The Exploitation of Relationships in Financial Distress: The Case of Trade Credit

Transcription

1 The Explotaton of Relatonshps n Fnancal Dstress: The Case of Trade Credt Benjamn S. Wlner * * LECG, Inc. Ths artcle s taken from Chapter 2 of my dssertaton completed at Northwestern Unversty. I would lke to thank Susan Chaplnsky, Peter DeMarzo, Patrck W. Duthe, Mchael Fshman, Thomas George, Mort Kamen, Mtchell Petersen, Olver Rchard, and Andy Wnton as well as semnar partcpants at Concorda Unversty, Dartmouth College, the Federal Reserve Bank of Chcago, the Federal Reserve Bank of Phladelpha, the Federal Reserve Board, Unversty of Iowa, London Busness School, Norwegan School of Management, Northwestern Unversty, and Notre Dame for valuable comments. I would also lke to thank René Stulz (the edtor) and an anonymous referee for ther thoughtful suggestons. All mstakes are due to the author.

2 The Explotaton of Relatonshps n Fnancal Dstress: The Case of Trade Credt ABSTRACT: Ths paper develops optmal prcng, lendng, and renegotaton strateges for companes n relatonshps where one frm s hghly dependent upon the other. Long-term trade credtor-frm relatonshps nduce dependent trade credtors to grant more concessons n debt renegotatons than non-dependent credtors. Antcpatng these larger renegotaton concessons, not only do less fnancally stable frms prefer trade credt, but all frms agree to pay a hgher nterest rate for trade credt. The model also explans the exstence of teaser nterest rates and convenence classes. Fndngs are consstent wth those of the relatonshp-lendng lterature.

3 Trade credt s the largest source of short-term fnancng for Amercan corporatons. In 993, trade credtors extended almost $.5 trllon n credt to ther customers. In the same year, the Internal Revenue Servce (997) estmates that for every dollar n short-term fnancng provded by credt markets, $.94 n trade credt was outstandng. Most frms extensvely use trade credt despte ts apparent greater cost; trade credt nterest rates commonly exceed eghteen percent. Petersen and Rajan (994, 995) post that frms take trade credt when cheaper sources of fnancng have been exhausted. However, ths does not explan why frms wth fnancal slack use trade credt. Ths paper provdes a ratonale for trade credt use by analyzng the effect of blateral relatonshps on debt renegotaton. In partcular, optmal prcng, lendng, and renegotaton strateges are determned for companes, ther trade credtors, and other credt market lenders. Petersen and Rajan (994, 995, 997) descrbe how relatonshps can be benefcal. Ths paper demonstrates that relatonshps can be detrmental f one party s dependent upon another. For example, a frm n fnancal dstress can take advantage of a credtor f t generates a large percentage of the credtor s profts. Ths logc s appled to trade credt. Consstent wth the evdence of Evans (998), trade credtors, desrng to mantan an endurng product market relatonshp, grant more concessons to a customer n fnancal dstress than would be granted by lenders n a compettve credt market. Antcpatng these larger renegotaton concessons, the debtor frm agrees to pay a hgher nterest rate to a trade credtor than to a credt market lender. Ths s not to say that trade credt s more expensve than credt market loans; nstead, the hgher trade credt nterest rate s far compensaton for the frm s recevng larger concessons f fnancal dstress occurs. Therefore, when contractng, a borrower should ask a prevously unexplored queston: wll t generate a large percentage of ts partner s profts? If so, the borrower should be wllng to accept what appears to be a less favorable contract, antcpatng more power n renegotatons 2

4 should fnancal dstress occur. Ths model makes addtonal predctons that are consstent wth emprcal observatons. Consstent wth the evdence of Petersen and Rajan (994, 995, 997) and Wlner (997), ths paper shows that frms wth larger probabltes of default are more wllng to pay the hgher trade credt nterest rate as the assocated renegotaton concessons are more lkely. In addton, Petersen and Rajan (994, 995, 997) and Wlner (997) demonstrate that the ntertemporal varablty of the trade credt terms s less than the varablty of credt market rates. Ths paper shows that renegotaton concessons are nversely related to macroeconomc nterest rates, whch dampens trade credt nterest rate fluctuatons. All other theoretcal papers prove the opposng result: f a frm takes trade credt, the correspondng terms were always more varable than the terms the credt market would have charged the frm. 2 Ths paper also accurately predcts that convenence classes, whch consst of credtors who are less lkely to be dependent on the bankrupt debtor, grant fewer renegotaton concessons n Chapter Bankruptcy. Most of the modelng n ths paper assumes that the trade credtor possesses market power and the credt market s perfectly compettve. Under these assumptons, the trade credtor earns postve expected profts whch forces a dependence on the debtor frm; the credt market does not earn postve expected profts, nor possess a smlar relance. Bulow and Shoven (978) and Petersen and Rajan (994, 995) argue that n certan nstances the credt market may not be perfectly compettve as one partcpant, a bank, can generate profts and a resultng dependence on the debtor frm. The model n ths paper s extended to allow for ths case. Ths extenson demonstrates that the nterest rate charged by a credtor vares cross-sectonally wth the degree of dependence. In addton, the paper s ntuton can be extended to show that, consstent wth Petersen and Rajan (995), f a debtor could be dependent upon ts credtor, the credtor offers teaser rates and/or relaxed terms n order to create the 3

5 dependence relatonshp. The paper proceeds as follows. The characterstcs of trade credt are dscussed n Secton I. The baselne model s descrbed n Secton II. In Secton III, optmal trade credt and credt market rates are derved; trade credt nterest rates are shown to exceed credt market rates n the baselne model. Comparatve statcs are performed n Secton IV. Model extensons are provded n Secton V. Secton VI concludes by usng ths paper s fndngs to summarze the relatonshp-lendng lterature. I. Trade Credt Interest Rates The nterest rate charged on trade credt loans vares wth the terms of sale and the degree to whch they are volated. Wlner (997) and Ng, Smth, and Smth (999) show that trade credtors often do not drectly charge nterest on ther trade credt sales; nstead they offer a dscount for early payment. Common terms of sale are 2-0 net 30. The net or full purchase prce s due n thrty days; a two-percent dscount s obtaned f payment occurs wthn ten days of sale. 3 The dscount for early payment can be consdered an nterest charge for late payment. Wth a $.00 purchase 2-0 net 30, the frm receves a $0.98 loan for twenty days; the nterest charge s $0.02. Therefore, 2-0 net 30 mples an annual nterest rate of 44.6 percent. Whle some trade credtors extend terms of 8-30 net 50 mplyng rates of 358 percent, others offer no dscount for early payment mplyng nterest-free loans. However, terms of sale are often volated as, for example, frms delay payment. Because terms of sale usually do not nclude an explct tardness penalty, 4 Wlner (997) shows that delayed payment reduces the aforementoned rates by two-ffths. Even wth ths reducton, the nterest rate on most trade credt loans far exceeds the June 25, 998 commercal paper rate of 5.48 percent. 5 Trade credt rates have also been shown to be ntertemporally stable. The Credt Research Foundaton (965) notes the prevalence of 2-0 net 30. Wlner (997) demonstrates that whle 4

6 volaton-adjusted trade credt rates fluctuate, they vary less than other nterest rates. That paper shows that whle commercal paper rates dropped about 30 percent from 983 to 993, effectve trade credt rates contemporaneously decreased by only 7 percent. 6 II. The Baselne Model Ths paper descrbes a three-perod, three-player sequental decson model. The three players are a suppler/trade credtor, a manager of a frm, and a compettve credt market. The trade credtor s a monopolstc producer of a pershable commodty. The manager s the sole owner of a frm that purchases from the trade credtor and sells to a product market. In order to solate the trade credtorfrm relatonshp, t s assumed that the frm s ether the trade credtor s only customer or the trade credtor can perfectly prce dscrmnate between hs customers. (Ths assumpton s relaxed n Secton V.A.) The frm has no costs of producton other than the prce charged by the trade credtor. The frm's manufacturng process s one-to-one, t s unable to store goods for more than one perod, and the frm s assumed to be a prce taker when sellng ts good. Whle the trade credtor s not cash constraned, the frm requres a loan to purchase ts nputs. The frm has two potental sources of fundng: the trade credtor and the credt market. The manager s assumed to ssue debt to purchase her frm s nputs. In order to prevent the frm from entrely nsulatng tself from uncertanty n the product market, t s assumed that a three-perod loan contract cannot be wrtten. Fgure dsplays the sequence of events. In perod 0, the trade credtor produces one unt of hs product and assumes the cost of producton v. He/she sets two prces: a cash prce (d) and a credt prce (p). 7 The nterest rate he/she charges, tc, s mplct n the formula: p = d ( + tc). Gven these prces, the credt market compettvely sets an nterest rate, r. The frm then purchases one unt of 5

7 product from the trade credtor ether wth cash or on credt. If credt s selected, the frm agrees to pay the trade credtor p n perod. To pay n cash, the frm borrows d from the credt market, uses the borrowed funds to pay the trade credtor, and assumes a loan due n perod wth face value of d( + r). At the end of perod 0, cash flows are dscounted at the rate of, where s the rsk-free rate. In perod, the frm sells to a product market wth stochastc demand. The market prce, whch s publcly observed and verfable at ths tme, s ether hgh, a > 0, or zero. The hgh prce occurs wth probablty q. If the market prce s zero, the frm s forced to renegotate ts debt as t has no revenues. If the hgh market prce occurs, the frm has the choce to renegotate or repay ts credtor. The renegotaton game s dscussed n Secton III.A. After repayment or renegotaton, all profts are dstrbuted as dvdends and consumed. Then a second sale occurs as long as the frm s not lqudated n perod. 8 The events n the second sale are dentcal to those n the frst sale except the prces and nterest rates are denoted by p2, d2, tc2, and r2, respectvely. After the second sale, the game ends. Let πt tc, πt m, and πt cm be the expected profts, ncludng and subsequent to sale t, of the trade credtor, the manager, and the credt market, respectvely. These profts are gven n tme t dollars. III. Solvng the Baselne Model Ths secton shows that trade credt rates dffer from credt market rates when the trade credtor earns postve expected profts from a contnung relatonshp. The model s solved by backwards nducton. Sale 2 results are determned frst, then the soluton to sale s ascertaned. A. Renegotaton Before determnng optmal strateges, renegotaton must be dscussed. It can occur ether 6

8 prvately or n the Bankruptcy Courts. It s assumed to be mmedate and costless. If the frm and ts credtor(s) agree to reorganze the frm s debts, the frm contnues to operate. If the frm and ts credtor(s) cannot agree, the frm s lqudated and all partes receve nothng. 9 Trade credtors and credt market lenders both provde unsecured short-term loans, whch have equal prorty under the Bankruptcy Reform Act of 979. However, Predcton 2 demonstrates that even though the law mples that both credtors should grant dentcal concessons, dependence on the fnancally dstressed frm causes the trade credtor to grant greater concessons n sale renegotaton than a smlarly postoned credt market lender. In other words, the trade credtor receves a smaller fracton of cash and/or equty n the fnancally dstressed frm n sale renegotaton than the credt market lender. By usng an unconventonal methodology to calculate the amount receved by the credtor(s) n renegotaton, ths paper demonstrates the relatonshp between the trade credtor s dependence on the fnancally dstressed frm and the renegotaton concessons. Instead of alterng the fracton of the money at stake conceded by each credtor, the model assumes that both the trade credtor and credt market lender concede the same fracton but the amount of money at stake n renegotaton vares. To smulate equal prorty, the credtors, rrespectve of type, are assumed to receve the same fracton, 0 < s <, whle the debtor receves - s. Bebchuk and Chang (992), Brown (989), and Gammarno (989) derve partcular fractons n ther theoretcal models. The money at stake equals the fnancally dstressed frm's current and expected future profts plus ts credtors expected future profts from tradng wth the frm. The credtors expected future profts are ncluded because they are a relatonshp-specfc asset that affects renegotaton. 0 Therefore, n sale renegotaton, the money at stake s larger f trade credt s beng negotated, as Theorem 2 shows that the trade credtor earns postve expected profts n sale 2 whle the credt market lender does not. The fact that the trade 7

9 credtor s expected sale 2 profts are at stake only f trade credt s taken n sale s explaned n greater detal n Secton V.D. Contrary to sale, n sale 2 renegotaton, rrespectve of the credtor type, the money at stake equals the frm s current profts snce there are no future profts as the game ends after sale 2. The amount receved by the credtor results by multplyng the money at stake wth the fracton conceded. Ths dstrbuton, whch vares wth the perod, demand state, and credtor dentty, s gven out n cash and/or equty n the frm. Let e tc be the fracton of the frm's equty awarded to the trade credtor and let e cm be the fracton of the frm's equty awarded to the credt market f renegotaton occurs after sale. Snce the frm only has one credtor n sale, e tc and e cm are not smultaneously postve. If renegotaton occurs after sale 2, the credtor receves no equty as the game subsequently termnates. Credtors receve cash dstrbutons only f renegotaton occurs when the market prce s hgh as no cash s generated when the zero demand state occurs and profts are assumed to be dstrbuted at the end of each sale. B. Sale 2 The amount of money at stake f renegotaton occurs after sale 2 equals ether a or 0, dependng upon the sale 2 market prce, but not on the sale 2 credt source. If a trade credt loan s renegotated n sale 2, renegotaton awards the trade credtor, sa or 0, whch equals a fracton s of the money at stake. The credt market receves the same amount f ts loan s renegotated n sale 2. Thus, the frm retans ether ( - s)a or 0. Snce the amount at stake s credtor ndependent, the renegotaton payoffs are credtor ndependent as well. Therefore, when there are no future profts from a contnung relatonshp, both credtor types receve the same amount n renegotaton as ntended n the Bankruptcy Reform Act. Theorem dsplays ths sale 2 renegotaton result. 8

10 Theorem : If sale 2 renegotaton occurs when the market prce equals zero, the credtor (credt market or trade credtor) and the debtor all receve nothng. If sale 2 renegotaton occurs when the market prce s hgh, the credtor receves sa and the debtor receves ( - s) a. Gven the sale 2 renegotaton outcome, the manager s sale 2 strategy s explored. When the market prce s zero, the frm s forced to renegotate as t has no revenues. Therefore, the manager of the frm s left wth two decsons: the source of credt and whether or not to renegotate when the market prce s hgh. As renegotaton s a zero-sum game between the frm and ts credtor(s) wth no moral hazard, the manager optmally selects the strategy that mnmzes the dstrbuton to her credtor. Profts from ths strategy are gven n Lemma. All proofs of subsequent Lemmas and Theorems are dsplayed n the Appendx. Lemma : Gven d2, r2, p2, e tc, and e cm, the manager's sale 2 profts equal: { } m tc cm π tc cm 2 (e,e d 2,p 2,r 2 ) = (- e - e )q a - mn[sa, d 2 ( r 2),p 2]. () + If d2 ( + r2) s mnmal, the manager s optmal strategy s to borrow from the credt market and not default n the hgh demand state. If p2 s mnmal, the manager s optmal strategy s to take trade credt and not default n the hgh demand state. If sa s mnmal, the manager s optmal strategy s to borrow from ether source and default n the hgh demand state. Antcpatng the manager s credt and renegotaton choces, the credt market determnes ts nterest rate, r2. Because the credt market s compettve, Lemma 2 determnes the r2 that grants the credt market zero expected profts. 9

11 Lemma 2: In sale 2, r2 = f ( + )d 2 q > sa and p2 sa. Otherwse, r = + 2 q -. The sale 2 cash prce, d2, and credt prce, p2, are determned next. Because the credt market earns zero profts and there s no moral hazard, the trade credtor earns maxmal profts when the manager's earnngs are mnmzed. Theorem 2 derves optmal nterest rates, manageral strateges and the resultng profts. Theorem 2: Gven 0 e tc, e cm, and qsa - v > 0, n sale 2:. The trade credt and credt market nterest rates are: tc 2 = r 2 = + q -. (2) 2. The frm only defaults when the zero market prce occurs. 3. The frm s ndfferent between both sources of credt. 4. The equlbrum expected profts for trade credtor, credt market, and manager are: tc tc cm π tc 2 (e,e ) = qsa v + e ( s)qa, cm tc cm π cm 2 (e,e ) = e ( s)qa, m tc cm π tc cm 2 (e,e ) = ( - e -e )( s)qa. + (3) (4) (5) The trade credtor s sale 2 profts can be decomposed nto two parts: the money he/she earns from the sale of hs product, qsa - v, and the money earned from holdng e tc of the frm's equty, [(-s)qa]. The frst term drves most of the later results; as stated n the assumptons of Theorem 2, ths term s assumed to be postve. The second term arses f trade credt s 0

12 renegotated n sale ; ths renegotaton awards the trade credtor e tc of the frm s equty. The credt market s profts n sale 2 result from the equty t holds f renegotaton occurred on a credt market loan n sale. Lastly, the frm retans what t has not dstrbuted to the credtors. Theorem 2 ndcates that the nterest rates both credtors charge exactly compensate for the tme value of money and the probablty of default. The paper s frst predcton mmedately follows. Predcton : When the future profts of both credtors from a contnung relatonshp wth the frm are zero, the trade credt and credt market nterest rates are dentcal. Therefore, the standard Modglan-Mller (96) result arses where, n absence of frctons, the manager s ndfferent between credt sources and all credtors charge the same nterest rate. As s shown n Predcton 3, ths result does not hold when there are future profts as n sale. C. Sale Lke sale 2, the results of renegotaton are frst determned. More money s at stake n sale renegotaton f trade credt s taken than f the frm renegotates wth the credt market because the trade credtor s sale 2 profts are only at stake n the former case. Therefore, unlke sale 2, the equty and cash payments to the credtor are credtor as well as demand dependent n sale. Let TC and CM represent the sale credtor, trade credtor or credt market. R ndcates that renegotaton occurs after sale. Let H and Z denote the sale hgh and zero market prce respectvely. Thus, e cm (CM,R,Z) equals the equty receved by the credt market f the frm renegotates a credt market loan when the sale market prce s zero. Theorem 3 dsplays the sale renegotaton results. Theorem 3: When the sale market prce equals zero, no cash s dstrbuted to the credtor. If a sale credt market loan s renegotated when the market prce equals zero, the credt market receves

13 e cm (CM,R,Z) = s. If trade credt s renegotated n sale when the market prce equals zero, the trade credtor receves e tc (TC,R,Z) = s qsa v. (6) qa The cash and equty payoffs for sale renegotaton when the hgh market prce occurs are dsplayed n the Appendx. As the dfference between the two equty payoffs s proportonal to the trade credtor's expected sale 2 profts from sellng the good, qsa + v, Theorem 3 demonstrates that the fnancally dstressed frm explots the trade credtor s dependence by makng hm/her take less equty than the credt market n renegotaton. 2 Theorem 3 also shows that trade credtors grant less concessons as the rsk free rate,, ncreases. Intutvely, ths relatonshp exsts because as macroeconomc rates rse, the trade credtor cares more about present profts than about protectng contnung relatonshps. Predcton 2 results drectly. Predcton 2: Trade credtors assst ther customers n fnancal dstress more than the credt market by grantng larger concessons n renegotaton. The amount of addtonal assstance vares wth the dependence of the trade credtor on the fnancally dstressed frm. As the rsk free rate,, ncreases, trade credtor concessons decrease. Evans (998) provdes evdence consstent wth ths predcton. She demonstrates that trade credtors grant more concessons n Chapter bankruptcy than smlarly postoned banks. Snce trade credtors receve a lower sale renegotaton payoff, Predcton 2 mples that the manager s renegotaton payoff s hgher f trade credt s renegotated than f a credt market loan s renegotated. Therefore, gven that renegotaton occurs, the manager ex post prefers to possess trade 2

14 credt n sale renegotaton. However, Theorem 4 demonstrates that prces are set to compensate for ths preference, causng the manager to be ex ante ndfferent between the two forms of credt. Antcpatng the sale renegotaton results, sale prces and strateges are determned usng a methodology smlar to the one used to fnd the sale 2 equlbrum. Due to the notatonal complexty of the terms, Lemmas 3 and 4 that determne the manager's and credt market s strateges are left to the Appendx. Equlbrum nterest rates as well as the resultng manageral strateges are contaned n the Theorem 4. Theorem 4: In sale equlbrum,. The trade credt nterest rate s: 2. The credt market nterest rate s: tc = ( ) ( ) sa + (-s)v qsa + (-s)v 3. The frm s ndfferent between both forms of credt. 4. Renegotaton only occurs when the market prce equals zero. -. (7) r = q - -q (-s)qsa -. (8) q qsa + (-s)v Snce there are no renegotaton costs and no moral hazard, the model acheves frst best. Predcton 3 formally states the exstence of the trade credt nterest rate premum. Predcton 3: The trade credt nterest rate exceeds the credt market rate. Proof: Combnng equatons 7 and 8, algebra leads to the followng expresson: tc- r = -q (-s)( )( qsa - v) +. (9) q qsa + (-s)v 3

15 Snce 0 < q, s <, > 0, and qsa - v > 0, tc - r > 0. QED Ths nterest rate premum compensates the trade credtor for grantng the larger concessons n sale renegotaton descrbed n Predcton 2. Ths premum also makes the manager ndfferent between trade credt and a credt market loan. Ths ndfference provdes theoretcal support to Petersen and Rajan s (994, 995, 997) observaton that frms take trade and other forms of credt smultaneously. IV. Comparatve Statcs In ths secton, comparatve statcs on the sale trade credt nterest rate, the sale credt market nterest rate, and the dfference between the two are performed by dfferentatng Equaton 7, 8, or 9. Whle the frst two comparatve statc results are not surprsng, the latter two results ntroduce two mportant nsghts of the model. Predcton 4: The trade credt and credt market nterest rates, tc and r respectvely, rse wth the trade credtor s and credt market s cost of captal,. As macroeconomc nterest rates rse, the trade credtor and the credt market rase ther nterest rates to compensate for ther ncreased cost of captal. Ths result s consstent wth the fndngs of Long, Maltz, and Ravd (995), Petersen and Rajan (994, 997), and Wlner (997), who all fnd that trade credtors restrct credt terms when macroeconomc nterest rates rse. Predcton 5: As the probablty of the hgh demand state, q, ncreases, the trade credt nterest rate, tc, falls, snce default s less lkely. The paper now nvestgates the effect of parameter changes on the dfferental between trade credt and credt market nterest rates. Predcton 6: The nterest rate dfferental decreases as the cost of captal for the credt market and 4

16 trade credtor,, ncrease. An ncrease n real macroeconomc nterest rates has two counteractng effects. Predcton 4 shows that the trade credtor and credt market lender rase ther rates to compensate for the hgher cost of captal. Conversely, Predcton 2 demonstrates that the trade credtor grants fewer renegotaton concessons, whch dmnshes the trade credt nterest rate. In equlbrum, the frst effect domnates; an ncrease (decrease) n the macroeconomc rate causes trade credt nterest rates to rse (fall). However, the combnaton of the two effects causes the change n the trade credt nterest rate to be less than the change n the credt market rate. Ths mples that trade credtors dampen the effects of macroeconomc nterest rate fluctuatons. Therefore, consstent wth the evdence n Secton I, trade credt rates are less responsve than credt market rates to changes n the rsk-free rate. Ths result contrasts wth that of Kyotak and Moore (997) who theoretcally show that trade credtors exacerbate credt shocks by demonstratng that credt ratonng propagates n a small closed economy. Propagaton does not occur n ths model as credt provders are assumed to be n a large economy and/or are not cash constraned. Predcton 7: The hgher the trade credtor's sale 2 expected profts from sales, qsa - v, the larger the dfference between the trade credt and credt market nterest rates. Predcton 7 results drectly from combnng Predctons 2 and 3. Predcton 2 demonstrates that greater sale 2 proftablty ncreases the trade credtor s dependence on the frm as well as the amount conceded n renegotaton. Predcton 3 shows that the trade credtor charges a hgher rate to compensate for grantng larger renegotaton concessons. Whle Petersen and Rajan (994, 995, 997) mostly observe the opposte result: larger profts mply less restrctve lendng terms, they show that Predcton 7 holds for the most proftable credtors n ther sample. 3 In addton, they nvestgate borrowng by small busnesses. Wlner (997), who nvestgates larger Compustat frms, fnds evdence consstent wth Predcton 7. Sectons V.C. and V.D. of ths paper dscuss why Predcton 7 mght not 5

17 hold for low proft credtors and young, small customers. V. Model Extensons. A. Manageral Type. Ths secton alters the model by assumng there are two dfferent manageral types: good and bad. The manager prvately observes her own type at the begnnng of the game. 4 The probabltes of the hgh market prce for the good and bad managers n sale are qg > qb, respectvely. Whle manageral type affects sale, type s assumed not to affect sale 2; the hgh prce probablty equals q n sale 2 rrespectve of type. Results follow almost drectly from the model n Secton III. Snce sale 2 s unaffected by ths extenson, Lemmas and 2, as well as Theorems, 2, and 3 hold dentcally. Lemma 5, whch presents optmal manageral strateges for sale, s smlar to Lemma 3 wth q τ, τ = g or b, substtuted n approprately. Lemma 6 determnes the credt market nterest rate. Lemmas 5 and 6 appear n the Appendx. Theorem 5 presents the resultng equlbrum. Theorem 5: In sale, there s a unque subgame perfect separatng equlbrum where the good manager borrows from the credt market whle the bad manager takes trade credt. Default only occurs when the market prce equals zero. The ntuton behnd ths equlbrum derves from Predcton 2, whch notes that trade credtors grant more concessons n renegotaton than credt markets. Because the bad manager has a greater probablty of defaultng, he/she s more lkely than the good manager to receve these renegotaton benefts. Therefore, the bad manager s wllng to pay more than the good manager for trade credt. 6

18 Snce the trade credtor s unable to set dfferent prces for dfferent customers, a separatng equlbrum where the bad manager takes trade credt and the good manager borrows from the credt market arses. Predcton 8 results. Predcton 8: Frms wth a greater probablty of default prefer trade credt to a credt market loan. Thus, trade credt can be used to dscrmnate between frms wth dfferent default rsks. Ths predcton s consstent wth most models of trade credt. 5 However, these models derve separatng equlbra by assumng some form of credt ratonng. Ths secton demonstrates that separaton can occur even wthout credt ratonng. If ratonng occurs, the dscrmnaton result would be even stronger. B. Systematc Shocks Ths secton assumes the frm s unable to nsulate tself from the rsk of the zero demand state. Credt ratonng can nduce ths systematc rsk. In ths case, a relatonshp between the nterest rate dfferental, credtor proftablty, and the probablty of the hgh demand state arses. Predcton 9: Whle the effect of a change n the probablty of the hgh demand state, q, on the dfference between the trade credt and credt market rates cannot be unambguously determned, the effect dmnshes as the trade credtor s expected sale 2 profts ncrease. 6 There are two counteractng effects of an ncrease n the probablty of the hgh demand state. Frst, the trade credtor s expected sale 2 profts ncrease. Predcton 7 mples that the nterest rate dfferental would subsequently ncrease. Second, the probablty of perod default decreases mplyng renegotaton becomes less lkely. Therefore, the trade credtor provdes less renegotaton concessons and would charge a lower nterest rate. Predcton 9 mples that as the trade credtor s expected sale 2 profts ncrease, the second 7

19 effect becomes more domnant. If the profts are large enough, the second effect domnates, and Predctons 2 and 9 mply that trade credtors assst the customers n two ways. Predcton 2 shows that trade credtors help ther customers n renegotaton. Predcton 9 demonstrates that trade credtors ease credt terms more rapdly than credt markets as the lkelhood of customer default dmnshes. Conversely, f the trade credtor s sale 2 profts are small enough, the dfference between the trade credt and credt market nterest rates ncreases wth the probablty of the hgh demand state. Ths concluson s consstent wth Petersen and Rajan (995) observaton that as a small frm ages, ts borrowng costs fall faster n compettve lendng markets. C. Dfferng Compettve Assumptons Smlar results arse f the compettve assumptons are relaxed. In the baselne model, the trade credtor s monopolstc and the credt market s compettve. If the trade credt market becomes more compettve, the proportonalty of the nterest rate premum and trade credtor s expected future profts shown n Predcton 7 stll exsts. However, as the latter probably decreases wth ncreased competton, so does the former. As was mentoned n the ntroducton, Bulow and Shoven (978) and Petersen and Rajan (994, 995) show that one partcpant n the credt market, banks, could generate profts and a resultng dependence on a debtor frm. In ths case, the nterest rate dfferental s proportonal to the relatve dependence of the trade credtor and the bank on the debtor frm. Ths mples Predcton 0. Predcton 0: If the bank's future profts from a contnung relatonshp are larger than the trade credtor's, bank nterest rates exceed the trade credt rate. Predcton 0 mples that trade credtors ease ther terms relatve to bank rates when banks possess wth relatonshps wth ther customers. Rajan and Zngales (995) provde evdence consstent 8

20 wth ths predcton n countres where bankng relatonshps are mportant. The combnaton of Predctons 3 and 0 s consstent wth the observaton that trade credt rates are sometmes hgher and sometmes lower than comparable credt market rates. Together these two predctons suggest that as an ndustry s compettveness ncreases, a credtor s expected renegotaton concessons decrease, whch causes credt terms to be eased. Ths paper develops models where a credtor s dependent upon a debtor. If the opposte dependence exsts, accordng to the logc of ths paper, a credtor should be able to extract rents from a dependent debtor. Therefore, credtors could offer teaser rates and/or relaxed terms n order to attract dependent debtors. Petersen and Rajan (995) theoretcally and emprcally demonstrate that credtors ntally ad small busnesses by chargng the low rates, expectng to earn profts by chargng hgher rates n the future. D. Robustness of the Results and the Exstence of Convenence Classes The key nsght of ths paper s that n debt renegotatons trade credtors bargan to protect past loans as well as future profts. As dscussed n Secton III.A., ths ntuton s formalzed by demonstratng that the trade credtor s future profts are a part of the money at stake n debt renegotatons only f trade credt s taken. Some mght argue that a trade credtor s future profts should be ncluded even f the frm borrows from the credt market. Accordng to ths argument, the credt market would threaten to lqudate the frm f the trade credtor does not grant concessons. However, ths argument s contradcted by backward nducton as the credt market s threat to lqudate s not credble. Assume the trade credtor gnores the credt market s threat. Snce ths model descrbes a one-shot game, t s optmal for the credt market to accept the postve amount descrbed n Theorems and 3 as opposed to lqudatng and recevng zero. Thus, the trade credtor can gnore the 9

21 credt market s demand for concessons and the trade credtor s future profts would not be at stake f the frm borrows from the credt market. By a smlar backward nductve argument, the trade credtor s threat of refusng to sell to a frm n the future unless he/she receves a certan amount n debt renegotatons s not credble. The above rebuttal assumes that credtors fght for every dollar n debt renegotatons. However, f the fnancally dstressed frm does not generate a large percentage of the credtor s profts, the credtor s threats descrbed above become more credble. Consequently, these credtors who are less dependent on ther fnancally dstressed customers are also less apt to grant renegotaton concessons. In practce, ths s observed as Chapter allows the creaton of a convenence class that conssts of credtors owed less than a certan amount. As ther threats are more credble, convenence classes usually grant less concessons than other unsecured classes. Fabozz, Howe, Makabe, and Sudo (993) dscuss convenence classes. In addton, the nterest rate charged by a credtor should vary wth the credblty of ts threats. Wlner (997) emprcally demonstrates that the trade credt nterest rate s parabolc n customer sze. If a customer s very small, whch mples that t does not generate a large percentage of the credtor s profts and s lkely to depend on ts credtor, the trade credt nterest rate decreases wth customer sze. If the customer s very large, whch means t s more able to extract renegotaton concessons from ts credtors, the trade credt nterest rate ncreases wth customer sze. Ths argument also provdes a ratonale for Petersen and Rajan s (994, 995, 997) observatons that credtors ease terms to young, small frms whose proftablty ncreases and that young, small, and unproftable trade credtors ease terms as ther own proftablty ncreases. 20

22 VI. Concluson Whle ths paper has concentrated on trade credt, more generally, t proves that dependence n blateral relatonshps explan many phenomena about lendng. Frst, a dependent credtor grants more concessons n renegotaton than a credtor wthout such a dependence. To compensate for these concessons, the nterest rate charged by the dependent credtor ncreases wth the degree of dependence. These concessons also cause the dependent credtor s nterest rate to fluctuate less than the non-dependent credtor s rate n response to changes n the rsk-free rate. In addton, dependent credtors reduce the rates they charge more rapdly as ther customer s lkelhood of default decreases. When a dependent credtor can completely dscrmnate, ts customers are ndfferent between all loan types. If complete dscrmnaton cannot occur, desrng the assocated renegotaton benefts, a fnancally dstressed frm borrows from the dependent credtor even f the non-dependent credtor offers lower rates. In summary, the lendng relatonshps lterature can be understood by notng that dependence alters the prcng of fnancal contracts. If one party generates a large percentage of ts partner s profts, t should be wllng to enter nto a seemngly unfavorable contract antcpatng more power should problems arse. Petersen and Rajan (994, 995, and 997) provde evdence consstent wth the above theory by nvestgatng small busnesses, whch are lkely to depend on ther credtors. Specfcally, ther 995 paper demonstrates that credtors offer teaser rates n order to attract dependent customers then subsequently charge hgh rates. Alternatvely, ths paper demonstrates that frms receve two benefts from acceptng a hgh nterest rate loan from a dependent credtor. Frst, consstent wth the evdence n Evans (998), a dependent credtor grants more concessons when a customer s n fnancal dstress. Second, a credtor reduces the rates t charges more rapdly as a customer s lkelhood of default decreases. Fnally, f dependence does not exst, as n the case of convenence classes n Chapter 2

23 Bankruptcy, ths paper accurately predcts that large renegotaton concessons are not granted. 22

24 Appendx Proof of Lemma : Snce the manager ams to maxmze her profts, the proof enumerates the manager's strategy choces, determnes the resultng profts, and selects the maxmum. If the market prce equals zero, there are no revenues and the partes receve nothng rrespectve of the manager's strategy choce. When the market prce s hgh, whch occurs wth probablty q, the frm receves revenues of a. The amount t pays ts credtor s strategy dependent. If trade credt and no renegotaton s chosen, the frm pays the trade credtor the cash prce of p2. If the credt market and no renegotaton s chosen, the frm pays the credt market d2 ( + r2). If the frm renegotates ether form of credt when the market prce s hgh, Theorem states that the frm must pay ts credtor sa. Snce the trade credtor and the bank possess e tc and e cm of the frm's equty, respectvely, the manager receves only - e tc - e cm of the frm's profts. By selectng the optmal strategy, the manager's sale 2 profts equal: { } [ ]. tc cm (-e -e )max q(a - sa),q[a -d ( r )],q(a - p ) + = tc cm (-e -e )q{ a - mn sa,d 2( r 2),p + 2 } (A) Because the manager receves and transfers cash n perod 3 and the manager s sale 2 profts are measured n perod 2 dollars, dscountng at the rate of occurs. QED Proof of Lemma 2: If d2 ( + r2) mn (p2, sa), the manager borrows from the credt market and does not default when the market prce s hgh. Under ths condton, the frm borrows d2 n perod. In perod 2, wth probablty 23

25 q, the frm repays the loan plus nterest, d2 ( + r2); wth probablty - q, the credt market receves nothng. The credt market s expected zero proft condton mples that d 2 = 2 2 qd ( r ) or r 2 = q -. Therefore, ths nterest rate s set f d 2 mn(p 2,sa). q If p2 mn {sa, d2 }, the manager takes trade credt and does not default when the market q prce s hgh. Snce trade credt s taken, the credt market s zero proft condton s trvally satsfed. Therefore, the credt market can set any nterest rate, r2 p2 /d2 -. One such rate that satsfes ths condton s r 2 = q -. If sa mn {p2, d2 q }, the manager defaults when the market prce s hgh on ether form of credt. In ths case, f a loan s extended by the credt market, n perod the credt market loans d2 and, n perod 2 the frm defaults and credt market receves sa wth probablty q. The credt market s expected profts n ths case are cm π 2 = 2 qsa - d. If these expected profts are negatve ( sa < ( )d2 q ), the credt market charges an nfnte rate. QED Proof of Theorem 2: Antcpatng the frm's and the credt market s strategy choces, the trade credtor chooses a cash prce and a credt prce to maxmze hs profts. Frst I assume that prces are set so that the credt market offers a fnte nterest rate. Then I show that the trade credtor never prefers to set prces so that the credt market sets an nfnte rate. 24

26 Assumng ( + )d 2 q sa or p2 < sa, by Lemma 2, the credt market nterest rate, r2, equals q -. By Lemma, the trade credtor s revenues equal q mn(p 2,d 2 +,sa). The trade + q credtor always pays the cost of producton, v. The trade credtor also receves a fracton e tc of the frm's profts. Therefore, the trade credtor s profts are gven by: tc tc cm π 2 p,d 2 2 tc (e,e ) = max q mn(p,d +,sa) v + qe a mn(p q 2,d 2 +,sa) q (A2) + Because e tc <, trade credtor s sale 2 profts are maxmzed when p2 = sa and d2 = qsa. Wth these prces, the trade credt nterest rate equals the credt market rate, 2 2 tc 2 = p - d = 2 d2 q - = r ; and the frm s ndfferent between takng both forms of credt and between defaultng and not defaultng n the hgh demand state. In addton, ( + )d 2 sa and p2 < sa, q as ntally assumed. Substtutng these prces nto Equaton A2, trade credtor profts become: tc tc cm π tc 2 (e,e ) = qsa v + e qa( s) (A3) Conversely, f p2 sa and sa < ( + )d 2, Lemma 2 mples that r2 = and the manager takes q trade credt and defaults n the hgh demand state. In ths case, the trade credtor s profts equal the profts n Equaton A3. Therefore, ths strategy s not strctly preferred. QED Proof of Theorem 3: The manager s owed a fracton - s of the sum of the frm s current revenues and the perod 2 profts of the debtor and credtor, whch are lsted n Column 4 of Table I. The manager receves her expected 25

27 sale 2 profts. The manager also receves - C of the cash at stake f the hgh market prce occurs when trade credt s renegotated. The manager receves - B of the cash at stake f the hgh market prce occurs when a credt market loan s renegotated. The sum of what the manager receves s gven n Column 3 of Table I. When the frm borrows from the credt market n sale, e tc equals 0. When trade credt s taken, e cm equals 0. The equty dstrbutons, e tc and e cm, whch are dsplayed n Columns 5 and 6, respectvely, of Table I, are obtaned by settng what the manager receves equal to what the manager s owed. The followng two condtons must be satsfed for the fractons C and B to be between 0 and : [ ] s v( s) max 0,s qa v C s, a + a 2 q( s) ( s)qs max 0,s B s+ (A4) (A5) QED Lemma 3: Gven p, d, and r, the manager's cumulatve profts equal: max {( s) [( + )qa v ]}, { + [ + + ]} { q[a d ( r )] + ( s)( s + sq) qa}. q(a p ) ( s) qa ( q)v,. (A6) If the frst term s maxmal, the frm chooses trade credt and renegotates when the hgh prce occurs. If the second term s maxmal, the frm takes trade credt and does not renegotate f the hgh prce occurs. If the last term s maxmal, the frm borrows from the credt market and does not renegotate f the hgh prce occurs. 26

28 Proof of Lemma 3: The frst step s to determne the manager s profts correspondng to the sale strategy of defaultng on trade credt when the prce s hgh. Wth probablty q, the hgh demand state occurs and the manager receves - C of the sale cash flow, a, plus her sale 2 profts whch are obtaned by tc substtutng e (TC,R,H) from Table I nto the manager s sale 2 proft functon gven n Equaton 5. Wth probablty - q, the zero demand state occurs and the manager receves her sale 2 profts whch tc are obtaned by substtutng e (TC,R,Z) from Table I nto the manager s sale 2 proft functon. Therefore, the manager's combned sale and sale 2 profts from ths strategy equal: {(-s)[( )qa v ]} +. + The manager's profts for her other sale strateges can be calculated n a smlar manner. These calculatons reveal a domnated strategy. Manageral profts from renegotatng trade credt n the hgh demand state exceeds the profts from renegotatng a credt market loan n the hgh demand state by ( ) ( s) qsa v > 0. Therefore, the manager never selects the latter strategy. QED Lemma 4: Gven p and d the credt market sets ts nterest rate, r, to be: r = q - -q q (- s)qsa -. (A7) d Proof of Lemma 4: The manager never defaults on a credt market loan when the prce s hgh. If trade credt s taken, the credt market trvally earns zero profts. 27

29 If the frm borrows from the credt market and does not default when the prce s hgh, the credt market sets ts costs equal to ts revenues, or [ ] d = qd ( r ) + (-q)(-s)qsa. (A8) + + The credt market loans d at the begnnng of sale. It receves d( + r) wth probablty q. Wth probablty - q, default occurs and the credt market receves equty that has a value of (-s)qsa. The credt market nterest rate, r, s mplct n Equaton A8. r = q - -q q (-s)qsa -. (A9) d QED Proof Theorem 4: Snce ths s a zero sum game between the trade credtor and the frm, the trade credtor maxmzes hs profts by settng prces, p and d, to mnmze the earnngs of the frm. Therefore, the trade credtor s problem can be wrtten as: mnp,d max {( s) [( + )qa v ]}, { + [ ]} { qa ( )d + ( s)qa}. q(a p ) ( s) qa ( q)v,. (A0) The thrd term s obtaned by substtutng the credt market nterest rate nto the formula for the manager s profts from borrowng from the credt market and not defaultng n the hgh demand state. One set of equlbrum credt and cash prces are : p = sa + (-s)v, (A) 28

30 Therefore, the trade credt nterest rate equals The credt market nterest rate s r = q { } d = qsa + ( s)v. (A2) [ ] tc = p - d ( ) sa + (-s)v = -. (A3) d qsa + (- s)v --q q (-s)qsa - d q - -q (-s)qsa = q qsa + (-s)v -. (A4) QED Lemma 5: Gven p, d, and r, the manager of type τ's cumulatve profts, τ {g, b} equal max q ( s) (q + )a v, τ { + [ ]} + τ τ { q [a d ( r )] + ( s)( s + sq ) τ τ qa}. q (a p ) ( s) qa ( q )v,. (A5) If the frst term s maxmal, the manager chooses trade credt and renegotates f the hgh prce occurs. If the second term s maxmal, the manager takes trade credt and does not renegotate f the hgh prce occurs. If the last term s maxmal, the manager borrows from the credt market and does not renegotate f the hgh prce occurs. Proof of Lemma 5: Apply the same steps as Lemma 3 wth q τ properly substtuted for q. QED Lemma 6: Gven p and d, f the bad manager takes trade credt and the good manager borrows from the credt market, the credt market nterest rate s: 29

31 g r = - -q qg qg (-s)qsa -. (A6) d If the good manager takes trade credt and the bad manager borrows from the credt market, the credt market nterest rate equals: b r = - -q qb qb (-s)qsa -. (A7) d Proof of Lemma 6: See the Proof of Lemma 4. Proof of Theorem 5: There are two potental separatng equlbra. Case I: The good manager borrows from the credt market and the bad manager takes trade credt and both managers do not default n the hgh demand state. As n Theorem 4, the trade credtor s profts are maxmzed by mnmzng manageral earnngs. Therefore, the prces, p and d, are set to solve the followng constraned mnmzaton problem: Subject to Mn p,d θ + { q (a p ) ( s) b + [ qa ( q )v b ]} ( θ) { q [a d ( r )] ( s)( s sq ) g g qa} (A8) q b(a p ) ( s) + qa max + ( s)( q b )v q ( s) (q + )a v b, q b[a d ( r )] + ( s)( s + sq ). qa b, (A9) 30

32 q [a d ( r )] g max + ( s)( s + sq ) qa g q ( s) (q + )a v g, q (a p ) g ( s) + [ qa ( q )v]. g, (A20) g r = - -q qg qg (-s)qsa -. (A2) d The trade credtor sets prces to mnmze manageral earnngs n Equaton A8. θ equals the probablty the manager s bad. Equatons A9 and A20 are the ncentve compatblty condtons for the bad and good manager, respectvely. Equaton A2 s obtaned from Equaton A6. and d = { q sa ( s)v} The prces, p = sa + (-s)v g +, solve ths mnmzaton problem. Thus, Case I corresponds to a separatng equlbrum. Case II: The bad manager borrows from the credt market and the good manager takes trade credt and both managers do not default n the hgh demand state. The prces, p and d, are set to solve a mnmzaton problem whch s dentcal to the one n Equatons A8 - A2 except θ and - θ as well as qb and qg are reversed n all the expressons. Algebra demonstrates that there are no prces that solve ths mnmzaton problem. Therefore, a separatng equlbrum correspondng to Case II does not exst. QED 3

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