The Threat of Bankruptcy Can Eliminate the hold-up problem

Transcription

1 The Threat of Bankruptcy Can Eliminate the hold-up problem Eric Van den Steen February 15, 000 Abstract This paper shows that hold-up inefficiencies disappear completely when the firm making the specific investments goes bankrupt if no agreement is reached. It then studies the implications for further specialization of one firm to another, for the allocation of assets and activities, and the level of debt. The result might explain the sometimes surprising efficiency of close alliances and supply relationships. It also suggests explanations for the use of option-like rewards (and layoffs) as incentive mechanisms, and for the spin-off of certain activities. Finally, the model shows why, in the presence of limited liability, one has to be very careful when arguing that sunk investments do not play a role in the ex-post bargaining. 1 Introduction Close alliances often require large specific investments and their breakdown can be very costly to the parties involved. While this suggests major hold-up problems, Holmstrom and Roberts (1998) cite the alliance between Nucor and DJJ, and supplier relationships in the Japanese automobile industry, as examples where such issues seem to be absent. This paper discusses a John Roberts support and (from time to time) critical looks were instrumental in this and other work. I also got useful suggestions from Jeff Zwiebel. Financial support from the Interuniversitair Centrum voor Managementwetenschappen (ICM/CIM) and Stanford Graduate School of Business are gratefully acknowledged. 1

2 phenomenon that can make firms whose fates are tied invest efficiently 1, even in the face of certain hold-up. Using the incomplete contracting approach pioneered by Grossman- Hart-Moore (1986, 1990, 1995, henceforth GHM), the paper shows in particular that the hold-up problem disappears when the firm making the specific investment goes bankrupt if the cooperation breaks down. To see the intuition behind this result, consider a fully debt-financed firm. Note that, in the event that this firm goes bankrupt, the investment costs will in fact be borne by the debtholders. If management maximizes shareholder value, it will thus make the efficient investment, since it should consider only the situation where the parties cooperate. This intuition also suggests where arguments that are based on the idea that the investments are sunk, might go wrong : while the investment is indeed sunk, it is not clear whose money is sunk until it is determined whether the firm goes bankrupt or not. The idea that bankruptcy might alleviate the hold-up problem 3, has already been suggested by Baldwin (1993). It was demonstrated in principle by Spiegel (1996) for the case of firm-paid investments and by Dalmazzo (1996) and Subramaniam (1996) for the case of private investments 4. The key contribution of this paper is to identify a very simple and powerful mechanism that earlier researchers have either overlooked or confused with other phenomena. The paper is also the first to show how bankruptcy can completely eliminate the hold-up problem and to derive comparative statics on the level of inefficiency. A final, and more general, contribution 1 The theory of supergames has been suggested repeatedly as a possible explanation. While such solutions require coordination of strategies and close monitoring, the mechanism discussed here modifies inherently the nature of the hold-up problem and is thus automatic. In particular, firms make ex-ante investments but cannot contract on the ex-post division of the rents. In contrast to the GHM models, investments in this paper are not of a personal nature, but are paid for by the firm. Note that this does not necessarily exclude human or social capital or effort : with on the job training, formal training programs, and incentive schemes, firms bear a large part of such costs. 3 There exists a relatively broad literature on how debt and bankruptcy influence the division of surplus in bargaining, such as Bronars and Deere (1991), Perotti and Spier (1993), Cavanaugh and Garen (1997), and Sarig (1998). Brusco (1996) considers the effect of the fact that the firm might renege on implicit contracts in case of bankruptcy. Dasgupta and Sengupta (1993) consider a model where the hold-up inefficiencies get partially neutralized by opposite inefficiencies caused by bankruptcy-induced moral hazard. 4 Subramaniam seems to assume implicitly that the investments are of a private nature, since they are considered sunk by the time of the bargaining. We argued above and do so again in section, that this treatment of costs is correct only for private investments, when the costs are not borne by the firm.

3 of the paper is to identify a situation in which our intuition on sunk costs breaks down. After setting up the model and deriving these main results in section through 4, section 5 considers the implications of the model for rent-seeking behavior, specialization of one firm to another, and the allocation of assets and activities. The key to these analyses is the fact that disagreementbankruptcy 5 removes the outside option from the equation. One implication is that the residual control over assets loses its importance as an investment incentive tool, so that it can instead be allocated on the basis of moral hazard or direct operating efficiency. This result is consistent with the fact that Japanese automobile suppliers, who tend to be very dependent on their manufacturers and have high debt, often own the dies and take up very critical activities, such as design. Section 6 extends the result to the case where both firms have specific investments. Sections 7 and 8 show that the effects can be mitigated, or sometimes even reversed, when firms face exogenous borrowing restrictions or the other party can negotiate with the firm s creditors before or after bankruptcy. These conclusions suggest that we must be very careful when interpreting these results as a rationale for debt-financing. Section 9 demonstrates that the possibility of bankruptcy when the firms do cooperate, introduces again inefficiencies. Section 10 discusses how firms can eliminate the hold-up problem by internalizing the activities and emulate the bankruptcy conditions. One way to do this is to give managers option-like incentive schemes. A commitment to fire managers if they don t attain their targets or aren t able to come to an agreement can accomplish the same effect, but could backfire if the company cannot commit to giving successors the same deal. Throughout, this paper focuses on transparency of the underlying mechanisms. The concurrent simplifications in the models lead to some extreme conclusions, such as firms will be completely debt-financed. Adapting the models to get more balanced conclusions is straightforward 6, but goes a the cost of complicating the analysis without adding insight. All proofs are in appendix. 5 The terms disagreement bankruptcy and breakdown bankruptcy will be used to indicate bankruptcy that occurs after negotiations broke down. 6 In particular, a probability of bankruptcy both in case of agreement and in case of disagreement, together with some simple parametric assumptions does the trick. 3

4 The basic model Consider a firm A, incorporated and owned by a set of shareholders. For expositional reasons, we assume a separation of ownership and control, but abstract from any agency problems between managers and owners 7 : Assumption 1 Management maximizes shareholder value. A can take on a project, say developing a new product, which is its sole activity and requires it to invest up-front an amount of resources I R +, at cost c(i). We assume : Assumption The costs of investments are borne by the firm. This category of investments arguably constitutes the most important part of the hold-up problem 8. In marketing the product, A can work on its own (x = 0) or cooperate with company B (x = 1). Assume that A and B cannot write a complete ex-ante contract, but negotiate instead a price for B s support at the time the product is launched 9, according to the Nash bargaining solution. Let the companies discount factor as well as the risk-free interest rate be zero, and B s costs and outside revenues be normalized to zero 10. We also assume that : Assumption 3 B cannot negotiate with A s creditors, before or after bankruptcy. but discuss and relax the assumption in section 7. The gross profit, which accrues to A, is R(I, x, ɛ) where ɛ G[ɛ ɛ] is a random variable, with mean ˆɛ, that represents the uncertain market success. We assume throughout the paper : 7 On a more micro-level, we can support this assumption by assuming that managers do not derive any direct costs or benefits from the (investment) decisions they take and that they get a few shares at the time of incorporation. 8 Nearly all specific examples in the literature concern investments in physical capital, of which the costs are borne by the firm (e.g. Hart 1990, p6). Moreover, even the costs of building human and social capital are often borne by the firm, either directly (time lost by on the job training, formal training programs, visiting suppliers during work hours) or indirectly (as part of what you are being paid for ). 9 A might not be willing to discuss its plans with B before it has developed and patented the product. It is also difficult to specify ex ante what good marketing of an as yet nonexisting product is. 10 As long as B does not have to make any ex ante investments, this is without loss of generality. 4

5 Assumption 4 R(I, x, ɛ) is strictly increasing in all its arguments, strictly concave in the first and supermodular. c(i) is strictly increasing and strictly convex. and most of the time : Assumption 5 R(I, x, ɛ) = ɛ + ˆR(I, x) with ˆR(I, x) a deterministic function and 0 ɛ < ɛ. The positive cross-partial indicates that there are complementarities between A s development effort and B s marketing resources. The additive ɛ-specification introduces bankruptcy in its purest form: ɛ affects whether bankruptcy occurs or not, but does not change e.g. derivatives. The game unfolds as follows : I. The shareholders decide how much equity capital E to provide A with. A s management then incurs a further debt D with lenders (or bondholders). II. A s management invests resources I with c(i) C + D. III. The uncertainty ɛ is resolved. IV. A and B negotiate a price p. V. A gets R(I, x, ɛ), pays p to B and repays debt 11. Appendix A shows that the results extend to the cases where the benefit R(I, x, ɛ) accrues (partially or completely) to B and/or where ɛ is realized after the p-negotiation 1. Allowing the benefits to accrue to either party covers a wide range of cases : B being just a support in A s marketing, B really distributing the product, A doing contract-research, or A and B jointly distributing the product (e.g. via licencing or OEM agreements). The fact that the main results extend to the case where ɛ is revealed after negotiation is useful since the latter is often the more realistic assumption, 11 The clearest way to imagine this is to assume that A gets liquidated after receiving R(I, x, ɛ). If there are sufficient funds, all parties get paid and shareholders get what is left over. If there are insufficient funds, then bankruptcy priorities determines that other firms get paid before debt-holders. 1 The case where the contract can depend on ɛ is of course equivalent to ɛ being realized before the negotiation. 5

6 but goes at the cost of increased complexity. The results also readily extend to the situation where B is a union 13 rather than a different company. Most of the analysis focuses on the implications of there being a probability of bankruptcy when the negotiation or cooperation breaks down, which will be denoted breakdown bankruptcy or disagreement bankruptcy. Of course bankruptcy can also occur when the parties do cooperate. Since these have very different influence on the investments, it is useful to separate the effects, which can be done by the following Assumption 6 The primitives of the model are such that the probability of bankruptcy under cooperation is always zero. The proofs in appendix show that the following primitives are sufficient : Fact 1 Let A1-A4 hold and ɛ condition for A6 is : R(I, 1, ɛ) c(i) > 0 be revealed before p-negotiation. A sufficient I I where I solves R (I, 1, ɛ) = c (I ) Section 8 treats the effects of bankruptcy under cooperation. Since lenders only care about what happens in equilibrium, A6 also implies that they are willing to lend an unlimited amount at the risk-free interest rate. Section 7 studies the impact of exogenously imposed borrowing restrictions. Sometimes we also use the following technical assumption : : Assumption 7 The primitives of the problem are such that it has a unique and internal solution in I. which has fairly standard sufficient conditions. 3 A deterministic model Before launching into the analysis of the full model, it is useful to discuss and illustrate the main ideas and intuition using a very simple deterministic model. So assume that, in the above model, R(I, 1, ɛ) = R(I) R(I, 0, ɛ) = r(i) 13 Notice that the rule that employees have priority over debtholders in case of bankruptcy applies only to past wages and not to any future promises. As a consequence, it is more reasonable in the current context to assume that debtholders have priority over employees since the claims of the latter pertain to future wages. 6

7 and that, without cooperation, investments are not worthwhile : r(i) c(i) I. Consider first the case that A is financed completely with equity. Nash bargaining with B gives A a profit, net of bringing in equity capital E, of : π A,Eq = = (E + R(I) c(i)) + (E + r(i) c(i)) E R(I) + r(i) c(i) However, in equilibrium the parties will agree to cooperate so that the efficient investment solves max I R(I) c(i). It follows, by the assumptions on the cross-partials and monotone comparative statics, that there will be underinvestment under full-equity financing. This is of course the basic result of GHM. Consider next the same company but now financed completely with debt. By the earlier assumption, the company goes bankrupt if the parties do not come to an agreement to cooperate. Nash bargaining then gives A a payoff 14 π A,Dbt = = D + R(I) c(i) D) + 0 R(I) c(i) Comparing this to the earlier result shows two effects: 1. The negative term r(i) c(i) disappeared, so debt increases A s payoff (i.e. debt strengthens A s bargaining position by improving its payoff when no agreement is reached).. The distortion on incentives due to the term r(i) c(i) also disappears. Management thus makes the efficient investment. The latter is the key result of this paper. Intuitively, management cares only about the cooperation-payoffs since the impact on the breakdown-payoffs are for the debtholders. Notice especially that it is not the case that the first effect causes the second, i.e. it is not true that the firm makes a more efficient decision because it captures more of the surplus. The latter is the intuition suggested in most of the literature. One way to highlight the difference is to 14 Nash bargaining solves max[(d + R(I) c(i) p D) 0][p 0] p 7

8 notice that in our model, the breakdown-bankruptcy will reduce investments if hold-up causes over-investment 15. The result also highlights the ambiguity of the argument that investment costs are sunk, when there is a probability of bankruptcy and firms have limited liability. Using such sunkness reasoning, one might be tempted to argue that c(i) should not play a role in the bargaining since it is sunk, and thus that the payoffs of a debt-financed company should be π = R(I) c(i). However, while c(i) is indeed sunk, it was paid for by the debtholders in a fully debt-financed company. So it is sunk only from their perspective. But management cares about shareholders and realizes that they carry the cost only when the firm does not go bankrupt 16. So it is not sunk from a shareholder value perspective. 4 Analysis of the full basic model We now proceed with the full stochastic model. The first result allows for the general R(I, x, ɛ) specification, but its conclusions are limited to the extreme cases : Proposition 1 Let A1-A4, and A6 hold. If R(I, 0, ɛ) < c(i) I (i.e. the firm goes bankrupt for sure when cooperation breaks down) then the firm will be completely debt-financed and make the efficient investment. 15 I.e. when I and x are substitutes. 16 A different argument that shows why the latter equation can t be right uses the fact that r(i) is as sunk as c(i): no matter what happens, the firm will get at least that revenue. In particular, it should make no difference whether that money is received just after the bargaining (as it is assumed right now) or just before. It thus follows that we could define a new cost and revenue function č(i) = c(i) r(i) and Ř(I) = R(I) r(i). Doing now again the calculations, we find that the net payoff becomes E + r(i) + R(I) c(i) E which is different from the formula above. In fact, any transfer between the no matter what revenue r(i) and the no matter what cost c(i) will give a different solution. Finally, the argument could also be restated as follows. Limited liability saves the shareholders money in the case of bankruptcy. The amount of these savings depends on c(i) since that determines the loss that they would have incurred. Moreover, shareholders only get those savings if the firm indeed goes bankrupt, i.e. when no agreement is reached. It follows that these savings must be added to their outside option. 8

9 If R(I, 0, ɛ) > c(i) I (i.e. the firm cannot go bankrupt) then the investment levels and payoffs are independent of the financial structure, and A underinvests. The intuition behind these results was discussed in the section above. To get more complete but still transparent results, a specification how ɛ enters the payoffs, such as A5, is needed. Let BR denote the event that there is disagreement bankruptcy and NBR its complement, both of which depend on the realization of ɛ. For expositional reasons, the financing and investment decisions will be analysed separately. Considering first the choice of I for a given capital structure : Proposition Let A1-A6 hold. For a fixed level of equity capital 17, A s management under-invests relative to the socially efficient level when P [BR] < 1. For level changes 18 in c(i) or ˆR(I, 0) or any changes in E or G(ɛ) that affect P [BR] 19, I increases in P [BR] and is efficient at P [BR] = 1. With the additive specification, the only effect of bankruptcy is to change the weight attached to the outside option. Decreasing this weight makes the investment more efficient. With ɛ multiplicative, there can be overinvestment. If so, an increase in P [BR] is not necessarily socially beneficial. We also get the following implication for the financial structure : Proposition 3 Let A1-A7 hold. Investors strictly prefer the project to be financed maximally with debt if and only if doing so implies P [BR] > 0. The intuition, as mentioned earlier, is that debt increases the outside option, and thus the bargaining payoff. The result can also be given a useful interpretation in terms of hold-up, which will be used later in the paper: The relevant variables in the hold-up problem are any income-stream that an outside party can threaten to reduce by withholding its promised or expected support, and any investment of the focal party that was made to generate that income stream. Equity capital becomes subject to hold-up and will therefore be minimized. 17 Note that debt is riskless and therefore costless. It follows that the total level of capital will never be a restriction on the investment level. 18 Level changes refer to changes that affect the level of e.g. c(i) without changing its derivatives. If c(i) ĉ(i) + δ, then changes in δ are level changes in c(i). 19 Remember that P [BR] is the probability that the firm goes bankrupt conditional on the negotiations breaking down, and P [NBR] = 1 P [BR]. 9

10 Spin-offs and de-mergers Note that activities that are not affected by I or hold-up, would also show up as equity capital 0. They provide a source of capital and income that can buffer the losses that occur when the cooperation breaks down. In order to benefit from the extra aggressiveness and more efficient incentives that come with the disagreement-bankruptcy, it might thus be necessary to spin-off the unit that has to make the specific investments and is subject to hold-up. The analysis thus predicts that the units that are rather independent (so that there is little direct loss from spinning off), that have to make important specific investments and that can easily be held up, are prime candidates for spin-off. 5 Specialization and rent-seeking An obvious question is whether A can gain from making itself dependent on B. This turns out not to be the case 1. A s incentives to specialize towards B, however, do improve with the probability of bankruptcy. To see this, introduce a specialization parameter δ [δ δ] with ˆR(I, 0, δ) δ This gives < 0 < ˆR(I, 1, δ) δ and ˆR(I, x, δ) δ Proposition 4 Let A1-A6 hold. For level changes in c(i) or ˆR(I, 0) or any changes in E or G(ɛ) that affect P [BR] 3, we have that A s chosen level of specialization δ increases in P [BR], and is efficient at P [BR] = 1. The intuition behind this result is simple : bankruptcy makes A s outside option less important, which favors specialization. It can be formulated loosely as : The more firms are dependent on other parties, the more they are willing to specialize towards these parties. The result also suggests that firms will spend less effort on actions that improve their outside options but have no further added value. Indeed, introducing such a rent-seeking action θ which affects only the firm s outside option : ˆR(I, 1, θ) = 0, ˆR(I, 0, θ) > 0 and ˆR(I, x, θ) = 0 θ θ δ 0 I.e. the NPV of their profit stream can be considered equity capital in this context. 1 This follows by the envelope theorem. The assumption on the cross-partial excludes indirect I-influence. 3 P [BR] is the probability of bankruptcy when negotiations break down. = 0 10

11 and carries a cost c(θ), we get : Proposition 5 Let A1-A6 hold. For level changes in c(i) or ˆR(I, 0) or any changes in E or G(ɛ) that affect P [BR], A s chosen level of rent-seeking decreases in P [BR]. Allocation of assets The property rights approach (Grossman and Hart (1986), Hart and Moore (1990), Hart (1995)) essentially exploits socially beneficial rent-seeking : the allocation of assets only matters in these models since it motivates the agents to make investments in order to improve their outside options (which is essentially a form of rent-seeking). Assets are then allocated to the player whose rent-seeking activities are most beneficial to the enterprise as a whole. Notice, however, that when players can acquire such assets from the outside, there will often be inefficient duplication of assets. When outside options now become irrelevant, it is not necessary any more to base the asset allocations on these property rights principles. Duplicate assets can then be eliminated and others allocated in a more directly efficient way (e.g. following the moral hazard principle that he who cares for the asset should own it). Holmstrom and Roberts (1998) observe that Japanese suppliers often own the dies and perform critical activities, such as design. They suggest an explanation in terms of repeated games and reputation. The above conclusion provides a complementary explanation, which is consistent with the fact that Japanese companies tend to have much higher debt levels than their US counterparts. 6 Exogenous borrowing restrictions When A s borrowing capacity is limited, shareholders face a trade-off : equity capital is needed to make the investments, but becomes subject to hold-up by B. To explore the implications in more depth, let us introduce an exogenous borrowing restriction : Assumption 8 Lenders are willing to lend companies 4 an amount D βe, with β 0. Other approaches are possible, but seem to give the same qualitative results. Denoting the level of investment when there are no borrowing restriction by I nr, we have 4 At the risk-free interest rate since there will be no bankruptcy in equilibrium. 11

12 Proposition 6 Let A1-A6 and A8 hold, with β <. A will finance the project maximally with debt. The total funds (equity + debt) available to A restrict the investment I below I nr. The investors payoff and I increase in the borrowing capacity β. Overall, disagreement bankruptcy solves only part of the hold-up problem when there are exogenous borrowing restrictions, while the rest is shifted to the capital markets. This is relevant from an empirical perspective. 7 Negotiation with creditors Up to this point, the creditors (denoted by C) were passive money providers in the game. This section considers how the conclusions would be affected if they had a more active role. In particular, C could enter the game in any of the following ways : When A is at the point of going bankrupt, it might try to renegotiate debt with C. After A goes bankrupt, C can try to negotiate an agreement directly with B. Since A derives a bargaining advantage from its contract with C, B might try to neutralize that by cutting a deal (as discussed below) directly with C. 7.1 Debt renegotiation Debt renegotiation takes place if the company is at risk of going bankrupt but is worth (substantially) more as a going concern than in liquidation. While a full analysis of this issue would bring us too far, we will show with a very simplified model that this renegotiation-possibility might actually lead to over investment. Consider again the deterministic model of section 3. In case of negotiation breakdown, the firm has a liquidation value of r(i), as before. But now the firm also has a value ř(i) > r(i) as a going concern. For the latter, however, the shareholders agreement is needed. This implies that their outside option when negotiating with firm B is their expected payoff from this debt-renegotiation. Assuming also the Nash-bargaining outcome for this negotiation, their outside option is thus : ř(i) r(i) 1

13 Note that, since this term does not include any costs, its derivative is always positive. A simple monotone statics application then implies that the firm will indeed over-invest when shareholders have a chance to renegotiate debt. 7. Post-bankruptcy negotiations When A goes bankrupt after negotiations break down, B can try to cut a deal directly with A s creditors. The value of such a post-bankruptcy deal, however, tends to be lower than that of the original. It depends, among others, on the following factors : The time lapse between the breakdown of negotiations and B closing a deal with A s creditors. While the length of bankruptcy procedures plays a role here, the most important factor is probably whether and how long A can survive after the breakdown. The costs to B are then not only the discounting of profits, but also the cost of finding temporary substitutes (or working temporarily without A s inputs). The consequences of the latter might make this option altogether valueless. The ability to keep important resources in A. The diminished perspectives and threat of bankruptcy might cause key employees to leave, demotivate others, and lead A to sell off important complementary assets and activities. A might have specific know-how for running its business. B has to worry about its reputation for such preying and the broader competitive impact of acquiring a supplier or customer. Whether B survives a breakdown of negotiations (see section X). Allowing for such creditor-negotiations changes B s outside option. To study the impact, let the revenues after bankruptcy be κ R(I, x, ɛ), where κ [0, 1] indicates the relative value of an after-bankruptcy deal, and assume : Assumption 9 G is uniform It turns out that the earlier results get reduced or even reversed when such post-bankruptcy deal is very valuable to B: Proposition 7 Let A1-A, A4-A6 and A9 hold. There exist a κ such that the firms finances the whole project with debt if κ κ, and otherwise provides sufficient equity financing to prevent disagreement bankruptcy altogether. 13

14 Proposition 8 Let A1-A, A4-A6 and A9 hold and let E be given. There exists κ (E) such that investment increases in P [BR] if and only if κ < κ. This also suggests that full efficiency requires κ = 0. Indeed : Proposition 9 Let A1-A and A4-A6 hold. The investment is efficient if and only if P [BR] = 1 and κ = 0. To get some idea of the implications, consider the deterministic case of section 3, and assume that R(I, 0, ɛ) < c(i) so that the firm goes bankrupt if no agreement is reached. If the firm is fully equity-financed, the shareholders payoff is ˆR(I, 1) + ˆR(I, 0) c(i) while with full debt-financing, that becomes ˆR(I, 1) c(i) κ ˆR(I, 1) ˆR(I, 0) 4 At κ = 1, shareholders thus get exactly half of what they would get if they financed the whole firm with equity! 7.3 Pre-bankruptcy creditor negotiations (Leave this out?) Underlying the bargaining advantages of debt is the fact that A s contract with its creditors, provides it with a commitment. Such a ploy gives B an incentive, however, to try to cut a side-deal with those creditors. In particular, B could promise C that it would break off negotiations with A, so that the latter goes bankrupt, if C agrees to a division of the surplus that is better than what B can get by bargaining directly with A. Appendix C analyzes a possible model of this case. It concludes essentially that this ploy can strengthen the effect identified in the postbankruptcy negotiations, but only if carrying it out does not reduce the profitability of the firm too much. The earlier caveats on the reduction of firm value in case of bankruptcy thus apply. Moreover and more importantly, the ploy requires an explicit contract between B and C, something which would make their intentions clear and verifiable. Apart from the question whether such actions are legal, it would ruin their reputation, especially that of the creditor 5. Which firm would be willing to trust a bank that has ruined one of its former clients in this way? 5 Who, as can be seen from the proof, actually does not gain a dime 14

15 8 Bilateral dependency In many situations, both parties to the deal have to make specific investments. The results extend quite straightforwardly to that situation. Consider again the model of section, but let now both firms make an investment and get a payoff. In particular, firm j {A, B} makes investment I j with cost c j (I j ) and has direct payoff R j (I j, I j, ɛ), where I j = 0 upon non-cooperation and ɛ G[ɛ ɛ] is common to both firms. The firms make their decisions, on financial structure as well as investments, simultaneously. Note that the assumption of supermodularity of R now implies also that the investments are complementary. Results equivalent to these of sections 3-5 hold. Consider e.g. : Proposition 10 Let A1-A4 and A6 hold for both firms. If R j (I j, 0, ɛ) < c(i) I, j {A, B} (i.e. both firms go bankrupt for sure when negotiations break down) then both firms will be completely debtfinanced and make the efficient investment. which is of course identical to the first part of proposition 1. If both firms go bankrupt for sure when the cooperation breaks down, then each will get half the surplus that they generate jointly. It follows that, as far as costs are borne by the firms, they will make the efficient decisions. This result can be formulated loosely as two parties that go bankrupt if their cooperation breaks down, start acting as one. 9 Bankruptcy under cooperation The main point of this paper has been that bankruptcy when no agreement is reached, can solve the hold-up problem. To highlight this result, it was assumed that the firm would never go bankrupt if it reached an agreement. This section shows that allowing for such bankruptcy would introduce inefficiencies. In order to highlight the effects, it is now assumed that the firm go bankrupt for sure when no agreement is reached. Consider again the model of section, with ɛ revealed before negotiation, but now allowing for bankruptcy under cooperation. With ɛ known 6, we have to be careful about the bargaining objectives of managers when they 6 When making the investment I, ɛ is still uncertain and managers have to maximize shareholder value according to their fiduciary duty. If we were to assume that ɛ is revealed after negotiation, managers should also focus on shareholder value. We conjecture that this would improve the shareholders payoff and the efficiency of the investment, relative to the situation where ɛ is revealed before the negotiation. 15

16 already know that the firm will go bankrupt no matter how good a deal they close. In particular, assume 7 : Assumption 10 Management maximizes shareholder value as long as there exists some deal p that would avoid bankruptcy. Otherwise, they maximize creditors value instead. Implicit in this assumption is that creditors start and win bankruptcy proceedings as soon as ɛ is revealed and it is such that future revenues will be less than the outstanding debt. To separate the effects of in- and off-equilibrium bankruptcy, also assume 8 Assumption 11 The primitives of the problem are such that if no agreement is reached, A goes bankrupt for sure. The key result of this section is : Proposition 11 Let A1-A5, A7, and A9-A11 hold, then A will underinvest. The effect is due to the fact that shareholders carry the full cost of financing. In particular, their payoff also depends on the deal the debt-holders get after the firm goes bankrupt. And this re-introduces the investment-distorting outside option. Overall we can conclude that the probability of bankruptcy in case of no agreement will reduce hold-up inefficiencies, but that the concurrent probability of bankruptcy even when an agreement is reached prevents us from achieving full efficiency. 7 To keep the model simple, we assume that B s outside option when bargaining with management-representing-shareholders is zero. In particular this implies that B will not be able to negotiate with creditors after breakdown. This might seem at odds with our assumption that such negotiations are possible if bankruptcy occurs after an agreement was reached. This is not necessarily the case : with bankruptcy under cooperation, shareholders know immediately that they will never be able to make a profit and so are willing to cede control quite easily; bankruptcy caused by a failure of negotiations might lead to a protracted effort to save the company nevertheless. It is also possible, at the cost of increased complexity, to adapt the model to bring the two situations more in line. The results seem to extend to such variations. 8 A sufficient condition is that R(I, 0, ɛ) c(i) I. 16

17 10 Solving the hold-up problem by internalizing activities The analysis also implies that firms can completely solve the hold-up problem by internalizing activities and using incentive schemes that emulate bankruptcy. To accomplish this, the firm should give the manager a share of profits 9 but only if these profits exceed a certain level. This is of course the payoff of an (call) option on the business unit profits. The value of such incentive schemes can be seen by comparing them to the effects of linear schemes as studied in Holmstrom and Tirole (1991). In particular, combined with either the M-form of the corrupted M-form, to use their terminology, this option scheme dominates all other alternatives in the absence of private (or non-monetary) costs 30. Except for options, emulating bankruptcy can of course also be achieved by giving the manager a share of profits but threatening to fire him if he cannot come to a (good enough) agreement. Note, however, that our earlier analysis implies that such threat might (unexpectedly) have the opposite effect if the firm cannot commit that all subsequent managers will get the same treatment. Such a strong commitment is rather difficult and might not even be subgame perfect 31. This issue would not play in the case of two internal managers, if both get fired when they do not reach an agreement. 11 Conclusion The main contribution of this paper is to identify the mechanism by which disagreement-bankruptcy eliminates the hold-up problem. The analysis immediately gave some further implications, such as the idea that strong dependence might make the outside options less relevant, which on its turn 9 Note that we assumed that investment costs are borne by the firm. Even an infinitesimal share of profits can then perfectly align the manager s incentives with these of shareholders. 30 At the end of that paper, the authors also discuss the possibility of rewarding the managers on the basis of the joint profits of both units. They suggest that an important disadvantage of such solution is the fact that it exposes the managers to the risks of both units. Note now that the option scheme implements in fact such profit sharing (i.e. through the bargaining each manager gets half of the joint profits), but that it insures a manager against the risk of the other unit for any uncertainties that will be resolved after the contracting. 31 The company is essentially bargaining by rejecting a proposal each time it fires a manager. We know from Rubinstein bargaining games that a commitment is generally not subgame perfect in discounted alternating offer games. 17

18 makes it optimal for a firm to specialize further. It also identified a simple way how organizations can eliminate the hold-up problem by internalizing activities. The analysis was positioned in the context of alliances, as one factor that might explain their smooth functioning. In terms of further research, this axis of the paper seem to be the most promising. At the current time, economics is fast developing its insights in internal organizations of firms, but the increasingly important fluid and network-like inter-organization linkages have got relatively little attention. References [1] Athey, S., Milgrom, P., and Roberts, J., (1998), Robust Comparative Statics, 1998, : [] Bronars, S. G., and Deere, D. R., (1991), The Threat of Unionization, the Use of Debt, and the Preservation of Shareholder Wealth, Quarterly Journal of Economics, February 1991, 106(1): [3] Bronars, S. G., and Deere, D. R., (1993), Unionization, Incomplete Contracting, and Capital Investment, The Journal of Business, January 1993, 66(1): [4] Bronars, S. G., and Deere, D. R., (1994), Unionization and profitability : Evidence of spillover effects, Journal of Political Economy, December 1994, 10(6): [5] Brusco, S., (1996), Bankruptcy, takeovers, and wage contracts, Journal of Economics and Management Strategy, Winter 1996, 5(4): [6] Cavanaugh, J. K., and Garen, J., (1997), Asset Specificity, Unionization, and the Firm s Use of Debt, Managerial and Decision Economics, May 1997, 18(3): [7] Dalmazzo, A., (1996), Debt and Wage Negotiations : A Bankruptcy- Based Approach, Scandinavian Journal of Economics, 1996, 98(3): [8] Dasgupta, S., and Sengupta, K., (1993), Sunk Investment, Bargaining and Choice of Capital Structure, International Economic Review, February 1993, 34(1): [9] Grossman, S. J., and Hart, O. D., (1986), The costs and benefits of ownership : A theory of vertical and lateral integration, Journal of Political Economy, August 1986, 94(4): [10] Hart, O. D., (1995), Firms, contracts, and financial structure, 1995, Oxford: Clarendon 18

19 [11] Hart, O. D., and Moore, J., (1990), Property rights and the nature of the firm, Journal of Political Economy, December 1990, 98(6): [1] Perotti, E. C., and Spier, K. E., (1993), Capital Structure as a Bargaining Tool : The Role of Leverage in Contract Renegotiation, American Economic Review, December 1993, 83(5): [13] Sarig, O. H., (1998), The Effect of Leverage on Bargaining with a Corporation, Financial Review, February 1998, 33(1): 1-1 [14] Subramaniam, V., (1996), Underinvestment, Debt Financing, and Long- Term Supplier Relations, Journal of Law, Economics, and Organization, October 1996, 1():

20 Appendix A Variations on the standard model This appendix considers two variations on the basic set-up : 1. When an agreement is reached, A gets η R(I, 1, ɛ) instead of the full R(I, 1, ɛ), while B gets (1 η) R(I, 1, ɛ). The payoffs when no agreement is reached and under bankruptcy are unchanged 3. ɛ is revealed after the p-negotiation, and the contract cannot depend on that future realization. It turns out that the basic results extend to these variations/generalizations : Proposition A.1 The results of sections 3-6 and 8-9 are not affected by the value of η and/or the timing of the ɛ revelation. Proof : It is sufficient to show that, starting from the end of period II, A has the same expected payoff for the rest of the game in all cases. Consider first the case that ɛ is revealed before the p-negotiation. At the time of the negotiation, it is thus known whether off-equilibrium bankruptcy occurs. The Nash solution solves : max[(e + ηr(i, 1, ɛ) c(i) p) max((e + R(I, 0, ɛ) c(i)), 0)] p.[p + (1 η)r(i, 1, ɛ) 0] Some easy algebra shows that the payoffs to A and B when bankruptcy occurs are : π A = π B = E + R(I, 1, ɛ) c(i) and when no bankruptcy occurs : R(I, 1, ɛ) + R(I, 0, ɛ) π A = E + c(i) R(I, 1, ɛ) R(I, 0, ɛ) π B = Let R(I, x) = E[R(I, x, ɛ)] and ɛ BR be the critical value for off-equilibrium bankruptcy 33 E + R(I, 0, ɛ BR ) c(i) = 0 Note that ɛ BR is function of both E and I. 3 When no agreement is reached A gets the full R(I, 0, ɛ), while B gets 0 (i.e. A goes it alone). In case of bankruptcy, both get zero. 33 If no such value exists, let ɛ BR = ɛ. 0

21 Prior to the revelation of ɛ, the expected payoffs are then (excluding the cost of bringing in equity capital) : π A = E + R(I, 1) c(i) + 1 max(ɛ,ɛbr ) max(ɛ,ɛ BR ) π B = E + R(I, 1) c(i)) 1 max(ɛ,ɛbr ) max(ɛ,ɛ BR ) (E + R(I, 0, ɛ) c(i))g(ɛ)dɛ (E + R(I, 0, ɛ) c(i))g(ɛ)dɛ which is independent of η. Consider next the case that ɛ is revealed after the p-negotiation. Nash bargaining solves [ max (E + η R(I, 1) c(i) p) p ] which gives max(ɛ,ɛbr ) max(ɛ,ɛ BR ) [ p + (1 η) R(I, ] 1) (E + R(I, 0, ɛ) c(i))g(ɛ)dɛ p = η R(I, 1) + 1 (E R(I, 1) c(i)) 1 max(ɛ,ɛbr ) max(ɛ,ɛ BR ) (E + R(I, 0, ɛ) c(i))g(ɛ)dɛ and thus the same expected payoff for both A and B. 1

22 Appendix B Proof of the propositions be revealed before p-negotiation. A sufficient con- B.1 The basic model Fact 1 Let A1-A4 hold and ɛ dition for A6 is : R(I, 1, ɛ) c(i) > 0 I I where I solves R (I, 1, ɛ) = c (I ) Proof : For given I, the Nash solution solves 34 : max[max((e + ηr(i, 1, ɛ) c(i) p), 0) p max((e + R(I, 0, ɛ) c(i)), 0)].[I (E+ηR(I,1,ɛ) c(i) p) (p + (1 η)r(i, 1, ɛ)) 0] In-equilibrium bankruptcy occurs when E + ηr(i, 1, ɛ) c(i) p at the optimum I, which implies that the value of the objective is non-positive. With E+R(I, 1, ɛ) c(i) > 0, however, there always exists a p such that the value is strictly positive 35. It thus follows that E + R(I, 1, ɛ) c(i) > 0 is a sufficient condition to have no in-equilibrium bankruptcy given some value E. Given A4 and the fact E 0, R(I, 1, ɛ) c(i) > 0 at the optimum I, is thus sufficient to get A6. By assumption A4, the results of the proof of proposition A.1, and monotone comparative statics, it also follows that the optimal I can never exceed I. This completes the proof. B. Analysis of the basic model Lemma 1 Let f(x) and g(x) be such that f (x) g (x), and let β 1, β > 0. Then argmax f(x) argmax(β 1 f(x) + β g(x)) in the strong set-order. If both have a unique and interior maximum, and f (x) > g (x), then the inequality is strict. 34 Appendix A explains the meaning of η: the share of revenue that goes to firm A. For all but that appendix, we have η = Take p = (1 η)r(i, 1, ɛ) + δ with arbitrarily small δ > 0.

23 Proof : that Take any x f argmax f(x) and x t argmax(β 1 f(x) + β g(x)). It is true x t argmax((β 1 + β )f(x) + β (g(x) f(x))) = argmax(f(x) δ(f(x) g(x))) with δ = β β 1 +β. Considering the last equation as an optimization problem in x with δ as parameter, it follows from robust comparative statics that the set of optimizers is decreasing in δ, so that that x f x t, as required. Let now x f and x t be unique and interior maxima. If x f = x t then we must have g (x f ) = 0, which is impossible when f (x) > g (x). Proposition 1 Let A1-A4, and A6 hold. If R(I, 0, ɛ) < c(i) I (i.e. the firm goes bankrupt for sure when cooperation breaks down) then the firm will be completely debt-financed and make the efficient investment. If R(I, 0, ɛ) > c(i) I (i.e. the firm cannot go bankrupt) then the investment levels and payoffs are independent of the financial structure, and A underinvests. Proof : From the proof of proposition A.1, the expected profit of A, net of the cost of bringing in equity capital, is : π A = E + R(I, 1) c(i) + 1 max(ɛ,ɛbr ) max(ɛ,ɛ BR ) (E + R(I, 0, ɛ) c(i))g(ɛ)dɛ E (1) where R(I, x) = E[R(I, x, ɛ)] and ɛ BR was defined in proposition A.1 as : E + R(I, 0, ɛ BR ) c(i) = 0 When R(I, 0, ɛ) > c(i) I the probability of off-equilibrium bankruptcy is zero, independent of the firm s financial structure. The net payoff becomes π A = R(I, 1) c(i) + R(I, 0) c(i) and the second set of conclusions of the proposition follow directly using lemma 1. Consider now the case where R(I, 0, ɛ) < c(i) I. From the above, it is clear that when E is high enough to prevent bankruptcy altogether, π A is given by (). When, on the other hand, E is such that there is a positive probability of offequilibrium bankruptcy, if follows from (1) and the envelope theorem that A will want to decrease E as long as E > 0, and thus finance the whole project with () 3

24 debt. The fact that R(I, 0, ɛ) < c(i) I then implies that bankruptcy occurs for sure off-equilibrium, giving a payoff : π A = R(I, 1) c(i) which can be seen 36 to be strictly larger than () when R(I, 0, ɛ) < c(i). Thus the firm prefers complete debt-financing. Moreover, it follows from the last equation that the investment will be efficient. Proposition Let A1-A6 hold. For a fixed level of equity capital, A s management under-invests relative to the socially efficient level when P [BR] < 1. For level changes in c(i) or ˆR(I, 0) or any changes in E or G(ɛ) that affect P [BR], I increases in P [BR] and is efficient at P [BR] = 1. Proof : From the proof of proposition A.1, A s payoff for R(I, x, ɛ) = ɛ + ˆR(I, x), net of bringing in equity capital, is : π A = E + ˆɛ + ˆR(I, 1) c(i) + 1 max(ɛ,ɛbr ) max(ɛ,ɛ BR ) (E + ɛ + ˆR(I, 0) c(i))g(ɛ)dɛ E with ɛ BR = c(i) ˆR(I, 0) E. For a fixed level of total capital that does not constrain investments, becomes : [ π A = 1 ˆR(I, 1) max(ɛ,ɛbr ) c (I) + ( ˆR(I, ] 0) c (I))g(ɛ)dɛ max(ɛ,ɛ BR ) π A then which can be written π A = 1 [ ˆR(I, 1) c (I) + δ ( ˆR(I, ) ] 0) c (I) P [NBR] with δ = 1. Lemma 1, applied twice, implies that Î (I 0, I 1 ) where Î solves the above equation while I x solves max I ( R(I, x) c(i)). A thus under-invests when P [BR] < Since () can be written : R(I, 1) c(i) + R(I, 0) c(i) where the second term is negative and the first term will be smaller since I is not chosen optimally. 4

25 Let y denote any parameter that increases P [BR] via level changes in c(i) or ˆR(I, 0) or any changes in E or G(ɛ). So we have : P [BR] y 0 and The cross partials on (I 0, I 1 ) are then : π A y = ( ˆR(I, 0) π A y E = 1 P [NBR] y y ( ˆR(I, x) c (I)) = 0 (3) c P [NBR] (I)) y π A E = 1 g(ɛ BR)( ˆR(I, 0) c (I)) ɛ BR E On [I 0 I 1 ], the first one is positive 37 while the latter two are negative. It follows that the investment increases in y. Finally, the very last conclusion of the proposition follows of course from proposition 1. Proposition 3 Let A1-A7 hold. Investors strictly prefer the project to be financed maximally with debt if and only if doing so implies P [BR] > 0. Proof : The total ex ante payoff to investors is : ˆπ A = E + ˆɛ + ˆR(I, 1) c(î) + 1 max(ɛ,ɛbr) max(ɛ,ɛ BR ) (E + ɛ + ˆR(Î, 0) c(î))g(ɛ)dɛ E where Î is the optimum I. Using the envelope theorem we find that : When P [BR] = 1, the second term drops and the payoff is strictly decreasing in E, which implies that E = 0 in this region. At P [BR] = 0 (which is always true for large enough E) the payoff is independent of E. When P [BR] (0, 1), the second derivative 38 is : d ˆπ A de = 1 g(ɛ BR) dɛ BR de 37 The first factor is negative on when I > I 0, while the second is negative since P [NBR] = 1 P [BR]. 38 The first (partial) derivative is : dˆπ A de because of the envelope theorem. = P [NBR] 1 < 0. Taking the partial is OK 5

26 The sign of dɛ BR de can be derived from ɛ BR = c(i) E ˆR(I, 0) and can be seen to be negative since I decreases with E (which follows from the proof of proposition ). It follows that ˆπ A is convex in E, so that the optimum must be an extreme value. It follows that the optimum must be at E = 0 or at a large enough E such that P [BR] = 0. The payoffs from these cases, assuming that E = 0 gives a positive probability of bankruptcy, are respectively : and ˆπ A = ˆπ A = ˆɛ + R(I, 1, ɛ) c(î) + ˆɛ + R(I, 1, ɛ) c(î) + 1 max(ɛ,ɛbr ) max(ɛ,ɛ BR ) ˆɛ + R(I, 0, ɛ) c(î) (ɛ + ˆR(Î, 0) c(î))g(ɛ)dɛ where the second is clearly the largest (since it equals the first, except for the (negative) losses off-equilibrium absorbed by bankruptcy). Thus A prefers full debt financing. B.3 Specialization and rent-seeking Proposition 4 Let A1-A6 hold. For level changes in c(i) or ˆR(I, 0) or any changes in E or G(ɛ) that affect P [BR], we have that A s chosen level of specialization δ increases in P [BR], and is efficient at P [BR] = 1. Proof : Let y denote any parameter that increases P [BR] via level changes in c(i) or ˆR(I, 0) or any changes in E or G(ɛ). So we have again (3), plus ˆR(I, x, δ) δ y = 0 The proof of proposition showed already that, on [I 0 I 1 ], π A y and π A E y 0. The other relevant cross partials are : π A δ y = 1 ˆR(I, 0, δ) P [NBR] δ y π A = 1 ˆR(I, 0, δ) P [NBR] δ δ π A δ E = 1 ˆR(I, 0, δ) P [NBR] δ E 6 0, π A E 0,