Debt Contracts in the Presence of Performance Manipulation

Transcription

1 Debt Contracts in the Presence of Performance Manipulation Ilan Guttman Stern School of Business New York University Iván Marinovic Stanford Graduate School of Business Stanford University August 10, 2017 Abstract Empirical and survey evidence suggests that firms often manipulate reported numbers to avoid debt covenant violations. The theoretical literature on debt contracting, by and large, has ignored the borrower ability to manipulate financial reports. Building upon a standard debt financing setting with continuation decisions based on reported signals, we study the effect of the borrower s ability to manipulate his report on the design of debt contracts and the resulting investment continuation and manipulation decisions. The model generates an array of novel empirical predictions regarding the covenant, the interest rate (face value), the efficiency of the continuation/liquidation decisions, and the likelihood of covenant violations. For example, the model predicts that firms with stronger corporate governance may set tighter covenants and, as a result, violate their covenants more often. It also shows that firms with stronger governance may face higher interest rates. We should expect covenants to be more prevalent in environments in which the cost of manipulation is relatively high and the firm s private information is more precise. Keywords: Asymmetric Information, Debt Contracts, Earnings Management JEL codes: D82, D86, G3, M12 We would like to thank Cyrus Aghamolla, Anne Beyer, Jeremy Bertomeu, Robert Miller, Stephen Ryan, Paul Povel, Andy Skrzypacz, Felipe Varas, and Jeff Zwiebel for helpful comments and seminar participants at U.C Berkeley, New York University, Colorado Accounting Research Conference and the Accounting Research Workshop in Basel. 1

2 1 Introduction The finance and economics literature has studied debt contracts extensively, both theoretically and empirically. This literature has nonetheless overlooked an important friction: managers can, and often do, manipulate financial reports to avoid debt covenant violations. 1 In this paper, we study the design of debt contracts in the presence of manager s ability to manipulate reports. Given the vast evidence of performance manipulation to avoid covenant violation, it is important to understand its effect on the design of debt contracting, the resulting likelihood of covenant violation and the expected amount performance manipulation. Absent theory that considers the ability to manipulate reports, it is hard to understand some features of debt contracts and interpret the evidence relating debt contracts to firms information systems. 2 For example, it seems intuitive that when the firm s information system is less reliable - namely, when it is less costly for the manager to manipulate reported numbers - the interest rate should be higher in order to compensate the lender for the expected loss of control rights caused by the manager s potential manipulation. On the other hand, one might think that a less reliable information system should lead to tighter covenants, i.e., greater control rights assigned to the lender, in order to offset the manager s reduced cost of misreporting. Both hypotheses are intuitive when considered in isolation, however as our model demonstrates these hypotheses cannot hold at the same time. We study how a cash constrained firm/entrepreneur, who needs to raise debt financing to pursue a positive NPV project, optimally designs a debt contract. The main inovation in our model is that the manager has the ability to manipulate financial reports to avoid a covenant violation. Manipulating the report is assumed to be costly to the manager. We analyze how the various aspects of the optimal debt contract are affected by the firm s ability to manipulate the performance measure on which the covenant is written. 3 These aspects include: the level of the covenant, the interest rate (face 1 For evidence of misreporting to avoid covenant violations, see DeFond and Jiambalvo (1994); Sweeney (1994); Dichev and Skinner (2002), Graham et al. (2008) and Dyreng et al. (2011). 2 There is a large empirical literature in accounting documenting the impact of corporate governance and accounting quality on debt contracts. See Bharath et al. (2008); Ball et al. (2008), Costello and Wittenwerg-Moerman (2011). 3 In this paper we restrict attention to debt financing and derive the optimal debt contract. While pure debt financing is not the optimal financing method in our setting, in additional analysis of an extended setting that includes hidden effort we numerically characterize the optimal mix of 2

3 value), the efficiency of the investment continuation/termination decision, and the tightness of the covenant or the probability of covenant violation. To gain further insight, we study how these aspects vary with firms characteristics, including: (i) how costly it is for the manager to manipulate the report - which may capture the quality of the firm s corporate governance or the reliability of the accounting system; and (ii) the precision of the firm s private information about future cash flows - which may capture the relevance of the firm s private information. Our model demonstrates that the answer to these questions is subtle and often counter-intuitive. Our setting is a simple debt contracting model with three periods. In the first period, a cash constrained manager offers a debt contract to a lender in a competitive capital market to obtain financing for the firm s investment project. The debt contract is characterized by a covenant and a face value (or equivalently interest rate or spread). In the second period, the firm s manager privately observes a noisy signal of the profitability of the investment project and reports it to the lender. The manager is not confined to truthfully report the signal and can potentially misreport it to avoid a covenant violation. However, manipulating the report is costly and the cost is increasing in the magnitude of manipulation. If the report is lower than the covenant, i.e., a covenant violation, the control rights are transferred to the lender, who may terminate the project. Termination of the project allows the lender to recover a fraction of the loan. If the project is continued, the firm s terminal cash flows are realized in the third period. Upon realization of the cash flow, in the third period, the lender receives the maximum of the face value and the realized cash flows, while the equity holders receive the residual cash flow. The overall quality of the reporting/accounting system is determined by the precision of the private signal obtained by the manager which represents the relevance of the firm s private information and the cost of manipulation which represents the reliability of the accounting system. Since termination of the project only partially recovers the initial investment, covenant violation is costly for the manager and existing shareholders. 4 As such, given the debt contract that was debt an equity. The optimal mix includes both debt and equity, and hence the trade-off we identify in the baseline model qualitatively holds even under the optimal mix of debt and equity. 4 While in the equilibrium of our model the manager s continuation value given termination is zero, the main results would qualitatively hold for any cost to the manager and existing shareholders from covenant violation. Beneish and Press (1993) document that, in their sample, following technical covenant violation firms experience increased interest costs ranging between 0.84 and 1.63 percent of the market value of firms equity and that costs of restructuring debt represent an average of 3.7% of the market value of equity. 3

4 signed in the first period, the manager always has an ex-post incentive to continue the project. Whenever the manager s private signal is higher than the debt covenant, there is no incentive to manipulate the report. When the private signal is lower than the debt covenant, the manager will manipulate the report upward to avoid violation of the covenant whenever the cost of the required level of manipulation to avoid covenant violation is lower than the manager s/equity holder s expected benefit from continuation of the project. As such, whenever a covenant is used as part of the debt contract, it entails a positive expected manipulation costs. In designing the debt contract, the manager considers the tension between investment efficiency (efficiency of the termination/continuation decision) and the expected cost of misreporting. As our model demonstrates, this tension is typically not resolved by setting a covenant that implements the first best termination/continuation decision. While a debt contract that implements the first best investment decision is feasible, it is almost always suboptimal because such a contract induces excessive expected manipulation costs. Interestingly, the model generates different qualitative predictions for different parameter values. In particular when the cost of manipulation is high (high quality of corporate governance) the optimal debt contract gives rise to over-continuation of the investment project. When the cost of manipulation is low and the precision of firm s private signal is intermediate the contract induces over-termination of the investment, which may initially seem counter intuitive, Finally, when both the manipulation costs and the level of precision of firm s private signal are low, implementing a covenant is costly and the quality of the signal is low, and hence the contract does not include a covenant. In addition to characterizing the optimal debt contract, the model also offers prediction of how cross sectional variation in firm s characteristics affects the optimal debt contract. One interesting parameter, that sometimes generates counter intuitive results, is the cost of manipulating the report. Cross sectional variation in the cost of manipulating the report whether it is via real manipulation which decreases the future cash flows, or accrual manipulation which are personally costly to the manager can arise due to differences in many firm characteristics, such as the quality of corporate governance; the reliability of the accounting system; the level of scrutiny by regulators, auditors, financial intermediaries and investors; regulatory enforcement; and litigation risk. The model predicts that an increase in the manipulation cost reduces the covenant but this does not necessarily imply a lower frequency of covenant violation. In equi- 4

5 librium, a decrease in the level of the covenant may be accompanied by an increase in face value. The increase in face value weakens the manager s misreporting incentives and the maximum manipulation cost that the manager is willing to bear in order to avoid covenant violation. If the effect of the increase in face value dominates, the likelihood of covenant violation decreases in the manipulation cost. We show that covenant violations are more likely when misreporting is more costly in environments characterized by relatively noisy private information. Note that changes in the cost of manipulation also affect the equilibrium efficiency of the investment. In particular, if the face value increases significantly, then an increase in the manipulation cost induces more termination of the investment project. If the effect of the decrease in covenant dominates then an increase in the manipulation cost induces more continuation of the project, even if conditional on the signal the project obtains a negative NPV. The (perhaps counter intuitive) phenomenon that the likelihood of covenant violation increases in the manipulation cost, or in the quality of corporate governance, arises when misreporting costs are relatively high, e.g., when corporate governance is relatively strong. This may explain why firms with stronger governance may violate their covenants more often: since their misreporting friction is weaker, they rely on tighter covenants, but they also violate them more often. The relation between the cost of manipulation and interest rates can also be counter-intuitive. The optimal debt contract resolves the misreporting friction by simultaneously adjusting the covenant and interest rate (face value). As we later show, these two levers must be substitutes in equilibrium. This means that a lower manipulation cost may lead to tighter covenants but at the same time a lower interest rate (face value). Thus, a more reliable firm which manipulates less on average, can face a higher interest rates than a less reliable one. This is the case when the precision of the firm s signal is high and the cost of manipulation is relatively low. One important implication of this result is that measuring a firm cost of debt by the observed interest rate is often misleading. This is because the interest rate does not take into account the total value promised to the lender, in particular in cases where the lender receives less than the face value following covenant violation. Moreover, a measure of the cost of debt should take into account the efficiency loss in investment caused by the possibility of misreporting. In summary, our model generates a rich set of empirical predictions, such as: In many industries we should expect a positive relation between the cost of manipula- 5

6 tion (which as mentioned above could be related to corporate governance, industry characteristic, country characteristic) and the likelihood of debt covenant violation; We should expect covenants to be more prevalent in environments in which the cost of manipulation is relatively high and the firm s private information is more precise. These predictions can be empirically tested either in an international setting (taking into account variations in regulations, enforcement, transparency, etc.), or in the US by dividing the sample to pre and post Sarbanes-Oxley, or across industries. 1.1 Related Literature We follow the Grossman-Hart-Moore property rights program by studying the optimal assignment of control rights given contractual incompleteness (see Grossman and Hart (1986); Hart (1995); Hart and Moore (1990)). The incomplete contracting literature (see Aghion and Bolton (1992)) considers the use of financial contracts to assign control rights across different states of the world. This literature takes the information structure as exogenous: information is public but non-contractible. In our setting, by contrast, information is contractible but potentially misreported by the firm, which sometimes results in information asymmetry. In addition, given that our model introduces the ability to manipulate the report, the likelihood and the extent of misreporting and the resulting information asymmetry depend on how control rights are assigned. There is a large literature in accounting studying the causes and consequences of earnings manipulation. This literature has followed two strands: the first strand takes the manager incentives as exogenous and focuses on the market reaction to earnings reports (see e.g. Dye (1988); Fischer and Verrecchia (2000); Guttman et al. (2006)). The second strand studies optimal contracts when managers have discretion to manipulate the reports (see e.g., Liang (2000),Beyer et al. (2014),Dutta and Fan (2014),Stein (1989)). We build on the second strand but restrict attention to debt contracts. Our paper is related to the costly state verification literature started by Townsend (1979), where debt contracts are optimal because they minimize verification costs. In our setting, lenders do not monitor, and the optimal debt contract seeks to minimize expected misreporting costs while maximizing investment efficiency. Unlike in Townsend (1979) the firm can obfuscate the information available to the lender via misreporting. Dessein (2005) studies the optimal allocation of control rights as a function of 6

7 the severity of information asymmetries. Garleanu and Zwiebel (2009) also study the design and renegotiation of covenants in a setting where the lender has private information at the contracting stage. In their settings, the informed party gives up control rights to the lender to signal congruent preferences. As Garleanu and Zwiebel (2009), we focus on debt contracts, and do not address the more general security design question. The optimality of debt contracts in moral hazard settings under limited liability was first established by Innes (1990). More recently Hebert (2015) proves the optimality of debt when managers effort and risk choices are unobservable. 5 Cornelli and Yosha (2003) study stage financing in a settings where managers can engage only in ex-ante window dressing that shifts the distribution of signals. The signal in their setting is non-contractible and they find that the optimal contract is a convertible debt contract which results in no window dressing. We consider a very different setting where signals are hard, privately observed by the firm, but manipulable at some cost. As such, firms reports about the signal are contractible. The empirical literature has provided ample evidence that managers take (costly) actions to avoid covenant violation. Some examples are DeFond and Jiambalvo (1994); Sweeney (1994) which finds that managers of firms approaching default respond with income-increasing accounting changes and that the default costs imposed by lenders and the accounting flexibility available to managers are important determinants of managers accounting responses. Dichev and Skinner 2002 and Dyreng et al. (2011) provide large-sample support to the debt covenant hypothesis. While companies try to avoid covenant violation, covenant violations are not rare. Dichev and Skinner document that covenant violations occur at some point to about 30 percent of the firms in their sample. Graham et al. (2005), on the other hand, focus on violations aimed at meeting earnings benchmarks, and find that the bond covenants hypothesis seems to be important primarily where there are binding constraints. Covenant violation is costly to the firm. The cost of covenant violation can vary substantially across firms in terms of the type of cost and its magnitude. For example, covenant violation costs can be due to: transfer of control rights; increased interest rate (that may lead to refinancing costs); lenders demand for partial or full 5 Sengupta (1998) notes that debt financing is the predominant form of external financing for publicly traded firms in the U.S. For example, during 1992, publicly traded companies raised approximately 2,764 billion through investment grade debt issue (which excludes mortgage and government-backed debt, convertible debt and junk bonds) in comparison to approximately 932 billion raised through common and nonconvertible preferred stock issue. 7

8 repayment (which may lead to restructuring costs and modification of operations); increased lender control and restrictions on assets sale, dividend payment and investment activities (see e.g., Beneish and Press (1993)). Note that our main results do not rely on the manager s payoff upon covenant violation being zero. As long as the manager has some personal cost from covenant violation, she will have an incentive to avoid violation of the covenant and our main results will qualitatively hold. 6 The paper proceeds as follows. Section 2 describes the model. Then section 3 develops the first best benchmark and Section 4 conducts preliminary analyses. In section 5 we analyze a contract without covenant, whereas Section 6 derives the optimal debt contract. Section 7 discusses the properties of the optimal debt contract. Sections 8 and 9 discuss empirical implications and theoretical underpinnings. Section 10 proposes several extension and Section 11 concludes. 2 Model We consider a debt contracting setting in which the borrower can misreport the firm s prospects to avoid the contractual consequences of a covenant violation. A liquidity constrained entrepreneur/firm has access to a project that requires an initial investment of I and pays out a stochastic future cash flow x F (x), if completed. In order to finance the investment opportunity, the firm needs to raise funds I through a debt contract. The debt contract specifies a covenant, z (as explained below), and a face value, K, which the borrower promises to pay the lender at the project s maturity. If the lender accepts the debt contract offered by the manager and the project is funded at t = 1, the sequence of events is the following. At t = 2, the manager privately observes the realization of a noisy signal of the project s future cash flows, s, which is the realization of the random variable s. Given the signal s, the manager issues a (potentially biased) report of his private signal, r. The manager is not confined to truthfully reporting his private signal, however, manipulating the report is costly. We assume the manager s misreporting cost equals c r s. 7 In the 6 In section 10.3 we study renegotiation following a covenant violation, which is an alternative way of introducing cost from covenant violation. 7 The specific cost function does not play an important role in the analysis. All the results qualitatively go through under any strictly increasing function of the magnitude of manipulation, e.g., quadratic cost function. 8

9 main analysis we assume, for simplicity, that the manipulation costs are personally born by the manager (as commonly assumed in the theoretical accrual management literature). In Section 10.4 we show that similar results hold when introducing the assumption that also the future cash flows are decreasing in the manipulation of the report, i.e., real earnings/performance management rather than just accrual manipulation. If at t = 2 the manager s report about his private signal is lower than the covenant, i.e., r < z, there is a covenant violation. When the covenant is violated the lender receives the project s control rights and can terminate the project. The termination/liquidation proceeds are assumed to be L, where L < I. If the project is not terminated, at t = 3 cash flow of the project is realized and payoffs are allocated. Upon realization of the cash flows (at the maturity of the project at t = 3) the lender receives min(k, x) and the borrower retains the residual cash, i.e., the manager gets max(0, x K). Figure 1 summarizes the timeline of our setting. Figure 1: Timeline t=1 The debt contract is signed, specifying {z, K}. t=2 The manager privately observes signal s and reports r. If the covenant is violated, the project is terminated. t=3 If continued, the project s cash flows x are realized and payments are made. Both the lender and borrower are risk neutral. For simplicity, and without loss of generality, we assume that future cash flows are not discounted. The debt market is competitive, so in expectation lenders break-even. Both the manager and lender maximize their expected payoff and obtain zero payoffs when the project is not financed. All the model s parameters, payoff functions, distributions of the signal and the cash flows are assumed to be common knowledge. 2.1 Information Structure The objective of this paper is to study the impact of misreporting on the design of debt contracts. We design a setting that focuses on this interaction, while trying to abstract from other potentially confounding effects. One such effect is the variation of the density of the distributions of cash flows and the manager s private signal (As indicated earlier, given a debt covenant, there will be an interval of signal realizations below the debt covenant, such that for all signals within this interval 9

10 the manager will manipulate his report upwards in order to meet the covenant. When designing the optimal contract in the first period, the manager considers the expected manipulation cost, which depends on the distributions of the private signal and the cash flows.) For simplicity, we assume cash flows are uniformly distributed. In Section 10.2 we demonstrate that our results hold under standard unbounded distributions, such as the Log-Normal distribution. 8 We assume that the manager s private signal, s, is a mixture: that is, with probability ρ the signal is equal to the cash flow x and with probability 1 ρ the signal is pure noise that is drawn from the same distribution as x. Thus, ρ can be thought of as the accounting system s precision. This is an important parameter impacting the design of debt contracts: Ball et al. (2008) documents that when a borrower s accounting information is more precise, this lowers the lender s monitoring cost. 9 In the sequel, we assume that both the cash flows x and the signal s are uniformly distributed over [0, 1], i.e., x U [0, 1] and s U [0, 1]. Hence, the conditional expectation of x given the signal s is linear in s and given by E( x s) = ρs + (1 ρ)e(x). 3 First Best: No-misreporting Case Before deriving the equilibrium, we provide as a benchmark the first best outcome. The first best (labelled F B) is achieved when misreporting is precluded, i.e., in the limit as misreporting becomes prohibitively costly (c ). Naturally, in the absence of misreporting, the optimal debt contract induces efficient continuation/termination. Since the expected cash flow given continuation increases in the signal s, the first best continuation strategy is a threshold strategy. We denote the threshold signal below which the project is terminated by τ F B. That is, for all s < τ F B the project is terminated, otherwise the project is continued. When the signal realization equals this threshold, the expected cash flow given termination, L, equals the expected cash flow given continuation, E ( x s = τ F B). 8 We verified that similar results hold also for truncated normal and exponential distributions, but for brevity we did not include these examples. 9 In particular, they hypothesize and document that when a borrower s accounting information possesses higher informativeness, information asymmetry between the lead arranger and other syndicate participants is lower, allowing lead arrangers to hold a smaller proportion of new loan deals. 10

11 The expected value of the firm when manipulation is prohibited, depends only on the efficiency of the firm s investment policy as captured by τ. Under the firstbest continuation policy, the expected value of the firm, which we denote by V (τ), equals V ( τ F B) = Pr ( s < τ F B) L + Pr ( s τ F B) E ( x s > τ F B). The first best continuation threshold, τ F B, is given by τ F B = 2L (1 ρ). (1) 2ρ Due to the option to terminate the project, the firm value is greater than E (x). Note that V ( τ F B) represents an upper bound for the firm value relative to the case where misreporting is feasible. Condition 1. Under an efficient continuation policy, the project has positive net present value, formally V ( τ F B) I. This assumption imposes an upper bound on I. As we shall argue, this assumption means that, no matter how small is c, the project can always be financed. Furthermore, for any c > 0 there is always a debt contract that implements the first best continuation policy and generates positive expected payoffs to the lender and the manager. To focus on the interesting case, we assume the signal is sufficiently informative such that termination is sometimes optimal. If the signal were not sufficiently informative the contract would not include a covenant and the project would never be terminated. Formally, a signal is sufficiently informative if there are realizations of s, such that E( x s) < L. Condition 2. Termination is sometimes optimal, or ρ > 1 2L. This assumption means the signal is precise enough, so in the absence of misreporting, the optimal debt contract always implements some termination. As we shall argue, misreporting may lead to a contract without covenants where the project is never terminated. 11

12 4 Preliminaries A debt contract can be defined as a pair {K, z} consisting of a face value K and a covenant z. The face value, K, determines the maximum amount the lender receives when the project s cash flows realize; the covenant, z, determines the report below which the covenant is violated and the lender is awarded control rights - following which the lender can terminate the project. Any contract {K, z} that is agreed upon results in an equilibrium termination cutoff τ (z, K). The cutoff τ defines the signal value below which the manager prefers to report truthfully and violate the covenant, transferring control rights to the lender who can terminate the project. An arbitrary contract {K, z} and the resulting termination cutoff τ (z, K) determine the enterprise s expected future cash flows (to the lender and the shareholders). We refer to this value as firm value and denote it by V (τ). Note that the firm value is independent of the expected manipulation cost, and hence, only depends on the efficiency of the continuation decision - which is determined by τ. The face value, on the other hand, only affects the allocation of surplus between the firm and the lender, and may affect the manager s misreporting behavior. The firm value is given by V (τ) = Pr (s < τ) L + Pr (s τ) E ( x s > τ) = τl + 1 τ E(x s)f(s)ds. For a contract {K, z} and the resulting termination cutoff τ (z, K), the expected cash flow to the lender, which we refer to as the value of debt and denote it by D(K, τ), is given by D (K, τ (z, K)) = τ (z, K) L + 1 τ E(min (x, K) s)f(s)ds. Naturally, for the lender to be willing to provide funding, the debt value must be no smaller than I, i.e., D (K, τ (z, K)) I. The termination cutoff τ (z, K) that results from a contact {K, z} must be incentive compatible from the manager s stand point when choosing the report. Hence, when s = τ (z, K) the manager must be indifferent between manipulating the report in order to meet the covenant and continue the project, and between saving the manipulation cost and violating the covenant. We currently implicitly assume that 12

13 when the covenant is violated the lender prefers to terminate the project. We later show that this indeed holds in equilibrium, so we can ignore incentive compatibility on the lender s part. Formally, the manager s reporting incentive compatibility constraint, which determines τ (z, K) is E [ (x K) + s = τ (z, K) ] = c (z τ (z, K)). (2) We refer to equation 2 as the misreporting IC constraint, but strictly speaking this is what the IC constraint reduces to given the fact that indifference at the threshold implies in this model no incentives to manipulate below. Given the above reporting incentive compatibility condition, the expected misreporting cost borne by the manager, which we denote by C (z, τ), is C (z, τ) z τ c (z s) ds. We can now define an optimal debt contract. Definition 3. An optimal debt contract {K, z } and the resulting termination threshold τ is given by the solution to Π max V (τ (z, K)) C (z, τ (z, K)) {K,z} subject to the lender s participation constraint D (K, τ) I (3) and the manager s misreporting incentive compatibility constraint given in equation 2. Intuitively, in equilibrium the lender s participation constraint binds. So for future reference, we define a function K (τ) representing the face value that exactly satisfies the lender s participation constraint given a termination cutoff τ, namely D (K, τ) = I. (4) In the remainder of this section, we derive and characterize the optimal debt contract. We start by analyzing the game backwards, in particular, we analyze the 13

14 manager s reporting strategy and expected manipulation cost for any given contract. We next derive the set of contracts that satisfy the lender s participation constraint as an intermediate step toward finding the optimal debt contract. 4.1 Expected Manipulation Costs A debt contract is designed to maximize investment efficiency while avoiding excessive misreporting costs. In this section, we study how the covenant and face value affect the manager s expected misreporting costs. As mentioned above, the covenant, z, in conjunction with the face value, K, determine a threshold signal τ (z, K) below which it is too costly to manipulate the report to meet the covenant. When the manager s signal equals that threshold, the manager is indifferent between meeting the covenant, by misreporting the true signal, and violating the covenant, thereby allowing the lender to terminate the project. In other words, for any given {z, K}, the threshold τ is such that the manipulation cost incurred by the manager to meet the covenant equals the manager s expected continuation payoff, as characterized by equation 2. Equation 2 characterizes the manager s reporting behavior, given an arbitrary contract {z, K}. The manager manipulates his report only if the signal belongs to s [τ, z], and over this interval the manager reports z and the bias in the report is z s. Otherwise, the manager truthfully reports his signal to the lender, even if this triggers liquidation. We can now consider the expected misreporting cost induced by the contract. We focus on the case τ K. (As it will turn out, this condition must be satisfied in equilibrium). For any given pair {z, K} equation 2 defines a termination threshold τ (z, K) = z (1 ρ) (1 K)2, (5) 2c such that managers with signals above τ = τ (z, K) will prefer to manipulate the report (if needed) to avoid a covenant violation. Notice that the distance between z and τ, hence the probability of manipulation, is independent of τ. This property holds for any cost function that increases in the magnitude of the manipulation. For simplicity, we assume a linear cost function Notice we do not restrict the covenant z to have the same support as the cash flows, i.e., z can be larger than one. This may seem unnatural, and is a limitation of using the Uniform distribution (or more generally of distributions that are bounded from above). We demonstrate the robustness of our results, with respect to distributional assumptions in Section

15 Given the characterization of the marginal type s misreporting cost, and the interval of types choosing to manipulate s [τ, min (z, 1)] (where the termination threshold τ is given by equation 5), we can now analyze the expected misreporting costs induced by an arbitrary contract {K, z}. Lemma 4. The expected misreporting cost for arbitrary {K, z} can be written as C (z, τ (z, K)) z τ c (z s) f(s)ds = { (1 ρ) 2 8c (1 ρ) 2 8c (1 K) 4 if z < 1 (1 K) 4 c(z 1)2 2 if z 1. (6) Consider the effect of increasing z when z < 1 (and keeping K constant). 11 Increasing z induces a one-to-one increase in τ, thus shifting to the right the location of the interval of manager types that manipulate the report but given the Uniform distribution it does not affect the probability of manipulation. Therefore, for a given face value, the probability of misreporting and expected misreporting cost is independent of the covenant level when z < 1. Now, let us consider the case of z > 1. Increasing z leads again to a one-toone increase in τ(z, K). However, now the probability of manipulation and the expected misreporting cost decreases because the upper bound of the interval of types who chose to misreport is fixed at one. Setting tighter (i.e., higher) covenants has the ability to reduce the likelihood of misreporting, ceteris paribus. The following corollary summarizes this result. Corollary 5. For a given face value K, a marginal increase in the contract s covenant z weakly reduces expected misreporting costs. dc (z, τ (K, z)) dz = { 0 if z < 1 < 0 if z 1 Also, for a fixed covenant z a marginal increase in the face value lowers expected misreporting costs, dc (z, τ (K, z)) < 0. dk 11 In general, the effect of z on expected misreporting costs is non-monotonic. This is intuitive: the contract can eliminate misreporting costs by setting z = 0. (Such a contract gives the manager all the control rights.) Alternatively, the contract can mitigate misreporting by setting a high covenant, so that misreporting is always unaffordable to the manager. (At the limit, such a contract awards all control rights to the lender.) 15

16 The effect of face value K is also intuitive. Increasing the face value, for a given z, reduces the manager s skin in the game, thus weakening his manipulation incentives and lowering expected misreporting costs. In the next section, we derive the face value that maximizes the manager s payoff when the contract implements a termination policy τ. 4.2 Lender s Participation In addition to the expected misreporting costs, a contract {K, z} determines the lender s expected payoff, which has two components. First, if the covenant is violated, the lender assumes control rights and can liquidate the project to recover L. Second, if the project is continued, the lender receives the maximum of the face value K and the cash flow x. The lender will accept the debt contract as long as his expected payoff is higher than the investment, I. Since the manager can always extract all the surplus from the lender, the optimal contract should offer a face value that keeps the lender s participation constraint binding, thus solving Pr (s τ) L + 1 τ E (min (x, K) s) f (s) ds = I (7) This equation represents the lender s participation constraint when debt markets are competitive. Lemma 6. The face value that satisfies the lender s participation constraint when the contract {K, z} induces termination threshold τ, denoted by K (τ), is given by K (τ) = (I Lτ) + ρτ 2. (8) 1 τ + ρτ For any τ [0, ˆτ] the face value K (τ) is a continuous U-shaped function with the following characteristics: K (τ) > I; K (0) = 1 1 2I; 16

17 and the unique minimum of K ( ) over the interval [0, ˆτ], denoted τ +, is given by τ + arg min s [0 ˆτ] K (s), where ˆτ = L+ L 2 +2ρ 4ρI 2ρ. The value of ˆτ is defined by K (ˆτ) = 1, and represents the termination threshold that makes the lender indifferent when he has 100% rights over the firm cash flows. The function K ( ) defines the face value that satisfies the lender s participation constraint when the project is terminated for signals s τ, in which case the lender receives L (notice that the function K (τ) ignores whether τ is incentive compatible from the lender standpoint) A contract is feasible for a given cutoff τ if K K(τ) Figure 4 shows the region of feasible contracts. Figure 2: The lender s participation constraint. Parameters: ρ =.95, I =.45, L =.4. The U-shape of K (τ) means that for low τ the face value and control rights are 17

18 substitute ways of paying the lender: the manager can increase the lender s payoff by either increasing the face value or by increasing the covenant. However, when τ is large, face value and control rights are complements. To gain some intuition for the U-shape of K (τ), note that a low value of τ (i.e., when the probability of continuation is high) means the lender is unlikely to get control rights. As such, for low values of τ the lender demands a large face value to break-even. As τ increases, the lender gets extra control rights: we add more signals under which the project is terminated which is consistent with the lender s ex-post incentive for s = τ and hence the lender is willing to accept a lower face value. This continues up to a certain value of τ for which the termination threshold, τ, is expost optimal from the lender s standpoint, that is, for s = τ the lender is indifferent between continuation and termination. As we further increase τ, the contract starts inducing excessive termination, even from the lenders s ex-post standpoint, and hence, the lender demands additional compensation in terms of face value (recall K ( ) is derived assuming the lender can commit to terminating the project when he acquires control rights). As such, the face value for which the lender breaks even is a U-shape function of τ. As mentioned above, the U-shape of K ( ) implies that, when keeping the lender s constraint binding, for values of τ such that τ < τ + the face value K and the termination threshold τ are substitutes. By contrast, for higher values of τ, an increase in τ requires a higher face value to satisfy the lender s participation constraint. Hence, for τ > τ + the termination threshold τ and the face value K (τ) are complements. In the next section we demonstrate that in any equilibrium the face value and the threshold must be substitutes. 4.3 Covenant and Face Value: Substitutes or Complements? Given any debt contract, the manager always has an ex-post incentive to continue the project. For any given face value, the lender has an interior optimal continuation threshold. Lemma 6 proves that the face value that keeps the lender s participation constraint binding is U-shaped in τ. The minimum of K (τ) is obtained at τ = τ + where the lender s ex-post optimal continuation threshold coincides with s = τ +. For τ < τ +, given s = τ the lender faces higher incentive to terminate the project (and requires increase in the face value) and hence, τ < τ + results in ex-post over continuation from the lender s standpoint. For τ > τ +, given s = τ the lender faces lower incentive to terminate the project (and requires increase in the face value) and 18

19 hence τ < τ + results in ex-post over termination from the lender s standpoint. The following lemma shows that the equilibrium threshold τ is lower than τ +. This implies that evaluated at the equilibrium threshold the face values decreases in the termination threshold and that for s = τ the lender wishes to terminate the project. Lemma 7. The equilibrium threshold signal, τ, satisfies dk(τ) dτ 0. τ=τ The reason why face value and covenant must be substitutes in equilibrium is easier to see in the case when z < 1 where for a fixed face value the expected misreporting costs are independent of the termination threshold τ. Assume by contradiction that dk(τ) dτ > 0. Then, by lowering the termination threshold τ=τ while keeping the same face value the lender s participation constraint would still be satisfied while the manager would be strictly better off - in contradiction to the original contract being optimal. The case where z > 1 is more subtle, and hence it is deferred to the proof in the appendix. The ex-ante benefit from having a covenant is that it enables to induce termination of the project for sufficiently low signals. However, a covenant always comes with a cost - positive expected misreporting costs. For some set of parameters, the cost exceeds the benefit, and hence the optimal contract will not include a covenant. The following section identify the conditions for such contract. In Section 6 we derive the optimal contract when having a covenant is optimal. 5 A Contract without Covenant The following lemma identifies a condition under which the optimal contract does not include a covenant and provides the general expression for the optimal contract, the lender s participation constraint, and the manager s incentive compatibility constraint. We denote by τ, z, K the equilibrium termination threshold, covenant, and face value respectively, and by Π the manager s expected payoff. Lemma 8. If ρ is sufficiently low, then the project is never terminated and the contract does not induce misreporting. Hence τ = 0, z = 0, the face value K is given by 1 0 E (min (x, K ) s) ds = I, 19

20 or, equivalently, K = 1 1 2I. This contract generates manager payoff Π = E (x) I (note that the only relevant solution is 0 < K 1 and that 0 < I < E (x) = 0.5). In general, the debt contract maximizes the firm s expected cash flows net of expected misreporting costs, subject to the lender s participation constraint, and the manager s (misreporting) incentive compatibility constraint. If ρ is small, namely the signal is not very informative, the benefit of implementing a covenant to terminate the project under bad news is very low and the misreporting cost triggered by the presence of a covenant outweighs the expected benefit. In contrast, when ρ is high, the real option to terminate the project has high value, and the benefit of implementing a covenant outweighs the associated misreporting costs. 6 The Optimal Debt Contract Without the possibility of misreporting, an optimal contract induces efficient termination, no negative NP V projects are ever continued, hence τ = τ F B. However, when misreporting is possible, efficient termination policy can generate excessive misreporting costs. To balance this trade-off, the debt contract must optimize over two dimensions, control rights, z and interest rate, K. By controlling these aspects of the contract, the firm effectively determines the termination threshold, τ. It is convenient to formulate the contract as a single variable optimization program that depends only on the termination threshold τ. For this purpose we define the expected misreporting costs induced by threshold τ as χ (τ) C (ζ (K (τ), τ), τ), where ζ is the covenant value z = ζ (K, τ) such that ζ solves the misreporting incentive compatibility constraint: E [ (x K) + s = τ ] = c (ζ τ). χ (τ) thus represents the expected misreporting cost when the contract induces termination threshold τ and the face value is such that the lender breaks even. 20

21 An optimal contract can be represented as follows: Π = max {V (τ) χ(τ), E (x)} I. (9) τ [0,ˆτ] The existence of a maximum is immediate, given the bounded support and continuity of Π ( ). Uniqueness is not obvious because in principle one could think of multiple thresholds as being optimal, some of which implement relatively inefficient investments but, in return, induce lower expected misreporting costs. In the next section, we shall derive the optimal debt contract and show that it implements excessive continuation for some parameter values and excessive termination for others. The following proposition summarizes some of these results. Proposition 9. There exists a unique optimal debt contract characterized as follows. (i) If c is large, the equilibrium always entails over-continuation. Furthermore, the likelihood of covenant violation increases in c, and the face value decreases in c. (ii) If c is small, the optimal contract can have one of the following patterns: it may include no covenant, i.e., z = τ = 0 (for small ρ); or may entail overtermination (for intermediate ρ) ; or may entail over-continuation (for high ρ). When the contract entails over termination, the likelihood of covenant violation decreases in c, and the face value increases in c. Figure 3 illustrates the proposition. Note that the manager would like to increase his cost of manipulation. In fact, in this model, the entrepreneur wants (ex ante) to be unable to manipulate the signal. So we can think of this problem as a commitment problem, i.e. the manager cannot commit to being always truthful. In the following section, we formally derive the statements in Proposition 9 and develop the intuition for these results. 7 Properties of the Optimal Debt Contract We now turn to the efficiency of the contract s termination policy. This aspect is tied to the (endogenous) expected misreporting as is apparent from the first order condition V (τ ) = χ (τ ). (10) This equation underscores the main trade-off facing the optimal contract: investment efficiency versus misreporting costs. The left hand side, captures the marginal 21

22 Figure 3: The effect of misreporting costs c. Parameters: ρ =.8, L =.36, I =.4. The upper panels depict the effect of reliability on the contract s termination threshold (τ ) and face value (K ). The bottom panels depict the effect of c on the covenant (zˆ*) and manager s payoff (Π ). effect of the termination cutoff on the firm s expected cash flows. V ( ) is a hillshaped function of τ, that attains a maximum at τ F B > 0. The right hand side captures the marginal effect of the termination threshold on the expected misreporting costs. Evaluated at the first best we have V ( τ F B) = 0. Hence, if V (τ ) = χ (τ ) > 0, the equilibrium entails excessive continuation and excessive termination otherwise. We next study whether χ (τ ) is positive in equilibrium. 7.1 Overinvestment or Underinvestment? We first note that if a debt contract optimally implements some termination (i.e., τ > 0) it must necessarily induce misreporting. However, the presence of misreport- 22

23 0.95 τ = τ F B Π(τ ) = E(x) Precision ρ over-termination over-continuation no covenant Reliability c Figure 4: Accounting properties and investment efficiency. The blue line is defined as the set of c, ρ such that τ = τ F B. The red line is defined as the set of c, ρ such that max τ {V (τ) χ (τ) E (x)} = 0. Parameters: I =.45, L =.4. Notice that the over termination area is very small. This is due to our parametric assumption that x is uniformly distributed over [0, 1]. ing on the equilibrium path does not imply termination decisions will be distorted. 12 Generically, though, (namely for almost all parameter values) the possibility of misreporting distorts termination choices away from first best. It is however not clear whether the possibility of misreporting will induce excessive continuation or excessive termination. To address this question we first prove two useful lemmas. Lemma 10. (i) For sufficiently high values of c, the optimal contract includes a covenant 0 < z 1 and τ > 0. (ii) By contrast, for lower values of c, either there is no covenant (τ = 0 and z = 0) or the covenant is z > 1 and τ > 0. The above result indicates that for c sufficiently large, both termination and misreporting take place in equilibrium. Similarly for c sufficiently small both ter- 12 As we show, continuation decisions can be efficient in equilibrium (τ = τ F B ) even in the presence of equilibrium misreporting. 23

24 mination and misreporting happen in equilibrium, unless the signal is sufficiently imprecise (ρ is sufficiently low) that the misreporting cost outweighs the benefit from termination, and hence it becomes optimal to remove any covenant by setting τ = z = 0. For a given contract, it s clear that introducing the possibility to misreport would increase continuation. However, the contract s covenant depends on how costly it is for the manager to manipulate performance. When the endogeneity of contracts is taken into account, the ability to manipulate performance could lead in equilibrium to tighter covenants - making termination even more likely than under first best. To understand whether the equilibrium entails excessive continuation or excessive termination, we need to study the behavior of the expected misreporting costs. Specifically, we next ask whether more termination (i.e., a higher τ) increases expected misreporting costs C (τ) or not. The answer depends on whether z < 1, hence it depends on the level of the cost coefficient c. Indeed, when z < 1 the expected misreporting cost depends only indirectly on τ. Inspection of equation (6) shows that χ (τ) (1 K (τ)) 4. Furthermore, we have established that in equilibrium the face value and the threshold must be substitutes, i.e., K (τ) < 0. This means, that an increase in the continuation threshold will enable to decrease the face value without violating the lender s participation constraint. As a result, the manager retains a larger part of the realized cash flow, which increases the manager s incentive to manipulation the report in order to continue the project. As such, the expected misreporting cost increase in τ for all z 1. When c is sufficiently high z 1. Starting from the covenant that implements the first best continuation, an increase in the termination threshold will increase the expected manipulation cost and will also decrease the efficiency of termination (moving away from first best). As such, for sufficiently high c the the termination threshold is lower than the first best threshold, so the equilibrium entails excessive continuation. The following Lemma formalizes this result. Lemma 11. When c is large the equilibrium entails excessive continuation. Formally τ < τ F B. The converse is not true: a low reliability c does not necessarily lead to excessive termination relative to first best and may even lead to efficient termination. 24