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Essays in debt covenants

Amadou Nicolas Racine Sy

Faculty of Management McGill University, Montreal

~ ~ r i l , ' 1998

A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfilment of the requirements of the degree of Ph.D..

O Amadou Nicolas Racine Sy, 1998.

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Abstract

Essays on Dcbt Covenants

Amadou Nicolas Racine Sy McGill University, 1 998.

The common justification, in financial theory, for the existence of debt covenants is their use as contractual devices that reduce agency problems between borrowers and lenders. The thesis first examines the extent to which debt covenants alleviate these agency problems, and how they affect a borrower's debt fmancing decisions. Then, building on recent theories on the costs of bank financing, the dissertation suggests a new economic rationale for debt covenants as instruments that can reduce these costs. The thesis consists of three essays:

The first essay shows that, debt covenants create underinvestment incentives while reducing the overinvestment costs of debt. It also finds that the borrower's choice between different contracts with, and without covenants, depends on the magnitude of the agency problems, and the quality of the lender's monitoring technology.

The second essay shows how debt covenants reduce the costs of banks information monopoly. In fact, contingent contracting with debt covenants can be used by banks to precommit against using their informational advantage to hold up borrowers and extract rents, thus giving borrowers incentives to exert greater effort.

The third essay shows that the renegotiation that debt covenants permit, can reduce liquidity risk defined as the risk that a solvent but illiquid borrower is unable to obtain refinancing. It also shows that a debt contract with covenants is similar to a mix of debt contracts with different maturities. The thesis concludes with a review of the determinanrs of corporate debt maturity structure, and the literature on corporate reliance on bank financing and suggests hture research in this area.

Candidates have the option of including, as part of the thesis, the text of one or more papers submitted or to be submitted for publication. or the clearly- duplicated text of one or more published papers. These texts must be bound as an integral part of the thesis.

If this option is chosen, connecting texts that provide logical bridges between the different papers are mandatory. The thesis must be written in such a way that is more than a mere collection of manuscripts; in other words, results of a series of papers must be integrated.

The thesis must still conform to all other requirements of the "Guidelines for Thesis Preparation". The thesis must include: A Table of Contents, an abstract in English and French, an introduction which clearly states the rationale and objectives of the study, a review of the literature, a final conclusion an summary, and a thorough bibiliography or reference list.

Additional material must be provided where appropriate (e-g. in appendices) and in sufficient detail to allow a dear and precise judgement to be made of the importance and originality of the research reported in the thesis.

In the case of mauscripts co-authored by the candidate and others, the candidate is required to make an explicit statement in the thesis as to who contributed to such work and to what extent. Supervisors must attest to the accuracy of such statements at the doctoral oral defense. Since the task of the examiners is made more difficult in these cases, it is in the candidate's interest to make perfectly clear the responsibilities of all the authors of the co-authored papers.

Acknowledgements

I am most grateful to God for having given me the opportunity and the motivation to write this thesis.

1 am grateful to my supervisor, Dr. Jer6me Detemple for his guidance. His rigor and his dedication to research will always be an inspiration for me.

I would like to thank my other committee members, Dr. Kris Jacobs, and Dr. Jean-Guy Simonato, as well as an anonymous external examiner for their relevant and valuable comments.

I am deeply indebted to Dr. Jean Fa& whose moral support and insightful comments have been very valuable, and have led to a real friendship.

I would like to thank my fellow doctoral students at Mc Gill University: Raza Ahmed, Anthony Aboagye, Faisal Bari, Sudheer Gupta, Basma Majerbi, Monia Mazigh, Carlton Osakwe, Atiqur Rahman, Nidhi Srinivas, Mirjana Vajic and Yuxing Yan for their encouraging me, and for contributing to my intellectual curiosity.

I would also like to thank Dr. Sanjay Bane j i , Dr. Alex Citanna, Dr. Robert Hauswald, Dr. Lawrence Kryzanowski, Dr. Sumon Mafll~lldar, Dr. Arthur Moreau, Dr. Shankar Nagarajan, Dr. Kazuhiko Ohashi, Dr. Michel Poitevin, Dr. Calvin. W. Sealey, Dr. Clifford W. Smith, Dr. Minh Chau To, and the participants of the Doctoral Seminars in Economics at the Universite de Montdal, especially Kdis Dachraoui, for their usehl comments.

I would like to thank Dr. J. C. Duan, Dr. Richard Loulou, Dr. Alan Lee, Dr. Jorgensen, Dr. Mao Wei Hung, and Dr. M. Yalowski for their support.

Last but not least, this work would not have been possible without the support of my mother, my father, my family and my friends

Sommaire

Clauses Contractuelles et Contrats Financiers.

La theorie financiere justifie habituellement I'existence de clauses dans les contrats de dette par le r6le qu'elles pourraient jouer dans l'allkgement des coQts d'agence qui existent entre creanciers et debiteurs. Dans un premier temps, cette thbe mesure l'effet de ces clauses contractuelles sur les coirts d'agence et sur le choix de financement des ernprunteurs. Puis, s'appuyant sur les theories recentes sur les cofits du financement bancaire, ce travail suggere une nouvelle justification Cconomique de la presence de clauses dans les contrats de dette. La presente these est divide en trois partie.

Dans la premitre partie, nous montrons que l'existence de clauses contractuelles reduit effectivement les coilts de sur-investissemeat mais au prix d'une incitation au sous- investissement. Nous montrons Cgalement que le choix d'un emprunteur entre diflerents contrats de dette avec ou sans clauses depend de I'irnportance des problemes d'agence et de la qualite de la supervision menee par le cdancier.

Dans la seconde partie de la these, nous montrons comment les clauses contractuelles aident a reduire les coiits lies au monopdle informatiomel des banques. En effet, ces instruments peuvent constituer pour les banques un moyen de s'engager a ne pas utiliser leu avantage informatiomel pour s'approprier une partie indue des rentes. En outre, ces clauses peuvent donner aux ernprunteurs une incitation a foumir un effon accru.

Dans la troisieme partie? nous montrons que les clauses contractuelles, griice a la renegotiation qu'elles permettent, entrainent une reduction du risque de liquiditd. Ce risque est d d f ' c o m e I'incertitude qu'un ernprunteur solvable mais a court de liquidite soit dam l'incapacite de trouver du refinancement. Nous montrons Cgalement qu'un contrat de dene incluant des clauses contractuelles est similaire a un portefeuille de contrats de dette de rnaturitks diffirentes. Nous concluons cette these par une revue de la litterature sur les determinants de la maturid des contrats de dette et sur la place priviligiee de I'endettement bancaire dam les sources de financement des corporations et suggerons un agenda de recherche pour le futur*

Contents

1 Introduction

2 Debt Covenants. Maturity Structure and Agency Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 The Model . . . . . . . . . . . . 2.2.1 Timing and Information Structure

. . . . . . . . . . . . . . . . . . . . . . 2.2.2 Debt Covenants . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Renegotiation

. . . . . . . . . . . . . . . . . . . . . 2.3 Optimal Debt Contracts . . . . . . . . . . . . . . . . . 2.3.1 The First-Best Contract

2.3.2 Long-Term Debt Contract with No Renegotiation . . . . . . . . 2.3.3 Long-term Debt Contract with Renegotiation

. . . . . . . . . . . . . . . . 2.3.4 Short-Term Debt Contract . . . . . . . . . . . . . . . . . . . . . . . 2.4 Empirical Predictions

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Conclusion

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Appendix . . . . . . . . . . 2.6.1 Long-Term Debt With Renegotiation

. . . . . . . . . . . 2.6.2 Effects of Relaxing Assumption (9)

3 Bank Information Monopolies and Debt Covenants . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 The Project

. . . . . . . . . . . . . . . . . . . . . . 3.2.2 The Financiers . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Information

. . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Covenants . . . . . . . . . . . . . . . . . . . . . . . 3.3 The Basic Trade-off

. . . . . . . . . . . . . . . . . . . . 3.3.1 First-Best Solution . . . . . . . . . . . . . . . . . . 3.3.2 Ann's-Length Contract

. . . . . . . . . . . . 3.3.3 Bank Contract with no Covenants . . . . . . . . . . . . . 3.3.4 Bank Contract with Covenants

3.4 Bank Debt with and without Covenants: A Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Conchsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Appendix

4 Liquidity Risk and Debt Covenants 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2 The hlodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Debt contracts . . . . . . . . . . . . . . . . . . . - . . . . . .

4.3.1 Information Arrival . . . . . . . . . . . . . . . . . . . 4.3.2 Debt Contracts . . . . . . . . . . . . . . . . . . . . . .

4.4 Liquidity Risk and Debt Covenants . . . . . . . . . . . . . . . 4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Summary of Notation . . . . . . . . . . . . . . . . . . . . . . . 4.7 Proofs . . . . . . . . . I . . . . . . . . . . . . . . . . . . . . .

5 Conclusions and Future Research 5.1 Models of Choice between Public and Private Debt . . . . . .

5.1.1 Costs and Benefits of Bank Lending . . . . . . . . . . . 5.1.2 Determinants of the Maturity of Corporate Debt Issues

5.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 Introduction

Debt covenants are provisions, which restrict a borrower from engaging in spwified actions, after the contract has been signed. The constraints imposed through covenants Limit a firm's investment, payout, and financing policies, and their violations accelerates the maturity of the contract. Bank loans, venrure partnership agreements, publicly, and privately placed bonds are ex- amples of financial contracts that include various covenants with differect degrees of stringency. A common justification for the existence of covenants in h a n & l economics is their use as contractual devices that reduce agency problems between borrowers and lenders. The goal of the dissertation is to &= evarnine the extent to which debt covenants reduce agency problems, and how they affect borrowers' debt financing decisions. Then, building on recent theories on financial intermediation, it will attempt to find a new rationale for debt covenants. In that context, the role of covenants, as con- tractual instruments that can reduce the costs of bank financing, such as bank information monopolies, and liquidity risk, will be investigated.

The dissertation is divided in three parts. In the first section, the use of covenants to reduce the agency problems of debt is analyzed. Covenants while redrlcing the overinvestment costs create underinves tment incentives. At the optimum, the marginal reduction in overinvestment costs is equal to rhe marginal increase in underinvestment costs. The choice of borrowers from a menu of debt contracts with different covenant and maturity structure is then considered. It is fonnd that when the monitoring technology of the lenders is high enough and agency problems are negligible, borrowers prefer Bank Debt to Privately Placed Debt while Public Debt is the least preferred option. Ruthermore, firms with lots of growth options in their investment opportunity set will prefer private debt to public debt.

While the benefits of bank debt are well understood, less attention has been paid to its costs. The second sec.tion offers a new rationale for debt covenants and discusses how these contractual arrangements can reduce the agency costs of delegated monitoring. It shows how contingent contracting with debt covenants can be used by banks to precommit against using their informational advantage to hold up firm and extract rents. It is argued that, by giving the borrower incentives to exert greater effort, introducing

covenants in bmk debt can be socially optimal. Recent theories on the cost of bank financing also analyze the tmde-off

between a borrower's preference for short-term debt due to private informa- tion about her future credit rating, and liquidity risk. The focus of the last section is on the role that debt covenants can play in mitigating such c0st.s of bank financing. The main result shows how these contractual arrangements can reduce liquidity risk, and are positively valued by firms with invest- ment grade credit ratings. Furthermore, it is shown that debt contracts with covenants are similar to a mix of risky short- and long-term debt contracts. This result is consistent with the current literature in banking which suggests the use of a mix of debt with different maturities to reduce the costs of bank financing. The dissertation concludes with a review of the literature on the corporate reliance on bank financing, and the determinants of corporate debt maturity structure, and suggests future research in this area.

2 Debt Covenants, Maturity Structure and Agency Problems

2.1 Introduction

Debt covenants are provisions which restrict a borrower from engaging in specified actions, after the contract has been signed. The constraints im- posed through covenants limit a firm's investment, payout and financing policies1. Bank loans, publicly and privately placed bonds as well as ven- ture partnership agreements are examples of contracts t hat include various covenants, with different degrees of stringency.

A common justification for the existence of covenants in debt contracts is their use as contractual devices that reduce the agency problems between borrowers and lenders. In his seminal article, Myers (1977) separates the value of a firm's assets in place from the present value of its growth opportu- nities. This distinction allows him to show that the presence of debt in the capital of the firm creates an underinvestment problem. To reduce this debt overhang problem, Myers (1977) suggests, among other solutions, the use of monitoring coupled with protective covenants.

Similarly, Jensen and Meckling (1976) analyze the conflicts that can arise between debtholders and equityholders. They point out that a debt contract may give equityholders an incentive to invest in negative-net-present-value project. To alleviate this overinvestment or asset substitution problem, they also suggest the use of bond contracts coupled with various covenants.

An exhaustive typology and analysis of bond covenants is offered in Smith and Warner (1979) who suggest four major sources of conflicts that debt covenants can control: dividend payment, claim dilution, asset substitution

'Debt covenants can be found in bank loan agreements, in bond indentures for publicly traded bonds and in securities purchase agreements for privately placed debt. They are conventionally divided into (I) affirmative covenants, which require firms to maintain specified levels of accounting- based ratios, and (2) negative covenants, which limit certain investment and financing activities unless specified accounting-based conditions are met . For instance, negative cmenents restrict the payments of dividends, the disposition of assets, the issuance of additional debt, and merger activity; ahnative covenants specify minimum working capital and net worth requirements.

and imderinvestment. More recently, Hart and Moore(1995), Park ( l9W), Gertner and Scharfstein (1991), Berkowitch and Kim (1990) and Chang (1990) analyze the importance of dividend covenants and seniority rdes in financial contracts.

Another strand of the literature on bond covenants is related to the the- ory of delegated monitoring. Berlin and Loeys (1988) compare contracts with covenants to loan contracts enforced by a monitoring specialist whereas Rajan and Winton (1995) motivate the use of covenants as contractual d+ vices that increase a lender's incentive to monitor. The literature on debt covenants has, so far, focused on two types of agency problems that debt covenants may alleviate, namely dividend payment and claim dilution.

In this paper, I address the role of debt covenants when overinvestment problems are present. Then, taking into account the existence of such re- strictions, I analyze the choice of a manager from a menu of debt contracts with different maturities.

Firms have existing assets and growth opportunities in the form of new projects that arise in the future. In the simple model used in this paper, firms have two types of projects: Type G projects are positive-NPV new projects that are marginally more productive than the old assets while Type B projects are negative-NPV new projects that are marginally less produc- tive than assets in place. For ease of notation, firms with type G (type B) projects will be denotxt Type G (Type B) h s . Type G firm can be considered as Growth Firms whose value consists primarily of investment opportunities whereas Type B firms can be thought of as mature companies with few profitable investment opportunities and whose value come primarily from assets in place. As in Diamond (1991), I assume that managers earn non- transferrable control rents whenever they accept a new project. Conse- quently, they face liquidity risk defined as the risk of losing nonassignable rents due to excessive liquidation incentives of lenders2. For instance, a lender may liquidate a project when the borrower would not choose to if she were the sole owner of the firm. Because of the control rents, the manager of a Type B firm may undertake negative-NPV projects, thus creating an overinvestment problem.

21n so doing, I am ignoring the possibility of executive compensation policies. The effects of managerid compensation will be to reduce the size of the control rents, thus affecting the manager's source of financing choice. Smith and Watts (1992) document that firms with more growth options in their investment opportunity set have higher executive compensation and make a greater use of stock-options plans.

To redl ice i he o\-erini-es tment problem, the lender includes a covennn t. in the loan contract reqtliring the manager to invest a minim~im verifiable amount of the fun& borrowed in the existing assets3. I find that such covenants reduce the overinvestment incentives but create an mderinvest- ment. problem by prrvenoing the manager of a Type G firm from investing as much as she can in positiveXPV projects'. The optimal covenant is such that the maro$.nal reduction in overinvestment costs is equal to the marginal increase in underinvexment costs.

In this setring, I a n a l j ~ e the choice of the manager from three sources of debt financing that M e r in their covenants as well as their maturity struc- ture. First, long-term debt contracts are considered and a contract which d o n s for renegotiation when the covenants are violated is compared to a contract with no renegotiation. These contracts share several characteristics with Privately P!aced and Publicly Placed bonds, respectively. Second, a short-term debt contract, which can be seen as a contract with forced rene- gotiation at the debt maturity, is then analyzed. This contract can be seen as a bank debt contract.

Using a contracting structure similar to Berlin and Mester5 (lggl), I End that borrowers value the option to renegotiate covenants embedded in pri- vately placed debt. In the presence of agency problems, they will prefer a p r h t e placement of debt to a public issue if the monitoring technology of the financier is high enough. However, the flacibility offered by privately placed debt comes at the cost of imposing more stringent covenants. This result provides an explanation for the empirical facts documented by Carey et al. (1993) that private placement covenants often impose significant restrictions on borrowers whereas public issues have few restrictive covenants.

I also find that, when potential agency problems are important, (that is when the manager's control rents are high), long-term debt, whether public or prilate, is preferred to short-term debt. In fact, short-term bank debt forces

3 ~ n practice, this is similar to writing covenants requiring the maintenance of the firm's properties. For example. Srnith and Warner (1979) document the case of the shipping in- dustry, where bond covenants hequent1y explicitly include service and dry-docking sched- ules in the indenture. "In the m e vein, Berkonritch and Kim (1990) show that restrictive dividend covenants

alleviate underinvestment incentives while exacerbating the overinvestment incentive. =Their main purpocie is to analyze, by comparing debt contracts with and without rene-

gotiation, the impact of a firm's credimrthiness on the value of the option to renegotiate. They do not address agency problems and focus solely on long-term debt contracts.

the manager to renegotiate the terms of the loan at matmity whereas in the case of private and pliblic debt, maturity is accelerated only if the covenants are violated. This suggests that a manager would prefer longterm rnatmity only if agency problems are important enough. Such a reason would be negatively perceived by investors. This resulto is consistent with the empirical evidence provided by James (1987) who finds t.hat. a firmk announcement of a new bank loan leads to significantly positive abnormal stock returns while a firm that announces a bond issue or a private placement of debt for the purpose of retiring a bank loan experiences a significantly negative abnormal return.

Finally, I find that, when agency problems are negligible and the mon- itoring technology is high, managers of Growth Firms will prefer private debt to public debt. Alternatively, they m i l l shy away from ba& debt when agency problems are serious and will prefer pri\ately placed debt or public debt. Ths result is consistent with the empirical findings in Houston and James (1996) who find, for firms with a single bank relationship, a negative and statistically significant relation betwwn the reliance on bank debt and the importance of growth options where these options measure the potential agency problems. As they point out, this finding is not consistent with the hypothesis that firm with larger information aqmmetries or greater agency problems of debt rely more on bank financing6. This finding, however, is consistent with the argument that potential information monopolies limit a firm's reliance on a single bank borrowing as in Rajan (1992) and Diamond (1991).

The rest of the paper is organized as follows. Section 2 describes the model in more details and Section 3 solves for rhe optimal contracts. Em- pirical results are obtained in Section 4 and comparative statics results are derived. Finally Section 5 presents the conclusion.

61n contrast to theories on the agency costs of delegated monitoring, these theories focus on the agency costs of debt and argue that h s ni th a high potential for underin- vestment (Myers, (1977)) or asset substitution (Bamea. Haugen and Senbet (1980)) have an incentive to borrow short-term debt. Barclay and Smith (1995a) empirically test these theories but do not separate between firms borrowing from a single bank and those with multiple banking relationships.

2.2 The Model

-4 risk-neutral manager is hired by shareholders of a firm which has assets in place at t = 0 and growth oppor tmi t i~ . consisting in new indivisible projects, that will arise at t = 1. The manager has no funds and needs to contract a loan at t = 0 to invest in the old assets as well as in the new investment projects. I assume that there are no conflicts between the manager and the shareholders of the firm.

The market for loanable funds is competitive and the lender has a reqired face value of debt of d which gives her a resenation utility. For simplicity, the discount rate is assumed to be zero. If she borrows. the manager will not have access to new financing at t = 1 and niU invest an amount z in the old assets which will earn her a known positive return of R ( r ) and 1 - z in the new projects whifh have a Net-Present-Value of r (1 - r ) . Whenever she takes a new project, the manager will also earn non-transferrable control rents of size C. The return hnctions R (.) and r (.) are assumed to be increasing and concave in their arguments. That is R, (2) > 0, RzL (z) < 0 and -r, (.) > 0, and -r,= (.) < 0.

Firms have two types of projects and the set of feasible types is denoted T = { t g r t b ) . Firms with type G projects. denoted as Type G firms, are such that they have only positive-NPV projects and any revenue they can produce is greater than their liquidation value L9. Furthermore, their new projects have always a greater marginal return than t.heir old assets. Type G firms can be considered as Growth Firms whose value consists primarily of investment opportunities. More precisely:

Firms with type B projects, denoted Type B firms, are such that they have only negative-NPV projects and their assets are worth more if used in other activities. Their old assets are marginally more productive than their new projects. Type B firms can be thought of as mature companies with few profitable investment opportunities and whose value come primarily from assets in place. That is

rb (1 - 2 ) < 0, vz (4)

R ( z ) + rb (1 - z ) < L~ < _d, Vz ( 5 )

2.2.1 Timing and Information Structure

At t = 0, nature7 draws a type for the manager horn the set of feasible types T = { t g , t b } and assigns a probability p of being trpe G and a probability 1 - p of being type B. Both the lender and the manager share these prior beliefs.

At t = 1 the manager observes a private signal s E {s,, s b ) about the type of the project. Conditional upon this information, the manager updates her beliefs and assigns a probability pij p ( t i I sj)of the project being of type ti given the signal s j * Suppose that s is such that p,, = P& = 1, pgb = pbg = 0 so that the manager knows the type of the project with certainty. I will refer to a manager who observes s, as the manager of a Type G Firm and one that observes sb as the manager of a Type B Firm.

At t = 0, the lender bears some fixed monitoring costs8 k which permits her to observe the signal s with probability 8. That is the monitoring tech- nology is such that, with probability O, the lender and the manager become symmetrically informed at t = 1. I refer to this state as the informed state. With probability 1 - 6, the manager's information remains private and I re- fer to this state as the uninformed state. Assume that when the manager observes the signal s, she also knows whether it will remain private or not. After having observed the signal s, the manager makes her investment deci- sion and invests z in the assets in place and 1 - z in the new asset. At t = 2, all uncertainty is resolved and the payoffs are realized.

In this setting, underinvestment and overinvestment problems arise. Even t,hough the manager of a Type B firm can choose solely among projects with negative NPV, she will invest in new projects if her control rents are such that her expected payoffs are greater than the loan rate d , that is if

'IPlease, see Figure I. 8The monitoring decision is not endogenow in the model. Howwer, when the debt

contract includes covenants, monitoring is useful. In fact, since covenants are based on ex- post verifiabe information, the lender can if she monitors collect the information necessary to prove if there has been a violation or not. Rajan and Winton (1995) show how covenants can be motivated tu~ contractual devices that haeases a lender's incentive to monitor.

R (z) + T' (1 - r ) i C - I; > d . If the manager of a Type B firm is not. prevented from investing in the new projects then there is a loss of efficiency that I refer to as a11 overinvestment problem. In this case. the lender may want to restrict investments in the new project. On the other hand, the manager of a type G firm always invests in positive-net-present-vahe projects because r9 (1 - Z ) > 0, hence, if she is prevented to invest as much as she wants in the new project, there will be a loss of efficiency which 1 refer to as an underinvestment problem. The purpose of the paper is to analyze to what extent debt covenants can be used to mitigate these agency problems and to study the manager's choice between debt contracts that differ in their

covenant and maturity structures.

2.2.2 Debt Covenants

Debt covenants are provisions which restrict a bomower from engaging in specified actions after the contract has been signed. To be enforceable, debt covenants must be based on verifiable information and easily verifiable by courts of lawg.

In this paper, the focus is on debt covenants that contractually require the manager to invest a minimum of the borrowed funds in existing assets. A debt covenant is a minimum verifiable investment in assets in placelo at date 1, r, required by the lender. Following Rajan and Winton (1995), i t is assumed that if the lender monitors then she can also obtain information on

gThe constraints imposed through covenants are frequently specified in terms of ac- counting numbers.Violation of a debt covenant other than promised payments is conven- tionally called technical default. Current accounting standards mandate disclosure of debt covenant defaults. For example, SFAS No. 59 specifies that default is a basis for a going concern warning, and SFAS No. 78 requires disclosure of a breach when long-term debt is reclassified as a current liability. SEC rules also require that any violation that exists at the date of a balancesheet filing must be disciosed in the notes to the financial statements. For a review of the cunent research on covenants in the accounting literature, see Smith (1993).

' O ~ h i s is similar toa maintenance covenant in practice. Smith and IVarner (1979) docu- ments that maintenance services are frequently found in the shipping industry where bond covenants explicitly include service and dry-docking schedules in the indenture. Another restriction pointed out by these authors is a covenant requiring that the firm stay in the same line of business. For example, the Associated Dry Goods Credit Corporation Notes of 1983 require that the firm not engage in any business other than dealing in Deferred Payment Accounts. In this paper, such a covenant can be obtained by putting a constraint s u c h a s z = z = l * -

whether there is a breach or not with the additional cost of wqdr ing this information equal to zero. A b r e d of covenant occurs when:

and there is no breach when: z > z r (8)

At t = 1, the borrower is audited and in case of a breach of covenant, the lender can demand repayment and the control of the firm may be transferred to her. If there is no b r e d , the borrower retains control of the firm. To avoid liquidation if the covenvt has been violated, the borrower can seek renegotiation. The next section explains the simple model of renegotiation used in this paper.

2.2.3 Renegotiation

I assume that the manager can propose a new contract by making a take- it-or-leaveit offer" to the lender at t = 1, after she knows the type of the 6rm and after she has invested. The lender audits the firm and accepts or rejects the offer. If the lender accepts the offer, the borrower is permitted to continue the operations of the firm until date two. If the lender rejects the offer, the borrower is audited and there is liquidation if the covenant has been violated.

It is not efficient for the lender to liquidate a type G h because the cash flows it generates are greater than its liquidation value. The liquidation of a Type B firm, on the contrary is optimal because its assets are worth more when they are used for other activities.

In this context, the lender will always accept an offer from a type G firm and reject an offer horn a type B finn if she knows the type of the borrower,

l1 Smith (1993) summarizes empirical results on technical default. The evidence suggests that technical default generally is caused by deteriorating corporate performance, that it almost exdusively invoives h a tive covenants, that a substantial fraction of the defaults involve the breach of multiple constraints, that default is more likely in private than public debt issues. In practice, lenders choose from a wide array of measures to respond to technical default. Smith (1993) documents that these actions range from granting a permanent waiver without fiuther modification of the contract to accelerating the maturity of the debt and forcing the borrower to obtain financing elsewhere.

that. is, in the informed state When the lender is iminforrnccl, I 'assume that.. she will reject any offer and liquidate the firm1':

In this setting a debt contract is of the form (2, d) and specifies the face value to be repaid at date 2 as well as the restrictive covenant z , required by the lender. The next section addresses in more details how debt covenants may increase or reduce the overinvestment and underinvestment problems.

2.3 Optimal Debt Contracts

2.3.1 The First-Best Contract

If the lender could write contracts contingent on the borrower's type but could not liquidate selectively then, by equations (1)-(6), the first-best con- tract would make type G managers invest all the debt proceeds ( 2 9 = 0) in the new project while type B managers invest all in the old assets, (zb = 1). Since this type of contract is not feasible, the analysis is restricted to second- best contracts.

First, a long-term debt contract with no renegotiation, similar to a pub- licly placed bond, is analyzed. In the banking literature, it is almost always assumed that publicly sold bonds, even though they incorporate covenants, are seldom renegotiated because of the great number of bondholders that would make an agreement between bondholders almost impossi bleI3. Later, a long-term debt contract with renegotiation is analyzed and compared to a long-term debt contract with no renegotiation. This contract can be seen as a privately placed debt. In a private long-term debt contract, the manager chooses to renegotiate whereas a short-term debt contract forces the borrower to renegotiate when the lender demands repayment. This type of contract will be analyzed and compared to both types of long-term debt contracts.

12The effects of relaxing this assumption are analyzed in the appendix. It is shown that under plausible parametric restrictions, the r e d ting contracts will be infeasible.

'=The Trust Indenture Act of 1939 limits the discretion that may be allocated to the trustee in a public debt issue. It is thus costly to renegotiate covenants in public debt agreements outside the bankruptcy process.

2.3.2 Long-Term Debt Contract with No Renegotiation

Consider a long-term debt contract of the form (2') d') specifying a loan rate d' and a minimum investment in old assets z*. Assume that renegotiatiorl outside of bankruptcy is impossible and that a violation would be detected by the audit at date 1. In this case, the manager would lose the control rents if she does not comply. Hence the covenant constraint is binding. The lender does not monitor and the auditing costs are assumed to be zero. By assumptions (3) and (6)) the incentive compatible decisions of a manager who has observed signal s are

The manager of a Type G firm will not invest more than required in the assets in place because they are less productive then the new projects. The manager of a Type B firm has no incentive to invest more then what is required and complies to avoid liquidation. The manager will then maximize her expected payoff subject to her incentive compatible decision and the lender's participation constraint. That is,

st. pd' + (1 - p) [R (2') + rb (1 - z*) ] 2 d

The first order conditions of this maximization problem are such that :

p [ (z') - (1 - ) + 1 - ) [ R ( 2 - (1 - z ) ] = 0 (14)

Forcing the manager of a Type G fmn to invest in the assets in place rather than in the new projects creates a loss of efficiency. However, forcing the manager of a Type B h n to invest in the old assets instead of the new projects reduces the loss in efkiency. At the optimum, the expected marginal underinvestment costs are equal to the expected marginal overinvestment costs where expectations depend on the prior b&& of the lender, p. Denote the first order conditions V'(z) so that equation (14) can be rewritten as V' (z') = 0.

Some long-term debt. contxacts do allow for renegotiation. this is t . 1 ~ case, for excmple, of privately placed long term debt cont.ractsl". The next section takes a closer look at, a long-term debt contract, when renegotiation is possible.

2.3.3 Long-term Debt Contract with Renegotiation

Consider a long-term debt contract (d",zn) consisting of the covenant, zn, and the face value of the debt, d", that has to be repaid at date 2. At t = 1, the manager can make an offer (d;, r;) after she has observed her type sj and after she has invested in the new project. Two situations can occur: either the lender is informed with probability 8, in which case she will reject an offer from a type B manager and accept an offer horn a type G manager, or the lender is uninformed and, given assumption (9), she rejects any offer1=.

Informed Lender When the manager knows that the lender will be in- formed, her incentive compatible investment decisions are as follows:

Type G firms The manager of a type G fum, if she complies, will not invest more than what the lender requires in the assets in place since r? < 0, R, > 0 and R, < I T ! ) . The solution of her optimization program is a corner solution and is such that 29 = z". At t = 2, the borrower gets a payoff of R (z9) + r9 (1 - zg) + C - k - d" and the lender receives the face value d". Intuitively, if the manager of a type G firm decides to comply, she is not going to invest more in the old assets than what is required by the lender. The reason is that she always prefers to invest in the new projects because

14See M. Carey et Al. (1993) for a comprehensive study of the private placement market. They report that private placements tend to be long term and fixed rate, Most public issues have few restrictive covenants whereas private placement covenants often impose significant restrictions on borrowers. The carenants of public issues are rarely renegotiated whereas at least half of all private placements are renegotiated at least once.

l S ~ v e n though the lender chooses to liquidate when she is uniformed, actual liquidation does not happen in equilibrium. Section 1.1.2 derives the unique equilibrium outcomes that exist when the lender is uninformed. When assumption (9) is relaxed, it can be shown that there is a pooling equilibrium where both lenders choose to renegotiate the contract. However, under plausible parametric restrictions, the renegotiable contract is unfeasible. These restrictions are such that d +k > pL9 + (1 - p) Lb. That is, the lender will not - invest funds and bear the costs of monitoring just to have the option to liquidate the firm- See section 1.2. of the Appendix.

they are more productive than assets in place and give her non-trmsferrable control rents.

If she does not comply, the manager makes an offer ( r i , 4) where zk < zn. Since the manager makes a takeit-or-leave-it offer, she offers the lowest rate that the lender is willing to accept. That is, the manager offers a new contract with no investment in old assets and a new face value of the debt equal to its liquidation value, L? This new contract, (0, Lg), will be accepted16 by the lender since the maximum she can gain if she rejects it is L? At t = 2, the borrow receives a payoff of R (0) + rg (1) + C - k - L, and the lender gets

4

Type B firms If the type B manager complies, she will choose a level of investment in the old assets equal to rn for the same reasons as the manager of a type G firm. In that case, the lender cannot force liquidation because the covenant has not been violated. Even though at date 2 the lender will own all the revenues produced by the firm, the manager will still receive control rents of a value of C. If the manager of a type B firm does not comply and the lender is informed, she will force liquidation and earn Lb. Hence, the manager will never breach the covenant when the lender is informed because she will lose the control rents, C. The manager's investment decision is zb = zn . At t = 2 the borrower receives the control rents, C and the lender gets R (2") + (1 - zn) .

When the lender is informed, a separating equilibrium, where the man- ager of a type G firm breaches the covenant and make an offer while the manager of a type B firm complies, exists. On the other hand, when the lender is uninformed, only pooling equilibria are feasible.

Uninformed Lender When the lender does not know the type of the firm, she will reject any offer and force liquidation, by assumption (9). In this case, the managers of both firms will comply and zb = zg = zn. A pooling q ~ i l i b r i u m ' ~ where the managers of both firms choose the same action obtains.

1 6 ~ h e lender could decide not to liquidate and let the firm continue its operations. In this case, the lender would earn d" > L9. However, since in this paper, the renegotiation process is a simple take-it-or-leavle-it offer from the borrower, this situation is not considered.

17See section 1.1. of the Appendix for a detailed proof.

Optimal Long-Term Debt Contract With Renegotiation Given the sitliations studied above, the optimal contmct solves the following program where the expected profit to the manager is being maximized:

st.

Given assumptions (5) and (8), the h s t order conditions are:

(1 - 8) [R, (zn) - r: (1 - rn)] + ( 1 - p ) [R, (2") - rp (1 - I")] = 0 (17)

At the optimum, the expected marginal underinvestment costs are equal to the expected reduction in marginal overinvestment costs. Expectations depend on the prior beliefs, p, as well as the probability of the lender being informed i.e. the monitoring technology, 0. In this model, it is always more efficient to let the manager of type G invest in the new project rather than in the old assets. The fist term on the RHS of equation (18) is negative because the marginal revenues from the old assets are smaller than the net present value of the project for a type G firm. The second term on the RHS of this equation is positive because for type B firms, the old assets yield always marginally more than the new project. The optimal contract is such that the marginal revenues are equal to the marginal costs. If we denote the first order conditions Vn (I), it can be shown that:

Proposition 1 The long-term debt contract with renegotiation has more stringent covenants than the contmct with no renegotiation ie.

Proof: V' and Vn are both downward sloping fiinction that intersect the horizontal axis at z' and zn, respectively. Furthermore Vn ( 2 ) > V* (2) since Vn (2) - V' (2) = -0p [Rz ( z ) - T: (1 - z ) ] > 0, VZ. It follows that Z" > Z'

should hold. More stringent covenants will reduce the overinvestment problem by putting

more restrictions on the Type B manager, reducing her investment in non

profitable projects. However, by giving the Type G manager the optiotl to renegotiate, the lender can decrease the underinvestment problem since the Type G manager can invest more in the new project when her offer is accepted in the informed state.

A long-term debt contract with renegotiation gives the borrower the op- tion to renegotiate the terns of the contract by choosing to violate the initial covenant. A short-term debt contract, on the other hand, by allowing the lender to demand repayment based on any information, contractible or not, may force the manager to renegotiate. The next section derives the optimal short-term debt contract.

2.3.4 Short-Term Debt Contract

Consider a short-term debt contract with a specified loan rate dS to be repaid at t = 1. Because the firm has no cash flows at t = 1 (payoffs are realized only at t = 2), the lender can demand repayment or roll over the debt? If the lender demands repayment, assume that the manager makes a take-it-or- leave-it offer, d". That is, she offers to pay d" at t = 2. in this case, based on her beliefs, the lender accepts the offer or rejects the offer and liquidate. As before, the investment decision is made before the renegotiation starts and the monitoring technology is such that the lender knows the borrower's type with probability 0 at t = 1.

When the lender knows the type of the firm, she demands repayment to the Type B manager and rejects any offer thereby forcing liquidation since by assumption, the liquidation value of a Type B Firm is greater than any revenues it can produce. In this case the lender gets a payoff of L' and the manager loses her control rents and receives no payoff. The lender rolls over the debt of a Type G Firm because if she demands repayment to a Type G manager, she would receive an offer worth L9, which is the Type G manager's best response. However, if she rolls over the debt, the lender can receive R (zi) + r g (1 - z:) which is more than Ls by assumption. If the lender rolls over the debt, the incentive compatible decision of the manager of a Type G firm is to invest ti = 0 in the assets in place and every-thing in the new projects. The lender will receive a payoff equal to dS at t = 2 and

181n practice, short-term debt contracts have the most stringent covenants and the lender has the option to accelerate debt maturity and force contract renegotiation. Since the short-term debt contract matures at t = 1 in the model, I m e that there is always renegotiation at maturity whether covenants are violated or not.

the manager will receive R (0) + TP (1) + C - d3 . When she is uninformed, the lender, given assumptions (2) , (5) and (9)

rejects any offer and liquidates the firmIg. In that. case, the lender's espectd payoff is pLg + (1 - p) Lb and both managers expect no payoff.

At t = 0, the lender will require a loan rate for the short term debt, contract, such that,,

In the next section, the manager's expected profits from each type of debt contract are ebtained and compared.

2.4 Empirical Predict ions

First the long-term debt contract with renegotiation is compared to the long- term debt contract with no renegotiation. The ex-ante value of the option to renegotiate, nl, can be obtained as the difference between the expected profits associated with each contract.

Denote ?rn the borrower's expected profit of a long-term debt contract with renegotiation and n' the borrower's expected profit associated with a long-term debt contract with no renegotiation. The following obtains:

n* =- p [R (I*) + rg (1 - r*)] + (1 - p) [R (r') + $ (1 - r e ) ] + C - (21)

The ex ante value of the option to renegotiate, q = rn - R' is:

I9If assumption (9) is relaxed then the lender chooses to always roll over the debt of the firm, in the uninformed state, In that case, it can be shown that such a contract is infeasible if (k+ d ) > L (p) + (1 - p) 8 [ L ~ - (R (0) + rb (I))] . That is, the lender will not - invest funds and bear the cmt of monitoring only to have the option to liquidate the finn even if, by doing so, she is ignoring the potential benefit of liquidating a bad firrn in the informed state. Note that if 8 = 0, that is when the lender is totally uninformed, this restriction becomes (k+ d) > L ( p ) . -

Since the long- term debt contract with renegotiation has more restrictive covenants than the long-term debt contract with no renegotiation, zn > z*, the second term on the RHS of the equation is positive and represents the gain in efficiency of reducing the Type B h ' s investment in the new projects. The sign of the first term on the RHS is ambiguous. It represents the net expected gains of a Type G firm where expectations depend on the probability of the lender being informed. The Q p e G borrower faces a trade- off between being able to invest as much as possible in the new projects when the lender is informed while facing too restrictive covenants when the lender is uniformed. However,

Proposition 2 The ex-ante value of the option to renegotiate, nl is positive if:

8 ( R (2") + ~g (1 - 2")) - (R (z') + r g (1 - 2')) > - 1 - 8 ( R (0) + ~9 (1)) - ( R (2') + ~9 (1 - z * ) ) (23)

Moreover, a suficient condition for the ez-ante valve of the option to renegotiate to be positive is that the monitoring technology is such that: 20

Furthermore, the better the monitoring technology, the greater is the value of the option to renegotiate :

20To prove this proposition, rewrite the first term on the RHS of equation (22) as

and me assumptions (1) and (3).

Indeed, the underinvestment problem is smaller the higher the probability of the lender being informed. When the monitoring technology improves, the lender accepts more often the offer from a type G manager to invest. the maximum possible in the new project. This potential gain in efficiency makes the option to renegotiate more attractive. However, it can be easily seen that the value of the option to renegotiate has a lower value when the monitoring costs increase.

It is important to notice that the control rents do not have any impact on the option to renegotiate because under both contracts, the borrower can always avoid losing them by complying.

Ex-ante, the effect of the type of the borrower on the option to renegotiate can be obtained by differentiating equation (22) and using the Envelope Theorem:

As the probability of being a Type G type increase, the option to rent+ gotiate will be more valuable only if the net expected gains of the Type G borrower, where expectations depend on the monitoring technology, are greater than the benefits of imposing a more stringent covenant to the type B borrower. It can be shown that, d r l / d p > 0 if

[R (zn) + rb (1 - zn) - rb (1 - z*)] - [R (zn) + r g (1 - zn) - r g (1 - z* ) ] 0 >

[ (R (0) + rg (1)) - ( R (zn) + rg (1 - zn))] (27)

That is, Growth Firms will prefer Privately Placed Debt to Public Debt, if the monitoring technology is high enough.

The following section compares the long-term debt contract with covenants with a short-term debt contract. In the tirst contract, the manager has an option to renegotiate whereas in a short-term debt contract, the lender can force her to exercise the option at the maturity of the debt contract. The borrower's expected benefit horn the short-term debt contract2', T"

that:

21Since the lender Bcpeets zero profit, it is assumed that the lender makes

is such

upfiont

Proposition 3 The dzfference between the ezpected benefits of a short-term debt contract and a long-term debt contract with renegotiation, 1 ~ 2 = ns - nn zs such that:

The first term represents the expected costs of an inefficient liquidatior. of a type G firm while the second term represents the expected benefits of liquidating a type B h. The last term represents the expected loss of control rents.

It can be shown that when the control rents are ignored, the short-term debt contract is preferred to the long-term debt contract22, (?r2 > 0) . Because of assumption (9), the short-term debt contract induces a smaller loss of efficiency and since the lender expects zero profit, x.2, the net expected surplus of the borrower is positive. However, if control rents are considered, the long- term contract can be preferred to the short-term debt contract, (r2 < 0) , because by complying, the manager can avoid losing them. h thermore , the greater the potential agency problems, that is the higher the control rents, the less attractive the short-term debt contract is (s < 0).

payments to the borrower. Rajan (1992) analyzes Banks' ability to control and their ability to idhence the division of surplus. He shows how borrowing from multiple sources and appropriately setting priority are ways of circumscribing the Banks' ability to extract surplus without diminishing their control.

22Rewrite

that is q = [ L ( p ) - # ( p ) ] +pB[R(tn) ++(I -2") -Lo] > 0; by (9) the k t term is positive and by (2) the second term is poeitive.

I t can be shown that:

The expected benefits of a short-term debt contract relative to a lone- = term debt contract with covenants are increasing in the efticiency of the monitoring technology. That is, the gains captured by the Type G borrower when there is an improvement in the monitoring technology are higher for a short-term debt contract than for a long-term debt contract with renegotiation. The intuition is that, when she borrows short-term, the Type G borrower can move horn a situation where there is no investment because of liquidation to a situation where she can invest all the funds in the new projects. If she borrows long-term, she will go from a situation where she faces stringent covenants to a situation where she can invest all the funds borrowed.

The effect of the firm's type is such that:

(30) When the control rents are ignored, 2 < 0 by assumptions (2) and

(5). As the probability of being of a Type G type increases, the short-term debt contract becomes less attractive because of the loss of revenues from excessive liquidation. High control rents can however reverse the inequality.

Finally, the long-term debt contract with no renegotiation is compared to the short-term debt contract.

Proposition 4 The dzflerence between the ezpected benefits to the manager of borrowing short-term rather than signing a long-ten- debt contract with no renegotiation is 7r3 = 7rd - r* such that:

The first term represents the expected gain of the type G manager, where expectations depend on the monitoring technology. The second term shows

the expected gain in efficiency due to the liquidation of the t,ype B manager. Finally the last terms represent the loss of control rents.

I t can be shown, as before, that a > 0 when there is no agency problems or equivalently when C = 0 and that, when the monitoring costs are high enough, the expected profit of the long-term debt contract can be higher than the short-term debt's expected profit. Also, the ains of better monitoring are higher for a short-term debt contract, (s > 0 f , control rents reduce the attractiveness of short-term debt contra& as well as high monitoring costs, (s < 0 and 9 < 0) .

Finally, the effect of the borrower's type on the ex-ante profit from bor- rowing short-term rather than long-term is

The sign of this derivative is ambiguous and depends on the monitoring technology. Better firm will prefer a short-term debt contract to a long-term debt only if the probability of the lender being informed is high enough to make the Type G borrower's expected net gains greater than the gain in efficiency due to the liquidation of the type B h.

It can be shown that, when control rents are ignored, 9 > 0 if

That is, Growth Firms will prefer Bank Debt to Public Debt if the mon- itoring technology of the lender is high enough.

2.5 Conclusion This paper analyzes the role of covenants in reducing overinvestment prob- lems. The covenants considered in the model restrict the firm's investment policy. They control overinvestment incentives by reducing investment in negativeNPV risky projects. However, in so doing they create an underin- vestment problem by preventing investment in positiveNPV projects. The optimal debt contract with covenants is such that it balances, ex ante, the margirial gains form a reduction in overinvestment with the marginal costs horn an increase in underinvestment.

In practice, a borrower has the choice between debt. contracts with differ- ent covenant and maturity structures. The effects of snch debt characterist.ics on the borrower' s choice of source of financing are analyzed. The long-term debt contract with renegotiation modeled in this paper shares many charac- teristics with Privately Placed Debt while the long-term debt contract with no renegotiation is comparable to Public Debt. As for the short-term debt contract, it can be thought of as a Bank Debt.

Comparing the borrower's ex-ante profit from Privately Placed Debt to those kom Public Debt, it is shown that the borrower values positively the option to renegotiate embedded in Privately Placed Debt. However, this enhanced flexibility is costly in the sense Privately Placed Debt has more stringent covenants than Public Debt. . It is shown that, when agency problems are not important, or equivalently,

when the manager's control rents are negligible and the lender's monitoring technology is high, the borrower's ex-ante profits from Bank Debt are higher than those from Privately Placed Debt while Public Debt is the least valuable contract. However, when agency problems are considered, Bank Debt is the least valuable contract. This is the case because both Public and Privately Placed Debt permit a firm to continue operating as long as the covenants are not violated. Bank Debt, on the contrary, forces the manager to renegotiate the terms of the loan at the maturity of the contract. In this setting, the liquidation of a type B Exm and the subsequent gain in efficiency is more likely for a Bank Debt. Since in this paper the lender earns zero-expected profit, all the surplus goes to the borrower who prefers Bank Debt to long-term debt contracts. Also, Privately Placed Debt is preferred to Public Debt because, by having more stringent covenants, it reduces the efficiency losses due to the type B firm investing in negativ+NPV projects. However, when control rents are considered, Bank Debt is not preferred because of the higher liquidity risk .

it entails. The model suggests that a manager would prefer Privately Placed Debt or Public Debt to Bank Debt only if agency problems are high enough. Such a reason would be negatively perceived by investors which is consistent with empirical evidence.

It is also shown that, when control rents are ignored and the monitoring technology is high enough, growth firms' managers prefer private debt to public debt. However, Bank Debt can be less attractive than Privately Placed Debt because of the risk of excessive liquidation.

Barclay and Smith (1992,1995a, b) provide interesting stylized facts which show that, in practice, all debt financing is not the same. Debt contracts

differ in several important, respects like mat,urit.y, convertibility, covenant. re- strictions, call provisions, security and whether the debt is privately placed or publicly held. In this paper, the focus has been on covenant restrictions and maturity. An interesting avenue would be to analyze how debt covenants affect the manager's choice of debt in the presence of bank information mo- nopolies as analyzed by Diamond (1993) and Rajan (1992). This topic is analyzed in the next section.

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[19] Smith C. W., A Perspective on Accounting-Based Debt Covenant Viola- tions, The Accounting Review, April 1993, Vo1.68, No.2, pp.289-303.

[20] Smith C.W. and R. L. Watts, The Investment Opportunity Set and Corporate Financing, Dividend, and Compensation Policies, Journal of Financial Economics, 1992, 32, pp.263-292.

[21] Smith C. W. and J.B. Warner, On Financial Contracting: An Analysis of Bond Covenants, Joumal of Financial Economics, June 1979, 7(2), pp117-161.

The manager and the lender have prior beliefs p about h e type o f the fm

Borrower receives signal a b u t the type of the fm and knows whether the lender will k informed or not

Lender learns bonowcr's type with probability 8

All uncertainty is resolved

Date

Contract (d,z) is signed Lender invests k in mc>- nitwing apparatus

Borrower invests z in OM assets and 1-2 in new project

Borrower may offer a new contract (z ' ,d ' ) if renegotiation is possibk

Lender may accept and waive the covenant (K

refuse and liquidate. h e firm

Payoffs arc realized

Fig. 1. The model

Bad Firm Good Firm

* 5. i $1,.

I .

comply; 'a, do not cowply' . do not i \i, comply \\ comply

$ ,i' '\

2'. '., z

Lender 1.

/ \ accept / \ reject offer

and audit \ and audit / \. I

Firm j \. producer' i.

I \ ?

Ltndcr

A . .

/ ' accept: ';reject offer

and audit/ !, and audit \;

i F'um 1

\ '!; produces i \..

i

Fig. 2. Fully Informed Lender

Long-Term Debt with Renegotiation

! '. 8 .

I ' \ . b I ,

comply,.. ': do not comply/ :., do not ,

I comply I # '. comply 2'; ' t b z?' '., 4

I I #

# b

I I

\

I

I I

I ; Firm makes offer i , Firm makes offer I

I i e' ' W b . 2'3 4 btd“ . z ' J

[ R ( f ) + y I d ) - d') +C C

Fig. 3 . Uninformed Lender

Long-Term Debt with Renegotiation

2.6 Appendix

2.6.1 Long-Term Debt With Renegotiation

Fully Informed Lender Refer to Fig. 2: consider the type B firm first. If the manager chooses to comply, she invests zn in the old assets. If she does not comply, she makes an offer (r', z') to the lender. In this case, the lender, if she accepts, receives a payoff equal to [R (2) + rb (1 - z')] compared to Lb if she rejects. So the lender rejects the offer since R (z')+rb (1 - 2') < L ~ . Given that the lender rejects her offer, the manager decides to comply because she can get the control rents C rather than a payoff of 0 if she makes an offer. So there is a unique equilibrium involving the following strategies:

{Type B Firm complies ; Lender rejects).

Next, consider the Type G firm. If the manager makes an offer (2, d'), then the lender gets L9 if she rejects the offer. If she accepts the offer she gets d'. So the lender accepts the offer if d' > L? Suppose the lender accepts the offer. In that case, the manager will comply if

[R (2") + rg (1 - 2") - d"] > [R (2') + + ( I - 2') - d']

and d' > L9

then the firm makes the offer (2, dl) which the lender accepts. In this case, the manager would receive [R (2) + r g (1 - 2) - d'] + C and the lender dl.

Assume that if the lender is indifferent between liquidating and not liq- uidating, she chooses not to liquidate. In this case, the manager's best offer is z' = 0 and d = L? So if the lender accepts an offer, the manager will indeed want to make an offer. In that, case the lender's profit is L9 which she accepts.

The manager will make that offer if her payoff is higher than the payoff she gets if she complies i.e.

[R (0) + @ (1) - d'] > [R (2") + f l (1 - zn) - d"]

From eq~iation (20). it. can be seen that the (P that makes tllc ic11t1e1- earn, ex-ante, her i1t~i1it.y of reserve is such that,

It can be verified that the manager will always make the offer as long as the ex-ante expected return horn liquidating the firm is less than the reserve utility 4 or in other terms as long as always liquidating is a negative net present value project. Proof. We have to show that

or equivalently

To do so, notice that

0 Therefore, one Nash equilibrium involves: {Type G Firm chooses z = 0 ;Type G Firm offers (d t , 2') = L9; Lender

accepts offer}. Suppose now that the lender rejects the offer, that is d' < Lg . In this case,

the manager loses her control rents and earns a zero payoff if she does not comply. Therefore, she decides to comply since [R (zn) + r g (1 - zn) - P] > 0.

So if the lender rejects the manager's offer, the manager complies. There is another Nash equilibrium where

{Type G Firm complies ; Lender rejects offer). However in this case, the lender's node is never reached. Whenever the

lender's node is reached, it is optimal for the lender to accept the offer. So, the unique sequential equilibrium is:

{Type G Firm chooses z = 0 ;Type G Firm offers (6, z') = L g ; Lender accepts offer).

Uninformed Lender Pooling Equilibrium Refer to Fig. 3. and let zb the choice of the manager of a type B firm and z, that of the rnanager of a Qpe G firm if they do not comply. First check the existence of a pooling equilibrium. Both managers make the same offer (d', z') and when her information set is reached, the lender assigns a probability q to a Type G firm and 1 - q to a type B firm. If the lender accepts, then the maximum profit she can receive is

If she rejects the offer, the lender receives (1 - q) Lb + qP. So if

the lender will reject the manager's offer. Suppose the lender's belief q is such that she rejects the offer, then the best response for the managers of both firms is to comply since

and ( R (2") + 7' (1 - 2") - 7'") + C > 0

In that case, the lender's information set is never reached and Bayes' n ~ l e need not to be applied. There is a continuum of sequential equilibria:

{Type G Firm complies, Type B Firm complies, Lender rejects offer, q satisfies (*)I

Separating Equilibrium

Check the exist,ence of n separating eqllilibrium. ..\ssume that the Ty c I3 firm makes an oRer (d ; , 2:) and the Type C. firm makes an oRer (d ; , .~ ; ! . Suppose that if the lender is indifferent between liquidating and not liqwdat- ing, she will choose not to Liquidate. Soz if the lender saw the offer she would place a probability 1 that the firm is Type G and would offer as long as d i 2 L9. The best action the manager of a Type G firm can take is to offer a new contract 219 = 0 and rb = LP since it would maximized her payoff giving her R (0) + rg (1) - Lg + C.

If the lender saw the offer (d i , i,), she would place a probability 1 that the manager is from a Type B finn and would reject any offer since, Lb > R (2;) + rb (1 - 2;) .

The manager of a Type B firm would then comply since she would get a payoff of zero if she makes an offer i.e. C > 0.

So, there can be no separating equilibrium.

2.6.2 Effects of Relaxing Assumption (9)

See Berlin and klester (1992) for a similar proof in a different context. If

p [R (2) + rg (1 - t)] + (1 - p) [R ( z ) + rb (1 - z ) ] 2 pL9 + (1 - P) Lb

then the renegotiable contract is infeasible provided that

That is, a lender would not invest funds and bear the costs of monitoring merely to have the option to liquidate the firm in states where the covenant binds.

Lemma 1. There exists a critical value p' E [0, 11 such that

Proof. Define:

and L ( p ) r p L 9 + ( 1 - p ) ~ b

Notice that,

by assumption (5) in the text and

by assumption (2) in the text. Therefore if 4' ( p ) - L' ( p ) 2 0 then the proof is complete.

To show that Q (p) - L' ( p ) 2 0 notice that 4 (p) - L @) 2 0 e

that is

(1 - P) [R (z' ( p ) ) + rg (1 - z* ( p ) ) ] - Lg 2 - [Lb - R (y ((p)) + rb (1 - Z* ( p ) ) ] P

Also,

= [R (2 ( p ) ) + +9 (1 - z' ( p ) ) - Lg] - [R (2' (p)) + r"1- 2' (p)) - L ~ ]

using the kt-order-condition of the non renegotiable contract, equation (17) in the text.

Therefore, Vp, such that 4 (p) - L ( p ) 2 0, we have

- P I [ L ~ - R (z' ( p ) ) + rb ( 1 - z* ( p ) ) ] 0' (PI - L' (PI 2 - P

- [R (r' ( p ) ) + rb (1 - L* ( p ) ) - L'] 1

= - [ L ~ - ( R ( z * @ ) ) + r b ( i - z ' ( ~ ) ) ) ] 2 o P

by assumption (5) in the text.0

L e m m a 2. In the uninformed state, only pooling equilibria are possible when

Proof. Similar to the proof when [4 (p) - L ( p ) ] < 0 given in section 1.1.2 of the Appendix.

Lemma 3. In the uninformed state, if

then both types choose 4 = z; = zit < zn in period 1, and the contract is renegotiated.

Proof. Given Lemma 2, only pooling equilibria are considered. .\ssume that the manager chooses < = z: = z" < zn at t = 1 and offers

contract (zt ' ,d") where d" is the minimum d that will be accepted by the lender.

That. is d" satisfies:

.A necessary and sufficient condition for this pooling equilibrium to exist is that. the manager of a Type G firm prefers (z", dtt) to ( rn, d") which requires that

D ( p ) s [R (2") + rg (1 - z") - 61 - [R (2") + P (1 - 2") - d"] > O

It is possible to show that there is unique z* satisfymg

2. =argmax D ( p ) s.t.pr" -F ( 1 - p) R' (2'') = L ( p ) z"

If D ( p ) evalaixed at z" = z' denoted D ( p ; z" = 2') is positive, then the pooling equz briuru will esist.

To show rhis. differentiate D ( p ; r" = z * ) with respect to 0 :

Rwall that rn solves

p [ 8 ~ ' + ( l -0)d"]+(1-~) [ ~ ( z " ) + r ~ ( l - z ~ ) ] - k - d = O

Substituring, we get

J

( R (r") + rb (1 - tn))]

By the firstader condition for the renegotiable test, the firs term is zero. Therefore

contract, equation 30 in the

dD (P. d + k - p L g - ( l - p ) ( ~ ( z " ) + r ~ ( l - ~ " ) ) ] } sign {dB} = 519" { ~ ( 1 - el2 [

Since we assumed that

and

then

Therefore, if D (p) cvalllilted a t 2" = z* is greater than 0 at. 0 = 0. the11 D ( p ) evaluated at st' = z' is greater than 0 at ,111 19.

To show D ( p ; 2" = r') > 0 at 0 = 0,note that at 0 = 0, z' is the imiqtle soh t ion of the first-order-conditions

b p[R, (z*) - r: (1 - z ' ) ] + (1 - p) [R, (z ' ) - r, (1 - z')] = O

whereas zn is such that

b p [Rz (2") - r: (1 - zn)] + (1 - p) [R, (2") - r, (1 - z")] = O

That is when 6 = 0, we have zn = z*. Furthermore, since d + k > L ( p ) , we have cF > d".

Therefore, D (p; 2" = r') at B = 0 is equal to d" - dl' > 0 .

Thus,

is a pooling equilibrium.0

Proposition. If 4 ( p ) > L @)and d + k > L (p) ,then the renegotiable contract is infeasible.

Proof. Given Lemmasl-3, the lender's expected profit at t = 0 is

+(1 - 0) ( ~ ( z " ) + rb (1 - Z"))] - (d + k)

= e [*u + (1 - p) ( R (zn) + 4 (1 - zn))] + (1 - 6) L (p) - (d + k)

= eL(p ) + (1 - e ) L ( p ) - (d+k) = L (p) - (d + k) < 0 by Assumption

Thus the contract is infeasible since the lender's expected profit at t = 0 is negative. 0

3 Bank Information Monopolies and Debt Covenants

3.1 Introduction

While the benefits of bank financing have been extensively investigated, less attention has been paid to its costs. Financial economists23 have shown that, bank financing, by mitigating adverse selection and moral hazard and by providing flexibility through covenants can be less expensive than borrowing horn public (arm's length) lenders . However, they have also pointed out that, monitoring costs and bank regulatory taxes can potentially offset these benefits.

Recently, Diamond (1991), Sharpe(l990) and Rajan (1992) have exam- ined other costs of bank hancing. Diamond (1991) argues that relying exclusively on bank debt can be costly because of liquidation risk. He points out that, a lender, sometimes, liquidate while the borrower would not choose to do so if she were the sole owner of the firm. Rajan(1992) and Sharpe(l990) discuss another cost of borrowing solely from a single bank. In these models, information acquired by a bank as part of an ongoing relationship can create a hold-up problem in that it is costly for the borrower to switch lenders. In Sharpe (1990), banks' ex-post monopoly arises because, in the process of lending, a bank learns more than others about its own customers. More precisely, firms stay with the same bank because high quality ftms are in-

23~heoretical and empirical studies on the role of banks in the corporate capital acqui- sition process focus on their information production and control functions. Monitoring of private information is most efEciently delegated to a financial intermediary? rather than collected directly by many investors (Diamond (1984)). The clientele of banks are those borrowers whose rating is high enough for monitoring to eliminate moral hazard (Diamond (1991)). Later, by threatening to deny credit, a bank provides the firm with incentives to take the right investments (Stiglitz and Weiss (1983)). Better ex-ante information and in- creased creditor control reduce adverse selection (through information) and moral hazard (through control of the h ' s investment decision) and enable the bank to provide cheap (informed) funds as opposed to costly (uninformed) or arm's-length funds (James (l987), Lummer and McConnell (1989), Hoshi, Kashyap, and Scharfstein (1990, 1991)). By in- cluding covenants in their contracts, banks can improve the flexibility of their contracts (Berlin and Mester (19921, Berlin and Loeys (1988), Sy (1997)). Finally, a positive loan renewal si& implies that other agents with fixed-payoff claims need not take a similar costly evaluation (Easterbrook (1984) and Fama(l985)) -

formattionally captured. Their own bank docs make the best, offer. blir this is due to difficulties firms face in conveying information about their superior performance to other banks. Adverse selection makes it, difficult to draw off another bank's good customers without attracting the less desirable ones as well. These inefficiencies are shown to be reduced when lenders can develop reputations. Indeed, if a bank exploits its captured customers, it. is likely to lose market share as potential new customers learn such practices. Broken agreements in the past would be punished by the loss of future credibility. If it is costly to write multiperiod contingent contracts but banks make non- binding promises, and future market participants learn about the banks's propensity to keep its promises, theg, implicit contracts arise. These com- mitments will be characterized by prices which more closeiy approximate the optimal prices and, thus, lead to more efficient allocation of capital. Building on Sharpe (1990), Rajan (1992) focuses not only on the costs of the inside bank's rent but also on the benefits of the inside bank's control. He argues that, while informed banks make flexible decision which prevent a firm's projects from going awry, the cost of this credit is that banks have bargain- ing power over the firm's profits, once the projects have begun. The resulting expropriation of rents distorts the firm's investment decisions by limiting the entrepreneur's gains from successful projects. In his model, the h ' s choice of borrowing sources and the choice of priority for its debt claims attempt to optimally circumscribe the power of banks.

In this paper, I argue that debt covenants, which are a frequent feature of bank loans, c w reduce the types of bank information monopolies discussed earlier. Previous studies on debt covenants have focused on their role in reducing the agency problems of debt. For example, the seminal work of Smith and Wamer (1979) discusses the role of debt covenants in controlling four major sources of conflicts between a borrower and a creditor, namely dividend payment, claim dilution, asset substitution and ~nderinvest~ment. More recently, Berlin and Mester (1992) argue that covenants improve the flexibility of bank debt, while Sy (1997) analyzes the role of covenants in reducing the agency problems of debt. Rajan and Winton (1995) rationalizes the existence of covenants as instruments that give banks an incentive to gather information by maximizing the difference between the value (to the bank) of public information and private information.

This paper departs from the literature on debt covenants by giving a new rationale for the existence of these contractual restrictions. It shows how covenants, by permitting contingent contracting can be used by banks

LO precommit against. using their information advantage; t h m reducing tthc costs of delegated monitoring discr~ssed by Rajan (1992) and Sharpe (1990).

The model considers a who has to finance externally an invest- ment in order to obtain a stochastic payoff. After making the investment, the manager exerts costly effort which affects the distribution of project payoffs. The state of the world, which is privately observable by the owner. is then realized. Depending on this information, continuing the project may have positive or negative present value. As the owner has a residual claim, and all financing is through bank debt, she always wants to continue the project. Typically, an informed bank will be able to control the owner's decision such that the project is continued only if it is profitable. In the process of doing so, however, it adversely affects the owner's incentive to exert effort. As an illustration, consider a short-term bank debt, where the bank requires repay- ment of the loan after the state is realized. As the bank is also informed about the state, it can prevent the owner from continuing a negative net present value venture by demanding repayment. Unfortunately, it can also demand repayment when continuing is efficient. If the owner has only the bank as a source of finance, she has to share some of the surplus from the project with the bank in order to persuade it to continue lending. As the owner no longer obtains all the s~lrplus from the project, she exerts lower effort than optimal, thus reducing the project returns.

The main point of this paper is that covenants can reduce such an ad- verse effect on the manager's effort. To see this, note t.hat the level of effort and the state of nature can be observed only by the owners and insiders but not by a court of law. However, an indicator of the state is verifiable by courts, which ensure the penalty structure of reneging, and hence can be contracted upon. In practice, the constraints imposed through covenants are frequently specified in terms of accounting numbers. Furthermore, the violations of debt covenants are more generally caused by deteriorating per- formance, and generally involve the breach of multiple constraints a t the same time. Following Berlin and Loeys(1988), a covenant can be written as a filnction of the state and the indicator. Contractually, the bank has the right to demand repayment of the loan, only if the covenant has been violated, otherwise, the project is permitted to mature. In case of a breach of covenant, the situation is the same as for a bank debt with no covenants.

24The manager operates in an owner-managed firm or there is no agency problems between the manager and the owners.

That, is, the firm is liquidated in the b C d state anti held up in the gooti state. When the covenant is not violated, the bank has no liquidation rights and cannot accelerate the maturity of the contract.. In this case the borrower will appropriate all the surplus. This, will give the manager an incentive to produce greater effort comparatively to a bank contract with no covenants. Covenants are, however, costly for the bank. Indeed, when the covenant. is not breached in the bad state, the bank cannot demand repayment. In this case, there is inefficient continuation and the owner's incentive to exert greater effort to avoid bad states is reduced. A rational lender will anticipate this and will demand a higher face value than if the continuation decision were efficient. This will reduce the surplus available to the owner in the good state and her incentive to exert effort. Moreover, the residual value accruing to the owner in the bad state increases the attractiveness of the bad state, further reducing effort. However, the inefficiency introduced by covenants is decreasing in their informativeness. A covenant is more informative when it is breached more often when the state is bad. It is perfectly informative when a breach always indicate that the sate is bad. In this case, a bank debt contract with covenants gives the manager an incentive to exert greater effort. Thus, introducing covenants in bank debt contracts can be socially optimal.

The rest of the paper is structured as follows. Section 2 describes the basic model. Section 3 discusses the First-Best solution and analyzes the debt contracts with the focus being placed on the characteristics of a bank debt contract with covenants. Section 4 compares the different contracts from the point of view of a borrower and section 5 concludes.

3.2 The Model 3.2.1 The Project

At an initial date 0, a manager-owner invests a fixed amount I in a project. She then makes an effort /3 a t a unit cost of 1. The assets can be liquidated at date 1 for a value of L where L < I. At date 2, the assets depreciate to a value of zero.

There are two possible states at date 1, t E {tc, t s } such that q = p (t = to) and (1 - q) = p ( t = t B ) .The state is good with probability q and bad with probability (1 - q). At date 2, in the good state, the project pays out X with probability 1. In the bad state, it pays out X with probability

p~ and zero with probability (1 - p B ) . Asslime that ,. > I 2 L > p,X. The manager's private effort /3 E [0, oo) along with an exogenow quali t.y

parameter 0 E [ O , l ] , affects the probability q of the good state occlirring. Assume that q = q ( & B ) , where q has the following properties:

where the subscript k denotes the partial with respect to the kth argu- ment.

Assumption (1) states that the probability of the good state being realized is increasing and concave in the effort of the manager and is increasing in the quality 0. Assumption (2) states that the marginal benefit of effort decreases to zero from a large number and assumption (3) is a standard separability assumption.

3.2.2 The Financiers

Assume that all agents are risk-neutral and that the riskless interest rate is zero. The manager has no initial funds and must borrow to finance the project. The date 0 credit market is competitive and there are two types of lenders.

i. Banks enter the market at date 0 to acquire information and make loans. If a bank makes a loan to a firm at date 0, it gains access to the internal records the firm maintains (and henceforth it will be referred to as the inside bank). During this period, the bank monitors the firm's books and the accounts the firm maintains with the bank. Much of the information obtained this way is not verifiable by courts and cannot be contracted upon. However, in the process of monitoring, Bunks observe a noisy interim indicator of the firm's future ability to repay. These indicators may be in the form of financial ratios and are verifiable by courts. Covenants are written as f'mctions of these indicators, and the firm's inability to satisfy these covenants put the

firm in defadrt'5. ii. Arm 's-length investors lend at date 0 and return to collect. repayments

at, date 2. They do not monitor because of high private cost of monitoring as compared to banks or because the smCd size of each investors loan will create a free-rider problem.

.4lthough the paper focuses on bank loans, the analysis of arm's-length contracts will prove useful to understand the bank contract with covenants.

3.2.3 Information

At date 0, the exogenous parameter B is public information. Once the project starts, the owner knows B the effort exerted. She also learns the state before deciding whether to continue the project at date 1.

The inside bank learns the effort provided and the state a t the same time as the owner. Insiders also learn y, the value of a noisy indicator of the state. Following Berlin and Loeys (1988), I assume that the indicator is independent across projects and is denoted by y E {yc, ys) . Both the inside bank and the manager know the conditional distribution of the state for each value of the indicator and the prior distribution of the indicator. Let pij denote the conditional probability of ti given y j . Given the simple structure of uncertainty, a useful parametrization of the probability distributions is as follows:

Pcc Pce

and P (YG)

[ P b ; ] = [ A ] where 0 < q < 1 and 0 < p < 1. In this parametrization, q is both the

prior probability of a favorable indicator and the prior probability of the good state being realized. The parameter p measures the informativeness of the indicator with p = 1 corresponding to a perfectly informative indicator and

15Vioiation of a debt covenant other than one specifying promised payments is conven- tionally called a technical default. For a review of the related empirical literature, see Smith (1993).

p = 0 corresponding to a totally u~~infor~llative indicat.or2% The indicat,or may be interpreted as a bdnnce-sheet. ratio, or the firm's ability to make a debt, payment.. If the indicator is a very good predictor of the firm's ultimate ability to repay, then p is close to one.

Arm'slength investors observe only public signals, which are assumed uninformative.

3.3.4 Covenants

Efforts and the state can be observed only by the owner and insiders, but not by the courts. However the indicator y of the state is verifiable by the courts and hence can be contracted upon. A covenant can be written as a function of the state t i and the indicator yj:

d ( t i , yj) E {O,1) for 2 , j = G, (38)

If the lender can prove that d (.) = 1, then the project is permitted to mature, and, if d (a) = 0, then the lender has the right to demand repayment of the loan, forcing liquidation if it so chooses. I assume that d (ti, ys) = 0 and d ( t i , gc) = 1 for i = G, B that is the covenant is violated only when the bad indicator y~ is observedz7. Modeling covenants in this way permits contingent contracting. The penalty structure for reneging is exogenous and is ensured by courts of law28.

26See Berlin and Loeys (1988) and Blackwell (1951) for a detailed analysis. An indicator with higher p is more informative in Blackwell's(l951) sense. In addition if tc = 2, t = 1, and y c = 2 and ys = I, then p is the correlation coefficient between s and y.

"The contract with covenant described is similar to the Harsh Contract of Berlin and Loeys(1988). In their model, only Harsh and Lenient contracts are optimal. The Harsh contract places the firm in default only when the bad indicator is observed and the Lenient contract never puts the h in default. They show that contracts which place the firm in default when a good indicator is observed cannot be optimal for the following reasons. One that imposes default only when the good indicator is observed is never optimal because a good indicator is good news about the project. If it is optimal to impose default when the good state is obeserved, then the same must be true when the state is bad. (See Milgrom (19S1) for the definition of good news.) However, default will not always be imposed because, by assumption, storage strictly dominates any contract that always places the firm in default. In this paper, a Lenient contract is similar to a long-term bank debt with no covenants.

2s~n practice, the constraints imposed through covenants are kequently specified in terms of accounting numbers. Debt covenants that employ accounting numbers are con- ventionally divided into (1) affirmative covenants, which require the firm to maintain

3.3 The Basic Trade-off

3.3.1 First-Best Solution

The First-Best. solution is such that the owner continues in the good state and closes the project down in the bad state. The expected total surplus at date 0 is such that:

The first term is the surplus in the good state, the second the depreciation losses in the bad state and the third represents the cost of the effort. The project should be financed only if the surplus is positive for some eEort level. The effort &,, which maximizes this surplus, is obtained by solving the first-order condition (FOC)

Assumptions (1) and (2) ensure existence and uniqueness of the solution. On the one hand, a contract close to the First-Best contract should on

the one hand give the owner the incentive to liquidate voluntarily the project and face all the losses in the bad state. A1 ternatively, the lender should have the ability to coerce or persuade the owner to liquidate in the bad state. On

specified levels of accounting- based ratios, and negative covenants, which limit certain investment and hancing activities unless specified accounting-based conditions are met. For example, negative covenants restrict the payement of dividends, the disposition of assets, the issuance of additional debt, and merger activity; afbnative covenants specify minimum working capitai and net worth requirements. Rajan and Winton (1995) argues many covenants are standard boiler-plate, fleshed out as much by lawyers as by loan offi- cers or treasurers, My personal discussions with lawyers confirm this assertion. However, Rajan and Wmton (1995) also documents that, courts penalize lenders both for taking action when covenants have not in fact been violated and for exercising powers beyond those allowed by the covenants. Violation of a debt covenant other than one specifying promised payments is conventionally called technical default. Reviewing several empirical studies, Smith (1993) argues that evidence shows that technical default is more generally caused by deteriorating corporate performance, that a substantial fraction of the defaults involve the breach of multiple constraints, that default is more likely in private than p u b lic debt issues, and that lenders choose a wide array of measures to respond to technical default. For the lender, these actions range from granting a permanent waiver without turther modification of the contract to accelerating the maturity of the debt and forcing the borrower to obtain b u n g elsewhere.

the other hand, the contract shodd allow the owner to obtain all the slirplus from the good state.

3.3.2 Arm's-Length Contract

The results derived in this section are similar to those obtained by Rajan (1992). At date 0, the owner borrows an amount I to invest in the project and promises to repay Do* at date 2. By assumption, the arm's length lender neither receives information nor can he act upon it. In this framework, the owner has no incentives to liquidate the project in the bad state and will always opt for a continuation decision at date 1. The owner's program is then:

Let solve the corresponding FOC and let the lender's conjecture of the owner's effort be P,C

The arm's-length investors's lends provided she finds it individually ra- tional, that is if

and provided the contract is feasible, X > A Rational Expectations Equilibrium will require that the lender's conjecture be correct, that is

Assuming a competitive credit market permits equation (9) to be met with equality. So, if a feasible contract exists, the FOC obtained horn (8), (9) and the equilibrium condition (10) taken together imply the optimal2" effort is defined implicitly by

for B = & and qi = q (P:, 8 ) . Note that the effort exerted by the owner is less than the £irst best solution. Intuitively, this result obtains because of

%Note that a solution may not always exist. But if it does then, ssaumptions (1) and (2) with a single crossing condition would ensure that the solution is unique.

the owner's decision to always cont.in~ie in tlie bad state even though i t may be inefficient to do so. A rational lender who anticipates this inefficiency charges the owner a higher face value than if the continuation decision were efficient hence decreasing the owner's part of the surplus in the good state. Furthermore, the owner has another incentive to reduce her effort because by doing so, she can increase the probability of the bad state occurring thereby increasing the expected residual payoff, p~ (X - DO2=) .

Finally, the owner's ex ante expected utility with arm'slength debt is:

The first term is the expected surplus in the good state and the second term is the cost of inefficient continuation.

3.3.3 Bank Contract with no Covenants

The owner borrows and invests I at date 0. The bank observes the effort exerted and then the state. If the state is bad at date 1, then the bank chooses to liquidate the project for a value of L. If the state is good, then the bank has no such rights. However, the date 0 contract does not oblige the bank to lend. It can use this discretion to hold up the owner and demand a share of the surplus in returns for the funds needed to continue the project. Following Rajan(1992)) the solution of this bargaining game is such that the owner gets p (X - L) while the lender gets (1 - p) (X - L) + L, where p E [O, 11 denotes the owner's bargaining power3! The FOC for the owner's effort decision at date 0 is

30A firm can be locked in a relationship with one inside bank because of its informational advantage. Sharpe (1990) building on a traditional view of bank lending behavior, first spelled out by Hodgman (1961) and Kane and Malkiel (1965) and elaborated upon by Wood (1975) as well as Fama (1985) shows how information monopoly can endogenously arise because of information asymmetry between banks. Similarly, Rajan (1992) shows that an inside bank's informational advantage over outside lenders can endogenously lock the firm to it.

Alternatively, a firm can be held-up if banks agree not to poach each other's clients and such collusive practices may be reinforced by a government that wants to restrain de-stabilizing competition in the banking sector as in Macrae (1990) and Modigliani and Perotti (1990). In a recent empirical study of 250 firms observed in 1980, 1985 and 1990, Houston and James (1996) h d that 66 percent of the firms in their sample maintain multiple banking relationship. The average number of bank relationships reported is 5.22. 34 percent of these firms have multiple banking relationship because they borrw through syndicates of banka. However, they also h d that the likelihood of multiple reletionships is

for = &, provided it is individually rational for the bank to lend:

The effort induced by the bank contract with no covenants is lower than the First Best solution. Note that if p is high (z 1) the bank will not be able to recover the depreciation losses (1 - qi ) ( I - L) . If p is low (-- 0) then, the owner, faced with poor incentives, will not exert much effort.

The owner's ex ante utility from a bank debt with no covenants is

The first term is the expected surplus in the good state while the second term represents the depreciation losses. In the next section, a bank debt contract with covenants is analyzed.

3.3.4 Bank Contract with Covenants

The owner borrows I at date 0 and exerts a level of effort P . The bank observes the effort exerted and then the state as well as the value of the indicator. At date 1, the bank has the right to liquidate only if the indicator is bad. If the value of the indicator is bad, and the state is also bad, then the bank liquidates the firm and obtains a payoff of L. However, if the - - --

positively related to firm size. For example, among firms with assets below the median, 43 percent have multiple banking relationships. In contrast, among firms with assets greater than the median, 88 percent have multiple banking relationships. Not surprisingly, in an empirical study of the borrowing behavior of 3,404 small firms from 1988 to 1989, Petersen and Rajan (1994) find only 18 percent of firms with multiple banking relationships. They explain that relationships with a unique institutional lender are valuable and appear to operate more through quantities rather than prices. They find that the primary benefit of building close ties with an institutional creditor is that availability of financing increases. Moreover, attempts to widen the circle of relationships by borrowing horn multiple lenders increase the price and decrease the availability of credit. Finally, Davis and Pinches (1997) argue that debt covenants appear to be less important for larger firms, due to the larger number of financing options available to them, the greater availability of public information about the firms, and the constant scrutiny they face from the financial markets, security regulators, underwriters, and bond-rating agencies.

value of the i~ldicator is b d but. the state is good then the bank can use its liquidation right to hold up the owner and demand a share of the surplus. If the indicator is good. then the bank has no liquidation rights <uld cannot. accelerate the maturity of the contract.

Given this contractual arrangements31, the owner chooses her effort level by solving the following program:

P

The bank lends provided it is individual rational

P (YG) [PGG + PBG (PB)] Doz=-P(YB) [PCB ((1 - P ) ( X - L) + L ) + PBBL] 3 I (50)

and provided the contract is feasible, X > Daze. The optimal effort P: is defined implicitly by

where the denominator is

and

Result 1 T h e owner's ez ante utility from a bank debt with covenants is equal to the ez ante ufikty from a mix of bank debt with no covenants and arm's-length debt where the weights am the prior pmbabilitzes of being in Me good state and in the bad state.

31Carey et Ai-? comparing the characteristics of bank loans, privately placed debt and pubiic bonds, document that bank debt has the tightest, and the most number of covenants. The contract modeled here can also be seen as a debt privately placed to a bank.

The owner's es ante utility from a bank debt with covenants can be written as:

4: [pGZ (X - I ) - PBC (1 - P B X ) ] + ( ~ - 9:) [PCB (X - I ) - PBB ( I L11-9: (54)

The expression in the first squared brackets is similar to the owner's ex ante utility from arm's- length financing with the priors replaced by con- ditional expectations. It represents the expected surplus in the good state minus the cost of inefficient continuation. The surplus is due to an efficient continuation policy while the cost of inefficient continuation is due to in- ac ien t control. Indeed, covenants are a source of inefticient control when the indicator is good and the state is bad because control rights are not transferred in this case.

The expression in the second square brackets is similar to the ex ante utility from bank debt when there are no covenants but with conditional expectations rather than priors. The terms in brackets represent the expected surplus in the good state minus the depreciation costs. The surplus is due to an efficient continuation decision while the depreciation costs are due to an efficient Liquidation decision. Note that the effort level induced by the bank debt with covenants is different from the one given by the two other contracts.

The owner's ex ante utility f ~ o m a bank debt with covenants can be seen as the utility from a mix of outside and inside debt, where expectations are conditional on the value of the indicator. The weights are the prior proba- bilities of being in the good state, q:, and in the bad state (1 - 9:). As q: increases, the manager's ex ante utility &om a bank contract with covenants resembles more that from an arm's-length debt contract. Alternatively, the manager's ex ante utility horn bank contract with covenants gets closer to that from a bank debt with covenants as q: decreases. Intuitively, when the probability of being in the good state is high, control becomes less important and the debt contract with covenants approaches an outside debt contract. When the bad state is more probable, the value of control increases and the contract gets closer to an inside debt contract.

The owner's ex ante utility depends on the informativeness of the indica- tor and can be written as a function of the parameter p which measures its precision:

Result 2 The owner's ez ante utility from a debt contract with covenants, rC, is a strictly incrensing function of p, the precision of the indicator. That is, 5 > 0

Proof: See Appendix. In other words, the payoffs to the owner increase with the precision of

the covenants. On the one hand, the efficiency losses decrease with the precision of the indicator. Indeed, as the indicator becomes more precise, the probability of being in the good state given a bad signal, decreases. This will reduce the instances in which the bank can extract rent when there is a covenant violation and will diminish the expected loss of rent due to an hold- up game. Similarly, the probability of being in the bad state given a good signal decreases with the precision of the indicator. The states where the firm can continue in spite of the state being bad because there is no covenant violation will be less frequent, thereby reducing the cost of an inefficient continuation.

On the other hand, the gains in efficiency increase with the precision of the indicator. Indeed, the probability of a good state given a good indicator and the probability of a bad state given a bad indicator both approaches one as the indicator becomes more precise. This will result in more frequent covenant violation and thus more efficient liquidation when the state is bad and in less frequent hold-up that is more efficient continuation when the state is good.

For a perfectly informative indicator32, ( p = l) , the conditional probabil-

o or a totally uninformative indicator, that is when p = 0. the solution becomes

and the owner's ex ante contract expected utility is:

q q x I ) - (1 - - P I + - - 1) - (1 - 9 - I - (56)

Note that q: is the probability of the good state occurring, the first term in square

ities reduce to [ ] = [ ] , and the solution of the manager's PBC P B B

optimization program becomes

Note that the effort exerted by the owner is less than first best. The owner's ex ante contract expected utility is:

When the indicator is perfectly informative, the owner's ex ante contract expected utility reduces to the expected s-uplus in the good state minus the expected depreciation losses in the bad state. There is no inefficient continuation and no hold-up game because both the probability of being in the good state given a bad indicator as well as the probability of being in the bad state given a good indicator are equal to zero.

Result 3 The Bank Debt contract with covenants achieves First-Best when assets do not depreciate over time, ( L = I ) , or alternatively when debt is riskless, (Do?= = I ) , and the indicator is perfectly informative, ( p = 1) .

ProoE See Appendix. When the indicator is perfectly informative ( p = 1) , both the probability

of a good state given a bad indicator (pcs) and the probability of being in the bad state given a good indicator (pBC) are nil. Alternatively, both the probability of being in a good state given a good indicator and the probability of being in bad state given a bad indicator are equal to one. In t h s case, control rights are never transferred to the lender when the state is good because there is no covenant violation. Furthermore, all the surplus goes to the owner since the debt is riskless. When the indicator is bad, that is when the state is bad, control rights are always transferred to the lender who asks for repayment thereby forcing the owner to face all the losses.

In other words, when the debt is riskless and the indicator is perfectly informative, covenants contractually guarantee that the lender has no liqui- dation rights when the state is good so that the owner gets all the surplus.

bracket is the ex-ante utility from arm's-length financing while the second term in square brackets is the ex ante utility from Bank financing when there is no covenant.

They also g~larantee that the owner faces all the losses when the state is bad by giving liquidation rights to the lender. This is exactly what the First Best. contract accomplishes33. Note that, if the debt is not riskless, then the lender will face depreciation losses (I - L) even though the indicator is perfectly in- formative. A rational lender would expect this, and make the borrower bear the expected costs. Hence, a perfectly informative indicator is not sufficient to obtain the First-Best solution.

3.4 Bank Debt with and without Covenants: A Com- parison.

The U-aer's ex ante utility with bank financing when there are no covenants is given by equation (15) and the owner's ex ante utility with bank financing when there are covenants is given by equation (20). The difference between these two expressions can be written as:

The first two terms represent the Merences of expected surplus and de- preciation losses between the two contracts due to the difference in incentives to exert effort. The third term represents the difference between the effort levels implied by the two contracts. The last term is negative and represents a loss of efficiency due to the inefficient continuation that covenants permit when the indicator is good in spite of the state being bad.

Result 4 Ex ante, the manager prefers a bank debt covenants to a bank debt with no covenants if the ez post loss of ineflciency intmduced b y covenants is outweighed by the gains j b m exerting a higher efort level.

In other words, the difference between the ex ante utility from the two contracts is positive if:

(9: - qb.1 (x - I ) + (qf - qb.)(I - L) - (8: - > Q: [PBC (L - P B X ) ] (60)

"The recent literature on the theory of inaomplete contracts suggests the use of either short-term contracts with renegotiation design or long-term renegotiation-proof contracts to mjtjgate under-investment problems. For a extensive review of this literature, see Faris, (1 997).

Cove~iants int,rodnce a loss of efficiency because they allow ineffiricnt. cont,inuation when the indicator is good in spite of the state being bod. In other words, there is inefficient continuation when there is no covenant, violation even though the state is bad. A rational lender will anticipate this and will demand a higher face value than if the continliation decision were efficient,. This will reduce the slirplus available to the owner in the good state and her incentive to exert higher effort. Moreover, the residual value, X - Do*,, accruing to the owner with probability p s increases the attractiveness of the bad state, further reducing effort34.

But covenants also give the manager an incentive to exert higher effort since she can get all the surplus in the good state, when there is no covenant violation. Hence, a bank debt with covenants is preferred to a bank debt with no covenants when the benefits from exerting greater effort are higher than the loss of inefficiency introduced by covenants.

Note that this loss of efficiency can be written as a function of the preci- sion of the indicator, that is q: (1 - p - q: (1 - p ) ) (L - psX) . Differentiating equation (22) with respect to p and noting that L > peX, shows that the difference between the ex ante utility from a bank contract with covenants and from a bank contract with no covenants is an increasing function of the indicator's informativeness. In other words, the more precise the indicator the greater the benefits of including covenants in the bank debt contract, ceteris paribus.

Result 5 When the indicator is perfectly informative, ( p = I), a bank debt with covenants gives the manager an incentive to ezert greater effort than a bank debt with no covenants if her bargaining power, p, is low

I-L - enough. That is if p < 1 - 7 = p, qc(X L)

Proof: See Appendix When the indicator is perfectly informative, the payoffs to the manager

from a contract with covenants are the same as the payoffs from a contract with no covenants whenever the state is bad.

The situation is different when the state is good. Indeed, when there are no covenants, the payoffs to the manager depend on her bargaining power. The prospect of being held up and of bargaining over the surplus reduces the manager's incentives to exert higher effort. However, when there are covenants, the lender cannot extract rents.

"Rajan (1992) shows that the same effect obtains for the arm's-length debt contract.

53

When her bargaining power is low enough, a bank contract with covenants will give the manager an incentive to exert greater effort then a bank debt. with no covenants since she can increase the probability of being in the good state thereby getting all the surplus, by exerting higher effort.

Result 6 The owner's ex-ante utility from a bank debt with covenants is greater than the utility from c bank debt with no covenants, when the indicator 2s perfectly informative, ( p = I), and the omer ' s bargaining power is low enough ( p < pc) .

ProoE See Appendix When the indicator is perfectly mformative, the probability of the state

being bad given a good value of the indicator is zero. In this case, there is no ineaicient continuation and the resulting cost disappears. When the state is bad, the indicator is bad and there is efficient liquidation. Alternatively, when the state is good, the indicator is good but unlike the bank debt with no covenants, the bank has no control rights and cannot hold up the manager who will appropriate all the surplus. If the manager's bargaining power is low enough as shown in Result 6, she will exert more effort and the probability of success of the project will be greater when there are covenants. In this case, her ex-ante utility will be greater than that obtained in the absence of covenants and she will prefer a bank debt with covenants to a bank debt with no covenants.

3.5 Conclusion

This paper gives a rationale for the existence of covenants in loan contracts issued by banks. As a matter of fact, covenants reduce the cost of bank financing by contractually preventing banks from engaging in opportunistic behavior. In a context where there is collusion by banks, it is shown that it is socially optimal to include covenants in bank debt contracts.

Covenants are a source of inefficiency by allowing inefficient continuation, when they fail to indicate that a bad state has occurred. However, covenants are a source of efficiency when they restrain the lender from using her bar- gaining power, thereby dowing the borrower to obtain all the surplus in the good state. A bank debt contract with covenants is preferred by the bor- rower when these efficiency costs are outweighed by the gains from exerting a higher effort.

The inefficiency costs introduced by covenants .are a decreasing function of their precision. When the covenants are perfectly informative and the debt. is riskless, it is shown that a bank debt with covenants achieves First Best by contractually ensuring that the borrower faces all the losses in the bad state and all the gains in the good state. In addition, when the covenants are perfectly informative, a bank contract with covenants gives a borrower with low bargaining power an incentive to exert greater effort and is preferred to a bank debt with no covenants.

More informative covenants can be obtained, in practice, when accounting ratios indicate more accurately the true state of nature. Thus, this paper also shows that, for covenanis to increase the a c i e n c y of bank debt, accounting information has to be reliable and accurately measure the firm's financial health. When there is collusion between banks, as in emerging markets, policy makers should encourage the use of covenants coupled with sound accounting practice since these instruments can increase social welfare.

Diamond (1991) analyzes another type of cost of bank financing which is due to a short-term lender's actions at the refinancing date. The next section discusses the role of debt covenants in mitigating such costs.

3.6 Appendix

Proof of Result 2 Note that 5 = q: [(I - q:) (L - psX)] which is nonnegative since by as- sumption L > pBX.

Proof of Result 3

When p = 1, [ ] = [ ] and the optimization problem PBG PBB

Using the fact that I = L, it is can be shown that the solution of the opti- mization problem is ql ( P , 0) = A, which is exactly the First-Best solution.

Proof of Result 5 By assumption (I), ql (P, 9 ) is a decreasing function of P. The result is

then obtained by comparing the value of q l ( . ) at P: and P,' such that ql (BE) < q1 (Pi3

Proof of Result 6 This is a direct application of the previous result. The difference between

the ex-ante contract utility bct ions Lorn bank debt with covenants and from bank debt with no covenants is:

which is positive by Result (5).

References

[I] Berlin M. and J. Loeys, Bond Covenants and Delegated Monitoring, Jour- nal of Finance, June 1988, XLIII(2), pp. 397-412.

[2] Berlin M. and L. J. Mester, Debt Covenants and Renegotiation, Journal of Financial Intenedzatzon, 1992, 2, pp.95-133.

[3] Blackwell F., Comparison of Experiments, Proceedings of the Second Berkeley Symposium in Mathematzcul Statistics and Probability, Berkeley: University of California Press, J. Neyman (ed.), 1951, pp93-102.

[4] Carey M. S., S. Prowse, J. Rea, and G. Uddel, The Economics of the Private Placement Market, Board of Governors of the Federal Reserve System, December 1993.

[5] Davis A. H. R, and G. E. Pinches, Canadian Financial Management, Third Edition, 1997, Addison Wesley.

[6] Diamond D. W., Financial Intermediation and Delegated Monitoring, Review of Economic Stadzes, 51, pp393-414.

[7] Diamond D. W., Debt Maturity Structure and Liquidity Risk. Quarterly Journal of Economics, August 199 1, pp. 709-737.

[8] Easterbrook, F., TwwAgency Cost Explanation of Dividends, American Economic Review, 74, pp. 650-659.

[9] Fama, E., What's different about banks?, Journal of Monetary Eco- nomics, 15, pp. 29-39.

[lo] Far& J., Specific Investment, Incomplete Contracts, and Renegotiation, Mimeo, Dhpartement de Sciences ~conomi~ues, Universit6 de Montrkal, 1997.

(111 Hodgman, D., Commercial Bank Loan and Investment Policy, 1961, (Bureau of Business and Ekonomic Research, University of Illinois Chicago Preps, Chicago)

[12] Hoshi T.? A. Kashyap and D. Scharfstein, The Role of Banks in Reducing the Costs of Fin.mciai Distress in Japan, Journal of Financial Economics, 27, pp. 67-88.

[U] Hoshi T., A. KashyaP and D. Scharfstein, Corporate Structure, Liquidity and Investment: Evidence Lorn Japanese Industrial Groups, Quarterly Journal of Economics, 1991, 106, pp. 3560.

[14] Houston J. and C. James, Bank Information Monopolies and the Mix of Private and Public Debt Claims. Journal of Finance, December 1996, LI(5), pp1863-1889.

[15] James C., Some Evidence on the Uniqueness of Bank Loans, Journal of Financial Economics, 1987, 19, pp. 217-235.

[16] Kane E. and B. Malkiel, Bank Portfolio Allocation, Deposit Variability, and the Availability Doctrine, Quarterly Journal of Economics, 1965, 79, pp. 113-134.

(171 Lummer S. L. and J. J. McConnell, M h e r Evidence on the Bank Lend- ing Process and the Capital Market Response to Bank Loan Agreements, Journal of Financial Economics, 1989, 25, pp. 99-122.

[18] MacRae N., Sweaty Brows Slippery Fingers, The Economist, 1990, September 8, pp. 21-24.

[19] Milgrom P.R., Good News and Bad News: Representation Theorems and Applications, Bell Journal of Economies, Autumn 1987, (12), pp. 380-391.

[20] Modigliani F. and E. Perotti, The Rules of the Game and The Develop ment of Security Markets, 1990, Mimeo, M.I.T.

[21] Petersen M. A. and R. G. Rajan, The Benefits of Lending Relation- ships: Evidence from Small Business Data, Journal of Finance, March 1994, xLm(l), pp. 3-37.

[22] Rajan R., Insiders and Outsiders: The Choice between Informed and Arm'eLength Debt, Journal of Finance, September 1992, XLVII(I), pp. 1367-1400.

[23] Rajan R. an: -4. Kintor.. Covenanr-s and Collateral as Incentives to Monitor, -jourr..- of Finance. September 1995, L(4), pp.1113-11.16.

(241 Sharpe 5. A.. .L>mmetni Information, Bank Lending, and Implicit Contracts: A C-;Lized Mod< of Customer Relationships, Journal of Fi- nance, 19W. 4.5. ?p. 1069-105;.

[25] Smith C. W.. -k Perspective on Accounting-Based Debt Covenant Viola- tions, The -4cco~~~~~tin.g Revieu-. April 1993, Vo1.68, No.2, pp.289-303.

[26] Smith C. W. a d J.B. Wa-er, On Financial Contracting: An Analysis of Bond Covenz~s, Journal of Financial Economics, June 1979, 7(2),

[27] Sy A.N-R, k j t Covenanrz. Alaturity Structure and Agency Problems, Unpublished PiD. Dissertationt 1997, Faculty of Management, McGill Universih-.

[28] StigIitz. J. ui -4. Weiss. kcentives Effects of Terminations: Applica- tions to Credit ~d Labor Markets, American Economic Review, 1983, 73, pp. 912-927.

[29] Wood J...., C~mmerczal 3ank Loan and Investment Behavior, 1975, (John Wiley 8i Sms. London .

4 Liquidity Risk and Debt Covenants

4.1 Introduction

The costs of bank financing that are traditionally studied in financial eco- nomics are monitoring costs and bank regulatory taxes. However, the recent literature pays a particular attention to other limitations of bank financing. Diamond ( 1993) argues that relying exclusively on short-term private debt can be costly because borrower control rights are not considered by the lender when determining whether to roll over a loan or call the loan back and force liquidation. By borrowing from both public and private sources, borrowers can reduce the private lender's control and reduce costly liquidations. Rajan (1992) and Sharpe (1990) discuss another cost of relying exclusively on pri- vate debt called information monopoly. The risk of not being able to refund debt because of deterioration in financial or economic conditions can moti- vate firm to lengthen the maturity of their debt. In Sharpe (1991), Diamond (1991) and Titman (1992) bad news arrive at the refinancing date, causing investors not to extend credit or to raise the default premium on new debt. Even if this extreme outcome is not realized, short-term debt can still cause a loss of project rents if it has to be refinanced at an overly high interest rate because of credit market imperfection [see F'root, Scharfstein and Stein (1993)]. Finns may also experience deadweight indirect costs of financial d i s tress, (e.g. loss of customers and distraction of management when they lose access to attractively priced credit). Guedes and Opler (1996) empirically validate Diamond's model (1991b). They find that large firms with high credit ratings borrow short and long-term maturity debt whereas speculative grade credit ratings firms borrow debt with an intermediary maturity.

While liquidity risk gives some firms an incentive to borrow long-term, they may not be able to do so because the rate of return required to com- pensate investors for bearing long-term credit risk can induce substitution into risky low-quality projects [see Diamond (1991) and Stiglitz and Weiss (198 I)]. Diamond ( 1991) argues that speculative grade credit ratings issue the lAgest possible term in order to avoid the risk of costly premature liq- uidation. However, these firms are not able to borrow as long-term as they would like because they are screened out of the long-term bond market by

moral hazard problems that, arise when the required rate of return induces risk-shifting. Thus, low quality firms can be screened out of the lon, = term debt market and only stable firms with high credit quality (e.g. large firms) may end up being able to borrow in the long-term credit market. This effect is similar in the corporate bond markets [see Rizzi (1994)l.

This paper is an extension of Diamond (1991) and includes long-term debt contracts with covenants in the analysis of liquidity risk. Diamond (1991) analyzes debt maturity choice as a tradeoff between a borrower's preference for short-term debt due to private information about the future credit rat- ing, and liquidity risk. Liquidity risk is the risk that a solvent but illiquid borrower is unable to obtain refinancing. For example, liquidity risk arises when some borrowers who are Liquidated would invest their own capital (if it were available), even without using their private information, to avoid de- fault. Short-term lenders liquidate too often from the borrower's point of view because there are constraints on pledging future rents to lenders: the amount that can be pledged to lenders may be less than the value from liquidation, yet the total future rents exceed the liquidation value. These constraints arise from many possible sources like private information by bor- rowers, moral hazard, and monitoring costs.

The focus of this paper is on the role that debt covenants can play in mitigating such costs of bank financing. The main result shows how these contractual arrangements can reduce liquidity risk, and are positively vdued by firms with investment grade credit ratings. The intuition is that covenants give control rights to the lender only when they are breached, whereas short- term debt always assigns all the control rights to the creditor at maturity date. When covenants are always breached, the debt contract with covenants is similar to a short-term debt. But, in the case where a downgrade of credit ratings does not imply a breach, the borrower avoids losing her control rents. The conflict region due to excessive liquidation by short-term lenders is thereby decreased when covenants are introduced. The resulting reduction in liquidity risk can give an incentive to a bank, who cannot lend to some good borrowers because of liquidity risk, to include covenants in the debt contract, in order to attract such debtors. F'urthermore, it is shown that, such a debt contract is similar to a mix of risky short- and long-term debt contract. This result is consistent with the current literature in banking which suggests the use of a mix of debt with different maturities to reduce the costs of bank financing.

Section 2 outlines the basic model, and section 3 describes the idormation

arrival stnicture, as well as the different debt contracts that will be analyzed. Section 4 analyzes the role of covenants in reducing liquidity risk. Finally section 5 concludes the paper.

4.2 The Model A borrower with no initial capital seeks to fund an indivisible investment project. The project's ex-ante prospects and the ex-post cash flows are pri- vate information and are observed only by the borrower. The borrower's project can be liquidated. If it is liquidated, the borrower can be prevented from consuming its current or future cash flows and control rents. In this case, an optimal financial contract is a debt contract enforced by the right to liquidate if the debt is not repaid in fdl.

Borrowers and lenders are risk neutral. Lenders consume at date 2 and have a constant returns-to-scale investment technology that returns R per unit invested per period. One unit invested at date 0 returns R units at date 1; and if invested until date 2, the terminal value is R2. A borrower with a given credit rating can borrow as long as lenders receive an expected retum of R per period, per unit loaned.

There are two types of projects, and each borrower has one type of project. The borrower's type is his private information. Both types require $1 in (outside) capital at date 0 and produce cash flows only on date 2 (none on date 1). Each project yields a cash flow of X > 0 when successful, and each project also produces nonassignable control rent of C if the management has control at date 2. All projects can be liquidated at date 1 for a value of L. A successful project yields a higher retum when not liquidated, because L < 5. Projects have no liquidation value at date 2. The two types of project differ only in the probability that the return X is received. Finally, the two types of borrowers are as follows: type G borrowers have a project that returns a cash flow of X > R2 for sure at date 2. This is a positive net present value project in terms of cash flows. Type B borrowers have a project that returns a cash flow of X with probability w and returns zero with probability 1 - T .

F'urthermore, nX < RZ and the project has negative net present value in terms of cash flows.

Lender's information about a borrower is the credit rating. As of date 0, it is as follows. A borrower has credit rating f if lenders assign the borrower a probability f to being type G and 1 - f to being type B. Recall that the borrower knows her own type- The lower a borrower's credit rating, the

higher is the promised interest rate, due to the higher default rate of type B. As of date 0, the probability of repayment of a loan maturing on date 2 is x + f (1 - a). Information about each borrower arrives at date 1 as described in the next section. A summary of the notations used is available in the appendix.

4.3 Debt contracts

4.3.1 Information Arrival

Information about borrowers arrives privately to lenders at date 1 and is not verifiable, so contracts written contingent on the information cannot be enforced. However, a contract based on an indicator of the true state of nature can be written. If borrowers refinance or renegotiate at date 1 the terms of the new contract will depend on the information, since the credit rating will be either updated or downgraded.

Assume that there are only two realizations of information at date 1. Denote the credit rating (conditional probability that a borrower is of type G) given an upgrade by fu and rating given a downgrade by f d , such that f > f > f the probability of being of type G is greater given an upgrade than given a downgrade.

Assume also that type G borrowers receive downgrade or an upgrade but all type B borrowers receive a downgrade, implying that fu = 1 because only type G borrowers receive an upgrade. Let e denote the probability that a type G borrower receives a downgrade (1 - e is the probability of an upgrade for a type G). Because all type B borrowers are downgraded, Bayes' Law implies that e = [f (1 - f )] / [f (1 - f d)] where f is the credit rating given a downgrade and f is the initial (date 0) credit rating of the borrower.

4.3.2 Debt Contracts

Long-Term Debt Contract with no covenants Long-term debt with- out renegotiation is debt floated at date 0 that matures a t date 2, with no renegotiation at date 1. The face value p of this debt is set so that lenders who lend $1 at date 0 get an expected return of R2, realizing that debt is repaid with probability r + f (1 - r) . The face d u e of a long-term bond is

given by

if p 5 X. If p > X then borrowers with credit rating f cannot borrow long-term because they cannot provide lenders with an expected return of R2.

Let FU and qd denote the date 1 market value of the long-term debt given, respectively, an upgrade and a downgrade. Given an upgrade, the long-term debt is repaid for sure, and its date 1 market value is

Given a downgrade, the long-term debt is repaid with probability qd e R + f (1 - T ) , and its date 1 value is

Because long-term lenders do not have liquidation rights, the information at date 1 does not influence the face value of the long-term bonds and does not lead to liquidation. However the information does influence the secondary market value of that debt. If pU is the date 0 probability of an upgrade and pd is the date 0 probability of a downgrade, then the lender will require that pUV;Y + pd&d = R2. The face value of the long-term debt contract with no covenants can be written as:

Short-Term Debt Contract Short-term debt is financed at date 0 and matures at date 1 with face value T I . The date 1 repayment comes either fiom refinancing at date 1 at interest rates contingent on the realization of date 1 information or fiom the proceeds of liquidation at that date. Refinanced debt issued at date 1 matures at date 2. Let rU and P (with no subscript) denote the face value of refinanced short-term debt that matures on date 2, given respectively, an upgrade and a downgrade at date 1.

The face value of short-term debt issued at date 1 is set so that given information about a borrower at that date, lenders at date 1 get an expected return of R per unit invested. The mount that must be raised at date 1

depends (among other things) on r , , the face value of short-term debt issued at t = 0.

When the borrower cannot repay in full at date 1, the decisions made at. that time serves the interests of date 0 short-term lenders, because they have the control rights to force liquidation when they are not paid in full. Suppose that the face value of the refinanced debt at date 1, given a downgrade is rd. The debt issued by downgraded borrowers at date 1 will be repaid at date 2 with probability qd = 7r + fd (1 - T ) (and repays 0 with probability 1 - q d ) . Debt with face value rd raises $$ on date 1. The debt maturing

at date 1 can be repaid in full by a new debt issue if $$ > r l , because X is the most a borrower can pay. At date 1, if the maturing debt cannot be repaid in M, lenders choose the resolution that maximizes their payment and either liquidate to get a value of L or accept the maximum that a new debt issue can raise i.e. G. The value of date 1 repayment received by a date 0 short-term lenders given a downgrade is

Short-term borrowers who receive an upgrade rehance to pay the full value of their date 0 debt: they pay rl on date 1, and the value on date 1 of date 0 short-term debt to an upgraded borrower is V: = r l . this debt maturing at date 2 is riskiess because it is repaid with probability 1; the face value of debt issued at date 1 with good news is then ru = rlR.

Let p' be the probability that news j arrives for a borrower of unknown type. Note that the probability that a borrower of unknown type receives an upgrade is pU = (1 - e) f and the probability that a borrower of unknown type receives an downgrade is pd = 1 - pU. The expected return of a t = 0 short-term lender is purl + pd v. Since the lender expects a return of R per unit invested,

Using the same model, Diamond (1991) shows that, when there is no liquidation on a downgrade, type G borrowers of all credit ratings prefer the short-term debt contract to the long-term debt contract with no covenants. The intuition is as follows. When the liquidation decision is not affected, increasing the payment by those who get a downgrade lowers the expected financing costs of type G borrowers who are less likely than average to get a

downgrade. In this case, type G borrowers desire the largest possible value of Vd, the value of the amount received by lenders from borrowers who get a downgrade, when there is no liquidation. Since Vd is always higher for short- term debt than for long-term , because either the face value of the debt is increased, or there is liquidation that yields more than increasing the face value. type G borrowers will prefer the short-term debt contract. Similarly, when there is liquidation on a downgrade, Type G borrowers of all credit ratings prefer the short-term debt contract, when their control rents (C) are zero.

However, when there is a liquidation on a downgrade, but the control rmts are positive, there may be a conflict between some type G borrowers and the short-term lender over the Liquidation decision. The disagreement is due to the fact that short-term lenders liquidate whenever type G borrowers - would desire it, and at other times a s well. The reason is that lenders cannot benefit from the control rents C, since they cannot be pledged. Diamond suggests the use of a mix of riskless senior short-term debt and junior long- term debt to solve this c o ~ c t .

The next sections characterize a long-term debt contract with covenants and show how it can reduce excessive liquidation. The intuition is that, covenants, by denying control rights to the lender when they are not violated, will enable type G borrowers to consume their control rents. Furthermore, it will be shown, that the long-term debt contract with covenants is similar to a mix of risky short- and long-term debt contracts.

Long-Term Debt Contract with Covenants Long-term debt with covenant is debt Boated a t date 0 that matures at date 2. To avoid cumbersome nota- tion, I denote the face value of this debt +R so that its date 1 present value is $. If this debt has no covenant, then it is similar to the long-term debt contract described above. By adding covenants, the lender will be given some power to accelerate maturity by demanding repayment, but only if there has been a breach of covenant.

Following Rajan and Winton (1995), I assume that a covenant is a private verifiable signal such that a t date 1 there is either a breach of covenant with probability @ or there is no breach with probability 1 - 4. Whennore, collecting evidence for the verifiable private signal q5 allows the lender to observe the credit rating of the borrower at no additiond cost.

First suppose that there is a breach of covenant, then two situations

can occur. The credit. rating of the borrower may have been upgraded or downgraded. In the first case, the lender waives the covenant and rolls over the debt, since only type G borrowers receive an upgrade. The date 1 value of the long-term debt contract given a breach and an upgrade is then

If the borrower's credit rating has been downgraded, then the lender takes the action that maximizes her payoff. The date 1 value of the long-term debt contract given a breach and a downgrade is then

Now, suppose that the covenant is not breached. In this case, the lender has no rights whatsoever to demand repayment or liquidate the finn. The date 1 market value of the long-term debt contract given no breach and an upgrade is

v; = + (70)

and the date 1 market value of the long-term debt contract given no breach and a downgrade is

At date 0, the lender requires a one-period return of R so that,

The face value3' of the long-term debt with covenant can thus be written as

" ~ l ternatively, one can arri t e:

so that,

since fU = 1, by assumption.

The following propositions analyze the debt. contmct with respect. t o the stringency and precision of t-he covenants

Proposition 1 (Stringency) If the covenants are extremely stringent, so that they are always breached, (4 = 1) , then the long-term debt contract with covenants is equzvalent to a short-term debt contract. If the covenants are ext~emely lenient, so that the covenants are never breached, ( 4 = 0 ) , then the long-term debt contract with covenants is similar to a long-term debt contract with no covenants.

When the ex-ante probability of a breach is one, i.e. 4 = 1, the ma- turity of the long-term debt with covenants is always accelerated at t = 1, as covenants are always breached at this date . The long-term debt with covenants collapses then, to a short-term debt since both the lender and the borrower are in the same situation as in a short-term debt contract. Contrac- tually, the lender has the right to force repa ent at date 1, thus deciding to roll over the debt or liquidate the h, @ = v:). Such a case occurs when the covenants are so stringent that they are always violated at date 1. Alternatively, when the ex-ante probability of a breach is nil, that is when 4 = 0, the long-term debt with covenants collapses to a long-term debt with no covenants. Since covenants are never breached, the lender has no right to accelerate the maturity of the debt, and cannot act upon date 1 information. The lender is then, in the same situation as a the lender of long-term con- tract when there are no covenants. The following proposition obtains similar results for extreme values of precision of the covenants.

Proposition 2 (Pmision) If the covenants are very precise, so that there is always a breach on a downgrade, (1: = 1) , then the long-term debt with covenants is equivalent to a short-term debt. If the covenants are very im- pncise, so that them is never a breach on a downgrade, (ff = 0 ) , then the long-term debt utith covenants is equivalent to a long-term debt contract with no covenants.

Covenants can be seen as extremely precise, when they indicate that the bad state has occurred with probability one. When the probability of a breach given a downgrade is one, (ff = 1) , a downgrade will automatically trigger a breach of covenants, thus giving the lender control rights. In this case, forced repayment by the lender at date 1, accelerates maturity and the long-term debt with covenants is similar to a short-term debt contract. When

covencants are so imprecise, that they totally fail to indicate that, the bad state of nature has occurred, when it actually does occur. the lender has no contractual rights to demand repayment and cannot use date 1 information to adjust the face value of the debt. This situation arises when the probability of a breach given a downgrade is nil, (f,d = 0) .

The next results show that, when there is a conflict over the liquidation decisions between the short-term lender and Type G borrowers, the intro- duction of covenants in a debt contract can reduce liquidity risk. Recall that when there is no liquidation on a downgrade, Type G borrowers prefer the short-term debt contract. Suppose that type G borrow short-term, and that there is liquidation on a downgrade. If type G borrowers could instruct lenders as of date 0 on their prefened resolution of debt given a downgrade (when there is liquidation on a downgrade), then they would request a liq- uidation if L > + (which is equivalent to f d 5 :,";'zY = P ) .

- -

However, the condition for lenders to liquidate is L > (which is equiv- alent to f d 5 = A, set . A > p). Type G are not in agreements with lenders over liquidation decisions when f d E (P, A) because the lender does not consider the control rents while deciding whether to liquidate or not. When this conflict arises, Type G borrowers whose downgraded credit rating f d , is such that f E (& A) will not borrow from a short-term lender. The foilowing analysis is restricted to the case when there is a liquidation on a downgrade, and there is a conflict between the short-term lender and Type G borrowers, as characterized by Diamond (1991). In this context, it will be shown that debt covenants can reduce liquidation risk.

4.4 Liquidity Risk and Debt Covenants

Lemma 1 Type G borrowers prefer a liquidation when there is a breach on a downgrade zf their control rents are such that:

w h e ~ cp = -1 is the of o bamtuer being of type G r-lte pd/f

given a loss of control rights. Pmot See appendix.

The next lemma uses this result to show that, type G borrowers will prefer a liquidation on a downgrade if lenders take into account their control rents.

Lemma 2 Suficient conditions for type G borrowers to prefer liquidation when there is a breach on a downgrade are the absence of control rents, C = 0, and liquidation yielding suficiently high proceeds: L > ( g d ~ + @) / R . Lenders liquidate on a breach follouring a downgrade zf L > qdX/R. If L E [ q d ~ , ( q d ~ + c p ~ ) ] , then lenders liquidate too often.

Proof: See appendix.

Lenders liquidate whenever the proceeds of liquidation exceed the gains From continuation. Since control rents cannot be pledged, financiers do not take them into account when assessing the liquidation decision. Type G borrowers make a trade-off between the loss of control rents when they lose their control rights, versus the extraction of higher repayment horn borrowers who are liquidated given a downgrade on a breach. As a consequence, there is a conflict region where lenders liquidate when Type G borrowers would have preferred them not to do so.

Lemma 3 If there is liquidation when there is a breach on a downgrade, then the long-term debt with covenants is a weighted average of the short-term debt and the long-term debt with no covenants, that is,

= + (1 - a) (p/R) where a = puff E [0, 11 pU + pdfidQd

(76)

Pmofi See appendix.

The value of the long-term with covenants, given a breach on a downgrade is = max is also the value of a short- term debt contract when downgrade. When there is liquidation on a downgrade, the value of the long-term debt with covenants given a breach on a downgrade is similar to the value of the short-term debt given a downgrade, (v: = Kd = L) . Noting that, the face value of a long-term debt with no covenants is not affected by date 1 information, it is possible to show that long-term debt contract with covenants is a mix of short-term debt and long-term debt with no covenants. The weight, a, can be interpreted in the following fashion. First, note that the lender of a long-term debt contract with covenants expects to receive the face value r(,

with pobability pU + pd f2dqd, and the value = m a s [q, L] with proba-

bility pd f ,d. Rewriting pU + pd ft$ as pu f f + (pu + pdqd) f& it is possible to interpret cr as the conditional probability of repayment of r,, the face valt~e of the short-term debt, and (1 - a) as the conditional probability of re- payment of p/R, the face value of the long-term debt with no covenants,

The numerator of a is the ex-

ante probability of repayment of rl multiplied by the probability of a breach given a downgrade, while the numerator of 1 - a is the ex-ante probability of repayment of p/R, multiplied by the probability of no breach given a down- grade. Note that the results found earlier are obtained, that is if f,d = 1

? (ff = 0) then a = 1, (a = 0). In short, when there is liquidation following a breach on a downgrade,

the long-term debt with covenants is similar to a mix of short- and long- term debt contracts with no covenants. The lender expects to receive the face value of a short-term debt with probability a, and the face value of a long-term debt with no covenants, with probability 1 - a. The parameter a is the conditional probability of repayment of a short-term debt, where expectations depend on the probability of a breach given a downgrade which is also the probability of the lender having control rights. Next, the main result of the paper is obtained using the previous lemmas. It shows how debt covenants can reduce the conflicts between type G borrowers and lenders over their liquidation decisions.

Proposition 3 When there is liquidation on a downgrade, a debt contract with covenants reduces the conpicts due to liquidity risk, if the probability of a bzach given a downgrade (ft) is such that 0 < f,d < 1. The resulting debt contract is comparable to a mix of short-tern and long-tern debt contract with no covenants.

Proof. See Appendix.

As can be seen from Figure 1, covenants can reduce the conflict between type G borrowers and lenders. In fact, note that, when the probability of a breach given a downgrade is one, (f ,d = 1) , the long-term debt contract with covenants collapses to a short-term debt. In this case a breach of covenants is equivalent to a loss of control rights, and the confiict region is the area be- tween the vertical line (L = # XI R) , and the line (L = (#XI R + cp (1) C/ R) ). As the probability of a breach given a downgrade decreases, (0 < ff < 1) ,

Type G borrowers lose their control rights only if there is a breach of covenants following a downgrade. This can be seen as forcing the lender to take into account the borrowers control rents, when there is no breach. The con- flict region is then reduced and is now the area between the vertical line (L = g d ~ / ~ ) , and the line (L = ( q d ~ / ~ + cp (f;') CIR)).

Type G borrowers who had refused a short-term debt contract can now be attracted by a lender who includes covenants in the contract. Furthermore, the debt contract with covenants is similar to a mix of short- and long-term debt contracts.

4.5 Conclusion

This paper offers a new rationale for debt covenants as contractual arrange- ments that can mitigate the costs of bank financing. In particdar, it has been shown that Liquidity risk can be reduced by assigning control rights to a lender, only when covenants are breached. In contrast, short-term debt always give all the control rights to the lender at the maturity date. In this context, borrowers with investment grade credit ratings, whose control rents are not negligible may shy away from short-term debt. The introduction of covenants, by reducing the events when the lender has control rights can prove attractive to such borrowers. In practice, this could be similar to a borrower placing debt privately. Models of private placement are very scarce in the financial literature (see Carey et Al., 1993). This paper can be seen as an attempt in this direction.

4.6 Summary of Notation

f = Probability that a borrower is of type G, given date 0 public information, (credit rating); f d = Probability that a borrower is of type G, given a downgrade at date 1; fu = Probability that a borrower is of type G, given a upgrade at date 1; n = Probability that a type B borrower repays at date 2, (probability that the project is successful) ; qd = Probability that a borrower who receives a downgrade repays at date 2, qd = r + fd ( l - R); X = Return of a successful project (Type G project succeeds with certainty) ; C = Control Rent of a project not liquidated before date 2; e = Probability that a type G borrower receives a downgrade, e =

f 1-fd , w p" = Probability that a borrower of unknown type receives an upgrade, pu = (1 -e ] f; pd = Probability that a borrower of unknown type receives an downgrade; R = Expected Return required by lenders on a one-unit investment, per period; p = Face value of long-term debt, maturing at date 2; T I = Face value of short-term debt, maturing at date 1; rd = Face value of short-term debt, maturing at date 2, issued after a down- grade at date 1; rU = Face value of short-term debt, maturing at date 2, issued after an upgrade at date 1; L = Date 1 proceeds of liquidation; Vd = Date 1 market value of a debt contract given a downgrade;

= Date 1 market value of a short-term debt contract given a downgrade; Kd = Date 1 market value of a long-term debt contract given a downgrade; V: = Date 1 market value of a short-term debt contract given a upgrade; KU = Date 1 market value of a long-term debt contract given a up&ade; 3 = Face value of long-term debt with covenant, maturing at date 2; 4 = Probability that a borrower of unknown type breaches the covenant; fr = Probability of a breach given an upgrade; j; = 1 - f? = Probability of no breach given an upgrade; f;d = Probability of a breech given a downgrade;

f! = 1 - ft = Probability of no breach given a downgrade p = Probability that, a borrower is of type G given a loss of contlrol rights

Tbe Conflict Region

4.7 Proofs

Proof of Lemma 1. The payoff of a type G borrower, when there is liquidation on downgrade

following a breach of covenants is:

The payoff of a type G borrower, when there is no liquidation on down- grade following a breach of covenants is:

X + C - -a v'R) + ~ ; ( X + C - $ R ) + (1 - e) [X + C -+R] Q

VP d = x+C-R[e (Vbf l +$f2") + ( ~ - e ) d ]

I = d d d P"+P f 2 q

VP = x+c- [ (e f t ) V, + ( I - 'f" pu +@fild

= X + C - R2

- pdf:vfl P" + pdfidsd (1 - eft) - R V ~ (ef,d)

d d d

where cp = P " + P f i 9 + e f f

PdfP (1 - eff)

Noting that f = ,$& and that sign {$ - $1 = sign { f f p d (1 - e) [qd - f ) ,

75

implies that. [$ - $1 > 0, since q" f d + K (1 - f d , > f d . 111 this case, dtn01'4 .- > 0.

Vt A type G borrower will prefer a liquidation on a downgrade following a

breach of covenant if her payoff is greater when there is liquidation, that is if

This RHS expression is decreasing in C, and decreasing in V'. The pa- rameter p is the probability of borrower being of type G given a loss of control rights. To see that, note that the probability of a loss of control rights given that the borrower is of type G Is efi? The unconditional probability of a loss of control rights is pdf,d, and the probability to be a type G borrower given a downgrade is f . The probability to be of type G given a loss of con-

efid f trol rights is then, $&. Realizing that the unconditional probability of no

loss of control rights is pu + $ figd = (1 - e ff) f ,and substituting for f implies that the probability lo be of type G given a loss of control rights is

Proof of Lemma 2.

Using Lemma 1, and noting that.. V: 5 $, a necessary condition for the type G borrower to prefer liquidation on a downgrade when there is a breach is:

Proof of Lemma 3. Rapd f vd The face value of a long-term debt with covenants is $ = pu+pdilddd where

= min [$+ax (q, L)] . Recall that the face values of the short-term

debt contract and the long-term debt contract are respectively, rl = 9, and p = Solving for a E [0, I] , such that 11, = arl + (1 - a) ( p l R) gives the following expression:

If there is always a Liquidation when there is a breach on a downgrade , then = = L, and

Proof of Proposition 3. If f ,d = 1, then the debt contract with covenants is similar to a short-term

debt contract and, cp = fd. Suppose that a type G borrows horn a short- term lender. If type G borrowers could instruct lenders as of date 0 on their preferred resolution of debt given a downgrade (when there is liquidation on a downgrade), then they would request a liquidation if L > + 9 (which is

equivalent t,o f 5 e;_"zy p, s.t.X > P ) , as shown in Lemma 2. However,

the condition for lenders to liquidate is L > (which is equivalent to . - fd < - p A).

Type G are not in agreements with lenders over liquidation decisions when fd E (0, A) because the lender does not consider the control rents while deciding whether to liquidate or not. When this conflict arises, Type G borrowers whose downgraded credit rating fd, is such that f E (P , A) will not borrow from a short-term lender. However, when 0 < f ,d < 1, they will accept a long-term debt contract with covenants. To see this, first note that:

- - e ( ~ - e) [ f d - qd] < 0, since

(1 - ef t )*

The conflict region behueen type G borrowers and a lender, can be seen as the following difference:

so that,

Since T (1) = [L - (4x1~ + fdc/~) - [L - ~ X I R ] ] is the conflict region for a short-term debt contract,

The conflict region is reduced as the probability of breach given a downgrade decreases. Lemma 2 shows that the debt contract with covenants is similar to a mix of short-term and long-term debt with no covenants.

References

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5 Conclusions and Future Research The first section of the dissertation analyzes the role of covenants in reducing overinvestment problems. The covenants considered in the model restrict the firm's investment policy. They control overinvestment incentives by reducing investment in negative-NPV risky projects. However, in so doing they cre- ate an underinvestment problem by preventing investment in positive-NPV projects. The optimal debt contract with covenants is such that it balances, ex ante, the marginal gains form a reduction in overinvestment with the marginal costs from an increase in underinvestment. In practice, a borrower has the choice between debt contracts with different covenant and matu- rity structures. The effects of such debt characteristics on the borrower' s choice of source of financing are analyzed. The long-term debt contract with renegotiation modeled in this paper shares many characteristics with Privately Placed Debt while the long-term debt contract with no renegoti- ation is comparable to Public Debt. As for the short-term debt contract, it can be thought of as a Bank Debt. Comparing the borrower's ex-ante profit from Privately Placed Debt to those from Public Debt, it is shown that the borrower values positively the option to renegotiate embedded in Privately Placed Debt. However, this enhanced flexibility is costly in the sense Privately Placed Debt has more stringent covenants then Public Debt.

The main results of this paper show that, when agency problems are not important, or equivalently, when the manager's control rents are negligible and the lender's monitoring technology is high, the borrower's ex-ante profits from Bank Debt are higher than those from Privately Placed Debt while Public Debt is the least valuable contract. However, when agency problems are considered, Bank Debt is the least valuable contract. This is the case because both Public and Privately Placed Debt permit a firm to continue operating as long as the covenants are not violated. Bank Debt, on the contrary, forces the manager to renegotiate the terms of the loan at the maturity of the contract. In this setting, the liquidation of a type B firm and

the subsequent gain in efficiency is more likely for a Bank Debt. Since in this paper the lender earns zer~expected profit, all the surplus go= to the borrower who prefers Bank Debt to long-term debt contracts. Also, Privately Placed Debt is preferred to Public Debt because, by having more stringent covenants, it reduces the efficiency losses due to the type B firm investing in negative-NPV projects. However, when control rents are considered, Bank Debt is not preferred because of the higher liquidity risk it entails. The model suggests that a manager would prefer Privately Placed Debt or Public Debt to Bank Debt only if agency problems are high enough. Such a reason would be negatively perceived by investors which is consistent with empirical evidence. It is also shown that, when control rents are ignored and the monitoring technology is high enough, growth firms' managers prefer private debt to public debt. However, Bank Debt can be less attractive than Privately Placed Eebt because of the risk of excessive liquidation.

The second section gives a rationale for the existence of covenants in loan contracts issued by banks. As a matter of fact, covenants reduce the cost of bank financing by contractually preventing banks born engaging in o p portunistic behavior. In a context where there is collusion by banks, it is shown that it is socially optimal to include covenants in bank debt contracts. Covenants are a source of indciency by allowing inefficient continuation, when they fail to indicate that a bad state has occurred. However, covenants are a source of efficiency when they restrain the lender from using her bar- gaining power, thereby allowing the borrower to obtain all the surplus in the good state. A bank debt contract with covenants is preferred by the bor- rower when these efficiency costs are outweighed by the gains from exerting a higher egort. The in&ciency costs introduced by covenants are a decreasing function of their precision. When the covenants are perfectly informative and the debt is riskless, it is shown that a bank debt with covenants achieves First Best by contractually ensuring that the borrower faces all the losses in the bad state and all the gains in the good state. In addition, when the covenants are perfectly informative, a bank contract with covenants gives a borrower with low bargaining power an incentive to exert greater effort and is preferred to a bank debt with no covenants.

Finally, the last section offers additional support to the thesis that debt covenants can be seen as contractual arrangements that can mitigate the costs of bank financing. In particular, i t has been shown that liquidity risk can be reduced by assigning control rights to a lender, only when covenants are breached. In contrast, short-term debt always give all the cont.ro1 rights to

the lender at the maturity date. In this context, borrowers with investment gade credit ratings, whose control rents are not negligible may shy away from short-term debt. The introduction of covenants, by reducing the events when the lender has control rights can prove attractive to such borrowers.

Barclay and Smith (1992,1995a, b) provide interesting stylized facts which show that, in practice, all debt financing is not the same. Debt contracts differ in several important respects like maturity, convertibility, covenant r+ strictions, call provisions, security and whether the debt is privately placed or publicly held. This dissertation is an attempt to analyze the importance. and role of debt covenants in this context. h t u r e research should consider empirical tests of the predictions of the theoretical models. A current exciting research agenda studies corporate reliance on bank financing, and the deter- minants of corporate debt maturity structure. The analysis of debt covenants in this framework could yield interesting insights. The next section reviews this hterature.

5.1 Models of Choice between Public and Private Debt Market hictions such as informational asymmetries and agencies costs may explain why capital does not always flow to firms with positive net present values. In their seminal work [Credit Rationing in Markets with Imperfect In- formation], StigLitz and Weiss(l981) argue that in most markets, price adjust to equate-demand and supply but this is not necessary true for the capital market. Indeed, the capitd market is special in that the interest rate need not always adjust to clear the market. They show, that the rate charged to an ex ante observationally equivalent group of borrowers, determines not only the demand for capital but also the riskiness of the borrowers. A higher interest rate either draws riskier applicants [Adverse Selection Effect] or in- fluences borrowers to choose riskier investment [Moral Hazard Efftxt). If an increase in the interest rate lifts up the average riskiness of borrowers: lenders may partially choose to ration the quantity of loans they gan t rather than increase the rate to clear the market.

Developing on this, Leland and Pyle (1977); Campbell and Kracan. (1980); Diamond (1984); Fama (1985); Haubrich (1989) and Diamond (1991a) de- scribe how large institutional creditors can partially overcome these frictions by producing information about the firm, and using it in their credit deci- sions. If scale economies exist in information production and information is durable and not easily transferred, then a firm with close ties to a financial

institutions should have a lower cost of capital and greater adab i l i ty of funds relative to a firm without such ties. These ties are usually referred to as relationships in the financial literature. Note however, that Blackwell and Santomero (1982) do not accept this thesis. Hoshi, Kashyap and Scharfstein, book (1990, 1991) provide evidence that firms in Japan with close ties are less liquidity cons trained. James (l987), Lumrner and McConnell ( 1989) and James and Wier (1990) h d that the renewal of bank loans is a good signal in the stock market. This result is also obtained by Shockley and Thakor (1992) for loan commitments. Diamond (1991a) argues that if lenders remain at arm's length, management can indulge in pet projects, shift risk toward the fixed claims creditors or otherwise misuse the borrowed funds. As a re- sult, small and young firms can rarely borrow in the public capital markets and we should expect h-credi tor relationships to be very important.

5.1.1 Costs and Benefits of Bank Lending

Models of choice between public and private debt generally argue that p u b Lic debt is diffusely held, while the ownership of private debt is concentrated in a few lenders. Furthermore, restructuring of public debt is governed by the Trust Indenture Act of 1939 which makes the modification of public debt contracts more difficult than private debt contracts. [see Smith and Warner (1979) and Gertner and Scharfstein (1991)l. Smith and Warner (1979); Blackwell and Kidwell (1988) and Diamond (1984, 1991) and Berlin and b e y s (1988) argue that these differences, ceteris paribus, imply that public debt has higher agency costs relative to private debt. This reduces the incentives of bondholders to engage in costly information production and monitoring. Monitoring by a large number of bondholders is also inefficient since it involves needless duplication of monitoring costs.

In contrast, the concentrated ownership of private debt claims reduces the free rider problems and increase overall information production as well as monitoring. It also increases control over investment and liquidation de- cisions of the borrower, [see Boyd and Prescott (1986) and Berlin and Loeys (l988)]. Diamond (1984) argues that better ex-ante information and in- creased control will reduce adverse selection and moral hazard problems. Smith and Warner (1979) and Barclay and Smith (1995) argue that smaller firms and firms with a higher proportion of intangible assets are expected to rely primarily on bank financing because if information asymmetries and agency costs of debt are large, then the benefits of private borrowing are

large too. In contrast, Diamond (1993) argug that relying exclusively on short-term private debt can be costly because borrower control rights are not considered by the lender when determining whether to roll over a loan or call the loan back and force liquidation. By borrowing from both public and private sources, borrowers can reduce the private lender's control and reduce costly liquidations. Rajan (1992) and Sharpe (1990) discuss another cost of relying exclusively on private debt called information monopoly. In fact, the costs of bank hancing that are traditionally studied are monitoring costs and bank regulatory taxes.

Lending Relationships and Information Monopoly Diamond, (199 la) argues that the longer a borrower has been servicing its loans, the more likely the business is viable and its owner trustworthy. Conditional on its past ex- perience with the borrower, the lender now, expects loans to be less risky. This will decrease the expected cost of lending and increase the willingness to lend. Interaction over time is also important in other ways. For example, the lender could get information from the firm's past interactions with other fixed claim holders like employees and prior creditors. In this case, the age of the firm should determine the lender's cost and availability of funds. Al- ternatively, the information may not be observable to outsiders. In this case, the length of relationship should exert an independent influence. Relation- ships, in addition to interaction over time, can be built through interaction over multiple products. This will increase the precision of the lender's in- formation about the borrower. For example, the lender can learn about the firm's sales by monitoring the cash flowing through its checking account or by factoring the h ' s accounts receivables. The lender can also spread any fixed costs of producing information about the firm over multiple products. Both effects will decrease the lender's costs of providing loans and services and increase the availability of funds to the firm.

However, Greenbaum, Kanatas and Venezia (1989); Sharpe (1990) and Rajan (1992) argue that this allows the lender to extract the rents at- tributable to knowing that the borrower is less risky than average. If in- formation is not transfernable and is private, then relationships decrease the interest rate by less than the true decline in cost.

5.1.2 Determinants of the Maturity of Corporate Debt Issues

Liquidity Risk and Screening The risk of not being able to refund debt because of deterioration in financial or economic conditions can motivate firms to lengthen the maturity of their debt. In Sharpe (1991), Diamond (1991b) and Titman (1992) bad news arrive at the refinancing date, causing investors not to extend credit or to raise the default premium on new debt. Even if this extreme outcome is not realized, short-term debt can still cause a loss of project rents if it has to be refinanced at an overly high interest rate because of credt market imperfection [see Froot, Scharfstein-and Stein (1993)l. Firms may also experience deadweight indirect costs of financial distress, (e.g. loss of customers and distraction of management when they lose access to attractively priced credit).

While liquidity risk gives some firms an incentive to borrow long-term, they may not be able to do so because the rate of return required to com- pensate investors for bearing long-term credit risk can induce substitution into risky low-quality projects [see Diamond (1991b) and Stiglitz and Weiss (1 98l)]. Diamond (1991b) argues that speculative grade credit ratings issue the longest possible term in order to avoid the risk of costly premature liq- uidation. However, these firms are not able to borrow as long-term as they would like because they are screened out of the long-term bond market by moral hazard problems that arise when the required rate of return induces risk-shifting. Thus, low quality firms can be screened out of the long-term debt market and only stable tirras with high credit quality (e.g. large firms) may end up being able to borrow in the long-term credit market. This effect is similar in the corporate bond markets [see Rizzi (1994)l.

Agency Costs of Debt Myers (1977) argues that short-term debt reduces the potential for underinvestment caused by debt overhang because lenders and borrowers recontract before growth options are exercised. Barnea, Hau- gen and Senbet (1980) show that short-term debt reduces the incentives for risky asset substitution because short-term bond prices are relatively insen- sitive to shifts in risk of the underlying assets. As a result, firms whose value derives to a large extent from investment opportunities or that are particularly sensitive to the degree of management effort and talent (e-g. creation and exploitation of risky growth opportunities as opposed to har- vesting assets-in place) have an incentive to borrow short-term. In contrast the liquidity risk hypothesis predicts that fins with risky growth opportu-

nities have an incentive to finance themselves with long-term to avoid the threat of inefficient liquidation.

Assets maturity (i.e. the pattern of cash flows generated from a firm's assets) also plays an important role in agency theories of debt maturity. Myers (1977) argues that firms schedule repayments to match the decline in value of assets in place as a way to lower the agency costs of debt. Thus, firms with more long-term assets in place can support more long-term debt. Maturity matching allows firms to extend debt maturity without sigdicantly increasing the agency costs of debt.

It is worth mentioning a study by Hart and Moore (1995) that shows that debt maturity choice can decrease the agency conflict between managers and shareholders. Noting that long-term is almost junior to short-term debt, they argue that a firm can select an optimal amount of junior and senior debt to offset management's incentive to invest in unprofitable projects.

Tax Benefits Mauer and LeweUen (1987); Emery, Lewellen and Mauer (1988) and Brick and Palrnon (1992) emphasize the tax-timing option in long-term debt contracts resulting from the opportunity to mark debt to market by repurchasing and reusing it. With a convex tax function, in- creased volatility of interest rate decreases the present value of tax shield born short-term debt but not long-term debt. However, Lewis (1990) ar- gues that taxes are irrelevant to maturity choice. Brick and Ravid (1985) show how the different time patterns of interest payments affect the com- bined taxes paid by borrowers and lenders. They argue that borrowers seek to accelerate interest payments to maximize the present value of tax shields, while lenders seek to slow down interest payments to minimize the present value of their tax liabilities. This implies that a maturity strategy that ac- celerates interest payments is more costly to the borrower, on a beforetax basis, than a maturity strategy that slows down interest payments since a premium has to be paid to lenders to induce them to accept a larger tax bill. As a cmsequence, borrowers prefer long-term debt when the term structure of interest rates is upward sloping because the present value of interest tax shields is highest then.

Asymmetric information Theories on asymmetric information focuses on cases where borrowers have private information about their credit quality [see Flannery (1986), Robbins and Schatzberg (1986), Kale and Noe (1990)

and Diamond (l993)]. They can be classified in two groups. Signalling mod- els assume that investors infer private information held by borrowers from the debt maturity choice. Because short-term debt is less sensitive to underpric- ing, firms that have underpriced liabilities choose to issue debt of a shorter term to maturity (and vice-versa). Flannery(l986) argues that if a debt is- sue is costless, only a pooling equilibrium is possible, because low-qualitly firm can costlessly mimic high quality h ' s debt maturity choices. As such the market undervalues high-quality firms and oveduies low-quality firms. With positive transaction costs, however, a separating equilibrium is possible. If lower quality firms cannot afford the cost of rolling over short-term debt, they will self-select into the long-term debt market. In the resulting sepa- rating equilibrium, high quality firms signal their type by issuing short-term debt.

Adverse selection models make the hypothesis that private information is not revealed and maturity is chosen to minimize the effect of private infor- mation on financing costs. Asymmetric information induces a bias toward short-term debt because hm with favorable inside information avoid lock- ing in their financing costs with long-term debt, since they expect to be able to borrow under most favorable terms later.

5.2 Conclusion

Numerous empirical studies have been made to test these theoretical models. Recently, Houston and James (1996) argue that the reliance on bank bor- rowing depend on firm size, growth opportunities and intangible assets, the number of banking relationships and firm's access to public debt markets. They find that size and overall leverage are negatively related to bank bor- rowing. Furthermore if the firm is in a single bank relationship then growth opportunities are negatively related to bank borrowing. The same effect is obtained in the case of multiple nonbank private debt. However, when the firm is involved in multiple banking relations, growth opportunities are positively related to bank borrowing. Cuedes and Opler (1996) empirically validate Diamond's model (1991b). They find that large firms with high credit ratings borrow short and long-term maturity debt whereas speculative grade credit ratings firms borrow debt with an intermediary maturity. Note also that, recent studies are also focusing on the determinants of a mix of private and public debt [see Hart and Moore(1995), b j a n (1992) and Dia- mond (1993)l. Fnture research relating these remits to debt covenants could

prove fruitful

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