Interest Rates in Trade Credit Markets

Transcription

1 Interest Rates in Trade Credit Markets Klenio Barbosa Humberto Moreira Walter Novaes December, 2009 Abstract Desite strong evidence that suliers of inuts are informed lenders, the cost of trade credit tyically does not vary with borrowing firm characteristics. We solve this uzzle by demonstrating that it is otimal for suliers to kee the riskier firms indifferent between trade credit and loans from uninformed lenders. Because these uninformed loans vary across industries but not with firm characteristics, the same attern alies to the cost of trade credit. The model redicts that the cost of trade credit is more likely to vary with firm characteristics in industries that are lagued by moral hazard roblems or financial distress. JEL: G30, G32 Key Words: Trade Credit; Information; Credit Risk. Toulouse School of Economics. Graduate School of Economics-FGV. Deartment of Economics at PUC-Rio.

2 1 Introduction In the U.S., suliers of inuts to roduction rocesses extend a significant amount of credit to their customers using standardized trade credit contracts. 1 In these contracts, interest rates are determined by a discount for early ayment. For instance, Petersen and Rajan (1994 and Ng, Smith and Smith (1999 show that a common trade credit contract combines a 30 day maturity with a two ercent discount for early ayment within 10 days of the invoice (2-10 net 30 loans. For all ractical uroses, foregoing the deadline for the discount is equivalent to acceting a 20-day extension of credit at an annual interest rate of 44 ercent. Suliers, therefore, can align the cost of trade credit with the borrower s risk by roerly varying the terms of the discount. Indeed, these terms do vary across industries. And yet, Giannetti, Burkart and Ellingsen (2008 cannot tie the discounts for early ayment to the borrowers credit risk. This finding is hard to reconcile with the common view that suliers are informed lenders, who, as Petersen and Rajan (1997 show, have a comarative advantage in identifying firms with growth otential. 2 Presumably, the suliers should use their informational advantage to increase the interest rates aid by the riskier firms. We solve this uzzle by arguing that cometition with uninformed lenders makes it difficult for informed suliers to align the cost of trade credit with their customers risk. More secifically, any attemt to selectively raise the interest rates aid by the riskier firms will induce them to borrow from uninformed lenders, whose interest rates overestimate the odds that the debt contract will be honored. We demonstrate that it is otimal for suliers to kee the riskier firms indifferent between trade credit and loans from uninformed lenders. Because the cost of these uninformed loans is likely to vary across industries but not with firm characteristics, the same attern alies to the cost of trade credit. To understand the main ideas of our aer, consider an industry with a continuum of firms, N suliers of inuts and a cometitive banking sector summarized by a reresentative 1 See Rajan and Zingales (1995 for the imortance of trade credit in the G7 countries (Canada, France, Germany, Italy, Jaan, U.K., and the U.S.. 2 A vast literature in cororate finance claims that the suliers informational advantage exlains why trade credit is ervasive. In articular, Smith (1987, Mian and Smith (1992 and Biais and Gollier (1997 argue that the sales effort of suliers makes it easier for them to assess their customers credit risk. 1

3 bank. The firms seek financing to undertake a rofitable roject, whose ossible outcomes are two: a ositive return on the investment (success or total loss (failure. While a bank loan is the standard source of external financing, some firms may have the otion of using trade credit to finance the roject. An informational advantage exlains why suliers offer trade credit in our model. We assume that the robability that the roject succeeds deends on firm-secific risk factors the tyes that are distributed in the ositive interval [t, 1]. Without loss of generality, the robability of success, t, increases with the firm s tye. When firms seek financing to the roject, they know their own tyes and so do their main suliers. The other suliers and the bank, on the other hand, do not know the tyes. Will the informed suliers vary the cost of trade credit with the firm-secific risk factors? To answer this question, we build uon a key observation: rivate information gives market ower to the informed suliers. As suggested by standard monooly ricing, a sufficiently inelastic demand for inuts (and, by extension, for credit makes it otimal for the informed suliers to raise the cost of trade credit until it reaches the cost of the borrower s outside otion, which, in our model, is the interest rate of a bank loan. 3 Since the bank cannot vary the cost of its loans with information that is rivy to the informed suliers, the latter cannot use their information either, if they match the cost of trade credit to the bank rate. Accordingly, we demonstrate that, in equilibrium, the cost of trade credit does not vary with firm characteristics, if the elasticity of the demand for inuts is below a certain threshold ɛ. If the elasticity of demand is larger than ɛ, then it is otimal for the informed suliers to lower the cost of trade credit for the safer firms in order to boost their demand for trade credit. Firms that have access to trade credit are therefore slit into two grous: The riskier ones get trade credit offers whose cost matches the interest rate of a bank loan, and the safer firms ay lower interest rates that decrease with their robability of success. This imlication of our model is interesting, for two reasons. First, there is evidence that suliers do not treat all customers alike when they negotiate trade credit contracts. For instance, Ng, Smith and Smith (1999 show that suliers occasionally waive enalties for 3 Brennan, Maksimovic and Zechner (1988 also argue that the elasticity of the demand for inuts determines the cost of trade credit. In their model, the sulier is a monoolist in the roduct market. 2

4 late ayments, which is equivalent to selectively reducing the cost of trade credit. Second, and more imortantly, testable models of interest rates in trade credit markets should redict when or where the cost of trade credit is more likely to vary with firm characteristics. As we argue below, three redictions of this sort arise from the equilibrium that allows for trade credit contracts to vary with firm characteristics. A standard tradeoff, between margin of rofit and volume of trade, determines the otimal interest rates in the trade credit markets. On the one hand, raising the interest rates increases financial rofits er unit of rofits. On the other hand, it decreases the demand for trade credit. All things equal, suliers have more to gain from trade credit if their cost of raising funds is low. Accordingly, these suliers have stronger incentives to rotect the volume of trade credit for their most valuable customers, namely, the safer firms. A lower cost of funds, therefore, makes it more likely that the cost of trade credit varies with firm characteristics. While a low cost of funds rovides incentives for suliers to reduce the cost of trade credit for the safer firms, financial distress reduces the exected debt reayment, thereby inducing the uninformed bank to increase interest rates. The higher bank rates let the informed suliers selectively raise the cost of trade credit for the riskier firms while rotecting the volume of trade credit for the safer firms. Our model, therefore, redicts that the cost of trade credit is more likely to vary with firm characteristics in financially-distressed industries. A similar argument imlies that the cost of trade credit is more likely to vary with firm characteristics in industries lagued by moral hazard. As Burkart and Ellingsen (2004 oint out, suliers can mitigate moral hazard roblems more efficiently than banks, because trade credit is extended in kind rather than cash. It then follows that moral hazard roblems weaken the banking sector s ability to comete with trade credit, increasing the margins of rofits of the informed suliers and, consequently, strengthening their incentives to vary interest rates with the borrower s risk. Hence, moral hazard doesn t exlain the existing evidence on the cost of trade credit, although it may exlain why trade credit is ervasive. This aer builds rimarily on Biais and Gollier (1997 and Burkart and Ellingsen (2004. In Biais and Gollier, suliers can identify firms whose credit risk is overestimated by banks. Knowing that these firms credit lines are unduly low, suliers are willing to fill their financing 3

5 needs. Burkart and Ellingsen s aer argues that loans in kind (as oosed to cash are less vulnerable to moral hazard roblems. As such, suliers may extend credit to firms that have exhausted their ability to borrow from banks. In Biais and Gollier as well as Burkart and Ellingsen s model, the cost of trade credit would vary with the suliers rivate information, were the customers to have different levels of credit risk. The remainder of the aer is organized as follows. Section 2 describes the basic model. Section 3 shows how firm-secific risk factors and industry characteristics determine the cost of trade credit. Section 4 introduces moral hazard roblems in the model and shows that they make the cost of trade credit more sensitive to firm characteristics. Section 5 discusses the robustness of the results to different information structures and richer trade credit contracts. Section 6 concludes. Proofs that are not in the text can be found in the aendix. 2 The Model 2.1 Sequence of events and information structure Consider a risk-neutral economy with a risk-free rate i, N suliers of inuts, a cometitive banking sector summarized by a reresentative bank, and a continuum of firms C with tyes in the interval [t, 1], where t > 0. In this economy, the firms seek financing to undertake a roject, whose ossible outcomes are two: a ositive return on the investment (success or total loss (failure. When we add firm-secific factors to those that are intrinsic to the roject, the robability that the roject succeeds, t, increases with the firm s tye: t = t, with (0, 1 and t [t, 1]. While a bank loan is the standard source of financing, suliers may finance the roject by extending trade credit. Neither the bank nor the suliers observe the roject s return without a verification cost. As in Townsend (1979 and Gale and Hellwig (1985, verification costs imly that outside equity isn t an otimal financing contract. Hence, firms rely on debt-like instruments to finance the roject, whether the lender is the bank or a sulier. 4 4 In our model, verification costs focus the financing decisions on the debt-like instruments that revail in the trade credit markets. In a multi-eriod setting, Fluck (1998 demonstrates that equity financing may be otimal, even if cash flows are not verifiable. 4

6 Figure 1: Timing of events Firms seek financing Take-it-or-leave-it offers by the main suliers Uninformed lenders/ Purchase of inuts Production/ Payoffs As figure 1 shows, the game begins at date 0, when the firms seek financing to urchase inuts for the roject. At this time, the firms know their own tyes, and so do their main suliers. The bank and the other suliers, on the other hand, know only that the tyes are distributed across [t, 1] with a cumulative distribution F 0 (t and density function f 0 (t. Intuitively, the informational advantage of the main suliers is the outcome of unmodelled reeated urchases that give rise to most-favored business relationshis. We model these secial relationshis by a set {T n } N n=1, where T n is the set of firms whose main sulier is n. We assume that each firm has one (and only one main sulier, that is, T l T m = for any l m and N n=1 T n = C. To ensure that the suliers are symmetric at t = 0, we also assume that, for any n, the tyes in T n belong to the interval [t, 1] with the cumulative distribution F 0 (t. The distribution F 0 (t, the roject-secific risk factor and the artition of firms {T n } N n=1 are all common knowledge. In addition to allowing a better assessment of the firms credit risk, secial business relationshis give the main suliers a first-mover advantage. At date 1, they may bundle sales of inuts to trade credit through take-it-or-leave-it offers to their referred customers. 5 main suliers know, however, that if they do not reach an agreement with their referred customers, then the latter may borrow from one of the uninformed lenders (the bank or the other suliers at date 2. After securing the funds, the firms buy the inuts and undertake 5 The main results of our aer hold under less extreme assumtions on how the main suliers and their referred customers reach an agreement over the terms of trade credit. The 5

7 the roject at date 2. The ayoffs realize at date 3, when the firms reay the debt (if ossible and distribute the residual cash flow to shareholders. 2.2 Technology In the U.S., trade credit contracts often let firms ay for the urchased goods after delivery, without charging a ositive interest rate. Of course, trade credit contracts at zero interest rates are costly for the suliers. For these contracts to make economic sense, they must benefit the suliers in some other way. 6 Regardless of the reason for suliers to subsidize trade credit, one would exect that the otimal subsidy varies with the borrower s characteristics. One way for suliers to vary the subsidy is to offer trade credit contracts with different discounts for early ayment. Giannetti, Burkart and Ellingsen (2008 show, however, that the borrowers risk characteristics do not exlain the terms of the discount for early ayment. To focus our analysis on the interest rate that is imlicit in the discount for early ayment, we assume that the market for inuts is cometitive and endow the suliers with a constantreturn-to-scale technology. While cometition rules out abnormal rofits in the market for inuts, constant returns to scale imly that the equilibrium inut rice is equal to the marginal cost, which we normalize to one. If the inut rice is constant, then the cost of trade credit is the only instrument available for the suliers to vary their ricing decisions with the borrowers characteristics. This is the worst-case scenario for a model that aims to exlain why the cost of trade credit does not vary with firm characteristics. Unlike the suliers, the buyers of inuts can fetch abnormal rofits in the roduct market. These firms are endowed with an investment oortunity whose ossible outcomes are two: success or failure. In case of success, the return of investing I units of inut in the roject is Q(I. The roduction function Q(I is increasing and strictly concave on the investment, satisfying Q(0 = 0 and the standard Inada conditions. 7 investment, once we take into account the verification costs. In contrast, failure destroys the 6 Daria and Nilsen (2009, for instance, argue that subsidized interest rates induce cash-constrained firms to kee higher inventory levels, thereby increasing their suliers rofits in the market for inuts. 7 The Inada conditions are lim I 0 Q (I = and lim I Q (I = 0. 6

8 2.3 Trade credit contracts Since cometition drives the rice of the inut to its marginal cost, suliers design trade credit contracts that maximize their exected financial rofits. We shall restrict our attention to linear debt contracts, which are ervasive in the trade credit markets. Assuming linear contracts from the onset may be interreted as a short-cut to focus the analysis on the most relevant determinants of interest rates in the trade credit markets. 8 To characterize the otimal trade credit contracts, we must take into account whether the borrowing firm is a referred customer or not. Trade credit transactions with referred customers are articularly aealing for the suliers, for two reasons. First, they can vary the interest rate with the borrower s risk. Second, they can make reemtive trade-credit offers. Of course, this first-mover advantage does not insulate the informed suliers from cometition in the credit markets. In articular, they cannot lend at an interest rate that is higher than the cost of the borrower s alternative source of financing. Leaving aside trade credit from a main sulier, what is the least costly financing alternative for the firms? As in Biais and Gollier (1997, we assume that the bank s cost of funds is the riskless rate i, while the cost of funds of the suliers is i + c, with c > 0. Uninformed suliers, therefore, cannot comete with the bank in the market for loans. A bank loan is the best alternative for a firm that does not agree with its main sulier with resect to the terms of trade credit. Note, however, that trade credit breaks down if the suliers cost of funds is too high. To assure that trade credit arises as an equilibrium outcome, we assume: Assumtion 1 The suliers cost of funds satisfies 1 + i + c < 1+i 1 t tdf 0(t. 2.4 The borrowing firms outside otion: A bank loan Free entry drives the bank s exected rofit to zero. To see what tye of restriction this zerorofit condition imlies, consider a standard debt contract (I, A(I, where I is the amount of the loan and A(I is the romised reayment. When the bank offers the debt contract, it knows that the borrower will ay A(I if and only if its investment in the roject ays off. 8 Section 5 demonstrates that the main insights of our aer are robust to otimal nonlinear contracts, if default imoses small economic losses on suliers. 7

9 From the bank s viewoint, the robability that the roject succeeds is E 1 [t] = 1 tdf t 1(t, where F 1 (t is the udated distribution of the tye of a firm that requests a bank loan. For the bank s exected rofit to be zero, its exected ayment, E 1 [t]a(i, must be equal to its cost of funds, (1 + ii, imlying that the interest rate of the debt contract is r B A(I I Equation (1 shows that the interest rate r B 1 = 1 + i 1. (1 E 1 [t] decreases with the exected tye of the borrowing firm (i.e., E 1 [t]. Cometition in the banking sector, therefore, elicits incentives for loan contracts that screen the borrowers tyes. It is easy to show, nonetheless, that, in our model, the bank cannot screen the tyes, because any loan contract that is otimal for a tye-t firm is also otimal for the other tyes. 9 This feature of the model reserves the informed suliers informational advantage, which is crucial to the uroses of our aer, while allowing for risk characteristics to vary across firms. It then follows from Gale and Hellwig (1985 that a standard debt contract with a romised return r B = 1+i E 1 1 is the least costly bank loan. In the otimal debt contract, the romised [t] ayment A(I varies with the loan amount, but its romised return doesn t. To characterize the otimal debt contract it thus suffices to in down the loan amount that maximizes the value of a reresentative firm that borrows from the bank, that is, the investment I E 1[t] that makes the marginal roductivity of investment, E 1 [t]q (I E 1[t], equal to its marginal cost, 1 + i. The necessary and sufficient condition that characterizes the otimal investment is Q (I E 1[t] = 1 + i E 1 [t]. (2 The otimal debt contract, therefore, lends I E 1[t], in exchange for the borrower s romise to ay (1 + r B I E 1[t] after the roject s ayoff realizes. 9 More formally, consider any two standard debt contracts, (I k, A(I k k {T, ˆT }, that finance I k in exchange for a romised ayment A(I k. For the debt contracts to screen some of the firms, there must exist tyes t T and ˆt ˆT such that t [Q(I T A(I T ] > t [Q(I ˆT A(I ˆT ] and ˆt [Q(I T A(I T ] ˆt [Q(I ˆT A(I ˆT ]. These two conditions cannot hold simultaneously, though, because t [Q(I T A(I T ] > t [Q(I ˆT A(I ˆT ] imlies that t [Q(I T A(I T ] > t [Q(I ˆT A(I ˆT ] for any t t. Hence, if a loan contract is otimal for a tye-t firm, then it is also otimal for the other tyes. 8

10 As it turns out, the otimal debt contract can be imlemented by a linear contract that lets the borrowers ick the loan amount. To see this, consider the investment roblem of a tye-t firm that finances the inuts at an interest rate r: ] max [Q(I t (1 + ri. (3 I The objective function (3 takes into account that the firm benefits from the roject if it succeeds. With robability 1 t, the firm gets into oerational roblems that destroy the roject s ayoff. The first order condition of rogram (3, which is also sufficient, is Q (I = 1 + r. (4 Plugging r = 1+i 1 into the first order condition (4 yields E 1 [t] Q (I = 1+i E 1, which is the [t] first order condition (2 for the value-maximizing investment of the reresentative tye E 1 [t]. Hence, we can assume, without loss of generality, that a linear debt contract at the interest rate r B = 1+i E 1 1 is the firms alternative for borrowing from the informed sulier. [t] 3 Equilibrium in the trade credit market This section is divided in three arts. The first art derives the otimal trade credit contracts, taking as given the udated belief F 1 (t that determines the cost of borrowing from the bank. In the second art, we obtain F 1 (t as art of the equilibrium of the game. The last art of the section investigates the likelihood that the cost of trade credit varies with firm characteristics. 3.1 The otimal trade credit contracts of informed suliers The focus of this section is on trade credit transactions between a firm and its main sulier of inuts. Consistently with Petersen and Rajan (1997, we argue that an informational advantage shaes these trade credit transactions: The main sulier is the only lender that knows the tyes of its referred customers. The main sulier of a tye-t firm thus solves ( max t (1 + r t (1 + i + c I (r t (5 r t subject to 1 + i + c t 1 r t r B. (6 9

11 The objective function is the informed sulier s exected rofit of extending trade credit to a tye-t firm at an interest rate r t. The loan amount, I (r t, is the otimal urchase of inuts given the interest rate r t (see the first order condition (4. With robability t, the borrower can ay rincial lus interest, (1+r t I (r t, but, with robability 1 t, oerational roblems destroy the roject s ayoff. Whether the roject succeeds or not, the sulier bears the cost of roducing the inut lus its own cost of funds, that is, (1 + i + ci (r t. When choosing the interest rate, the informed sulier takes into account that a necessary condition for lending to a tye-t firm to be rofitable is that r t is larger than 1+i+c t 1. The interest rate cannot be too high, though, or else the firm is better off borrowing from the bank at the interest rate r B. These two restrictions are summarized in (6. The only reason for a solution to Program (5 not to exist is the uer bound on the interest rate (r t r B. If r B is lower than the break-even rate, then the rogram s oortunity set is emty, meaning that the informed sulier will not offer trade credit to the tye-t firm. Using t = t, a necessary and sufficient condition for trade credit to be rofitable for the informed sulier is r B 1+i+c t 1, or equivalently t 1 + i + c (1 + r B. (7 Our next task is to characterize the interest rate that solves the maximization roblem (5, assuming that trade credit is rofitable (i.e., t 1+i+c. To do this, note first that (1+r B r t = 1+i+c t 1 yields zero exected rofits for the informed suliers, while any slightly larger rate imlies strictly ositive exected rofits. The otimal interest rate charged to a t-tye, therefore, is either r B or lies in the oen interval ( 1+i+c t 1, r B. A standard trade-off, between margin of rofit and volume of trade credit, determines the otimal interest rate. To rule out the uninteresting case that it is always otimal for the informed suliers to raise the cost of credit as much as ossible, we assume: 10 Assumtion 2 Let ɛ(r = Thus, ɛ(r is non-decreasing in r. di (r (1+r dr I (r be the interest-elasticity of the demand for inuts. Given Assumtion 2, Proosition 1 characterizes the interest rate that solves Program Assumtion 2 holds, for examle, if Q(I = I α with α (0, 1. 10

12 Proosition 1 It is rofitable for any informed sulier to offer trade credit if and only if the firm s tye is t 1+i+c (1+r B. In this case, a necessary and sufficient condition for rt to be the otimal interest rate is ɛ(r t ɛ(r t, t, where ɛ(r t, t = t(1+r t. The otimal interest t(1+r t (1+i+c rate r t strictly decreases with t, for any r t < r B. If r t = r B, then the otimal interest rate does not vary with the borrower s firm-secific characteristics. Proosition 1 shows that the cost of trade credit falls with t, unless the informed sulier raises the interest rate to the maximum level that firms are willing to ay, that is, the bank rate r B. From Proosition 1, the necessary and sufficient condition for r t = r B to be otimal is ɛ(r B ɛ(r B, t. Fixed r B, the cutoff ɛ(r B, t decreases with the firm s tye, t. Hence, ɛ(r B ɛ(r B, 1 ensures that the cost of trade credit never varies with firm characteristics. As Petersen and Rajan (1997 show, the demand for trade credit in the U.S. seems to be fairly inelastic; a finding that Proositions 1 relates to interest rates that do not vary with firm characteristics. Note, however, that Proosition 1 does not rovide a comlete characterization of the otimal trade credit contracts. trade credit, The cutoff tye that has access to 1+i+c, and the otimal interest rate, (1+r B rt, deend on the bank rate r B, which is an endogenous variable of our model. The next section integrates the trade credit market with the market for bank loans, thereby solving for the equilibrium of the game. 3.2 Characterization of the equilibrium To describe the normal form of the game, consider the following ure strategies and belief: { } } E = {(I B, r B, (I (r t, r t, 1 t t [t,1] bank, F 1 (t. (8 t [t,1] In the rofile E, the bank s strategy is a standard debt contract, (I B, r B, that is available to all firms. The debt contract lends I B, in exchange for a romised ayment that imlies an interest rate r B. Unlike the bank, the informed suliers know the tyes of its customers. Their strategies, therefore, consist of a set of trade credit contracts, (I (r t, r t, that can be tailored to the borrower s firm-secific risk factors. All trade credit contracts finance urchases of inuts that let the borrower imlement the otimal scale of the roject, I (r t, given the interest rate r t. In addition to varying the interest rate with the borrower s risk, 11 t [t,1]

13 the informed suliers can deny trade credit to tyes below a cutoff t [t, 1]. The firms { } strategies consist of the indicator functions 1 t bank. For each t, the indicator function t [t,1] takes value one if a bank loan maximizes the tye-t firm s exected rofit and value zero if trade credit is the rofit-maximizing loan. Finally, the cumulative distribution F 1 (t describes the bank s belief on the tye of a firm that asks for a bank loan. The equilibrium concet we use is Perfect Bayesian Equilibrium (PBE. For E to be a PBE, the strategies and belief must satisfy two conditions. First, each layer s strategy must maximize its exected ayoff, conditioned on the other layers strategies and the equilibrium belief F 1 (t. Second, F 1 (t must satisfy Bayes rule whenever ossible. Proosition 2 exhibits a PBE in which the informed suliers exloit their informational advantage to extend trade credit to their most imortant customers the safer firms while the bank takes advantage of its lower cost of funds to rovide financing for the riskier firms. Under a relatively mild assumtion, this equilibrium is unique. 11 Proosition 2 There exists a Perfect Bayesian Equilibrium in which a cut-off tye t (t, 1 determines whether trade credit or bank loans finance urchases of inuts. Firms with tye t [t, t urchase inuts by borrowing I (r B from the bank at the interest rate 1 + r B = 1+i E 1 = (1+iF 0(t [t], which is consistent with a belief F t 1(t = P rob(s t t t. In turn, any t sf 0(sds t [ t, 1] accets a trade credit offer to finance I (r t at the interest rate r t. Moreover, there exists ˆt [0, 1] such that r t = r B if and only if t [ t, ˆt]. If t > max{ˆt, t}, then the otimal interest rate is imlicitly defined by ɛ(r t = ɛ(r t, t, with r t strictly decreasing in t. Provided ( that d F0 (t dt f 0 > c, the cut-off tye t is unique and so is the equilibrium of the game. (t 1+i In Proosition 2, the equilibrium trade credit contracts follow trivially from the otimality restrictions of Proosition 1: the otimal interest rate is characterized by ɛ(r t ɛ(r t, t, and the safest tye that has access to trade credit is t 1+i+c. Likewise, the rincial amount (1+r B of the bank loan, I (r B, maximizes the borrower s net outut (as in Section 2.4, while Bayes rule and the cutoff tye t (t, 1 in down the udated belief, F 1 (t = F 0 (t/f 0 ( t, 11 The sufficient condition for uniqueness is slightly stronger than the monotone hazard condition; the hazard ( rate must increase with t at a ace faster than c/(1 + i. Under Assumtion 1, the condition d F0(t dt f 0(t > c 1+i holds if F 0 (t is the C.D.F. of a uniform distribution in the interval [t, 1]. 12

14 that ultimately determines the interest rate that leaves the bank with zero exected exected rofits, that is, r B = (1+iF 0(t t t sf 0(sds 1. The zero-rofit condition for the bank is a key to understand the cutoff t that searates the firms that borrow from the bank from those that use trade credit. In equilibrium, the bank s exected rofit with loans to the safer firms just offsets its exected loss with loans to the riskier firms. The interest rate r B, therefore, falls short of the informed suliers break-even rate for trade credit offers to the riskier tyes. Accordingly, informed suliers restrict trade credit offers to firms whose risk of credit is lower than the tyical firm that borrows from the bank. In articular, the risk of the cutoff tye t is sufficiently low to make the bank rate offset not only its exected default but also the higher cost of funds of the informed suliers. Given t, the cutoff ˆt slits the tyes with access to trade credit into two grous. The safer ones, t > ˆt, ay an interest rate r t that decreases with their robability of success. The riskier tyes, t > max{ˆt, t}, ay the interest rate r B that kees them indifferent between trade credit and bank loans. Excet for corner solutions, ˆt is imlicitly defined by ɛ(r B = ɛ(r B, ˆt, which imlies that the informed suliers marginal gains of increasing interest rates above r B are equal to their marginal cost of reducing the tye-ˆt s willingness to borrow. If all tyes ay r B then ˆt = 1 t, while ˆt < t if r t < r B, for any t. 3.3 The likelihood that the cost of trade credit varies with firm characteristics Tyically, interest rates in the trade credit markets vary across industries but not with firm characteristics. As such, a test with ower to reject our model should be centered around imlications that hel redict when or where the cost of trade credit varies with firm characteristics. This section shows that the cost of trade credit is more likely to vary with firm characteristics in financially-distressed industries and in industries with informed suliers that have a low cost of funds. To link the cost of trade credit to financial distress, our first task is to extend the model to create classes of risk. As such, slit the continuum of firms C in two sets, A 0 and A 1, such that A 0 A 1 = C and A 0 A 1 =. For simlicity, the suort of tyes in the two 13

15 sets is still the interval [t, 1], but the cumulative distribution varies across the sets. While the distribution of tyes in the set A 0 remains F 0 (t, the distribution in A 1 is G 0 (t, with density g 0 (t. We assume that the hazard rate of G 0 (t is always smaller than F 0 (t, that is, g 0 (t G 0 (t < f 0(t F 0 (t for any t (t, 1], (9 which imlies that the exected robability of success is smaller in A 1 than in A 0. From now on, we shall denote the sets A 0 and A 1 as, resectively, the F -class and the G-class. The uninformed lenders know which firms are in each class, but cannot distinguish the tyes of firms in the same class of risk. Proosition 3 below shows that the greater risk of the G-class carries through to the equilibrium in the credit markets. In articular, firms in the G-class ay a higher interest rate to the bank than firms in the F -class. More interestingly, Proosition 3 shows that, relative to the F -class, more firms in the G-class have access to trade credit and their cost of trade credit is more likely to vary with firm characteristics. Proosition 3 Assume that the distributions F 0 and G 0 satisfy the inequality (9. t G < t F Thus, and ˆt G < ˆt F, where t k is the riskiest tye in the class k {F, G} that has access to trade credit, and ˆt k is the safest tye in the class k whose cost of trade credit does not vary with firm characteristics. Moreover, firms in the G-class ay a higher interest rate to the bank than firms in the F -class. The bank s resonse to the higher robability of default in the G-class is quite obvious: It increases its interest rate. In turn, the informed suliers take advantage of the higher bank rate to selectively raise the cost of trade credit for the riskier firms in the G-class. By doing so, the informed suliers reserve the volume of trade credit for the safer firms, while offering trade credit at costlier terms to the riskier firms. 12 Proosition 3 suggests that the cost of trade credit is more likely to vary with firm characteristics in industries that are lagued by financial distress. This imlication of our model 12 An increase in risk does not necessarily increase the exected rofit of the informed suliers; additional restrictions on the riskier distribution G(t are needed to determine whether the greater leeway to raise the cost of trade credit outweighs the greater robability that trade credit is not aid. 14

16 is consistent with Wilner (2000, who argues that suliers have incentives to bail-out financially distressed customers in order to reserve long-term business relationshis. Anticiating their own incentives, suliers should embed the exected cost of the otential bail-out in the terms of trade credit. Clearly, this exected cost varies with the customer s risk and is more likely to be relevant in distressed industries. Of course, suliers of inuts may also become financially distressed. One might then wonder whether financially-distressed suliers are more rone to vary the cost of trade credit with firm characteristics. To answer this question, our starting oint is that financiallydistressed suliers have difficulties to raise the necessary funds to rovide trade credit. In our model, these difficulties ma into a higher cost of funds, whose imact on the suly of trade credit is summarized by Proosition 4. Proosition 4 An increase in the suliers cost of funds raises the cutoff tyes t and ˆt, reducing access to trade credit while lowering (ossibly weakly the fraction of firms whose cost of trade credit falls with the robability of success. The intuition for Proosition 4 lies in the trade off between margin of rofits and volume of loans. A higher cost of funds decreases the exected margin of trade credit, regardless of the borrower s firm-secific characteristics. The lower margin of rofits makes the volume of trade credit less imortant for the informed suliers, weakening their incentive to use the interest rate as an instrument to discriminate the demand for loans. Hence, suliers with a higher cost of funds rovide less trade credit ( t increases and make the cost of trade credit less sensitive to firm-secific characteristics (ˆt increases. Arguably, small suliers of inuts have a higher cost of funds and are more rone to financial distress. 13 If so, Proosition 4 redicts that small suliers are less inclined to extend trade credit and, when they do so, the terms of trade credit are less likely to vary with the borrower s credit risk. To illustrate Proosition 4, assume that F 0 (t is uniformly distributed in the interval [t, 1] and consider the roduction function Q(I = I α, which imlies an iso-elastic demand for 13 Rajan and Zingaless (1995, among others, find evidence that bigger firms have a larger debt caacity. 15

17 inuts: ɛ(r = 1, for any interest rate r. This roduction function satisfies our technological 1 α assumtions if α (0, 1. by t = From Proosition 2, the riskiest tye that has access to trade credit is imlicitly defined 1+i+c, or equivalently, t = 1+i+c E (1+r B 1+i 1 [t]. 14 If F 0 (t is uniformly distributed, then the exected tye of a firm that borrows from the bank is E 1 [t] = E[t t t] = t+ t, which imlies 2 t = 1 + i + c t. ( i c Equation (10 confirms that a higher cost of funds makes trade credit less ervasive, that is, t increases with c. To see that the cost of trade credit becomes less sensitive to firm ( characteristics as c gets larger, assume that α > 1+i+c = t 1+i+c to ensure an equilibrium (1+r B 1+i c in which the cost of trade credit may vary with firm characteristics. From Proosition 2, the safest tye that ays r B, i.e. ˆt, is imlicitly defined by ɛ(r B = ɛ(r B, ˆt. In the iso-elastic case, this condition becomes 1 1 α = ɛ(rb, ˆt, or equivalently ˆt = 1 + i + c α(1 + r B = 1 α ( 1 + i + c E 1 [t] = i α ( 1 + i + c t, ( i c which roves that ˆt increases with c because Assumtion 1 imlies that 1 + i > c. 4 Trade credit and moral hazard roblems Burkart and Ellingsen (2004 argue that trade credit is a ervasive source of external financing because loans in kind are less vulnerable to moral hazard roblems. This section demonstrates that although moral hazard may be an imortant reason for trade credit to exist, it doesn t exlain why the cost of trade credit tyically does not vary with firm characteristics. 4.1 The moral hazard roblem To introduce a moral hazard roblem in the model, we assume that shareholders may unduly divert art of the cash-flow generation that should be used to ay debt obligations. 14 To obtain t = 1+i+c 1+i E 1 [t], lug r B = 1+i E 1[t] 1 into 1+i+c (1+r B. 16

18 There are two constraints on the shareholders oortunistic behavior. First, we do not let them grab cororate assets and run: Diversion of cash is bounded by the firm s cashflow generation. Second, debt holders may sue the shareholders of firms that do not ay their debt obligations, unless the court believes that the breach of the debt contract was the unfortunate outcome of a risky but reasonable investment. To curb the risk of rosecution, firms must invest in a diversion technology that makes it more difficult for outsiders to detect oortunistic behavior. If firms ay B, then their shareholders can safely cature an amount [ ρb of the cash-flow generation. We assume that ρ, which imlies that the exected 0, 1+i return on the diversion technology does not cover the time value of the money, regardless of the firm s tye. Diverting cash is therefore socially inefficient. To characterize the incentives to divert cash, suose that a tye-t firm borrows I, romising to reay A(I when the roject s cash flow realizes. After receiving the roceeds of the loan, the borrower chooses how much to invest in the roject and how much to invest in the diversion technology. Investing B in the diversion technology, on the one hand, lets the shareholders cature an amount ρb of the firm s cash-flow generation, whether the debt holders are aid or not. On the other hand, it reduces the cash-flow generation from the roject by Q(I Q(I B. The otimal diversion olicy solves [ { } ] max B [0,I] t max Q(I B A(I, 0 + ρb. (12 Lemma 1 characterizes the otimal investment in the diversion technology. Lemma 1 Let B(I be the largest investment in the diversion technology that does not harm the debt holders, that is, Q(I B(I = A(I. Thus, the otimal diversion olicy is 0 if Q (I ρ and Q(I ρ + A(I, I I B(I, ρ = I B (0, B(I if Q (I B = ρ and Q(I B I B otherwise. ρ + A(I I B, The otimal diversion olicy, B(I, ρ, takes into account the two conflicting forces underlying the decision to divert cash: The efficiency of the roject and the shareholders gains from extracting value from the debt holders. These two forces are summarized by the average roductivity of the roject, Q(I I, and two marginal roductivities; one for the roject, Q (., 17 (13

19 and another for the diversion technology, ρ. The conditions on the marginal roductivities ensure that marginal deviations from B(I, ρ do not increase the shareholders exected ayoff. And the lower bounds on the average roductivity imly that the roject s exected return is sufficiently large to dissuade the shareholders from diverting all available funds. The otimal diversion olicy suggests that the bank may constrain its suly of loans to eliminate the agency costs of debt. By constraining the loan amount, the bank lowers the scale of the roject that the borrowers can undertake, raising its average roductivity to a level that dissuades the borrowing firms from investing in the diversion technology. To be sure, constraining the suly of loans imoses costs. Still, Proosition 5 shows that, in equilibrium, the bank designs a loan contract that revents any diversion of cororate funds. Proosition 5 In equilibrium, the bank designs a standard debt contract (I, A(I that dissuades the borrowers from diverting cororate resources, that is, B(I, ρ = 0. Proosition 5 imlies that the otimal debt contract must satisfy three conditions. First, firms must be willing to borrow from the bank (the articiation constraint. Second, the debt contract must induce the borrowers to invest all roceeds of the loan in the roject (the incentive-comatibility constraint. And third, the debt contract must imly zero exected rofits for the bank (the zero-rofit condition. Consider first the zero-rofit condition while assuming that the other two constraints hold. As in section 3, a firm s request of a loan udates the bank s rior on the borrower s tye to F 1 (t. If the bank correctly believes that the borrower will use the roceeds of the loan to invest in the roject, then its exected rofit is E 1 [t]a(i (1 + ii, where E 1 [t] = 1 tdf t 1(tdt is the exected tye of the borrower. The zero-rofit condition imlies that the romised return of the loan is 1 + r B = 1+i E 1, exactly as in the equilibrium interest rate that ignores agency [t] costs of debt (see equation (1. As a result, we can write the loan contract as a air (I, r B. To obtain the loan amount I, we move on to the incentive conditions that assure that the borrower is better off undertaking the roject rather than diverting the roceeds of the loan. From Lemma 1, incentive comatibility requires that neither the marginal roductivity nor the average roductivity of the investment is too small. As Proosition 6 shows, the lower bound 18

20 on the average roductivity of investment is the relevant restriction for the characterization of the equilibrium loan contract. Proosition 6 The equilibrium loan contract is (I (r B, r B if and only if I (r B ĪB (r B, ρ, where r B = 1+i E 1 [t], I (r B is the otimal investment in the roject given r B, and ĪB (r B, ρ is imlicitly defined by Q(ĪB (r B, ρ Ī B (r B, ρ = ρ + (1 + r B. (14 If I (r B > ĪB (r B, ρ, then the equilibrium loan contract is (ĪB (r B, ρ, r B, with ĪB (r B,ρ ρ < 0 and ĪB (r B,ρ r B < 0. The intuition for Proosition 6 lies on the marginal roductivity of the diversion technology, ρ. If ρ is close to zero, then the gains from diverting cash are small, making it unrofitable for the shareholders to sacrifice resources that could be used in the roject. The moral hazard roblem is therefore irrelevant: There is no credit constraint, and the bank offers the debt contract (I (r B, r B that finances the otimal scale of the roject. As ρ increases, the gains from diverting cash grow, raising the minimum roductivity of the roject that dissuades the shareholders from diverting cororate resources (see Lemma 1. Since the roduction function is concave, a necessary condition for the average roductivity to increase is that the investment in the roject falls. Hence, as ρ gets bigger, the largest investment in the roject that satisfies the roductivity condition, ĪB (r B, ρ, decreases. Credit constraint arises when the benefit of diverting cash, ρ, gets sufficiently large to make the bank offer a loan amount, ĪB (r B, ρ, that does not finance the otimal scale of the roject. The cutoff for ρ that imlies credit constraint is defined by Ī B (r B, ρ const (r B = I (r B. If ρ ρ const (r B then ĪB (r B, ρ I (r B, imlying that the bank can offer the first best contract, (I (r B, r B, without fearing agency costs of debt. Moral hazard is costly, though, if ρ > ρ const (r B. In this case, the bank offers the constrained contract (ĪB (r B, ρ, r B that kees the borrower as close as ossible to the otimal scale of the roject, without eliciting incentive for diversion of cash. We can thus write the value of a tye-t firm that borrows from 19

21 the bank as t Π B (r B, ρ ] [Q(I t (r B (1 + r B I (r B [Q(ĪB ] t (r B, ρ (1 + r B ĪB (r B, ρ if ρ ρ const (r B, if ρ > ρ const (r B. (15 Note that equation (15 does not rovide a comlete characterization of the value of a firm that borrows from the bank, because r B deends on the borrower s exected tye (E 1 [t]. The next section obtains E 1 [t] as art of the equilibrium of the game. 4.2 Equilibrium with moral hazard roblems As Burkart and Ellingsen (2004 oint out, loans in kind like trade credit do not give leeway for insiders to divert cororate assets. We assume, therefore, that suliers do not fear oortunist behavior. And yet, this section demonstrates that severe moral hazard roblems in the market for bank loans make trade credit more ervasive and increase the likelihood that the cost of trade credit varies with firm characteristics. A first ste to determine the imact on the trade credit markets of the bank s moral hazard roblems is to characterize the informed suliers oortunity set. Without moral hazard, the highest interest rate that informed suliers can charge is the bank rate r B. 15 Moral hazard may relax this uer bound, because credit-constrained firms are willing to ay a remium for larger credit lines. The largest interest rate that informed suliers can charge call it r kees the credit-constrained firms indifferent between a cheaer (but undersized bank loan and a larger (but costlier trade credit contract, that is, 16 ] [Q(I t ( r (1 + ri ( r = t Π B (r B, ρ. (16 The left-hand side of equation (16 is the exected rofit of a tye-t firm that invests in the roject, after acceting trade credit at the interest rate r. The right-hand side is the 15 In this section, we continue assuming that the roblem of the informed suliers is to design linear trade credit contracts that maximize exected financial rofits. 16 Severe moral hazard roblems may break down the market for bank loans. In this case, moral hazard cannot exlain the cross-sectional variation of the cost of trade credit because, in our model, suliers are insulated from moral hazard roblems, whether they have an informational advantage or not. Accordingly, we assume that a bank loan is always the firms outside otion to trade credit offered by their main suliers. 20

22 exected rofit of a tye-t firm that borrows from the bank. Using equation (15, one can check that r = r B, if moral hazard roblems do not imly credit constraint in the market for bank loans. Otherwise, r > r B. We have thus established: Lemma 2 The cost of trade credit cannot be higher than the interest rate r that is imlicitly defined by equation (16. If the firm is not credit constrained, i.e. ρ ρ const (r B, then r is the bank rate r B. Otherwise, r > r B. From Lemma 2, we can write the roblem of the informed suliers as ( max t (1 + r t (1 + i + c I (r t (17 r t subject to 1 + i + c t 1 r t r. The objective function (17 is the exected rofit of an informed sulier that extends trade credit to a tye-t firm at the interest rate r t. The interest rate r t must be larger than the break-even oint, 1+i+c t 1, but it is bounded by the largest interest rate r that the firm is willing to ay. The uer bound on the interest rate imlies that it is rofitable for informed suliers to offer trade credit if and only if the borrower s tye is t 1 + i + c (1 + r. (18 A straightforward comarison of Programs (5 and (17 shows that they are equal, unless the moral hazard roblems arameterized by ρ let the informed suliers raise the cost of trade credit above the bank rate. Accordingly, Proosition 7 identifies a cutoff value for ρ below which the moral hazard roblems have no imact on the trade credit markets. Proosition 7 There exists ρ const > 0 such that ρ ρ const imlies that the strategies and belief of Proosition 2 form a Perfect Bayesian Equilibrium. In this equilibrium, which is ( unique if d F0 (t dt f 0 > c, moral hazard roblems are irrelevant; the bank induces the borrowing (t 1+i firms to invest in the roject, without imosing credit constraint. In contrast, ρ > ρ const imlies that there is no equilibrium without credit constraint in the market for bank loans. 21

23 Proosition 7 shows that there is no equilibrium without credit constraint, if the shareholders gains from diverting cash are larger than ρ const. As it turns out, it is easy to exhibit technologies that imly credit constraint in the market for bank loans. It can be shown, for ( examle, that the iso-elastic roduction function, Q(I = I α, imlies that ρ const 0, 1+i, if ( ( 1 α., 1 For any ρ ρ const, 1+i and r B = 1+i 1+t E 1, the otimal unconstrained investment, [t] I (r B, is strictly bigger than the largest loan ĪB (r B, ρ that induces the borrowers to invest in the roject. Proosition 6 thus imlies that the equilibrium debt contract, (ĪB (r B, ρ, r B, does not let the borrowers imlement the otimal scale of the roject. Credit constraint does not change the essence of the suliers roblem, though. In articular, the otimal interest rate r t still solves a trade off between margin of rofit and volume of trade credit. Analogously to Proosition 1, the first order condition of Program (17 imlies that r t is otimal for the informed sulier if and only if ɛ(r t ɛ(r t, t t(1+r t t(1+r t (1+i+c. And a cutoff ˆt determines which tyes ay the interest rate r, defined in equation (16, that kees the borrowers indifferent between trade credit and a bank loan. If t ˆt, then r t = r. If t > ˆt, then the otimal interest rate is imlicitly defined by ɛ(r t = ɛ(r t, t, with drt dt < 0. Hence, a necessary and sufficient condition for the cost of trade credit not to vary with firm characteristics is ˆt = 1, or equivalently, ɛ( r ɛ( r, 1. To integrate the otimal trade credit contracts with the market for bank loans, we roceed as in Section 3.2 and consider the following strategies and belief {(ĪB ( { } } E(ρ = (r B (ρ, ρ, r B (ρ, I (r t (ρ, r t (ρ, 1 t t [t(ρ,1] bank, F 1 (t t(ρ. (19 t [t,1] E(ρ is a Perfect Bayesian Equilibrium (PBE if there exists t(ρ [t, 1 such that: (i The (ĪB debt contract (r B (ρ, ρ, r B (ρ ensures to the bank zero exected rofits under the belief F 1 (t t(ρ, while keeing the scale of the roject as close as ossible to the first best without inducing the borrowers to divert cash; (ii it is otimal for the informed suliers to lend I (r t (ρ to any tye t t(ρ, where r t (ρ is the interest rate that solves Program (17; (iii firms choose the financing alternative that maximizes their exected rofits; and (iv Bayes rule determines F 1 (t t(ρ from the equilibrium strategies, whenever ossible. Proosition 8 shows that, for any ρ (ρ const, 1+i, there exist t(ρ [t, 1 that makes E(ρ a PBE. 22