P i gets to buy the equity. However, this may not be the creditor for whom the value of the firm is the highest. But perhaps one gets closer than by other methods. Aghion, Hart, and Moore (1992) claim that this procedure solves the financing problem by allowing non-cash bids. It does not deal directly with the lack-of-competition problem, but they say that allowing non-cash bids is likely to mitigate it. It replaces structured bargaining by a simple vote. Unlike automatic financial restructuring, which leaves incumbent man- agement in place, incumbent management remains only if there is an explicit vote by shareholders to retain them. References: Aghion, Philippe, Oliver Hart, and John Moore. “The Economics of Bankruptcy Reform,” Journal of Law, Economics, and Organization 8(1992) 523-546. Hart, Oliver. Firms, Contracts, and Financial Structure (Clarendon Lec- tures in Economics). Oxford: Oxford University Press (1995). 4 CHAPTER 9. BANKRUPTCY PROCEDURES Bebchuk, Lucian. “A New Approach to Corporate Reorganizations,” Harvard Law Review 101 (1988) 775-804. 9.3 An equilibrium model of bankruptcy Suppose there is a single bid for the firm consisting of C ≥ 0 units of cash and the equity in the re-organized firm. If the bid is all cash then the distribution problemis trivial, sothere is no loss of generality inassuming that theamount of equity is positive. Without loss of generality we can normalize the number of shares to equal one. There are n classes of debt (i =1,...,n) arranged in decreasing order of seniority. The face value of the i-th class of debt is denoted by D i > 0.The equity in the original firm is the (n +1)-th class security. There is assumed to be one share in the original firm. There is a (non-atomic) continuum of agents A =[0,1] endowed with Lebesgue measure. The assumption that agents form a non-atomic contin- uum implies that an individual has no “market power”. Each agent a has w(a) units of cash, d i (a) units of the i-th class of debt, and d n+1 (a) units of equity. Let d(a) ≡ (d 1 (a),...,d n+1 (a)) represent the portfolio of agent a. Each agent has a linear utility function for cash and equity. If agent a holds x units of cash and e units of equity his utility is x + v(a)e.Inother words, v(a) is the monetary value agent a places on one unit of equity in the re-organized firm. We assume that the functions v(·),w(·) and d(·) are Lebesgue integrable. 9.3.1 Competitive equilibrium An allocation is a measurable function f : A→ R + ×R + ,wheref(a)=(x,e) is the portfolio of cash and equity allocated to agent a. An allocation f is attainable if Z f(a)da =(W + C,1), where W = R w(a)da is the aggregate initial endowment of cash. Let V be the equilibrium value of the equity. The equilibrium price of 9.3. AN EQUILIBRIUM MODEL OF BANKRUPTCY 5 the class i security is denoted by p i ≥ 0 and defined by p i = min n V + C ? P j<i p j D j ,D i o D i ,i=1,...,n, (9.1) p n+1 = V + C ? n X j=1 p j D j . (9.2) Let p =(p 1 ,...,p n+1 ) denote the vector of equilibrium security prices. A competitive equilibrium consists of the market value of the firm V, a vector of security prices p ≥ 0 satisfying (9.1) and (9.2), and an attainable allocation f such that, for almost every agent a ∈ A, f(a) maximizes x + v(a)e subject to the budget constraint Ve+ x ≤w(a)+p·d(a) and the non-negativity constraint (x,e) ≥ 0. An attainable allocation f is Pareto-e?cient if there does not exist an attain- able allocation f 0 such that f 0 (a) is weakly preferred to f(a) for almost every a and f 0 (a) is strictly preferred to f(a) for a non-negligible set of agents. Theorem 1 If (f,V,p) is a competitive equilibrium then f is Pareto-e?cient. This is just the first theorem of welfare economics, of course. The non- standard part is the definition of security prices to allocate the value of the firm among the di?erent creditors. These prices do not play any role in clear- ing markets; they merely serve to allocate the value of the firm according to the seniority of di?erent classes of debt and equity. An important observation is that any price vector p is consistent with e?ciency. In other words, the fact that debt claims can be used to purchase the firm increases the market value of the firm V but does not a?ect the e?ciency of the outcome. 9.3.2 Lex-e?ciency An attainable allocation f respects limited liability if f(a) is weakly preferred to (w(a),0) for almost every agent a. 6 CHAPTER 9. BANKRUPTCY PROCEDURES A vector of security prices p is said to respect seniority if p i =0=? p i+1 =0,i=1,...,n; p i+1 > 0=? p i =1,i=1,...,n. An attainable allocation f is said to respect seniority if there exists a price vector p that respects seniority and (1,v(a)) ·f(a)=w(a)+p·d(a), for almost every a. Let F denote the set of attainable allocations that respect seniority and limited liability. An allocation f is lex-e?cient if it is Pareto e?cient and belongs to F. The “lexicographic” part of the definition follows from the fact that allocations in F can be ranked “lexicographically” considering first the welfare of holders of class 1 debt, then the welfare of holders of class 2 debt, ... and finally the welfare of shareholders. Note how a lex-e?cient allocation di?ers from a competitive allocation: here the high valuation debt holders do not get any surplus. If f is lex-e?cient, then it must satisfy the following separation property: thereexistsaV such that for almost every a f(a)= ? (0,x) if v(a) <V (e,0) if v(a) >V . The separation property is su?cient for f to be Pareto-e?cient. Proposition 2 Suppose that f is attainable and satisfies the separation prop- erty. Then f is Pareto-e?cient. The proof of this proposition parallels the first theorem of welfare eco- nomics. So, an attainable allocation is lex-e?cient if (a) it satisfies the separation property, (b) respects limited liability and (c) respects seniority. 9.3. AN EQUILIBRIUM MODEL OF BANKRUPTCY 7 9.3.3 A strategic game Nowsupposethattheassetholdingsof all thedi?erent categories of claimants, creditors and shareholders, are common knowledge and that the preferences arecommon knowledgeamong the claimants, butnot to the receiver. Instead, the claimants report their cash endowments and valuations to the receiver, who then chooses a lex-e?cient allocation relative to the reported valuations. The claimants choose their reports to maximize their payo?s, taking as given the strategies of the other claimants and the receiver. A strategy profile is a pair of measurable functions (?w,?v):A → R + ×R + ,where?w(a) is agent a’s reported cash holding and ?v(a) is his reported valuation of the equity in the re-organized firm. For each strategy profile (?w,?v) the receiver chooses a lex-e?cient allocation f = Φ(?w,?v),wherelex-e?ciency is defined relative to the reported economy rather than the true economy. A technical problem in defining the game is that lex-e?cient allocations are only defined up to a set of measure zero. To get around this problem, we select one version of the allocation. The allocation is symmetric or anony- mous in the sense that the bundle received by an individual agent depends only on his report and the distribution of reports by other agents. Assume that the receiver chooses a market value for the firm V and a security price vector p and then gives an agent a reporting (?w(a),?v(a)), a bundle (x,e) satisfying x +?v(a)e =?w(a)+p·d(a), e =0if ?v(a) <V, x =0if ?v(a) >V. Feasibility requires ?w(a) ≤ w(a).Forany(V,p) it is a Nash equilibrium for agents to put ?w(a)=w(a) and ?v(a)=min{V,v(a)}. Proposition 3 Let (?w,?v) be a Nash equilibrium of the revelation game and let (V,p) be the prices defining the lex-e?cient allocation implemented by the receiver. Then ?v(a) ≤V for almost every a and ?w(a)=w(a) if v(a) >V for almost all a. Furthermore, there exists a Nash equilibrium in which ?w(a)= w(a) and ?v(a)=min{V,v(a)} for almost all a. If v(a) <V then agent a will receive none of the equity and so his reported valuation and wealth are (within certain bounds) indeterminate. For these agents, truth-telling is a best response, but only one of many. 8 CHAPTER 9. BANKRUPTCY PROCEDURES 9.3.4 Competitive equilibrium, once again Call f a competitive allocation if (f,p,V) is a competitive equilibrium for some prices (p,V ). Theorem 4 If f is a competitive allocation, then there exists a Nash equi- librium (?w,?v) of the revelation game such that f is lex-e?cient for the econ- omy represented by the strategy profile (?w,?v). Conversely, if (?w,?v) is a Nash equilibrium of the revelation game and f is the lex-e?cient allocation corre- sponding to (?w,?v),thenf is a competitive allocation. 9.3.5 Discussion Suppose there are three classes of claimants, senior debtholders (i =1), junior debtholders (i =2), and shareholders (i =3). Let D i denote the face value of the debt for i =1,2. There is assumed to be a unit measure of identical individuals in each class. Assume that w 2 >w 1 = w 3 =0 and v 1 >v 2 >w 2 >v 3 =0, where w i is the cash holding of a typical member of class i and v i is the valuation of the re-organized firm of a typical member of class i. (We assume that only a single plan to re-organize the firm is on the table). Consider first the case in which only cash bids are allowed. Since only class 2 has cash, the maximum cash bid will be w 2 which is less than class 2’s valuation. Thus, the market value of the firm is V = w 2 <v 2 . Thevalueofthedebtwillbe p 1 D 1 = V = w 2 ,p 2 D 2 =0. This outcome is ine?cient, because class 1 ends up holding cash, not equity, even though it values the equity more than class 2. Now suppose that a secondary market on which equity can be traded for cash opens after the resolution of the bankruptcy. What will happen? Class 9.3. AN EQUILIBRIUM MODEL OF BANKRUPTCY 9 2 will not sell for less than v 2 but class 1 cannot a?ord to buy all the stock at apricegreaterthanorequaltov 2 . Thus, the price on the secondary market must be V 0 = v 2 and class 1 will purchase a fraction α = V V 0 = w 2 v 2 of the equity of the firm. Class 2 holds the remainder, i.e., 1=α. Suppose that the opening of the secondary market had been anticipated when the bids for the firmwerebeingmade. Wouldthathavemadeany di?erence? Suppose that the bankruptcy procedure outlined above did not allow for non-cash bids? What would an equilibrium look like? Would the outcome be e?cient? One possibility is that only cash bids are recognized during the allocation process, but all proceeds are distributed ex post according to the standard procedure. In e?ect there is a credit constraint that prevents creditors from using anticipated receipts in order to bid for equity. Suppose that re-contracting is allowed, i.e., there is a second round of bidding once the proceeds of the liquidation or re-organization have been distributed. Does this guarantee e?ciency? What e?ect would the antici- pated second round have on the first-round bidding? Are all procedures equivalent with re-contracting? An important assumption in this model is that all valuations are common knowledge (except to the receiver). Would asymmetric information provide a rationale for the AHM-Bebchuk scheme?