Asymmetric Information, Debt Capacity, And Capital Structure *

Transcription

1 Asymmeric Informaion, Deb Capaciy, And Capial Srucure * Michael. emmon Universiy of Uah Jaime F. Zender Universiy of Colorado a Boulder Curren Draf: July 20, 2011 Very Preliminary and Incomplee Do No Quoe wihou Auhor s Permission * emmon: (801) , finmll@business.uah.edu; Robers: (215) , mrrober@wharon.upenn.edu; Zender: (303) , jaime.zender@colorado.edu. We would like o hank Mahias Kahl and Chris each for helpful discussions.

2 Asymmeric Informaion and Capial Srucure Absrac: We analyze a model of financing under asymmeric informaion ha includes deb covenans. Asymmeric informaion creaes an incenive o use deb financing. The use of deb financing, however, disors he coninuaion decision of equiy holders. Deb covenans become a valuable conracing device in his environmen. The model offers several predicions regarding he use of deb covenans and heir relaionship wih he capial srucure decision of he firm.

3 The radeoff heory of capial srucure is he predominan heory of capial srucure choice in he lieraure. I is buil on he fundamenal inuiion ha one finds an opimum a he equaliy of marginal coss and marginal benefis for a given choice variable; in his case he amoun of leverage uilized by a firm. Commonly, his opimum has been characerized on a value basis; a raio beween he values of he firm s exising deb and of he firm iself (he value of all he firm s forecased fuure cash flows) or he raio beween he values of he deb and he firm s equiy. By implicily assuming ha exising deb may be rolled over or renegoiaed if here is ever a need, his characerizaion ignores he iming of he expeced fuure firm cash flows as compared wih he required deb service. Viewing he MM proposiions as a version of he Coase Theorem he imporance of he assumpion of efficien and cosless renegoiaion of he financial conracs is clear. We develop a model ha explicily considers a fricion ha encourages he use of deb financing bu ha may impede he renegoiaion of hese conracs, specifically asymmeric informaion beween he firm and is lenders, as he primary facor in capial srucure choice. Assuming ha renegoiaion of deb conracs is no fricion free, one may obain a heory of leverage based on he informaion available concerning he firm s abiliy o service is deb, publicly available informaion concerning fuure cash flow, and he difficuly of renegoiaing resricive covenans associaed wih he deb. Empirically, he main ensions in he model can be measured eiher by examining proxies for he asymmery of informaion and he naure of he uncerain cash flows or by considering he marke s response o he presence of he asymmeric informaion; mos visibly he

4 change in he naure and he sricness of bond covenans and he firm s abiliy o renegoiae covenans ha become binding as leverage is increased. The heory is based upon a model of a firm wih an uncerain cash flow generaion process and asymmeric informaion beween he firm and he marke concerning his process. Given he asymmery of informaion and he need o make a coninuaion versus liquidaion decision a an inermediae dae, covenans, which delegae he righ o make he liquidaion decision, may be aached o he bond conrac when insiders cease o have appropriae incenives. As will be shown, he opimaliy of he use of resricive covenans is closely ied o he firm s abiliy o renegoiae hese covenans when hey resric he firm from aking efficien acions. The model is an exension of Myers and Majluf s (1984) classic model. While Myers and Majluf consider he implicaions of asymmeric informaion beween he firm and providers of capial a he ime of financing, his model considers ha he informaional asymmery exends o a fuure decision making dae. A ension beween he implicaions of asymmeric informaion a he wo daes develops. As Myers and Majluf demonsrae, he use of deb is moivaed by he presence of asymmeric informaion a he ime of financing. owever, because deb alers he incenives of he insiders in heir decision making, covenans ha ransfer conrol righs o he lender become valuable addiions o he deb conracs. The lender s has inferior informaion implies his ransfer of conrol will be cosly in some saes of naure. Primary ensions in he capial srucure decision are he impac of deb on he decision making incenives of insiders and he firm s abiliy o renegoiae he resricive covenans when he cos of uninformed decision making is high. The wo consequences of he informaional 2

5 asymmery in he model allow us o derive an opimal amoun of leverage for a firm. Our model is also closely relaed o ha of Garleanu and Zwiebel (2009) who consider he design and renegoiaion of deb covenans under asymmeric informaion. Our approach differs from heirs in ha we also address capial srucure choice. One perspecive on he naure of hese resuls is ha he model has developed an endogenous measure of deb capaciy ha complemens he pecking order of financing discussed by Myers (1984). Anoher perspecive is ha a more complee recogniion of he impac of asymmeric informaion on he choice of financing idenifies a balancing cos of deb financing under asymmeric informaion, placing he analysis back in he radiional radeoff heory framework. Relaive o he predicions of he sandard pecking-order heory, he model provides a conservaive opimum. The main issues limiing he use of deb in he model are he firm s liquidaion value and he marke s inferior informaion concerning he firm s qualiy. Deb levels are appropriaely compared o he level of guaraneed cash flow (liquidaion value in he model) based on he marke s informaion. As liquidaion value is dependen upon he sae of he overall economy we obain he imporan empirical implicaion ha firms will end o use more deb in economic expansions han in conracions. The model also derives oher ineresing empirical predicions concerning leverage choice and he naure of covenans associaed wih he firm s deb. 1. The Model wih a Binary Public Signal In his model, an enrepreneur/manager seeks funding for a firm. The enrepreneur s ype or qualiy is assumed o be known precisely and privaely by he 3

6 enrepreneur (we will alernaively alk abou an enrepreneur s ype or he ype of he firm run by he enrepreneur). Exernal invesors (he marke) know only ha enrepreneur s ype is drawn from a disribuion F(); where F() is defined on he inerval [B, G], wih 0 < B < G, and F() has a well defined mean, E(). Enrepreneurs wih ypes in his inerval are assumed o be observaionally equivalen o he exernal marke a ime 0. For simpliciy, in his version of he model, we assume here are only wo ypes and ha ypes are drawn from he se {B, G} where he ex ane probabiliy of a good (ype G) firm is θ. Iniial capial, I, is required o iniiae an invesmen projec and esablish a firm. The realized value of he invesmen projec, is ime 2 payoff, is assumed o depend upon he enrepreneur s ype and he value of a signal w ha is publicly observable (and verifiable) a ime 1, where he signal, w[ w, w] has a disribuion (w). In his secion, we consider he case of a binary signal where,, and prob(w = w 1 ) = p, and w 1 w 2 0. The realized signal can be considered an ex pos indicaion of he srengh of he overall economy or he indusry (where w 1 is ermed a srong marke and w2 as a weak marke) as i will affec he forunes of all observaionally equivalen firms. The expeced signal pw1(1 p) w2serves as an ex ane measure of expeced economic condiions. If he projec is funded and allowed o coninue unil ime 2 i generaes a cash flow of or where > > 0. The high cash flow (success) is generaed a ime 2 wih probabiliy given by he produc of he firm s ype and he realizaion of he public signal, Prob(cash flow = ype = and signal = w) = w, and he low cash flow (failure) is realized wih he complemenary probabiliy, 1 w. For inernal 4

7 consisency we mus furher assume ha Gw1 1 and Bw2 0. The random variables and w are assumed o be independen. An alernaive, available a ime 1, o allowing he projec o coninue is ha he projec may be liquidaed (or qui ). iquidaion of any firm will generae a ime 1 cash flow of Q wih cerainy. 1 The iming of he model is such ha he liquidaion decision is made dependen upon he realizaion of he public signal w. Because w is verifiable i can also be used as he basis for a bond covenan ha allocaes he conrol over he ime 1 liquidaion decision. In his sense we model he inclusion of a proscripive covenan ha requires, for example he mainenance of cerain accouning raios, failure o saisfy he requiremens resuls in defaul on he deb conrac. The srucure of he model implies ha if he bondholders are allocaed he liquidaion decision, hey will be making his choice based on inferior informaion. Iniially we will assume ha renegoiaion of his covenan is no possible (renegoiaion is infiniely cosly). We will hen consider he naure and impac of renegoiaion. In he model he enrepreneur/manager is assumed o own he righs o he projec bu has no capial. The required invesmen, I, may be raised by issuing equiy or deb. More precisely, he manager chooses he face value of deb, F, he level of he public signal (if any) a which o ransfer conrol of he liquidaion decision o he bondholders, w, and he proporion of he firm s equiy o be sold exernally, α, in order o maximize he value of his/her reained equiy, (1 α). Noe ha his is equivalen o assuming ha 1 Noe ha he firm can be liquidaed eiher as a going concern or piece-meal. To he exen ha i is more likely o be liquidaed as a going concern in a srong economy he level of Q will be relaed o he business cycle and is no likely o be consan across ime. This is no an issue in our saic version of he model, however, i will influence he empirical predicions derived from he model. 5

8 he manager acs in he ineres of shareholders (given his/her superior informaion). 2 Inuiively, he effec of his assumpion is o generae an agency problem, one ha increases wih he amoun of deb financing used by he firm. The asymmeric informaion a he ime of financing moivaes he use of deb (Myers and Majluf (1984)) and he bond covenan is used o (imperfecly) conrol he resuling agency problems and provides he implicaions for he asymmeric informaion a he ime of he liquidaion decision. The Firs Bes We begin by examining he firs bes decision making wihin he model. The ime zero informed (assuming knowledge of he enrepreneur s ype) value of he firm can be wrien (using an indicaor variable for coninuaion φ(w*) which akes he value 1 if he realized signal w w* and zero oherwise) as: I V E {( w (1 w) ) ( w*) Q(1 ( w*)} w prob( w w*)( E( w w w*) (1 E( w w w*)) ) prob( w w*) Q. If we assume a coninuous public signal, by maximizing his value wih respec o w*, i is sraigh forward o find he value of he public signal below which i is efficien for a firm of a given ype o be liquidaed. This signal value is w * Q. The cuoff ( ) level of he public signal has naural properies. I decreases in he enrepreneur s/firm s ype ( w w * * B G ); good firms should be coninued in worse economic environmens han should bad firms. The cuoff level increases in Q; all else equal, he more aracive is liquidaion he more frequenly you wan o liquidae firms. Finally he 2 We will leave for fuure work he incorporaion of an opimal incenive conrac in his ype of a model (see for example, Garleannu and Zwiebel (2008) as compared o Dybvig and Zender (1991)). 6

9 cuoff level is decreasing in he difference beween he coninuaion values for success () and failure (); he greaer is he upside poenial he more ofen you wan o allow firms o coninue. In order o capure he major ensions of he more robus model bu enjoy he simpliciy of he binary signal we will assume ha in good imes, if w = w 1, boh ypes of * * firms should coninue ( w w w ) while if w = w 2 only a good ype firm should * * coninue ( w w w ). The Agency Problem B 1 G 1 B G I is sraighforward o examine he liquidaion decision of an unconsrained (no covenan) enrepreneur wih deb ousanding who operaes a firm of ype. The enrepreneur acs o maximize he informed value of his reained shares for a given face value of deb. Assuming F Q, using he liquidaion decision o maximize he informed equiy value reveals ha he manager of a ype firm will coninue if he public signal is greaer han or equal o w M Q F ( F) and will liquidae he firm oherwise. Noe ha for any F > his value is less han * w and ha he difference beween * w and M w increases in F; in oher words he agency problem (risk seeking) inroduced by he use of deb financing increases in he deb s face value. Clearly for F < (riskless deb) he manager follows he firs bes policy and if F Q he manager will always coninue (equiy receives a payoff only if he firm coninues and is successful). Similarly, defining he agency problem o be he difference w w * M, for a given F, he agency problem is negaively relaed o firm ype. 7

10 In his model, assuming he iniial invesmen level is large enough, i will never be opimal o choose deb wih a face value less han ; his is simply Myers and Majluf s resul ha firms use financial slack or riskless deb as he firs choice for financing. Furhermore, here is no benefi o using deb wih a face value larger han Q. This is because issuing deb wih F > Q is, a he margin, equivalen o issuing exernal equiy (hey have he same informaional sensiiviy). When we examine he implicaions of he asymmeric informaion on a liquidaion decision, for an iniial financing decision or for any incremenal financing decision, asymmeric informaion beween he firm and is lenders does no provide a moivaion o issue deb in excess of he liquidaion value. This resul is discussed more compleely below. Finally i is useful o examine he behavior of he bondholders. If he bondholders were informed and in conrol of he liquidaion decision hey would ac o maximize he value of heir claim on he firm s cash flow. I D D D E {( wmin( F, ) (1 w) min( F, )) ( w ) min( F, Q)(1 ( w ))} w D D D prob( w w ) E( w w w )min( F, ) (1 E( w w w ))min( F, ) D prob( w w )min( F, Q). If F debholders are indifferen beween coninuaion and liquidaion. If < F Q, debholders always prefer o liquidae he firm; he limi on he upside poenial of heir claims causes he sandard preference for cerainy. Finally if F > Q (never opimal in his model) i is sraigh forward o show ha w D Q. In oher words for high F ( ) enough values of he public signal debholders will prefer o coninue and have a chance of capuring some of he upside poenial; a his poin he deb effecively becomes junk deb. 8

11 As is sandard in pooling models, a manager of he highes ype firm ype (ype G) chooses his preferred acion aking ino accoun he informaional asymmery and is impac on he oucomes of his choices. Bad firms mimic hese choices. For a good firm, he manager s decision problem can be wrien in erms of he expressions derived above. Furhermore we have assumed ha he required funding is sufficienly high ha he firm canno be financed enirely wih risk free deb. The Decision Problem No Renegoiaion For a ype G firm, he manager s problem can hen be wrien as: I Max (1 ) S ( F, w') w', F, G I I s.. E ( S ( F, w')) E ( D ( F, w')) I We can furher define he uninformed equiy and deb values as: U I U I S ( Fw, ') E( S( Fw, '))and D ( Fw, ') E( D( Fw, ')). The ype G manager selecs he level of exernal deb (described by he face value and a covenan ransferring conrol of he liquidaion decision o he debholders for realizaions of he public signal less han w ' ) and he proporion of he firm s equiy o sell exernally in order o maximize he (informed) value of his reained equiy, subjec o he consrain ha he required capial I is raised. Sricly speaking he capial consrain should be wrien as a weak inequaliy, however given ha he manager of a good firm sells securiies under asymmeric informaion i will never be opimal o raise more han is required. Finally, wih he consrain wrien as an equaliy, we can solve i for he necessary level of exernal equiy: U U S ( F, w') D ( F, w') I (1 ). U S ( F, w') 9

12 The manager s objecive funcion is simply his expression imes he informed value of equiy: U U S ( F, w') D ( F, w') I I Obj( F, w') SG ( F, w'). U S ( F, w') In he binary signal version of he model he opimal choices given he problem faced by he manager of a good firm are mos simply derived by comparing he value of he manager s objecive funcion for differen F and w'. By doing so we are able o illusrae he basic ensions underlying he model. A firs resul o noe is ha he value he objecive funcion for a he manager of a good firm Obj( F, w '), in he absence of any sae coningen ransfer of conrol righs o he lender ( w' w2 ) is larger a F F han i is a F ; Obj( F, w2) Obj(, w2). Q w2 B The value F 1 wb 2 Q is defined o be he level of he face value of deb a which a bad firm would be indifferen beween liquidaion and coninuaion when w w2 is observed (in oher words, he highes level of risky deb a which here is no cos associaed wih he bad manager s incenive problem given w 2 ). This resul illusraes ha his model capures he sandard pecking order noion ha he manager is beer off issuing risky deb raher han equiy. The qualificaion is ha his is a general prescripion on financing choice only as long as i does no aler he incenives of a bad enrepreneur by oo much. If we ignore he impac of deb financing on decision making we derive a limi on he use of deb financing. Proposiion 1: Asymmeric informaion a he ime of financing (ime 0) implies ha, all else equal, here is a pecking order for exernal financing in ha he enrepreneur prefers 10

13 o issue firs riskless deb o he exen possible (F = ) and hen risky deb o is poin of informaional equaliy wih exernal equiy (F = Q). Once his level of deb financing is reached, he enrepreneur is indifferen beween issuing more deb or exernal equiy. 3 Proof: See he appendix From Proposiion 1 we immediaely see ha by changing he model o include a liquidaion decision a version of he deb capaciy discussed by Myers (1984) is endogenously derived. A he poin F = Q here is no longer any moivaion derived from asymmeric informaion beween he firm and he marke o use risky deb raher han exernal equiy. An ineresing aspec of liquidaion value as a ceiling for deb capaciy is ha his value is sae coningen. During economic expansions, firms in financial disress will be more likely o be liquidaed as a going concern hen piece-meal. Thus liquidaion value may be very near firm value, implying a high ceiling. During conracions liquidaions will be more likely o be piece-meal, selling he firm for he highes value of is asses in an alernaive use, which may be quie low. When he coss relaed o he disorion of incenives from he use of deb financing and he assignmen of conrol righs o inferiorly informed debholders are considered, he opimal level of deb, in his simple version of he model, is below his ceiling. The innovaive feaure of his model is ha we also consider he implicaions of he asymmeric informaion beween he firm and he marke a he ime (ime 1) of he liquidaion decision. There are wo concerns o discuss. Firs is ha he use of risky deb in he iniial financing of he firm disors he incenives of he enrepreneur/manager of boh a good and bad ype firm in he ime 1 liquidaion/coninuaion decision. Second is 3 Noe ha he assumpion ha I > Q implies ha firms in his model will always find i opimal o issue some amoun of exernal equiy. 11

14 ha deb covenans, sae coningen changes in he conrol of he liquidaion decision, can help o limi he cos of he disored incenives. The use of bond covenans canno perfecly conrol he incenive problem because he lender always prefers liquidaion o coninuaion if he deb is risky (hey have heir own disored incenives) and because he lender makes decisions based upon inferior informaion. The ne cos of he incenive disorion associaed wih deb financing mus be balanced agains he adverse selecion benefis o he iniial sale of deb (raher han exernal equiy) in deermining he firm s opimal capial srucure. Given our assumpions, here are only wo poenial value added assignmens of he ownership of he liquidaion decision. The firs is equivalen o he absence of a covenan; because of how we have defined w', he manager owns he liquidaion decision whenever w w' his is wrien, w' w2. This arrangemen will end o be preferred if low levels of deb are used, F F as well as for high deb levels if he cos of uninformed decision making by he lender is larger han is he disored decision making by informed insiders. Because we have assumed ha i is efficien for boh good and bad ype firms o coninue in a srong marke ( w 1 ) and debholders will always wan o liquidae, i will never be efficien o allocae conrol of he liquidaion decision o he lender in his sae. Therefore, only an allocaion of conrol ha ses w' w1, leaving he manager in conrol of he liquidaion decision in a srong marke and allocaing his decision o he lender in a weak marke, is a second poenially opimal level of he deb covenan. Similarly, in he model wih a binary signal he poenially opimal levels for he face value of deb are limied. A low level of deb ( F F ) may be opimal if he cos 12

15 of inefficien decision making is large. By choosing he low deb level he incenives of insiders of boh good and bad firms remain efficien in he sense ha hey will make he righ decision in boh a srong and a weak marke (wih he manager of a bad firm being jus indifferen o coninuaion and liquidaion in a bad marke). For any face value of deb above F he manager of a bad firm will always wish o coninue, even in a weak marke. The manager of a good firm will also always wish o coninue, however, his is efficien. Therefore, if F F is chosen, here is no addiional expeced cos in added incenive problems and (as shown above) a sric gain in lowering he discoun for a good firm from issuing added deb. Therefore, if any F F is chosen i will be opimal o issue deb wih a face value of Q. We will label his he high deb level. Proposiion 2: If a low deb level is chosen, i is opimal o se w' w2. This arrangemen keeps conrol of he liquidaion decision in he hands of informed insiders and he low deb level, F, ensures efficien decision making in boh a weak and a srong marke. Proof: Obvious from he discussion above. Proposiion 3: Assuming a high deb level is chosen, F Q, i will be opimal o allocae he liquidaion decision o he lender in a weak marke if parameer values are such ha i is efficien for an average firm, G(1 ) B, o liquidae when w w 2 (if w * w ). If i is efficien for a firm of he average ype o coninue in a weak 2 marke hen i is opimal o allocae conrol of he liquidaion decision o he manager in all boh saes. Obj( Q, w1) Obj( Q, w2) if w * w2 and Obj( Q, w1) Obj( Q, w2) if w * w. 2 13

16 Proof: See he appendix The ensions ha influence he ime 0 capial srucure decision in he model are now clear. The ime 0 adverse selecion faced by he good ype firm provides a moivaion for he use of deb financing. The implied agency coss, ne of any benefis derived by he use of opimal bond covenans, inroduce a cos of deb. Given he lumpiness of he model wih a binary public signal, we will no expec a smooh radeoff o deermine he opimum bu raher expec o see parameer values for which here is a low deb opimum (F = F, when he ne agency cos of deb is large relaive o he adverse selecion benefi) and values ha indicae a high deb opimum (F = Q, when he reverse is rue). The simple srucure of his model wih a binary public signal, however, does no capure boh possibiliies. Proposiion 4: In he version of he model wih a binary public signal and infiniely cosly renegoiaion of deb covenans, i is always opimal for he good firm o choose deb wih a face value of F and o assign conrol of he liquidaion decision o he manager in boh saes of naure. I is never opimal o choose a high level of deb. Proof: See he appendix There is no high deb opimum in his version of he model. The model s srucure implies ha he low deb opimum is a corner soluion. Inuiively, one would expec ha when he adverse selecion benefi from issuing los of deb (he oal benefi of issuing deb wih F = Q raher han F = F ) was larger han he ne agency cos of he disored incenives here would be a high deb opimum. By choosing parameer values ha made he coninuaion decision of he bad ype firm ruly marginal i would seem possible o obain high deb as he opimal soluion. owever in his model, wha 14

17 deermines he imporance of he bad firm s coninuaion versus liquidaion decision imporan is he liquidaion value, Q. In oher words, when he efficiency of he liquidaion decision by he bad firm is no imporan (Q is low) here is also lile oal benefi from he use of risky deb raher han exernal equiy in he iniial financing decision. 4 The curren model shows ha when we exend a model of financing choice under asymmeric informaion o consider he coss associaed wih he use of risky deb, a good firm s incenive o use deb is limied by he disorion o he incenives of he bad ype firm. Because he firms are observaionally equivalen, he marke, anicipaing he disored incenives associaed wih large amouns of deb for a bad firm, will charge a good firm for he anicipaed inefficien decision-making. This makes he use of large amouns of deb subopimal. In his version of he model, here is a pecking order for financing choices bu he poin a which firm s urn o exernal equiy, F he firm s deb capaciy, is very low. Renegoiaion of Covenans Consider a good firm which has issued deb including a covenan ransferring conrol of he liquidaion decision in a weak marke. Wihin he exising model here is an inuiive renegoiaion sraegy ha a good firm may use o separae iself from bad firms in a weak marke (if w w2 is realized). A good firm is willing o offer o increase he ime 2 paymen o he lender in exchange for he lender waiving he covenan (no liquidaing he firm). For simpliciy we will assume ha he firm makes a ake-i-orleave-i offer o he lender in all renegoiaions and faces any coss of renegoiaion. We 4 The coninuous signal version of he model does no share his feaure and so allows he developmen of ineresing empirical implicaions for capial srucure choice under asymmeric informaion. 15

18 examine he renegoiaion sraegy in wha follows and derive he associaed capial srucure implicaion. In his model he covenans serve o miigae he coss of high deb levels. When renegoiaion is no allowed or is infiniely cosly, high deb levels, were hey beneficial, would ake full advanage of he low informaion sensiiviy of deb and se he face value of deb equal o he liquidaion value (F = Q). owever, if a good ype firm anicipaes a separaing renegoiaion sraegy in a weak marke i will no se F = Q. This is because a his deb level here is no way for a good firm o make a resrucuring offer ha he bad firm will no mimic (a F = Q a manager of a bad firm receives nohing in liquidaion and herefore will mimic any sraegy ha will waive he covenan). If, however, a ime 0 he manager of a good firm ses F Qhen because a good firm s cash flow disribuion in coninuaion sochasically dominaes ha of a bad firm here is always a separaing resrucuring offer, F S F, ha a bad firm will no choose o mimic and ha he lender will accep. The equiy value for a bad firm will be higher receiving Q F in liquidaion wih cerainy raher han aking a small chance on F S from coninuaion in a weak marke. Proposiion 4: Consider a good ype firm faced wih he violaion of a covenan in a weak marke. If he face value of deb, F, chosen a ime 0 is such ha Q F G B QGw (1 Gw ) 2 2 G B 1 here is a renegoiaion offer S ( Q F ) F ( F ) Bw 2 which a bad firm will no mimic and he lender will accep o waive he covenan. 16

19 Proof: See he appendix Ineresingly, raher han here being a sric benefi o issuing deb insead of exernal equiy, as long as he iniial face value of deb chosen a ime 0 saisfies he inequaliy given in Proposiion 4, he manager of a good firm is indifferen o a se of iniial deb levels ha are sricly less han Q. In oher words, here is no opimal F. Inuiively, for iniial levels of deb financing larger han F he savings a good firm receives on he ex ane adverse selecion problem from he use of more deb is jus balanced by he cos (in he form of a higher renegoiaion offer) imposed on he firm ex pos by he need o separae from bad firms. Proposiion 5: When renegoiaion of a bond covenan is cosless a manager of a good firm is indifferen beween any iniial deb level F such ha: Q F G B QGw (1 Gw ) 2 2 G B 1. Proof: See he appendix. We are now able o examine he full capial srucure implicaion of he exisence of a cosless and fully separaing renegoiaion in a weak marke. Ineresingly, in he case of cosless renegoiaion, asymmeric informaion does no provide a moivaion for he use of deb financing. Raher a good firm is indifferen beween low deb ( F F ) wih no covenan and high deb ( F F ) wih a covenan ha assigns conrol of he liquidaion decision o he lender in a weak marke (anicipaing he good firm will renegoiae in a bad marke). The benefi associaed wih iniially issuing a large amoun of deb is jus balanced by he cos o a good firm of separaing from bad firms in he even of a weak marke. 17

20 Proposiion 6: When he renegoiaion of bond covenans is cosless firms are indifferen o choosing high deb, F F wih a bond covenan iniially ransferring conrol of he liquidaion decision o he lender in a weak marke, and low deb, F F where he manager reains conrol of he liquidaion decision in boh saes. If high deb is chosen, in a weak marke, good firms will renegoiae he covenan choosing F F S while bad firms will liquidae. Proof: See he appendix. Noe when renegoiaion of covenans is cosless, i is no longer he case ha i is opimal o include a covenan ransferring conrol of he liquidaion decision o he lender only for cerain parameer values. The separaing naure of he renegoiaion implies ha i is always opimal o include he covenan when a high deb level is chosen. This resul mirrors he main resul in Garleanu and Zwiebel (2009) in ha covenans are opimally very resricive and over assign conrol righs o he less informed pary. Proposiion 6 illusraes no only he usefulness of bond covenans in conrolling he agency coss of deb bu also he imporance of he abiliy of firms o renegoiae hese covenans. In he model wih a binary signal, wihou an abiliy o renegoiae hese covenans hey will no be employed and only low deb levels are opimal. The limiing aspec of he model wih a binary signal is ha if he renegoiaion of covenans enails a cos hen he low deb soluion will be a unique opimum in he model and we will no expec o see covenans used o conrol he incenive problems caused by he use of high deb levels. 2. The Model wih a Coninuous Signal 18

21 In order o develop a richer se of predicions of he model we exend he curren seup by assuming he public signal w has a uniform disribuion ( w U[ w, w ]) raher han being governed simply by a Bernoulli disribuion. Oher han his change, he model in his secion is idenical o ha used above. This apparenly simple change increases he complexiy of he represenaions o such an exen ha we mus resor o numerical soluions of he opimizaion problem. owever, he added richness does allow us o develop siuaions in which firms will opimally use high levels of deb suppored by he use of resricive covenans and so more ineresing predicions. No Renegoiaion The represenaion of he problem becomes more complex when we assume ha he public signal has a coninuous disribuion. We firs presen he informed equiy and deb values and hen discuss he change o he problem. Using he same noaion as I above, S ( F, w '), he informed value of he equiy for a firm of ype, is given by: I M M S ( F, w') prob( wmax( w ( F), w'))( E( w wmax( w ( F), w'))( F)) M prob( w max( w ( F), w'))( Q F). Assuming ha he public signal is uniformly disribued his becomes: M M I wmax( w ( F), w') max( w ( F), w' w S ( F, w') ( F) w w 2 M max( w ( F), w') w Q F w w Similarly, he assumpion of a uniform public signal implies ha he informed value of I deb, D ( F, w '), is given by:. 19

22 M M I wmax( w ( F), w') max( w ( F), w') w D ( F, w') ( F ) w w 2 M max( w ( F), w') w F. w w U I I Finally, he uninformed values are simply S ( F, w') S ( F, w') (1 ) S ( F, w') and U I I D ( F, w') D ( F, w') (1 ) D ( F, w'). G B As is apparen from he equaions for he informed securiy values, a complicaion inroduced by he use of a coninuous signal is he quesion of wheher, for a given F, he covenan is se a a level of he public signal ha is greaer or less han he level a which a bad ype manager will volunarily liquidae he firm. This quesion was raised in he model wih a binary signal bu he srucure made i easy o address. As was rue in ha model, he relaionship beween w and G M wb limis he search o wo candidae opima. B If he covenan is opimally se so ha M w' w B he covenan does no effecively consrain he bad ype manager in he liquidaion decision. In his case, i will necessarily be opimal o se w' w and o selec a relaively low level of deb, F. If he covenan is * G se so as no o effecively consrain a bad ype manager in he liquidaion decision, hen he covenan will only serve o consrain good ype managers, herefore seing w' w * G is clearly opimal. As was rue above, if he covenan is se a his level i will also be he case ha F is opimally se a a low level. The opimal choice of F in his version of he model involves a smooh radeoff. Fixing w' w, as F is raised above in he ime 0 * G financing decision, a good firm benefis from selling an informaionally insensiive securiy. owever, he good firm faces a cos due o he fac ha he bad firm will now have disored incenives in he liquidaion decision and he good firm will pay for his 20

23 inefficiency in he price i receives for is securiies. As above we will label he low level of deb F. On he oher hand, if i is opimal for he covenan o consrain he manager of a bad firm, M w' w B, he same covenan will necessarily consrain he manager of a good firm. Given ha he liquidaion decision for boh ypes of firms is conrolled by he (same) covenan, here is no cos associaed wih he incenive disorion associaed wiah a high deb level. Assuming an inabiliy o renegoiae he covenan, he choice of deb ha maximizes he ime 0 benefi of selling he informaionally insensiive deb raher han exernal equiy is o se F = Q. Analyically, i is sraighforward o show ha if F = Q, hen i is opimal o se he covenan so ha conrol is ransferred o he lender a levels of he public signal ha are less han he level a which a firm of he average ype would opimally liquidae, w' Q w ( ) * where G(1 ) B. While i is clear ha wo ime 0 choices for deb srucure are possibly opimal, F F w w G and * (, ' ) F Qw w, a his poin we have no been able analyically * (, ' ) o derive he value F. Consequenly we are also unable o provide an analyical comparison of he value of he good manager s objecive funcion under hese deb srucures for differen parameer values. In wha follows, we herefore derive he value F numerically as well as numerically compare he value of he good manager s objecive funcion a he candidae soluions. Figures 1 3 demonsrae he naure of he soluions o he good manager s opimizaion problem when he public signal is assumed o be uniformly disribued. 21

24 Figure 1a compares he value of he good manager s objecive funcion a he candidae soluions for a given se of parameer values. Immediaely apparen is he resul ha wih a coninuous public signal boh he deb srucure ha includes a low deb level and a weak covenan F F w w G and he deb srucure ha includes a high * (, ' ) deb level and a resricive covenan F Qw w are opimal soluions o he good * (, ' ) manager s problem under differen parameer values. In he figure he verical axis represens he value of he objecive funcion while he horizonal axis represens differen values for Q he firm s liquidaion value. The black curve chars he value of he objecive funcion under he high deb soluion for a variey of levels of he liquidaion value of he firm, Q, while he grey curve chars his value a he low deb soluion. As discussed above, for low values of Q here is lile oal benefi o selling informaionally insensiive securiies available a ime 0 while he incenive based coss of he high deb soluion remain. Under he low deb soluion some of he benefi o selling informaionally insensiive securiies is exploied wih only minimal incenive coss. Therefore, for low values of Q he low deb soluion is he opimum. As he liquidaion value rises, he relaion beween he soluions reverses. As shown in Figure 1b, he low level of deb, F which srikes a balance beween he benefis of using risky deb raher han exernal equiy and he incenive coss inroduced by he deb, rises very slowly wih increases in he liquidaion value. This implies ha he value of he objecive funcion under he low deb soluion will also change relaively lile for increases in Q. Also as discussed above, as Q rises, he oal value of issuing deb raher han exernal equiy rises. While he cos of disorions in he liquidaion decision making also rise, 22

25 wih a coninuous public signal hese coss are more appropriaely managed (seing w' w ) han hey are wih a binary signal. Thus he value of he objecive funcion * under he high deb soluion will rise relaive o he value under he low deb soluion. 5 Figures 2a and 2b presen he same relaion as in Figure 1a wih a change in he value of he parameer θ, he probabiliy of a good ype firm/manager. There are wo inuiive changes in hese figures relaive o Figure 1a. The firs is he level of he curves. The value of he good manager s reained equiy decreases as he probabiliy of a good manager drops from 0.5 o 0.3 (Figure 1a versus Figure 2a) and increases as his probabiliy increases from 0.5 o 0.8 (Figure 1a versus Figure 2b). This effec is simply due o he effec ha changing θ has on oal value. Secondly, for relaively high levels of he liquidaion value, he dominance of he high deb soluion relaive o he low deb soluion varies inversely wih θ. In oher words, for low θ and high Q he high deb soluion is much more valuable o a good manager han is he low deb soluion, while for high θ and high Q he high deb soluion is only marginally beer han he low deb soluion. This difference is due o he change in he benefi of selling deb raher han exernal equiy as he mix of observaionally equivalen firms changes. When here are many good firms and only a few bad firms he adverse selecion discoun is relaively small. Therefore he benefi of he high deb soluion is reduced. owever, when here are many bad firms and few good firms he benefi received by a good firm from selling deb insead of exernal equiy is large. Renegoiaion of he Covenans 5 The general shape of he curves in Figure 1a may be explained as follows. Wih low Q he cos of disorions in liquidaion decision making are very low. As Q increases, holding he oher parameers fixed, here are wo effecs. Firs he cos of he disored incenives increases (he liquidaion decision is more imporan). Secondly, here is more oal value available (he NPV rises). The firs effec is responsible for he iniial decrease while he second soon becomes dominan. 23

26 To be wrien 3. Robusness To be wrien 4. Empirical Predicions and Analysis To be wrien 5. Conclusion The capial srucure decision is examined in a seing wih asymmeric informaion as he sole fricion. The model is an exension of Myers and Majluf (1984) where he implicaion of having deb in he capial srucure under a condiion of asymmeric informaion is considered a he ime of financing. We demonsrae ha an opimal capial srucure may be derived rading off he benefis of selling deb, based on is low informaion sensiiviy, and he coss of deb, derived from he inefficien decision making implied by ransfers of conrol o uninformed paries. 24

27 Appendix (proofs of he proposiions): Proof of Proposiion 1: The srucure of he model wih a binary public signal allows us o define he following values for he informed value of equiy (deb) for a good (bad) firm: S ( F, w ) pgw( F ) (1 p) Gw ( F ) I G and S ( F, w ) pbw ( F ) (1 p)( Q F ) pbw ( F ) (1 p) Bw ( F ), I B Q w2 B where he second equaliy derives from he definiion of F 1 wb 2 Furhermore he uninformed equiy value is wrien:. S ( F, w ) pw ( F ) (1 p)( Gw ( F ) (1 )( Q F )). U Similarly: D ( F, w ) pgw ( F ) (1 p) Gw ( F ) I G D ( F, w ) pbw ( F ) (1 p)( F ) I B 2 1 D ( F, w ) pw ( F ) (1 p)( Gw ( F ) (1 )( F )) U G Then Obj( F, w2) ( pw1( ) (1 p)( Gw2( ) (1 )( Q )) ( I )) Similarly we can wrie Obj(, w ) ( pw ( ) (1 p)( Gw ( ) (1 )( Q )) ( I )) pgw1( ) (1 p) Gw2( ) pw ( ) (1 p)( Gw ( ) (1 )( Q )

28 Direc comparison shows ha Obj( F, w2) Obj(, w2) whenever w * B Q w2 which is assumed (i.e. i is efficien o liquidae he bad firm in a B ( ) weak marke. Proof of Proposiion 2: Similar o he definiions in he proof of proposiion 1 we can wrie: G Obj( Q, w2) ( pw1( ) (1 p) w2( ) ( I )) and G Obj( Q, w1) ( pw1( ) (1 p)( Q ) ( I )) Q I is sraighforward o show ha Obj( Q, w2) Obj( Q, w1) iff w2. In oher ( ) words, if a high level of deb is chosen i is opimal o assign conrol of he liquidaion decision o he manager in boh a weak and a srong marke if and only if i is efficien for a firm of average ype o coninue in a weak marke. Similarly, i is opimal o assign conrol of he liquidaion decision o he lender in a weak marke if i is efficien for a firm of average qualiy o be liquidaed in a weak marke. Proof of Proposiion 3: Direc comparison shows ha Obj( F, w2) Obj( Q, w2) whenever w * B Q w2 and Obj( F, w2) Obj( Q, w1) whenever B ( ) w * G Q w2. Boh B ( ) of hese condiions were assumed o hold. Inuiively he firs inequaliy holds because if equiy conrols he liquidaion in boh weak and srong markes and a high deb level is chosen he inefficien coninuaion of he bad firm in a weak marke will be priced ino 26

29 he securiies. The second holds because when he lender owns he liquidaion decision in a weak marke, he inefficien liquidaion of he good firm in a weak marke is priced ino he securiies. Proof of Proposiion 4: Assume ha a covenan assigning conrol o he lender in a weak marke has been included in an iniial (ime 0) deb conrac wih a face value F F Q, and ha his covenan has been violaed, w w2. Noe ha in order for a S renegoiaion offer, F, from a good firm o be separaing i mus be ha ( S QF Bw ) 2 F. We will assume ha he minimal such increase in deb is offered by he good firm so ha a bad firm would be indifferen o coninuaion and liquidaion. This implies we can wrie he renegoiaion offer as S ( Q F) F. The Bw 2 offer S F mus also be accepable o he lender, given ha w w2. In oher words, i mus be rue ha ( S F Gw ) 2 F. Subsiuing for S F we find F G B QGw (1 Gw ), 2 2 G B 1 he requiremen in Proposiion 4. Noe, F may be chosen sricly less han Q as long as i is efficien for a good firm o coninue in a weak marke. If he renegoiaion offer S F saisfies he requiremen ha a bad firm will no have any incenive o mimic, hen as long as he iniial deb conrac has a face value F a leas as large as specified in he above inequaliy he lender will accep he renegoiaion offer. Proof of Proposiion 5: The proof of his proposiion comes simply by wriing he objecive funcion for he manager of a good firm for an arbirary F and assuming ha a separaing renegoiaion offer will be made by a good firm if a weak marke is realized. 27

30 I is sraighforward o show ha his objecive funcion is no dependen upon he iniial choice of F. The value of he objecive funcion for a manager of a good firm is, for an arbirary S F and he associaed ( ) F F given renegoiaion of he covenan if w w2, wrien as: S pw1( ) (1 p)( gw2( ) (1 )( Q )) ( I ) Obj( F, F, w1 ) S pw1( F ) (1 p)( Gw2( F ) (1 )( Q F ) S ( pgw ( F ) (1 p) Gw ( F )) 1 2 Imposing he requiremen for separaion by subsiuing ( S QF Bw ) 2 F ino he denominaor of he firs erm allows us o wrie he objecive funcion as: S G Obj( F, F, w ) pw ( ) (1 p)( gw ( ) (1 )( Q )) ( I ) which is independen of F. S Proof of Proposiion 6: Direc comparison shows ha Obj( F, F, w1) Obj( F, w2). 28

31 References Dybvig, Philip., and Jaime F. Zender, 1991, Capial Srucure and Dividend Irrelevance wih Asymmeric Informaion, Review of Financial Sudies 4, Garleanu, Nicolae, and Jeffrey Zwiebel, 2009, Design and Renegoiaion of Deb Covenans, Review of Financial Sudies 22, Myers, Sewar C., 1984, The capial srucure puzzle, Journal of Finance 39, Myers, Sewar C., and N. S. Majluf, 1984, Corparae Financing and Invesmen Decisions When Firms ave Informaion Tha Invesors Do No ave, Journal fo Financial Economics 13,

32 Figure 1a: Value of he objecive funcion for a good ype manager agains differen levels of Q. Oher parameers of he problem are held consan: = 4, = 1, w0.15, w1.2, θ = 0.5, G = 0.75, B = 0.60, and I =

33 Figure 1b: Numerical represenaion of he relaion beween Q and F. Parameer values are as repored in Figure 1a. 31

34 Figure 2a: Manager s objecive funcion agains Q for he parameer values used in Figure 1a excep ha θ = 0.3. Figure 2b: Manager s objecive funcion agains Q for he parameer values used in Figure 1a excep ha θ =

35 Figure 3: Manager s objecive funcion value versus θ. 33