Incomplete Draft. Accounting Rules in Debt Covenants. Moritz Hiemann * Stanford University. January 2011

Transcription

1 Accounting Rules in Debt Covenants Moritz Hiemann * Stanford University January 2011 * I would like to thank Stefan Reichelstein and participants at the joint accounting and finance student seminar at Stanford University for many helpful comments.

2 1. Introduction The objective of this research paper is to determine the optimal accounting rules that minimize the agency costs arising in debt contracts with accounting-based covenants. The paper seeks to characterize the relevant economic inputs to this problem, the optimal functional form of the accounting system, and the changes in the optimal accounting rules in response to shifts in economic parameters such as the variability of payoffs, the precision of information signals, and the profitability of investments. The results are intended to provide a better understanding of the usefulness of certain attributes of accounting numbers, such as relevance, reliability, and conservatism, in the context of this problem. Debt is a major source of financing for businesses, but its asymmetric payoff structure causes agency conflicts that can reduce firm value. Lender and borrower often have misaligned decision preferences, e.g. in trading off expected payoff and risk when choosing investment projects. Therefore, debt contracts frequently contain covenants whose violation leads to the imposition of restrictions on the borrowing firm or a transfer of certain decision rights to the lender. These may include the prohibition of any further increase in the borrower s leverage, the requirement of a minimum degree of liquidity, or the right of the lender to call the debt at once. Accounting plays a major role in these covenants because the technical default criteria tend to be stated in terms of accounting measures, such as book value of equity, leverage, working capital, or net income. The larger, primitive question underlying this setting is the problem of the optimal capital structure and its impact on firm value. One important conduit through which capital structure affects firm value is investors incentives when making operating decisions. 1 Operating decisions are both real economic decisions and reallocation decisions at the same time, i.e. they affect both total firm value and the distribution of this value between the holders of different securities. Many securities provide decision-making rights to their holders, either in general, e.g. to investors in voting equity, or under given circumstances, e.g. to debt investors after technical default, and hence the choice of financing affects how these decisions are made. 1 The term operating decisions refers to all discretionary actions that affect the value of an enterprise, e.g. investing in capacity, entering or exiting lines of business, or acquiring other firms. 1

3 The economic significance of the research question lies in the tension between the value creation and distribution effects of these decisions. From a social planner s perspective, only the maximization of firm value in total is of importance because any increase therein can be distributed to investors to achieve a Pareto improvement. However, to investors in a particular security, the value creation and distribution effects may not be aligned because investors seek to maximize their individual share of firm value, which is determined by the payoff function of the securities they hold and may or may not increase with total firm value. Between holders of debt and equity, this incentive misalignment gives rise to the well-known asset substitution problem, i.e. equity investors desire high and potentially inefficient operating risk while debt investors have the opposite incentive. This paper is concerned with the role of accounting in determining operating decisions in light of the asset substitution problem. Consistent with the social planner s objective of maximizing total firm value, the objective function throughout this paper is the efficiency of the debt contract. Efficiency measures the degree to which total firm value under a particular contract configuration approaches the theoretically attainable maximum from the social planner s perspective, and it is a function of the contracting parties incentives, the information structure, and the possibility of renegotiating the contract at later dates. The incentive asymmetry induced by debt financing generally prevents the implementation of the first-best outcome, and the accounting process in this model functions as a governing mechanism that mitigates the adverse effects of this asymmetry. The remainder of the paper is organized as follows. Section 2 lays out the conceptual approach taken in this paper in modeling the debt contracting problem. Section 3 surveys and comments on previous research on debt covenants and the use of accounting in debt contracts. The setup of the basic, two-period model with a linear accounting system is introduced in Section 4. The main results are presented both under symmetric information, shown in Section 5, and asymmetric information, shown in Section. Next, three variants of the model are examined. The effects of adding a project selection problem are discussed in Section. A generalized form of the optimal accounting system is developed in Section. Finally, Section extends the model to a multi-period setting. Section provides a summary and some concluding comments. 2

4 2. Conceptual Background The purpose of this section is to put the problem analyzed in this paper in the general context of financial contracting and outline some important assumptions and restrictions. The following discussion addresses reasons to choose debt over other forms of financing and the roles of accounting and information in this contracting problem. 2.1.Costs and Benefits of Debt Financing Various theories justifying the use of different securities to finance an enterprise have been developed since the work of Modigliani and Miller (1958). In view of the introductory discussion of decision rights and payoff functions, a financing contract must address two broad questions. First, how much of the investment s payoff does the investor receive? Second, what rights does the holder have in making operating decisions? Answering both questions in generality is a potentially complicated security design problem. Prior research in corporate finance, e.g. Aghion and Bolton (1992), has analyzed it in simplified settings. This paper has a somewhat different focus. Namely, the object of interest is the second question about operating decisions and decision rights and the role of accounting in this matter, while the answer to the first question is assumed to be a standard debt contract for exogenous reasons. Debt financing is one possible element of a firm s capital structure, and hence any analysis of its agency costs presumes that either debt confers benefits that outweigh these costs or alternative financing options incur even larger agency costs. This paper does not address a capital structure or security design problem and takes debt financing as given. But since alternative financing arrangements, in particular equity, can resolve the incentive misalignment and hence eliminate the inefficiency resulting from asset substitution, some motivation for confining this paper to debt financing is in order. The following discussion outlines several scenarios in which this truncation of the space of allowable contracts is a reasonable imposition, i.e. settings in which the payoff structure of debt imparts benefits that other contracts cannot provide. Corporate finance research has suggested various beneficial applications of debt. Jensen and Meckling (1976) observe that equity financing incurs an agency cost if insider owner-managers 3

5 can consume private benefits at the expense of total firm value and hence of outside equity investors. In contrast, if outside investors only provide debt financing, the consumption of private benefits reduces residual profits and hence only the owner-managers own share of firm value. A signaling role for debt is suggested in Ross (1977). A firm s manager whose compensation depends on the market value assigned to the firm in a capital market with uninformed investors may convey private knowledge of the firm s true value by financing the firm with debt. Based on the assumption that bankruptcy would be a costly event to the manager, managers of firms with higher true values would issue more debt. In Grossman and Hart (1982), managers issue debt in order to commit to taking some non-contractible action that maximizes firm value rather than managerial compensation. The effectiveness of debt as a bonding device in this setting is again based on the assumption that bankruptcy of the firm is costly to managers. Even absent private benefits and managerial compensation incentives, debt may be a useful device to overcome information asymmetry in capital markets. Myers and Majluf (1984) develop a pecking order of financing choices, whereby firms seeking to maximize the payoff of current investors prefer to raise capital by means unaffected by information asymmetry. To illustrate the idea in the context of this paper, one may envision a firm seeking capital in a competitive market and with the option to issue either debt or equity. If preferences over operating decisions constitute the only possible tension in this setting, full equity financing would attain the first-best outcome because incentive alignment between the firm s current owners and the new outside investors is achieved if all payoffs are shared proportionately. In contrast, debt financing would lead to inefficiency as a result of asset substitution. However, the firm may no longer prefer equity over debt if outside investors can only observe the distributional properties of the firm s payoff up to a threshold level. Issuing equity in this market would produce the standard adverse selection problem. In a pooling equilibrium, outside investors would demand a share of the firm s equity calculated to achieve their required return across all types of firms. Then high-type firms, i.e. those with favorable distributions above the threshold, would be forced to cede some of their economic profit to these investors in order to gain access to capital. In contrast, if the outside investors payoff function does not depend on realized payoffs above the threshold, the adverse selection problem can be averted. Hence, if debt can be issued at a face value below the threshold, its agency cost may be worth incurring for high-type firms in order to avoid ceding economic profit. 4

6 2.2.The Role of Accounting in Debt Contracts Accounting can serve two broad purposes in debt contracting. Its first role is that of an information transmitter. In this function, accounting may reduce the information asymmetry between the borrower and the lender and increase the set of contractible information. Accounting can thus reduce the need for potentially costly renegotiation of the contract at later dates, improve the efficiency of the renegotiation outcome, and provide information to the party in control of operating decisions and thereby reduce the cost of decision errors. In its second role, accounting serves as a decision mechanism. If covenant thresholds are based on accounting numbers, the likelihood of technical default and hence the triggering of sanctions or the transfer of decision rights depends on the properties of the accounting rules. The task of accounting in this context is to induce the most efficient operating decision given the underlying state of the world. This paper views accounting from the perspective of its second role. This is not to say that the information transmission dimension is unimportant. However, if agency costs decline and hence the efficiency of the financing arrangement increases when information asymmetry is reduced, the solution to the problem would likely simply involve the greatest possible enlargement of the uninformed party s information set. Unless one were to introduce further tension regarding the information transmission mechanism, it is not clear how the properties of accounting principles have any bearing on this problem because accounting is a process of measurement and interpretive summarization, whereas reducing information asymmetry is a question of communicating relevant information, not one of processing it. If accounting represents the set of communicated information, the optimal solution to the contracting problem would simply prescribe that it be as detailed and all-encompassing as possible. A direct corollary of this observation is that reductions, biases, truncations and similar outcomes of the accounting process that are often the focus of academic research would serve no purpose and may even be detrimental in this setting. The investigation into the benefits of accounting conservatism in debt contracting may serve as an example. The discussion tends to be cast in terms of the information content of accounting numbers, but as the discussion in Guay and Verrecchia (2006) shows, it is not easy to argue that the informational imbalance implied by 5

7 the asymmetric recognition of gains and losses under conservative accounting practices is superior to unbiased, full-information accounting. 2 Another important consideration in this context is that accounting information may not be entirely exogenous because the firm, i.e. the borrower, prepares the accounting report. Control of the accounting process is therefore in the hands of an interested party, which has two important implications. First, the firm would be able to undo any bias or reduction of economic information that may arise during the accounting process and would therefore not rely on accounting information unless it is complete and unbiased. Second, if accounting is assumed to add informational value beyond that of its inputs, e.g. because judgments and estimates made by the firm s accountants may reflect private information, the firm s optimal strategy would simply be to make biased judgments that maximize residual profits rather than total firm value. Scope for discretion in the accounting process would render it useless as an instrument to enhance contract efficiency. On the other hand, if accounting merely aggregates exogenous information and the process is verifiable, the firm s conflict of interest is not critical, but then any informational property of accounting can only be ascribed to the economic inputs and not to the accounting process and its underlying principles. In contrast, if the primary role of accounting in the debt contract setting is one of adjudicating operating decisions rather than conveying information, the optimal properties of the accounting process are not as obvious. In this setting, accounting implements a mapping from economic inputs, i.e. indicators of the state of the world, to decisions, either directly or via a delegation of decision rights to one of the contracting parties. In this setting, accounting can be represented as a mapping : Θ where is the accounting process, Θ is the set of contractible inputs, and is the accounting measure that implements the decision outcome. For example, Θ may represent cash flow data, interest rates, market prices and other observable information; may be the firm s net income or its book value of equity; is the set of accounting principles according to which Θ is translated into journal entries; and technical default might be defined to occur when falls below a certain threshold value. 2 Guay and Verrecchia suggest that the informational inefficiency of conservative accounting may be worth incurring because the cost of reporting verifiable information may be higher for gains than for losses. 6

8 The focus on this paper is on finding and describing the optimal function. One may argue that designing still leaves the task of choosing how ultimately implements the decision outcome. However, there is no loss of generality in fixing the latter part. For example, one can create a list of all possible sets of operating decisions, number them sequentially, and declare that a decision set is implemented whenever falls between the set s assigned number and the preceding set s assigned number. Since no restrictions are imposed on at this time, fixing the mapping from to decisions in this manner incurs no loss of flexibility and shifts the entire task of designing the covenant to. 3 The contracting problem described in Section 4 takes this approach. 2.3.Information Structure The contracting parties operating decisions and hence the efficiency of the contract are a function of both their incentives and their information. Consequently, if the covenant provides for a delegation of operating decisions to one of them, the functional form of is determined not only by Θ itself but also by the parties own information sets, their incentives, and the correlation of the two with Θ. It is therefore useful to preface the analysis with an outline of the information structure of the model and introduce some simplifying assumptions. The collection of all contract-relevant information in the world, which will determine the first-best benchmark for efficiency, will be denoted Θ; the information sets of the firm and the lender will be denoted Θ and Θ, respectively; and the collection of all contractible information, which is assumed to be reflected in the accounting measures used in the contract, will be denoted Θ, as discussed already. By construction, Θ and Θ constitute lower and upper bounds on the information sets of the firm and the lender because either knows at least the verifiable information captured by accounting but neither can know more than Θ. The parties information sets are unlikely to be equal in reality, and their disparity is an important source of tension in this contracting problem. The following assumption imposes some structure on this disparity. 3 One might think of this approach in analogy to a multinomial logistic regression, where choosing the mapping from to decision outcomes corresponds to assigning values to the categories of the dependent regression variable. 7

9 Assumption 1. The firm s information set i) contains all available information, i.e. Θ Θ. ii) is a superset of the lender s information set, i.e. Θ Θ ; and Part i) of Assumption 1 is a convenient simplification but does not affect the dynamics of the problem and its conclusions at all. Part ii), on the other hand, is an important premise because asymmetric information induces asymmetric decision-making and asymmetric renegotiation outcomes, which have important implications for the optimal set of accounting rules. Consistent with the observation that the firm is the insider in this problem and likely has access to proprietary information unavailable to the lender, the lender s information set is modeled as a subset of the firm s. In reality, lenders may also possess some proprietary information. The simplification made in Assumption 1 presumes that on average, the firm is in a superior informational position. One can now write the hierarchy of information sets as Θ Θ Θ Θ The tension in this model rests on two possible inequalities in the above relationships, namely that i) the contractible accounting information does not capture all information available to the contracting parties, and ii) the contracting parties information sets are not equal. In order to focus the analysis on these tensions, two simplified scenarios will be considered. The case of symmetric information, presented in Section 5, assumes that Θ Θ Θ Θ whereas the setting with asymmetric information, pres ented in Section, assumes that Θ Θ Θ Θ 3. Related Research The properties of accounting-based debt covenants have been studied extensively in empirical research. Beneish and Press (1993) document the consequences of technical violations of debt covenants for a sample of 91 firms during the period of 1983 to The authors find that technical default is costly to violating firms because subsequent renegotiation of the contract tends to result in higher interest rates, increases in collateral, or the prohibition of certain invest- 8

10 ing or financing transactions, and may force firms to divest part of their operations in order to meet payment obligations. In another survey of covenants, Begley and Freedman (2004) examine a sample of debt contracts between 1975 and 2000 and observe that covenants involving dividend and borrowing restrictions are frequently based on accounting measures during the earlier part of the sample period but infrequently used in later years. The role of accounting conservatism in debt contracting has received particular attention. Ahmed, Billings, Morton and Stanford-Harris (2002) present evidence that firms apply more conservative accounting practices when the conflict between shareholders and bondholders over dividend policy is severe. In addition, their results indicate that firms with more conservative accounting achieve higher credit ratings. In a similar paper, Zhang (2008) focuses on the relationship between accounting conservatism, covenant violations, and interest rates at the inception of the debt contract. The results show that borrowing firms with more conservative accounting practices are more likely to violate their debt covenants after negative stock price shocks but pay lower interest rates to their lenders. Both accounting conservatism and the restrictiveness of debt covenants increase the likelihood of technical default. Beatty, Weber and Yu (2008) investigate to what extent these two mechanisms are used as substitutes. The authors find that accounting conservatism and conservative covenant modifications are both frequently found in debt contracts and are often applied jointly, which suggests that the two are not completely substitutable in practice. Theoretical models of the debt contracting problem have generally focused on the properties of covenants that give control over some operating decision to either the borrower or the lender. Gârleanu and Zwiebel (2008) examine the problem of costly renegotiation of debt contracts under asymmetric information. In particular, the controlling party in their model can take an action at an interim date that, depending on the state of the world, increases or decreases the total payoff of an investment and at the same time transfers some wealth from the lender to the borrower, who is privately informed about the amount of the transfer. Control over this decision is assigned unconditionally at the inception of the contract. The contract can be renegotiated after both parties observe the state of the world but before the action is taken. When renegotiating, the uninformed lender incurs an exogenously determined, fixed cost in order to become informed, so that renegotiation ultimately occurs under symmetric information. The results of the paper show 9

11 that generally, contract efficiency is maximized when the uninformed lender has control. The findings in Section of this paper confirm this conclusion. In practice, renegotiation likely occurs without the complete resolution of information asymmetry, and the resulting inefficiency relative to the first-best outcome, represented in Gârleanu and Zwiebel by the cost of becoming informed, is endogenous. Even absent the opportunity to resolve the information asymmetry at a cost, both parties could renegotiate, and the efficiency of the outcome would be determined by the distribution of bargaining power, the allocation of control rights when no agreement is reached, and the severity of the information asymmetry. This observation does not affect the paper s results qualitatively, but in a setting with statecontingent control allocation, the sensitivity of the efficiency of renegotiation to the underlying state and its contractible correlates would become important. The discussion in Section of this paper can thus be viewed as a further development of the setting considered in Gârleanu and Zwiebel. Li (2009) also considers costly renegotiation of debt contracts, but in a setting with symmetric information and state-contingent control allocation via an accounting-based covenant. The paper adopts a reduced-form representation of accounting as a contractible random variable that is informative about the probability of success of the firm s investment. Both firm and lender observe the true probability after the inception of the contract. At this interim date, the decision must be made whether to liquidate the investment for a fixed amount or to continue the project to the end. The precision of the accounting information varies conditional on the true underlying state of the world, and accounting conservatism is interpreted as a specification of this random variable such that it is more precise when the underlying state is good, i.e. liquidating the investment is not optimal. The author concludes that conservative accounting is relatively more efficient when renegotiation costs are low and firm s liquidation value is high. Gigler, Kanodia, Sapra and Venugopalan (2009) also interpret conservatism as an asymmetrically precise signal about future payoffs. In their model, the firm and the lender are likewise symmetrically informed, but the accounting variable represents the only new information arising at the interim date between the inception of the contract and the realization of the firm s profit, i.e. a renegotiation-proof contract can be written. The authors conclude that conservatism reduces the efficiency of the debt contract in this setting, but a necessary condition for this result is the 10

12 assumption that the liquidation value of the firm s invested assets is below the expected continuation value ex ante. The conclusions from the Gigler et al. model are not limited to the debt contract setting. Symmetric information and the absence of non-contractible information at the interim date eliminate any debt-specific agency costs and thereby make the model applicable to any security type and capital structure. The fundamental question of the paper is for which underlying states of the world a decision-maker would desire more precise information about the outcome of interest. Control allocation via covenants is not relevant in this setting because the first-best outcome is always attained. In terms of the discussion in Section 2, accounting in the Gigler et al. model thus serves the role of conveying information rather than moderating operating decisions. Both Gigler et al. and Li model accounting as a random variable, posit certain of its statistical properties and analyze their benefits. An advantage of this approach is the conciseness of the representation, which allows for succinct conclusions. But the validity of these conclusions depends on the validity of the assumed properties. Hence, a disadvantage of this reduced-form representation is that it cannot explain how the posited properties of accounting arise during the accounting process in practice. In particular, if accounting is purely a process of summarization and transformation, it cannot produce information over and above what the inputs, e.g. cash flow data, already possess. Then the properties of the accounting information must ultimately be properties of the economic inputs to the accounting process rather than results of the accounting rules per se. On the other hand, if the proposed asymmetric precision of accounting arises because the accounting rules prescribe that economic inputs be condensed into a more or less precise summary statistic depending on the underlying state of the world, it is not clear why it should not be possible to produce an accounting statistic that is precise in both good and bad states, and why the firm, as the preparer of the accounting report, would rely on this information and, if discretion is permitted, refrain from manipulating it in its favor. In order to address these problems explicitly, this paper treats the accounting process itself as a design choice. While the above models consider the borrower s initial investment opportunity fixed and exogenous, Caskey and Hughes (2010) focus on the problem of non-contractible project selection. Similar to the liquidation-continuation decision after the initial investment, lender and borrower have asymmetric and inefficient incentives in the project selection decision. However, unlike the liquidation-continuation problem, the project selection problem involves an irreversible com- 11

13 mitment of capital and can hence not be resolved via renegotiation ex post. The authors conclude that if the borrower makes the investment decision, state-contingent control allocation based on interim information about the fair value of the investment should favor the lender. Of the fair value accounting schemes considered in the paper, choosing the minimum of the liquidation and continuation values is found to perform best, which the authors interpret as an indication that conservative accounting practices may be preferable in this setting. 4. Model Setup This section introduces the relevant information and payoff variables and their properties in this model, derives the contracting parties decision incentives, and describes the accounting process on which the debt covenant is based. The section concludes with the setup of the optimization program and a note on renegotiation. 4.1.Economic Variables A firm has an investment opportunity with positive expected net present value. 4 The project requires a capital outlay of at time 0 and yields uncertain cash flows of during the subsequent periods 1,2 if continued to the end. The cash flows are distributed over the intervals 0, with probability and an expected value of. Alternatively, the firm s owners can sell the enterprise after the first period for a liquidation value, which has a prior distribution with support 0, and an expected value of. The distributions of and are all mutually independent and common knowledge. For simplicity, the firm is assumed to undertake only this single project, so that the only operating decision to be made in this setting is the binary choice between liquidation and continuation at 1. In order to create an analytically tractable problem, the following assumptions are imposed on the probability distributions of the random variables in the model. 4 Throughout this text, the firm refers to the firm s owners and managers, who are assumed to seek to maximize the value of the firm s equity. Intra-firm agency conflicts between owners and managers are not considered in this model. 12

14 Assumption 2. The distributions, with 1,2,, have i) continuous and differentiable density functions ; ii) zero density at the boundary points of their support; and iii) a decreasing ratio. Properties i) and ii) are made for convenience and are not very limiting. Property iii) is satisfied by a large number of distributions, e.g. the normal distribution. The conditions in Assumption 2 are not strictly necessary for the qualitative conclusions in this paper, but they ensure that the critical point of the resulting optimization problem is unique and thereby permit an analytical treatment of the problem without reliance on numerical analysis. Assumption 2 also implies two further useful properties. Lemma 1. The density functions of the distributions, with 1,2,, are unimodal and satisfy the monotone hazard rate property, i.e. the ratios are increasing over their support. Proof. See Appendix. The firm s cash flows are assumed to be observable and verifiable for contracting purposes. In contrast, is observable to the firm and potentially also to outsiders but cannot be contracted upon. However, an observable and contractible estimate of the liquidation value is available at 1. The estimate has the same prior distribution as and induces a posterior distribution that is common knowledge. Depending on the nature of the firm s assets, may be more or less informative. In particular, as the precision of increases toward perfect accuracy, approaches a delta distribution with Pr 1 in the limit. Conversely, if is entirely uninformative about, conditional and prior distributions are the same, i.e.. The intermediate precision levels of can be expressed as linear combinations of these two corner cases. In accounting terminology, can be thought of as an estimate of the fair value of the firm s invested assets, constructed from observable inputs and some agreed-upon valuation model. For example, the value of a steelmaker s inventory may be determined by prices in the commodity market, the value of an office building by prevalent real estate prices, and the value of notes re- 13

15 ceivable by interest levels and historical default rates. The less an asset s value correlates with such observable inputs, the more imprecise will be, e.g. the value of an intangible asset such as some new, proprietary technology can likely only be estimated with substantial error. and The information sets introduced concept ually in Section 2 can now be specified. In particular, Θ,, Θ, To be precise, one could also include in both sets the distributional properties of all random variables in the model, but since this information is common knowledge at all times, it is omitted for notational simplicity. The first-best benchmark for an efficient liquidation decision is defined according to Θ. Since both parties are risk-neutral, the decision to liquidate should hence be taken whenever, i.e. when the liquidation proceeds exceed the expected continuation payoff. The maximum expected payoff theoretically attainable from the investment is therefore max, 4.2.Decision Incentives For lack of internal funds, the firm must obtain the requisite capital from an outside investor. The investor is assumed to break even in expectation, i.e. the firm raises in a competitive capital market. 5 All parties are risk-neutral and the risk-free interest rate is normalized to zero, so the terms of the financing contract are set so that the investor s expected payoff is, conditional on the liquidation or continuation decisions that are made at 1 across all possible states. In order to simplify the analysis, the financing contract is further assumed to prohibit the firm from issuing debt or equity, distributing dividends, and making new investments for the duration of the project. Permitting these decisions would complicate the analysis but not alter the fundamental dynamics of the problem. As noted in the introduction, the financing agreement between the firm and the investor must contain two main elements, namely a payoff function specifying how, and are to be di- 5 One could without loss of generality require that the investor obtain a positive economic profit in expectation. 14

16 vided between the two parties, and a decision rule concerning the liquidation option at 1. Consistent with the motivation in Section 2, the firm chooses debt financing for some exogenous reason, for example in order to circumvent an adverse selection problem due to information asymmetry in the capital market about the distribution of high outcomes of. 6 The payoff function is therefore that of a standard debt contract by assumption and is given by a maturity value, which the firm must repay upon conclusion of the project or at the time of liquidation. 7 If the firm s cash flows are insufficient to cover, the lender receives all payoffs. The decision rule over the liquidation option at the end of the first period, on the other hand, is a choice variable in this model. Before deriving the optimal form of this decision rule, it is useful to characterize the incentive effects of the standard debt contract s payoff function. The only operating decision, and hence the only instance in which incentives affect outcomes in this model, is the liquidation decision at 1. Conditional on the initial contract terms and the realized values of and, the firm prefers liquidation whenever max0, max0, where the left side is the firm s share of the liquidation proceeds, and the right side is its expected payoff under continuation. It is evident from the above inequality that liquidation can never be the firm s strictly preferred choice when the left side is zero. Similarly, the lender prefers liquidation whenever min, min, and thus continuation can never be the strictly preferred choice if the left side is equal to. If the above expressions hold with equality, the decision-maker is assumed to resolve the resulting indifference in favor of the decision yielding the higher total payoff to both parties. If the minimum and maximum constraints on the left sides of the above expressions do not bind, the parties preferences depend on the realization of. In this case, there exists a cutoff value of above which the party in control prefers liquidation over continuation. This cutoff value will be referred to as the liquidation threshold and is denoted for the firm and for the 6 This scenario does not contradict the assumption that the entire distribution of is known to the outside investor at the time of contracting as long as there is a fully revealing, separating equilibrium in the capital market. 7 In reality, the contract may specify a payment less than in case of liquidation at 1 because the debt is retired before maturity, but for simplicity, it is assumed that the firm does not receive such a discount. 15

17 lender. The functional form of the liquidation threshold can be obtained by solving the inequalities above for, which yields max0, (1) and min, for 0. If the outstanding debt amount is outside this range at 1, the firm is either bankrupt with certainty or the lender will be repaid in full with certainty. The first-best benchmark rule that maximizes the total expected payoff from the investment calls for liquidation whenever, and equations (1) and (2) suggest that the parties incentives do not generally coincide with this benchmark. The distances and thus measure the potential agency cost of the debt contract. This observation illustrates the importance of assuming the financing agreement to be a standard debt contract with a fixed maturity value in order to have a non-trivial agency conflict. If this assumption were relaxed, one could set different values of under liquidation and continuation, calculated as a function of such that everywhere. A possible reason that this may not be feasible in reality is that many potential operating decisions may not be known ex ante, and hence it may not be possible to condition the lender s payoff on them. Instead, the parties would have to rely on a statecontingent assignment of broad decision-making rights via covenants, as observed in reality and as modeled in this paper. The potential agency cost implied by and has several important properties, as the following proposition demonstrates. The distances and will be referred to as the inefficiency range. (2) Proposition 1. The firm never prefers an inefficient liquidation, and its inefficiency range is a decreasing, convex function of. Conversely, the lender never prefers an inefficient continuation, and its inefficiency range is an increasing, convex function of. Proof. See Appendix. The results in Proposition 1 provide important insight into the relationship between inefficiency and incentives. If the contracting parties were to make decisions based on their liquidation 16

18 thresholds, the firm would cause more inefficiency when is high and is low, while the opposite holds for the lender. This observation is a key determinant of the form of the optimal covenant and holds under any assumption about probability distributions. Figure 1 provides a graphical illustration of the liquidation thresholds. Proposition 1 is a general result in the following sense. A preference for an inefficient decision necessarily implies that this decision results in a wealth transfer to the decision-maker at the expense of the other contracting party, and that this wealth transfer exceeds the decision-maker s share of the resulting efficiency loss. For any particular decision, the wealth transfer can only benefit one of the two parties. Hence, if there exists only one possible inefficient action per state of the world, at most one party can have an incentive to choose it. Then one can partition the state space into two disjoint subsets according to which party has the inefficient incentive. Proposition 1 shows that the partitioning in this model is defined by the set of points, where. The liquidation thresholds reflect preferences and hence decision incentives, but as noted in Section 2, the ultimate decision outcomes are also a function of the decision-maker s information. In order to determine the optimal contract terms, the incentives derived above are therefore combined with symmetric and asymmetric information structures in Sections 5 and. Nonetheless, the liquidation thresholds describe fundamental the tension underlying the model in all of its following variants. Both parties prefer to maximize the investment s payoff ex ante but are unable to do so because neither can commit to taking the first-best action at Covenants and Accounting Both the firm and the lender may have incentives to make inefficient liquidation or continuation decisions at 1. Proposition 1 shows that these incentives are asymmetric, and so the debt contract must include a covenant specifying how the liquidation decision is made. This covenant can either provide a direct decision rule based on the available contractible information, or delegate the decision to either party, possibly via a state-contingent control allocation mechanism. The following result shows that the latter approach dominates the former. 17

19 Proposition 2. For any direct decision mechanism, there exists a state-contingent control allocation mechanism that achieves a more efficient outcome. Proof. See Appendix. The result of Proposition 2 is not surprising given the hierarchy of information sets laid out in Section 2. A direct decision rule can only be based on Θ, while delegating the decision to the firm or the lender results in a decision based on Θ or Θ, i.e. a superior set of information. Although the contracting parties do not always use their information to implement the first-best action, the perfect asymmetry of the liquidation thresholds, shown in Proposition 1, can be exploited to ensure that the outcome is never worse than under a direct decision rule. Thus, Proposition 2 has general validity in settings where for each state of the world, Θ can identify at least one party that has an incentive to make the first-best decision. The optimal covenant is thus a mapping from realizations of Θ to decision rights. As discussed in Section 2, accounting will implement this mapping by transforming Θ into an accounting measure that determines the control allocation and thus the decision outcome. This accounting measure is assumed to be the firm s book value of equity, denoted. 8 The accounting process can therefore be written as, for the critical period 1. The control allocation can now be implemented by setting a threshold value below which the firm is defined to be in technical default and the lender is given the right to make the liquidation decision at 1. Efficiency is minimized if for every element in Θ, the covenant awards control to the party that is more likely to make the optimal liquidation decision. The solution thus takes the form of a partitioning of the information space Θ into a sphere of control for the lender and a sphere of control for the firm. The optimal functional form of is determined by the shape of this partition. Exploring the properties of the optimal in generality will be deferred until Section. For the moment, the accounting book value of equity is assumed to take the simple linear form 8 It should be noted that book value of equity is merely a label at this point and hence no restrictions are imposed on the functional form of the accounting process yet. 18

20 1 1 (3) where is the firm s book value of equity at the inception of the contract. The remaining terms can be thought of as the firm s accounting income in period 1, where the constant term represents fixed accruals, e.g. depreciation and amortization of the invested assets or the accrual of interest on the debt, and is a weighting of cash flow and fair value information that may represent accruals that vary with and, e.g. allowances for uncollectible accounts receivable, accrued warranty costs or units-of-production depreciation. The coefficients of and in equation (3) are determined by the single parameter rather than modeled as two separate choice variables. This reduced-form algebraic representation does not incur a loss of generality, provided that one coefficient can be normalized because i) the problem is one of relative rather than absolute magnitude and ii) the sign of the normalized coefficient is known. Condition i) applies because is only evaluated relative to a single cutoff point. Condition ii) holds because Proposition 1 shows that and affect the contracting parties incentives with opposing signs, whereby the firm has an incentive for inefficient continuation at 1 only when and so higher values of should make default more likely. One may therefore limit attention to 1,1. The resulting accounting treatment of the estimated liquidation value may seem counterintuitive because higher realizations reduce the firm s book value for 1. The economic rationale for this lies in the interpretation of as a change in the opportunity cost of continuing the business, consistent with the common notion that accounting measures the value of the firm as a going concern rather than its disposal value. In reality, both the liquidation value and the expected continuation value may change over time, but for simplicity, has been fixed so that is informative about only. 9 The representation in equation (3) allows for a few simplifications. Both and are constant, and so without loss of generality, one can set 0, i.e. capitalize the investment at its cost initially and recognize the liability to the lender at the issue amount of the debt, which is also because the project is entirely debt-financed. Likewise, raising is equivalent to decreasing the technical default threshold by the same amount, and so the latter can be normalized 9 Conceptually, one could readily interpret the setting such that is also updated at 1 and reflects the difference between and. Then would enter this difference with a negative sign, and hence increases in would have the intuitive income-increasing effect. High realizations of can then be thought of as an indication of a particularly low realization of that leads to an asset write-down. 19

21 to 0 without loss of generality. The remaining parameters, will be referred to as the accounting rule and are specified as part of the debt contract. In sum, the debt contract is of the form,,,, where is exogenously given and the remaining three parameters are endogenous choices, subject to the lender s break-even constraint. To facilitate the derivation of the fo llowing results, it will be useful to define 1 1 as the cutoff value of above which technical default occurs. This expression is obtained by solving equation (3) for 0, which is the critical book value because the default threshold has been set at 0. If is very high or very low, can potentially fall outside the support of, i.e. the realization of may become irrelevant in determining whether default occurs. In particular, technical default is unavoidable when is b elow and it becomes impossible when is above max 1,0 (5) 1 min, 1 (6) The expressions for and are obtained by solving (4) for at the boundary points of the support of. For convenience, the cutoff value will be set to 0 for and for. (4) 4.4.The Optimization Problem The timeline of the model is summarized in Figure 2. At 0, both parties observe the distributional properties of,, and and agree on a debt contract with elements,,,. At 1, the firm prepares an accounting report according to, based on the realizations of and. 10 Control over the liquidation decision is determined based on, and the controlling party decides whether to liquidate the enterprise or continue the project through the second period, possibly after renegotiating the contract with the other party. If liquidation occurs, proceeds 10 The firm cannot manipulate the accounting report through discretionary estimates in this model because is solely based on contractible information and can therefore be verified via an audit. 20

22 in the amount of are realized and split between firm and lender according to. If the project is continued instead, is realized in 2 and the payoff is again split according to. Since the firm has the bargaining power at 0 by assumption and thus retains all of the economic profit, the problem can be cast as a constrained optimization program over equity claims, subject to the lender s break-even requirement. Both firm and lender rationally anticipate each other s actions at the liquidation decision stage at 1, and so during the initial contract negotiation at 0, the lender always insists on contract terms yielding debt payments of at least in expectation, conditional on the control allocation across states induced by the accounting rule. Ex-ante wealth transfers from the lender to the firm are therefore impossible, and hence the firm can only increase its profits by increasing total proceeds, including both debt and equity claims. The problem of maximizing the investment s total payoff is equivalent to minimizing the loss resulting from both parties incentives to make inefficient liquidation or continuation decisions at 1, relative to the first-best benchmark. The expected value of this loss represents the agency cost incurred under the contract and will be denoted by. Total firm value at 0, i.e. the expected payoff from the investment, can thus be writte n as where is the firm s expected payoff and is the lender s expected payoff. Solving the above equation for and adding the lender s break-even constraint yields the firm s optimization program max,,, (7) 4.5.Renegotiation A final note about the possibility of renegotiation at 1 should be made. The option to renegotiate affects the efficiency of the contract, in addition to incentives and information. Renegotiation may increase total payoffs if the gains relative to the original contract exceed the costs of renegotiating. Among other things, this cost may represent direct legal and administrative expenses, which are likely to be high when the debt is issued in the form of bonds and sold to a large number of investors. Renegotiation costs may also include negative externalities. For example, a major customer of the firm may become aware of the renegotiation, interpret the event 21

23 as a signal that the firm is in financial difficulty, and seek a new supplier that does not have a potential going concern problem. This paper is not concerned with the role of renegotiation costs. Therefore, the analysis is limited to the two corner cases of zero and prohibitively high renegotiation costs, whereby the latter case is meant to imply that renegotiation never occurs. Modeling the cost explicitly would lead to the predictable result that it decreases contract efficiency by preempting an otherwise profitable reconfiguration of the contract terms in certain states. The conclusions concerning the optimal accounting system would not be affected qualitatively. 5. Results Under Symmetric Information The optimization problem in a setting with symmetric information will be considered first. In particular, both the firm and the lender are assumed to observe the realization of at the end of the first period, i.e. Θ Θ Θ Θ Analyzing this information structure can only yield non-trivial results if barriers to renegotiation exist. Otherwise, if renegotiation is costless, the Coase theorem applies and the first-best outcome can be implemented. In particular, if the firm has not defaulted and has an incentive to continue the business when liquidation is optimal, it can offer the lender to liquidate the business in exchange for accepting a payoff of less than. Since liquidation yields a higher payoff than continuation, both parties can obtain their expected continuation payoffs and split the surplus according to the distribution of bargaining power. The case when the lender is in control and has an incentive to liquidate inefficiently is analogous. Then 0 regardless of the covenant-based control allocation scheme set out in the original contract, and it suffices to calculate such that the lender breaks even given the anticipated renegotiation outcomes. Accounting would have no role in this setting. In contrast, if renegotiation is prohibitively costly, both firm and lender execute their liquidation decisions in accordance with their incentives and their information sets. Since Θ Θ,, in this scenario, the liquidation thresholds in equations (1) and (2) determine the con- 22

24 tracting parties actions. Then 0 because the liquidation thresholds do not coincide with the first-best benchmark, and the optimal accounting rule is no longer an arbitrary choice. Solving the optimization program in (7) requires the derivation of and. The firm defaults whenever and makes an inefficient decision if,, according to Proposition 1. As noted in Section 4, the loss relative to the first-best benchmark is measured by the distance. Then conditional on, the firm s decisions result in an expected efficiency loss of The converse observations apply to the lender, which impli es an expected efficiency loss of Combining the previous two expressions and integrating over yields where and are as defined in Section 4. Equation (8) gives the total inefficiency of any given contract. The lender s expected payoff is affected by the same decision incentives that determine. Its functional form is therefore where min, is the expected debt payment when the lender is in control and min, is the expected debt payment when the firm is in control, conditional on. The functional form of shows that the lender s payoff is discontinuous in at. (8) (9) 23

25 Before proceeding to solve the firm s optimization problem, one should note the following useful observation, which states that higher fixed accruals increase the lender s expected payoff. Lemma 2. The lender s expected payoff is everywhere increasing in. Proof. See Appendix. This result is not unexpected because raising increases the probability of technical default unconditionally and thus results in a strict enlargement of the subset of states in which the lender has control. Given the incentive misalignment between the firm and the lender, either party s payoff increases in its sphere of control. The firm maximizes its profit by minimizing the sum of the inefficiency of the contract and its payments to the lender. While it can never pay the lender less than in expectation, one may conjecture that the firm could pay the lender more than the required amount if this results in a reduction of that outweighs this overpayment. After all, the firm has the full bargaining power at 0 and would reap the entire benefits of such an efficiency gain. The following result shows that this strategy is never optimal, i.e. the lender s break-even constraint always binds. Proposition 3. The firm always chooses its optimal contract such that the lender s expected payoff is. Proof. See Appendix. Proposition 3 is consistent with the previous observation that and are determined by the same decision incentives. But while the lender s payoff is determined by the entire state space, only depends on the region in which inefficient decision-making occurs. The lender would therefore receive more than one-hundred percent of the efficiency gained through any concessions in the contract terms by the firm. A general, closed-form solution to the optimization problem is unattainable given the general form of the probability distributions, but as the following results illustrate, the properties of the 24

26 optimal accounting rule can be characterized nonetheless. As a preliminary, the next lemma establishes the uniqueness of the solution to the firm s problem, which will be useful for the subsequent propositions. Lemma 3. The critical point for the optimal contract,, is unique. Proof. See Appendix. It is instructive to begin the discussion of the optimal form of the accounting rule by examining the two corner cases of perfect and uninformative liquidation value estimates. The former case implies that the state of the world is fully contractible, and thus leads to a straightforward implementation of the first-best benchmark result, i.e. 0. Proposition 4 provides the solution values of and for this case. Proposition 4. If is a perfect estimate of so that Pr 1, the optimal accounting rule is, 1, 2 and achieves the first-best outcome. Proof. See Appendix. The contrary case is an estimate that yields no information at all about. One might conjecture that adding noise to the accounting measure does no harm to the efficiency of the contract because both the firm and the lender are risk-neutral, and that adding or omitting from the accounting system is hence a matter of indifference. However, if is uninformative, its impact on the allocation of control is uncorrelated with and hence with the contracting parties incentives. Therefore, it can at most not overturn a control allocation that is efficient ex ante based on knowledge of, but it will do so in some cases. In other words, the most effective covenant should not rely on in this case. The next proposition formalizes this idea. Proposition 5. If is completely uninformative so that, the optimal accounting rule is 1. In addition, if and both distributions are symmetric, 2 at the optimum. 25

27 Proof. See Appendix. Proposition 5 states that in the absence of correlation between and, the optimal accounting measure is solely a function of cash flow information. This can be viewed as a form of pure historical cost accounting that does not rely on any forward-looking information in the form of fair value estimates. A corollary of the preceding two propositions is that the optimal value of decreases in the precision of. The results of Propositions 4 and 5 also combine in a natural manner with respect to for intermediate cases. Proposition 6. If and all three distributions are symmetric, and the optimal maturity value of the debt is, then the optimal accounting rule is Proof. See Appendix. Proposition 6 is a special case, but it allows for a number of important and general observations. First, the functional form of suggests that the optimal level of fixed accruals is a linear combination of the solutions to the corner cases of precise and uninformative. The weight of either component depends on and thus on the precision of. In this sense, illustrates the tradeoff between relevance and reliability of accounting information. Second, while the functional form of changes if the assumptions imposed in this proposition are lifted, the comparative statics it implies are nonetheless valid in general. In particular, increases with the firm s leverage and the expected second-period cash flows, and it decreases in the investment s profitability and the precision of the fair value estimate. The level of represents the amount of scheduled accrued expenses recognized at 1, such as depreciation. Higher values of can thus be interpreted as increases in unconditional conservatism, i.e. an accelerated recognition of expenses that are allocated over several periods. 26

28 References Aghion, P. and Bolton, P An incomplete contracts approach to financial contracting. Review of Economic Studies 59(3): Ahmed, A., Billings, R., Morton, R. and Stanford-Harris, M The role of accounting conservatism in mitigating bondholder-shareholder conflicts over dividend policy and in reducing debt costs. Accounting Review 77(4): Beatty, A., Weber, J. and Yu, J Conservatism and debt. Journal of Accounting and Economics 45: Begley, J. and Freedman, R The changing role of accounting numbers in public lending agreements. Accounting Horizons 18(2): Beneish, D. and Press, E Costs of technical violation of accounting-based debt covenants. Accounting Review 68(2): Berkovitch, E. and Israel, R The bankruptcy decision and debt contract renegotiations. European Finance Review 2: Caskey, J. and Hughes, J Assessing the impact of alternative fair value measures on the efficiency of project selection and continuation. Working paper: University of California, Los Angeles. Christensen, H. and Nikolaev, V Capital versus performance covenants in debt contracts. Working paper: University of Chicago. Décamps, J. and Faure-Grimaud, A Excessive continuation and dynamic agency costs of debt. European Economic Review 46:

29 Gârleanu, N. and Zwiebel, J Design and renegotiation of debt covenants. Review of Financial Studies 22(2): Gigler, F., Kanodia, C., Sapra, H. and Venugopalan, R Accounting conservatism and the efficiency of debt contracts. Journal of Accounting Research 47(3): Grossman, S. and Hart, O Corporate financial structure and managerial incentives. The Economics of Information and Uncertainty. Ed. J. McCall. Chicago: University of Chicago Press, Guay, W. and Verrecchia, R Discussion of an economic framework for conservative accounting and Bushman and Piotroski (2006). Journal of Accounting and Economics 42: Jensen, M. and Meckling, W Theory of the firm: managerial behavior, agency costs and ownership structure. Journal of Financial Economics 3: Li, J Accounting conservatism and debt contracts: efficient liquidation and covenant renegotiation. Working paper: Carnegie Mellon University. Li, N Debt contracting efficiency of accounting conservatism. Working paper: London Business School. Modigliani, F. and Miller, M The cost of capital, corporation finance and the theory of investment. American Economic Review 48(3): Myers, S. and Majluf, N Corporate financing and investment decisions when firms have information that investors do not have. Journal of Financial Economics 13:

30 Ross, S The determination of financial structure: the incentive-signaling approach. Bell Journal of Economics 8(1): Zhang, J The contracting benefits of accounting conservatism to lenders and borrowers. Journal of Accounting and Economics 45:

31 Appendix Proof of Lemma 1. All three distributions have support over 0, for some, with 0 0 by Assumption 2, and so by Rolle s theorem, 0 for at least one 0,. Since is a probability density, 0 for all and 0 for some 0,, and so if is defined to be the left-most 0 for which 0, must be a maximum. Then 0 for some, which implies that 0 for such. If had a second extremum at some point, 0 and the property that that 0 0 and hence lead to a contradiction. Therefore, must be unimodal. and so where and is decreasing would imply The decreasing ratio further implies tha t for any and positive integer for any,,,,, 1, 1. Then, lim, after setting 0, and so 30

32 Therefore, the decreasing ratio implies that is increasing, i.e. has a monotone hazard rate. Proof of Proposition 1. Based on equation (1), the firm s liquidation threshold is max0, and changes with respect to by 0 Therefore, is everywhere decreasing in and attains its minimum when. Substituting into the liquidation threshold shows tha t i.e. the firm never prefers liquidation below the first-best benchmark value. The convexity of the inefficiency range follows from 0 Likewise, the lender s liquidation threshold from equation (2) can be written as and changes with by min, 10 so that it attains its maximum wh en 0. Then and hence the lender never liquidates above the first-best benchmark value. The lender s inefficiency range is a convex function becau se 0 31

33 Proof of Proposition 2. Liquidation is efficient whenever. The only indicator of available in a direct decision mechanism is, and hence the optimal mapping from to decisions would prescribe liquidation whenever where is the expected total liquidation payoff. Alternatively, one can consider a state-contingent control allocation scheme by which the lender receives the right to decide whether to liquidate whenever and the firm retains control otherwise. The lender will choose liquidation if s where is the lender s information signal. By Assumption 1, Θ Θ, i.e. all information in is also reflected in in all states, and so. Then the expected payoff of the delegation scheme becomes 1 where Pr. The inequality must hold because by Proposition 1, and hence this delegation scheme achieves a higher total payoff than the optimal direct decision mechanism. The argument that delegating the liquidation decision to the firm when achieves a higher payoff than directly mapping to a continuation decision is symmetric. Proof of Lemma 2. The lender s expected payoff in equation (9) changes with respect to by where and The term min, min, 32 (A1)

34 1 1 0 is constant. The liquidation thresholds in equations (1) and (2) imply the identities and min, which can be applied to combine terms so that min, 0 for every. Hence, 0 for all. Proof of Proposition 3. The first-order condition of the firm s optimization program implies that Direct computation of the numerato r yields where d m and are as efined in Lem a 2. Then for every 0 analogous to the derivation in Lemma 2. Since 0 and 0 by Lemma 2, can therefore never be negative, and it can only be zero in the corner cases 0 and. By the complementary slackness condition, the lender s break-even constraint does not bind when 0. Then for any value such that, there exists some such that the lender s payoff declines without causing a violation of the break-even constraint. The firm must profit from this decline, net of any possible ensuing efficiency loss, because 0 as shown above. Thus, cannot be optimal. 33

35 0 0 Figure 1. Liquidation thresholds. The firm and the lender conclude a contract,,,. 0 1 The values of, and are realized. Default is determined according to,. The controlling party decides whether to liquidate the investment, possibly after renegotiation. 2 If no liquidation occurs at 1, is realized. Figure 2. Timeline. 34