RISK ANALYSIS WITH CONTRACTUAL DEFAULT. DOES COVENANT BREACH MATTER?

Transcription

1 RISK ANAYSIS WITH CONTRACTUA DEFAUT. DOES COVENANT BREACH MATTER? Emanuele Borgonovo Deparmen of Decision Sciences Bocconi Universiy Sefano Gai Deparmen of Finance and CAREFIN - Bocconi Universiy sefano.gai@unibocconi.i Absrac Mergers and acquisiions (M&A), privae equiy and leveraged buyous, securiizaion and projec finance are characerized by he presence of conracual clauses (covenans) ha rigger he echnical defaul of he borrower even in he absence of insolvency. Therefore, borrowers may defaul on loans even when hey have sufficien available cash o repay ousanding deb. This condiion is no capured by he NPV disribuion obained hrough a sandard Mone Carlo simulaion. In his paper, we presen a mehodology for including he consequences of covenan breach in a Mone Carlo simulaion, exending radiional risk analysis in invesmen planning. We inroduce a concepual framework for modelling echnical and maerial breaches from he sandpoin of boh lenders and shareholders. We apply his framework o a real case sudy concerning he projec financing of a 64-million euro biomass power plan. The simulaion is carried ou on he acual model developed by he financial advisors of he projec and made available o he auhors. Resuls show ha boh echnical and maerial breaches have a saisically significan impac on he NPV disribuion, and he impac is more relevan when leverage and cos of deb increase. Keywords: Invesmen Analysis; Projec Finance; Risk Analysis; Mone Carlo Simulaion; Coheren Risk Measures; Covenans; Risk Managemen; Business Planning. JE codes: C61, C63, G31. 1 Inroducion Risk analysis is a cenral ool for supporing decision-making in invesmen decisions. One of he main oucomes of a risk analysis is he disribuion of he valuaion crierion (henceforh, risk profile). Based on he risk profile, analyss esimae all risk measures concerning a given invesmen. Recen lieraure has raised he quesion of wheher covenan breaches affec an invesmen s risk profile. The answer is currenly he subjec of debae, wih some auhors arguing ha covenans do no maer in a quaniaive projec risk analysis, and ohers conending he conrary. To he bes of our knowledge, he quesion has no been addressed wih a direc invesigaion; in his paper, we aim o do jus his. Covenans characerize a vas porion of financial ransacions [Bengsson (2011)] represened by privae bank debs [Demiroglu and James (2009), Nini e al (2009), Sudarsanam and Moir (2007)], leveraged buyous (BOs) [Cumming and Johan (2003), jungqvis e al (2008)], privae equiy [Achleiner e al (2011)], corporae and projec bonds [Dailami and Hauswald (2003)], asse-backed securiizaion, syndicaed loans and projec finance [Corielli e al (2010), Finnery (2007)]. A relevan par of hese deals is financed on a srucured basis, 1

2 meaning ha he borrower is a special purpose eniy, differen from an already exising firm, frequenly known as sponsor or originaor. In his paper, we focus our analysis on projec finance which, ogeher wih securiizaion and BOs, is he prooypical example of a srucured finance ransacion [Megginson (2010)]. Crediors can rely only on he cash generaed by he iniiaive and only on he asses of he SPV as collaeral, bu no on he cash flows and asses of SPV s originaors/sponsors [Esy (2001), Esy (2004), Esy and Sesia (2004), Bonei e al (2009)]. The raionale behind including sric covenans in loan agreemens is, hen, o give he lender he righ o inervene in he managemen of he iniiaive o avoid financial disress (Rajan and Winon, 1995). Covenans impose on he SPV eiher obligaions o do somehing (posiive covenans) or o refrain from doing somehing (negaive covenans) [Smih (1993)]. Furhermore and his is he mos imporan implicaion for our work covenans specify financial raios ha mus be respeced hroughou he life of he loan (financial covenans). Because loan covenans are se ighly ex-ane, i.e. before he deal is closed or he credi agreemen wih lenders is signed, i happens frequenly ha a covenan is violaed even if he borrower is no in severe financial disress [Chen and Wei (1993)]. This siuaion is ofen referred o as echnical defaul. Crediors waive a echnical defaul only when hey do no consider he breach of covenans a maerial even [SEC (1999), Novo (2007)] able o disrup he orderly coninuaion of he deal. Esablishing a maerialiy es requires he ex-ane definiion of a range of values of he coverage raios. A one end of his range here is a prese value ha riggers echnical defaul bu allows crediors and SPV shareholders o coninue managing he ransacion wih enforced monioring or wih a renegoiaion of he loan erms; a he oher end is a final value below which he breach is considered maerial. A his poin, crediors consider he loan subjec o resoluion, accelerae he loan and force he deal ino bankrupcy wihou he possibiliy of renegoiaion. In his respec, covenan violaions expose on o an underhand risk, which, if overlooked, can lead boh shareholders and lenders ino severe consequences. The survey of Davison e al (2010) reveals maerial violaions in around 8% of he projec finance deals analyzed in heir sudy. For invesors analyzing a given ransacion, he exisence of a maerialiy es and he differen implicaions of he breach for lenders and sponsors challenge he resuls of sandard risk analysis obained hrough Mone Carlo propagaion. More precisely, hree issues raised are: 1) how frequen one expecs covenan breach o be, and 2) given a breach (eiher a echnical defaul or a maerial breach) wha consequences are sponsors and lenders incurring ino and 3) Is he modelling of covenan breach causing a saisically significan impac on he risk profile and, consequenly, on he risk measures. To answer hese quesions requires a modificaion of he sandard risk analysis procedures, which we address as follows. Firs, we design a concepual model of covenan breach. The model disinguishes a echnical from a maerial breach. In he case of a echnical breach, he model accouns for he change in deb schedule repaymen due o he fac ha lenders would demand ha dividend disribuion o sponsors be suspended and use all he available 2

3 cash o accelerae deb repaymen (cash sweep). Insead, in he case of a maerial breach, he model accouns for shareholders loss of he equiy cash flows deermined by he lenders enforcemen of he securiy package. Furhermore, lenders are in he posiion o ake over conrol of he projec, and can coninue he projec wih he objecive of recovering he amoun len o he SPV [Davidson e al. (2010), p. 44]. Second, we ranslae he model ino a simulaion mehodology ha ness he modelling of covenan breaches and heir differen consequences for sponsors and lenders ino radiional Mone Carlo Simulaion. Third, we apply he simulaion procedure o a real projec finance ransacion involving a recen biomass power plan locaed in Ialy worh around 64 million euro ha underwen financial closing in 2009 wih General Elecric-Inerbanca as lead arranger. For his projec, access o he financial model used by sponsors and he mandaed lead arranging bank in heir evaluaion of he deal was graned o he auhors. Thanks o he availabiliy of he financial model, we are in a favourable posiion o examine quaniaive resuls relying on real daa and no on ficiious or simulaed deals. Resuls show ha he effec of covenan breach on he cash flow disribuions o he SPV s sponsors is small if he violaions are echnical. Conversely, in he case of maerial breach, he cumulaive disribuion funcion of he equiy NPV exhibis a fa lef ail, wih a considerable change in he value of risk measures. Our conribuion o he exising lieraure on risk analysis and deb covenans is hreefold. Firs, available papers on covenans have analyzed conracual clauses almos exclusively in he conex of corporae finance seings, i.e. in case of bond or loan conracs beween lenders and already exising firms [Aghion and Bolon (1992), Beneish and Press (1995), Chava and Robers (2008)]. However, much less is known abou he imporance and he role of covenans included in lending agreemens designed for projec finance, and more generally for srucured deals. As we have said, he ypical srucured finance ransacion is a fully self-conained, one-ime financing even wih a definie economic life-cycle [Gai e al, (2011)]. Wih such a deal, he previous lending relaions beween lenders and he SPV shareholders are much less imporan han he soundness of he sand-alone deal o be financed. These characerisics are rue for no oher corporae financing sample, making projec finance deals ideal o sudy he disciplining role of covenans in isolaion from oher borrower-specific facors. Second, we discuss he use of covenans for a significan segmen of inernaional capial markes which is no exensively covered in previous heoreical and empirical papers. Thomson Reuers repors ha syndicaed loans amouned o US$3.9 rillion a he end of 2011, of which US$214.5 bn were PF loans. These figures compare wih US$180 bn of privae equiy invesed globally in 2010 and wih global securiizaion issuance of morgage and asse backed securiies of US$799 bn a he end of Third, we design a mehodology ha is useful o model he effec of echnical and maerial breach of covenans for sponsors and lenders. Knowledge of he expeced frequency of covenan violaions provides analyss wih a degree of confidence as o he projec s abiliy o susain sresses. This informaion can hen be used by lenders o fine-une he loan enor, he spread and he deb/equiy raio. Our mehodology can also help 3

4 crediors assess unexpeced loss and allocae equiy capial in accordance wih Basel II and Basel III rules [Basel Commiee on Banking Supervision., 2009]. The remainder of he paper is organized as follows. Secion 2 reviews he valuaion crieria, covenans of credi agreemens ypically used by lenders and sponsors, and sandard risk measures. Secion 3 designs he model ha includes he possibiliy of a covenan breach. Secion 4 illusraes how o urn he model ino a corresponding simulaion procedure. Secion 5 presens addiional risk analysis insighs and he Mone Carlo esimaion of he frequency of covenan breach and of risk measures. Secion 6 presens he case sudy analysis and resuls. Secion 7 offers conclusions. 2 Valuaion Crieria, Covenans, Risk Analysis and risk measures Throughou his work, we invesigae a projec finance invesmen srucured hrough an SPV funded wih equiy and deb provided by projec sponsors and a pool of banks respecively. In his secion, we describe he valuaion crieria used by lenders and sponsors o assess projec viabiliy, he covenans included in he credi agreemen and he risk measures we use in he simulaions included in Secion The Valuaion Crieria By he adjused presen value principle [Myers (1974)], analyss separae equiy from deb cash flows. We call free cash flow of period (FCF ) he line of he cash flow saemen a period preceding financial iems (deb service and dividends paid o sponsors). Specifically, leing R denoe revenues, Taxes he cash ouflow due o axes, OE operaing expenses, WC he correcion of working capial changes and Capex he capial expendiures for period, (=1,2,...,T), we have, FCF = R OE Taxes + WC Capex (1) FCF [eq. (1)] represens he cash produced by he projec in period. If he invesmen is financed fully wih equiy, hen FCF is enirely in he hands of shareholders. If he invesmen is financed parly wih equiy and deb, hen a par of FCF goes o lenders and a par o shareholders. More precisely, le P and I represen he principal and ineres on loan o be repaid in period, respecively. Then, he quaniy FCFE = FCF P I (2) represens he free cash flow o equiy a period (FCFE ). eing ShNPV denoe he shareholder NPV and assuming no fricions in he FCFE disbursemen, we obain ShNPV T FCFE = (3) = 0 (1 + k ) e 4

5 Knowledge of FCFE can also be uilized o esimae alernaive shareholders valuaion crieria as, for insance, he inernal rae of reurn (IRR) [For an overview abou he consisen uilizaion of IRR as valuaion crierion, see among ohers Hazen (2003) and Hazen (2009)]. As documened in Davidson e al (2010), he perspecive of lenders differs from ha of shareholders in several respecs. Firs, lenders do no have direc responsibiliy for he operaion of he projec. A he same ime, for lenders i is vial for he projec o say afloa so hey can be reimbursed as planned or wih limied deviaions from he original deb cash flow sream. This sream is deermined by he flow of principal and ineres and solves he equaliy where paymens, T P + I A = (4) 1 (1 + k ) = d A is he percenage amoun disbursed by lenders, P and I he corresponding principal and ineres T is he final repaymen dae of he loan and k d is he cos of deb. By eq. (4), he loan NPV is null oan ( NPV = 0 ) a k d. 2.2 Covenans of he credi agreemen Covenans are defined as... supplemenal obligaions of he borrower in addiion o he basic obligaion o repay he lenders he amoun due on he scheduled mauriy daes [...] These supplemenal obligaions may be eiher correlaed o loan repaymen--as in he case he borrower doesn' ake cerain acions ha will hamper deb repaymen a he scheduled daes--or required by lenders in order o monior heir credi invesmen and verify ha i is being managed properly [Novo (2007); p. 254]. The evidence available for sandard corporae finance seings (i.e. already exising firms wih a porfolio of ongoing asses) shows ha mos covenan violaions are acually eiher waived by he crediors or resolved by renegoiaions of he loan or refinancing wih a differen lender [Chen and Wei (1993)]. Indeed, Beneish and Press (1995) and Nini e al. (2009) demonsrae ha only a small fracion of violaing firms experience a disressed-exi. Moreover, a covenan breach is followed by he imposiion of furher consrains on he borrower s behaviour (like an increased spread on he loan [Smih (1993), Sweeney (1994), Sufi (2009)], reques of addiional collaeral and limiaions o dividend disribuions or o addiional capial expendiures [Nini e al (2009)]). Finally, credior inervenion in case of covenan violaion is in fac good for he borrowers shareholders as i is associaed wih operaing performance and share price increase. 1 While several of he findings in he exising lieraure can be exended o individual projec finance ransacions, here is one main difference. This ype of ransacion requires he lenders risk assessmen of a 1 In he same fashion, Demiroglu and James (2009) show ha shareholders respond more posiively o announcemens of loans wih igher financial covenans. However, Beneish and Press (1995) documen wealh losses o shareholders following he renegoiaion of loans riggered by a echnical defaul. 5

6 specific projec and no of an exising pool of real projecs, like in an ongoing corporae eniy. This fac has four imporan implicaions for sponsors and crediors ha we address in he paper, implicaions which, o he bes of our knowledge, have no been covered by previous sudies. Firs, he breach of covenans canno always be followed by a revision or renegoiaion of he conracual erms of he deb conrac. Examples are large infrasrucure projecs where he minimum values of he coverage raios discussed in Secion 2.2 are breached and very close o 1. In hese cases i becomes unfeasible for lenders o raise he level of spread on he loan ranches because operaing cash flows canno susain an increased deb service and here are no oher cash flows ha can be used for loan repaymen. Second, he reques for addiional collaeral is excluded by definiion, since hese deals are based on a norecourse clause o he originaors/sponsors of he SPV. Furhermore, lenders include in he credi agreemen a negaive pledge clause [Gai (2007)] ha obliges he borrower no o allow any oher lender ouside he pool of exising lenders o use he presen and fuure asses of he SPV as collaeral. Third, projec finance implies he financing of one single projec, so a very deailed securiy package is se up before he deal closing [Finnery (2007)]. This allows exising crediors (and no ohers) o ake over he conrol righs of he shareholders when no waiver or renegoiaion of he loan erms is possible. Furhermore, he securiy package grans lenders he opion o ake full conrol of he SPV, ake possession of all projec asses, expropriae shareholders conrol righs and capure he remaining enerprise value. Yescombe (2002) repors ha a ypical projec finance securiy package includes: 1) a pledge on he borrowers' shares, so ha banks have he righ o voe in he even of defaul; 2) a morgage on land righs, buildings, and oher angible and inangible fixed asses; 3) credi assignmen for proceeds coming from key conracs of he borrower [Bonei e al. (2009)]; 4) a pledge on all he bank accouns of he borrower; and 5) assignmen of insurance paymens in case of damages. Given such a igh package, he opion o refinance he loans wih oher crediors which is a possibiliy in sandard corporae finance seings following a covenan violaion is simply no possible in projec finance. Fourh, oher limiaions o managemen behaviour ha have been exensively documened in he lieraure do no apply in a clear-cu way o projec finance deals. The limiaion o dividend disribuions is included from he beginning in he original credi agreemen wih he lenders and no added afer a covenan breach. imiaions o increased capial expendiures afer a breach of covenans is no possible, because he SPV is creaed wih he sole purpose o complee one single projec ha requires exacly ha amoun of money. Should he level of capial expendiures be limied afer a breach of covenans, he projec would auomaically be erminaed and forced ino bankrupcy given he impossibiliy o complee consrucion and sar operaions. 2 2 The impossibiliy o resric capial expendiures upon violaion of financial covenans explains why very big infrasrucure projecs (like he Eurounnel) underwen several rounds of refinancing in order o complee he consrucion phase. See Esy and Sesia (2004). 6

7 A sandard caegorizaion of covenans is no available in he huge volumes of exising lieraure. However, mos auhors agree on he broader caegories of posiive, negaive, and financial covenans [Rosenbaum and Pearl (2009), Smih (1993)]. Wihin financial covenans, Demerjian (2007) and Nini e al. (2009) disinguish he caegories of coverage raios, curren raios/liquidiy raios, leverage raios, gearing raios, and ne worh raios. 3 Demiroglu and James (2010), insead, classify financial covenans as eiher incurrence or mainenance covenans. Incurrence covenans are designed o increase he recovery raios of lenders in case of borrower defaul and o impose resricions on borrower behaviour. Mainenance covenans, insead, mus be saisfied on an ongoing basis as a wealh-increasing measure for lenders and are linked o mandaory, posiive acions by he borrower. Among he various financial covenans ha can be included in a credi agreemen, one is paricularly relevan o our work: he deb service cover raio (DSCR) (Gai, 2007). 4 DSCR is defined as FCF DSCR = P + I DSCR represens he raio beween he cash available before deb repaymen (FCF ) and he amoun o be repaid in period. I provides lenders as a measure of he projec s capabiliy o repay he loan By eq. (1), 5 R OE Taxes + WC DSCR = P + I In addiion o DSCR, for lenders i is of ineres o know he minimum DSCR in all periods. This quaniy is here denoed as min DSCR = min DSCR (7) = 1... T (5) (6) From he decision-making viewpoin, mindscr is uilized by lenders in he loan negoiaion phase o help hem decide he opimal deb-o-equiy raio of he deal (Gai, 2007). They firs se he arge mindscr. Then, hey run he financial model and ieraively adjus he loan amoun in such a way ha mindscr is always greaer han he minimum required value. 3 Demerjian (2007) indicaes ha in highly leveraged ransacions (like projec finance), higher relevance is given o coverage raios and leverage. 4 A second cover raio ha is frequenly used in conjuncion wih DSCR is he loan life cover raio (CR). CR measures projec repaymen capaciy as he presen value of operaing cash flows plus he exising reserve accouns. The CR provides he invesor wih a measure of he number of imes he unlevered free cash flows can be used o repay he ousanding deb balance (O ) over he scheduled life of he loan. 5 I is imporan o remember ha he numeraor of eq. (6) does no include Capex as indicaed in eq. (1). The reason is ha in all projec finance ransacions, capial expendiures are concenraed only during he consrucion phase. Insead, he operaional phase is dedicaed o managing he projec and no addiional invesmens are required. See, among ohers, Corielli e al. (2010) and Yescombe (2002). 7

8 A ypical projec finance loan conrac usually includes wo ses of values for his financial covenan. The firs indicaes he minimum hreshold below which lenders can require an acceleraed repaymen of he loan; he second, which is lower han he firs, riggers he resoluion of he credi agreemen and represens he maerial breach of covenan. The join consideraion of he wo ses of values generaes a range of values for DSCR associaed wih a echnical defaul ha is frequenly waived by means of a renegoiaion of he loan repaymen erms. This renegoiaion is always available unil DSCR reaches he lower bound when he breach of covenans becomes maerial, forcing he projec ino bankrupcy. 6 The acual levels of coverage raios depend on he deal. For insance, Mariano and Tribo (2010) repor an average DSCR of 1.53x for a large sample of 1,352 lending non-projec finance agreemens. Gai (2007) repors average DSCR values beween 2x and 2.25x for merchan power plans, and beween 1.2x and 1.3x for waer and saniaion projecs. The maerial breach of covenans is frequenly associaed wih DSCR close o 1.03x- 1.05x. Eqs. (1)-(7) represen he basic equaions of financial modelling. In he pracice, R. OE, Taxes, P and I are, in urn, expressed as funcions of exogenous variables (e.g., macroeconomic variables, escalaion indices, ec.) here represened by vecor ω. The funcional dependence of he lenders and sponsors valuaion crieria on ω is, in he professional pracice, he resul of complex financial calculaions ha ake ino accoun echnical, operaional, fiscal, and accouning aspecs of he invesmen projec. These calculaions are implemened in a financial model validaed hrough exper opinion. As he valuaion of he invesmen progresses from he due diligence o he negoiaion phases, he model becomes he cenral ool for negoiaions beween shareholders and lenders. A deailed modelling of he invesmen projec characerisics is required and he financial model ends o become a complex mapping, usually known only numerically (Borgonovo e al., 2010). e us wrie he relaionship beween he decisionsuppor crierion of ineres and ω as Z(ω). Z(ω) is deermined if ω is known. However, his is seldom he case in pracice, as ω usually consiss of several uncerain random variables. Analyss, when performing daa analysis, reques forecass from specialized insiuions and informaion from consulans (Gai e al, 2007). This allows hem o assess disribuions for ω. By propagaing he uncerainy in ω hrough he Mone Carlo simulaion, we obain he disribuion of Z(ω). The cumulaive disribuion funcion (CDF) of Z(ω) is called he risk profile [Smih (1998)]. This is he firs sep in risk analysis. 6 In a recen PF loan in he renewable energy secor, he group of lenders se a minimum deb service cover raio of 1.45x. If in any year, he acual DSCR was beween 1.45x and 1.05x lenders forced sponsors o use he excess cash o repay he loan (i.e. cash sweep), considering repaid he farhes insalmens. Below 1.05x, no renegoiaion of he loan erms was allowed and he loan agreemen was subjec o resoluion. 8

9 2.3 Risk Analysis and Risk Measures The erm risk analysis originaes in he seminal works of Hillier (1963), Herz (1964), Hillier (1965), Van Horne (1966), Wagle (1967). These auhors propose he use of he Mone Carlo simulaion o obain he disribuion of an NPV or IRR. This has become bes pracice in he analysis of indusrial invesmens and business planning [see Carmichael and Balaba (2008)] More recenly, also he erm probabilisic sensiiviy is used as a synonym of risk analysis [Hazen and Huang (2006)]. Formally, given a probabiliy space ( Ω, B ( Ω), P ), we le he applicaion Z:Ω R represen a generic loss or profi funcion. The funcion F Z (z)=pr(z<z) is he cumulaive disribuion funcion of Z, also called he risk profile. From F Z (z) an analys obains a wide range of insighs abou he invesmen viabiliy and infers risk measures[rockafellar and Uryasev (2002)]. Generally speaking, a risk measure is a funcion of Z, ρ:z R; ρ becomes a coheren measure of risk if i saisfies he axioms of ranslaional invariance (Axiom T), subaddiiviy (Axiom S), posiive homogeneiy (Axiom PH), monooniciy (Axiom M), and relevance (Axiom R) of Arzner e al. (1999). The mos widely uilized risk measures in he pracice of indusrial invesmen, and consequenly our main ineres in his work, are he value a risk (VaR) and condiional value a risk (CVaR). VaR α is defined as follows. Given β (0,1) [Gourieroux e al (2000), Rockafellar and Uryasev (2002)]: { α} VaR : = inf z : Pr( Z > z) 1 (8) α In probabilisic erms, VaR α is he quanile corresponding o he upper bound of he α-ail of he disribuion of Z. Alernaively, VaR α can be seen as he maximum poenial loss, which is exceeded only in α% of he cases. VaR α is widely used as a risk managemen ool by corporae reasurers, dealers, fund managers, financial insiuions, and regulaors [Alexander and Bapisa (2004)]. According o Berkowiz e al (2009) [p.2-3], VaR α is associaed wih hree major fields of applicaion: porfolio choice, risk conrols and regulaory uses. I is probably in hese las wo areas, however, where some limiaions of VaR α became apparen [see Arzner e al (1999)]. To address hese limiaions, auhors have pursued wo lines of research. One approach addresses changes in axiomaizaions and condiioning ha make VaR α a coheren measure of risk wih no need o modify is definiion [see, among ohers, Garcia e al (2007)]. The oher approach modifies he definiion of VaR α, ransforming i ino a coheren measure of risk. For insance, in Naarajan e al (2008), VaR α is exended o Asymmery-Robus VaR α, which resuls in a coheren risk measure. One of he firs and mos sudied modificaions of VaR α - and he mos relevan for his work - is CVaR, inroduced by [Rockafellar and Uryasev (2002)] as follows: 9

10 CVaR : = E [ Z Z > VaR ] (9) α CVaR α is boh a coheren risk measure and a naural risk saisic [Hong and iu (2009), p. 281]. Rockafellar and Uryasev (2002) also asser ha CVaR α coincides wih expeced shorfall and is closely relaed o mean excess loss, which are also coheren measures of risk. Since is inroducion, CVaR has been inensively sudied, especially in comparison o VaR. A comprehensive review goes beyond he scope of his paper. However, we wish o highligh he following works. Benai (2003) addresses porfolio selecion wih coheren risk measure consrains. Alexander and Bapisa (2004) compare resuls for porfolio opimizaion in he presence of VaR and CVaR consrains. [Szego (2004)] offers a comprehensive overview of risk measures, presening a criical comparison of he concepual aspecs of VaR and CVaR. Opimizaion in porfolio selecion wih coheren risk measures is discussed in [Miller and Ruszczynski (2008)]. Robus opimizaion in CVaR porfolio selecion is presened in [Huang e al (2010)]. CVaR is also uilized as a risk measure in fields ouside finance. Ahmed e al (2006) and Gooh (2006) deail applicaions in invenory managemen. We are ineresed in sudying how/wheher hese risk measures are affeced by a covenan breach (echnical or maerial). The dual perspecive of sponsors and lenders is considered in he nex secion. α 3 A Concepual Model of Covenan Breach We consider an invesmen projec ha develops over T periods. For simpliciy of noaion in he nex equaions, he consrucion phase is assumed o be fully conained in period =0, while operaion akes place from periods 1 o T. We le A 0 denoe he invesmen coss. The invesmen is financed hrough equiy and deb, wih denoing he deb proporion o he oal invesmen coss. We le I dc represen he ineres capialized during consrucion, I and P he ineres and he principal repaid a ime. oan repaymen goes from period 1 o T, wih T T. eing τ be he income ax rae, and δ be he depreciaion rae, he expression of FCF is: ( ) FCF = (1 τ)( R OE ) + τ [ δ A + I + χ I ] = 1, 2,..., T (10) 0 dc where 1 χ = 0 if T if > T. Correspondingly, he free cash flow o equiy a period (FCFE ) is: ( ) FCFE = (1 τ)( R OE ) + τ [ δ A + I + χ I ] χ ( I +P ) (11) 0 dc Assuming no fricions in he equiy repaymen o shareholders, ShNPV becomes: 10

11 0 = 1 ( ) T (1 τ)( R OE ) + τδ [ A + I + χi ] χ( P + I ) ShNPV = (1 ) A + (12). 0 dc (1 + ke ) We assume ha R, OE, A0, Idc canno be deermined wih cerainy (bolded fons indicae vecors). Thus, we have ω=( R, OE, A0, Idc ), and ShNPV = Z ( ) 1 ω. Then, he decision crierion in eq. (12) becomes E [ ShNPV ] > 0, where he expecaion is aken over he join disribuion of ω. The loan agreemen includes a sandard clause on mindscr. For our reference invesmen model, we have: and (1 τ)( R OE) + τδ [ ( A + I ) + I ] 0 dc DSCR = if 1 < < T P + I (1 τ)( R OE) + τδ [ ( A + Idc) + I ] 0 min DSCR = min = 1,... T P + I (13) (14) Thus, min DSCR = Z2( ω ) is a random variable. As we will see, assessing he disribuion of mindscr provides analyss wih a range of imporan insighs concerning projec risk, boh for shareholders and lenders. In his respec, we observe ha financial models equip analyss wih all indicaors concerning he breach of financial covenans. However, in professional pracice, such indicaors are usually no included as par of a sandard risk analysis (In oher words, analyss do no look a he disribuion of hese indicaors.) Insead, hey are assessed a base case firs and hen subjeced o sress esing ha produces he values of he indicaors in correspondence wih pre-deermined scenarios. Ye, scenarios do no provide any informaion abou he probabiliy of covenan breach. Furhermore, no addiional modelling of he consequences of defaul accompanies he radiional risk analysis. Thus one canno quaniaively assess he effecs of covenan breach. The modelling of hese effecs from he dual perspecive of shareholders and lenders is discussed in he following wo secions. 3.1 The Shareholders Perspecive Following covenan breach, shareholders and lenders are exposed o differen consequences depending on he ype of defaul (echnical or maerial) and he conracual clauses. e us sar wih shareholders. If a covenan breach is deemed echnical by lenders, hey call for he suspension of remissions of cash flows o shareholders (i.e. dividend paymens) in he period of defaul, and measures like cash sweeps come ino force. e TB indicae he period of echnical breach occurrence. Then, he deb cash flows are equal o he originally scheduled ones for = 1, 2,..., TB 1. For =,..., T he cash flows will be hose corresponding o a cash TB sweep repaymen of he loan. e us denoe hem by P ' and I '. 11

12 Then ShNPV [eq. (3)] in he presence of echnical breach becomes: ShNPV FCFE FCFE (15) TB 1 T ' TB = (1 ) A = 1 (1 + ke) 1(1 k ) TB + + E where he 0 evidences he presence of a null repaymen a ime TB, and ' FCFE are he new free cash flows o equiy afer deb rescheduling. Because a leas one equiy cash flow repaymen is suspended and, afer TB, cash is redireced earlier owards lenders, shareholders will experience a loss equal o According o eqs. (11) and (15), we have: = 1 ( 0 ) ( 0 ) ShNPVTB ' ' ' (1 )( R OE ) + [ A + Idc + max(0, T ) I ] ( P + I ) max(0, T ) ShNPV. TB 1 (1 τ)( R OE ) + τδ [ A + Idc + max(0, T ) I ] ( P + I ) max(0, T ) (1 ) A0 + + (16) (1 + k ) + T = TB τ τδ ShNPV TB (1 + k ) E = E Consequences are more severe if he maerialiy es is posiive. A maerial covenan violaion riggers projec defaul. The securiy package implies ha he pledged shares of he SPV fall ino he hands of lenders. Then, he presen value of equiy cash flows from he momen of defaul o he projec end is aken away from sponsors and redireced o lenders. e MB represen he ime a which a maerial breach happens. Because shareholders receive cash flows up o he period preceding MB, ShNPV [eq. (3)] becomes (1 ) A + 0 MB 1 = 1 ShNPV MB MB 1 FCFE = (1 ) A0 + = (1 + k ) ( 0 ) = 1 (1 τ)( R OE ) + τδ [ A + I + max(0, T ) I ] ( P + I ) max(0, T ) dc (1 + k ) E E (17) Correspondingly, one can measure he loss incurred by shareholders as he presen value of he cash flows from MB o he end of he projec. e NPVoss MB = T FCFE (1 + k ) (18) mabreach In eq. (18), NPVoss MB denoes expecaion condiional on maerial breach. NPVoss MB represens he loss incurred by shareholders in a given scenario in which maerial breach happens. We consider he expecaion of his breach and have: E 12

13 In eq. (19), Shoss MB T FCFE : = EMB[ NPVloss MB] = E MB[ ] (19) (1 + k ) MB Shoss is he expeced loss for shareholders condiional on maerial breach, wih he expecaion aken over all scenarios in which maerial breach happens. 3.2 The enders Perspecive When a covenan breach happens, lenders and shareholders (beer sill, heir respecive legal advisors) mus assess he severiy of he breach. In mos cases, he aiude of lenders is usually o ry o allow shareholders o keep going on managing he projec by waiving he covenan breach [Chen and Wei (1993), Beneish and Press (1995), Nini e al (2009)]. In his case, he sole consequence is a cash sweep in favour of he lenders. As a resul, he projec s enire free cash flow of he period a which he echnical breach happens is redireced o lenders, he deb ousanding is correspondingly reduced and he remaining deb is repaid over he subsequen periods. Hence, in he case of a echnical breach, we have: NPV MB P + I P' + I ' 1 TB T oan TB = + = 1 (1 + kd) = (1 + k ) TB d where TB is he period when a echnical breach happens and E (20) P ' and I ' are he newly scheduled principal and ineres repaymen flows. Of course, he rescheduling is such ha no financial losses are incurred by lenders. In he case of maerial breach, insead, he siuaion for lenders is differen. Shareholders are, in principle, excluded from he projec and lenders now face he decision of wha o do. A firs possibiliy, denoed as a workou by Davidson e al. (2010), is o ensure he projec s operaional phase coninues. In fac, a maerial breach does no necessarily correspond o a siuaion of insolvency and he projec is poenially capable of producing enough cash o repay he loan. Thus, lenders work ou a resrucuring of he SPV,, which involves revising he conracual package and frequenly having new shareholders sep in. Of he 213 projecs sudied by Davidson e al (2010) ha underwen a maerial breach, 116 wen hrough a workou wih crediors. In hese cases, he ulimae recovery rae on he loan was 76%. In he remaining cases, bankrupcy was declared and lenders recovered he ousanding amoun on he loan only hrough disressed sales. In hese circumsances, he average ulimae recovery rae on he ousanding amoun was only 48%. Formally, le O MB denoe he value of he ousanding deb a MB, wih p Workou he probabiliy of a workou, and (1- p Workou ) he probabiliy of a fire sale, he expeced recovery for lenders equals: E[ W ] = p λ E[ O ] + (1 p ) λ E[ O ] = enders workou workou MB workou disressed MB = [ p ( λ λ ) + λ ] E[ O ] workou workou disressed disressed MB (21) where λ workou and λ disressed are he recovery raes on he loan in he case of workou and disressed sales, respecively. According o eq. (21), we can also deermine he percenage of he expeced recovery rae: 13

14 w E[ Renders ] = = p ( λ λ ) + λ E [ O ] (22) enders workou workou disressed disressed MB Eqs. (21) and (22) provide measures of expeced recovery for lenders given maerial breach. In paricular, only if λ workou > λ disressed and p workou is sricly non-null, lenders have he possibiliy of recovering more hrough workou han wha hey would oherwise recover hrough disressed sales. As discussed in Davidson e al (2010), when a maerial breach occurs, in a realisic applicaion, decision-making and negoiaion aspecs (i.e., he abiliy o lead he ransacion o a successful recovery) become he key concerns of he problem. We are now lef o describe how o nes he modelling of he consequences of defaul described in his secion in he conex of he Mone Carlo simulaion. 4 The Simulaion Procedure Sep 1: Probabilisic Sensiiviy for n=1:n shareholdercrierion(n)= value produced by financial model evaluaed a ω^(n) lendercrierion(n)= value produced by financial model evaluaed a ω^(n) CovenanIndicaor(n)= value produced by financial model evaluaed a ω^(n) end for n=1:n Sep 2: Maerialiy Tes Sep 3: Evaluaing he consequences of defaul if no breach is encounered Sore value of shareholder and lenders crieria esimaed a sep 1 elseif echnical breach U TB (n)=1; Reassess lenders and shareholders valuaion crieria modifying FCF and FCFE in accordance wih he provisions of he conracual clauses if maerial breach U MB (n)=1; Reassess lenders and shareholders valuaion crieria modifying FCF and FCFE in accordance wih he provisions of he conracual clauses End Sep 4: Esimaing Covenan Breach Frequency Sum U MB (n) o obain he probabiliy of maerial breach Sum U TB (n) o obain he probabiliy of echnical breach end Sep 5: Evaluaing Risk Measures and Risk Profiles Compare risk profiles wih and wihou covenan breach if Discrepancy Saisically Significan Reassess shareholders, lenders Crieria and Risk Measures end end Figure 1: Simulaion seps for modeling he effecs of covenan breach 14

15 In his secion, we describe how our concepual model can be urned ino a simulaion procedure. The firs sep consiss of running a probabilisic simulaion of he financial model regisering he values of boh lenders and shareholders crieria a he end of each simulaion (Figure 1). Then, he examinaion of covenan breach a scenarios n=1,2,,n sars. A each scenario, we analyse he value of he covenan indicaors produced by he model, and check he maerialiy es (Sep 2 in Figure 1). If no covenan breach is regisered, hen he value of he valuaion crierion obained in he probabilisic simulaion is regisered as final value of scenario n. Conversely, we have o simulae he consequences of maerial breach wih he differen perspecives of lenders and shareholders. If he covenan breach is echnical, we need o esimae he new FCF and FCFE. Wih eq. (16) we obain he value of ShNPV o be sored in scenario n. If he breach is maerial, eq. (17) applies. Simulaneously, we can uilize eqs. (20) and (21) o assess consequences for lenders. By comparing he NPV disribuions [risk profiles in Smih (1998)] obained wih and wihou modelling defaul, we have a way o assess he consequence of covenan breaches for he given ransacion. To quaniaively esablish wheher he effec is significan, several saisical ess are available. If he es provides a negaive answer (ha is, he separaion is no significan), hen he informaion on he original disribuion (he one obained wihou explicily modelling he consequences of defaul) can be mainained in furher projec evaluaion. Conversely, if he answer is posiive, conracual defaul has an impac and he new risk profile has o be uilized o assess risk measures for he projec. The above procedure can be also applied if we are evaluaing he model hrough a scenario analysis raher han a Mone Carlo simulaion, observing ha one Mone Carlo run can be inerpreed as a possible scenario. Boh echniques are well known and widely described in he lieraure, and i is no wihin he scope of his work o presen a deailed descripion. In eiher case he procedures available in he lieraure allow us o build disribuions or scenarios reflecive of he decision maker's sae of knowledge wih respec o he uncerain quaniies [in he case of disribuion assignmen in Mone Carlo simulaion; [Aposolakis (1990), Glasserman (2004)] or o fuure saes of he world [in he case of scenario analysis; [Jungermann and Thuring (1988), Tieje (2005).] 5 Esimaing Covenan Breach Probabiliies, Workou Probabiliy and Risk Measures In ligh of he simulaion procedure, we can infer several addiional insighs abou he projec risk wih and wihou inclusion of covenan breach. The firs is he frequency of echnical and maerial breaches. Definiion: Consider a financial ransacion wih covenans. e CB be he even any of he covenans is breached. Then, we le denoe he probabiliy of covenan breach. ν = Pr( CB) (23) CB 15

16 As menioned above, a covenan breach can be echnical or maerial, depending on he specific conracual clauses se forh in he loan agreemen. Thus, a maerial breach is acually associaed wih only a subse of he saes in which a breach occurs. Then, we can define he following probabiliies. Definiion: Consider a financial ransacion wih covenans. e TB and MB denoe he evens echnical breach and maerial breach of any covenan, respecively. Then, we le ν TB = Pr( TB) and ν = Pr( MB) (24) denoe he projec probabiliies of echnical and maerial covenan breach, respecively. Clearly, he se of he saes of he world corresponding o maerial breach is included or equal o he se of he saes of he world wih echnical breach. However, he wo evens are usually o be considered disjoined. In oher words, CB = TB MB, and herefore we have νmb + νtb = νcb. Elsinger e al (2006) (p. 1310) observe ha he relaive frequency of defaul across scenarios is hen inerpreed as a defaul probabiliy. e N be he number of Mone Carlo runs. Then, le n TB and n MB denoe he number of Mone Carlo runs a which covenan breach and conracual defaul are regisered, respecively. Then, by consrucing a Mone Carlo simulaion [see, for insance, Glasserman (2004)], we have: MB ν TB ntb ( N) nmb ( N) = lim, νmb = lim (25) N N N N Hence, a any sample size N we obain an esimae of ν TB and ν MB 16, ha we denoe as ν TB and ν MB, respecively. A procedure for readily auomaing he calculaion of hese wo variables in a Mone Carlo simulaion is he following. e us consider TB for simpliciy s sake. A each Mone Carlo run, we can inroduce he auxiliary Boolean indicaor of echnical breach U TB 1 if TB ( n) =. Then, i is 0 if no TB N n ( N) = U ( n). By we obain ν TB esimae a sample size N. Similar reasoning applies for obaining esimaes ofν MB. TB n= 1 TB N UTB ( n)/ N, We furher observe ha, from he simulaion, we can esimae an endogenous probabiliy of workou. In eq.(21), we choose he value of p workou ha bes maches he geographic locaion and indusrial secor of he projec a hand, resoring o he daa published by raing agencies, for example. However, a workou probabiliy can be endogenously generaed by our Mone Carlo simulaion. We consider scenario s in which a maerial defaul happens. We assume ha lenders will be able o coninue he projec operaions and find a new projec sponsor if he following wo condiions are me: a) ϕ mindscr<1.051; and b) he equiy NPV of he ousanding cash flows is posiive. Condiion a) is abou he severiy of he breach. In our simulaion, we impose ϕ=1, which corresponds o cases where he projec is no bankrup alhough in maerial breach. However, here migh be cases in which lenders aemp o rescue he projec even if mindscr<1, bu no far away from uniy. n= 1

17 Of course, ϕ can hen be modified in he simulaion. Boh condiions can be exraced from a Mone Carlo simulaion. Operaionally, we define he indicaor U WO 1 if workou condiions me ( n) = (26) 0 if workou condiions no me Which leads o he following Mone Carlo esimae of he workou probabiliy: N U ( n) WO n= 1 Workou (27) v = N I is also ineresing o consider he condiional frequency of workou given maerial breach. This can be esimaed by simply normalizing N UWO ( n) over he scenarios in which maerial breach has occurred: n= 1 N WO n 1 v = Workou MB = N (28) n= 1 U U MB ( n) ( n) Finally, based on our knowledge of he risk profile, we can esimae risk measures in he presence and absence of conracual breaches. In his paper, we focus on VaR and CVaR in eqs. (8) and (9). TheMone Carlo esimaion of hese indicaors is widely discussed in he lieraure [Rockafellar and Uryasev (2002), Ruszczy nski and Shapiro (2005), Jin and Zhang (2006)] and, herefore, can be omied in his work. Suffice o say ha by comparing he values of VaR and CVaR in wo ses of simulaions (one ha explicily includes covenan breaches and one ha doesn ), lenders and sponsors are able o form a comprehensive view of he invesmen a hand. 6 A Case Sudy 6.1 Projec Background and economic raionale In mid 2007, Bonollo Disilleries one of he mos renowned high-end liquor producer in Ialy sared sudying he projec of a biomass plan o be annexed o is already exising brewing facory. According o Bonollo Disilleries managemen, he plan was needed o reduce boh energy coss and polluing emissions and o diversify he energy sources currenly employed by he facory. A ha ime, Bonollo Disilleries already used some biomass energy o cover approximaely 30% of is hea energy needs and 40% of is elecrical energy needs. The remaining par of is requiremens was covered wih mehane gas and elecrical energy from he naional elecriciy Grid. The new plan was expeced o provide he 17

18 Disillery wih 10MW of clean hea and elecrical energy. This represened 97% of hea energy needs and 100% of elecrical energy needs. The energy surplus of 57 MWh per year would be sold o he elecriciy disribuion nework. Anoher key feaure of he biomass plan was ha i would enable he Disillery o reduce is emissions from a oal of 513,779 kg/year o less han 403,260. Furhermore, biomass combusion did no increase he level of CO 2 presen in he amosphere and herefore represened a clean and environmenal-friendly energy source. In addiion o hese advanages for Bonollo Disilleries, anoher elemen ha promped managemen o embark on he projec in quesion was he possibiliy o use he byproducs of he disillaion process as base feedsock for he power plan. The wase byproducs would be sold o he biomass plan by Bonollo Disilleries under a long erm raw maerial supply agreemen. Finally, he ashes deriving from combused biomasses could be used as ferilizers in he company s planaions, resuling in minimal wase and furher coss reducion. 6.2 Conracual srucure The conracual srucure underpinning he projec is as follows. The biomass plan was incorporaed in a new eniy (SPV), Bonollo Energia Spa, graned wih he righs o build and operae he biomass plan. The SPV had o be financed wih a deb/equiy raio of 4/1 wih equiy provided in equal pars by he sponsors Bonollo Disilleries and Alerion Clean Power. Alerion is a company lised on he Milan Sock Exchange specialized in he managemen and operaions of renewable power plans in Ialy and Cenral and Easern Europe. Deb was provided by a pool of banks headed by General Elecric (GE)-Inerbanca. Inerbanca was appoined as Mandaed ead Arranger (MA) of he bank syndicae in July 2008 and sared working wih projec sponsors on projec conracs and loan syndicaion during he hird and fourh quarer of The financial close ook place in February 2009 wih a syndicae composed by General Elecric-Inerbanca as MA, GE Inerbanca, MPS Capial Services, Banca Popolare dell Eruria and Cenrobanca as underwriers. GE- Inerbanca also aced as hedging bank, agen bank and deposiory bank. Plan consrucion was regulaed by an EPC (engineering, procuremen and consrucion) conrac signed wih STC Group as general conracor. STC was a leader in he consrucion of indusrial plans for power generaion on he Ialian marke. The consrucion conrac was signed on a fixed-price urnkey basis and was supplemened by guaranees provided o he SPV by he general conracor (iming of delivery and minimum performance sandards). Furhermore, he conracor was required o provide performance bonds and warrany bonds for 2 years afer consrucion.consrucion was expeced o sar a he beginning of 2009 and las a oal of 24 monhs, wih an addiional 6-monh esing and sar up phase. The wo projec sponsors played key roles in he conracual nework of he projec finance deal. Bonollo Disilleries was he seller of approximaely 142,000 ons/year of base feedsock (biomass) under a long erm raw 18

19 maerial supply agreemen of 16.5 years. Furhermore, Bonollo Disilleries would purchase around 116,000 ons of seam per annum and 13,000 MWh per annum of biomass-produced energy under a long erm power purchase agreemen. Alerion conribued o he projec in wo roles. Firs, a join venure was creaed by he wo sponsors in order o carry ou O&M (operaions and mainenance) services for he SPV. Second, Alerion had o ener a service agreemen wih he SPV for he sale of power and green cerificaes on he marke. Finally, as menioned, he energy surplus produced by he plan had o be sold on he Ialian elecriciy marke based on marke spo conracs. The sale of his surplus was carried ou by Alerion Clean Power pursuan he service agreemen wih he SPV. 6.3 Financial daa and covenans The agreemen beween sponsors and lenders required he projec o be financed wih a senior deb/equiy raio of abou 4/1, in line wih sandard marke pracice a he ime of he deal. The oal invesmen cos was expeced o be around 64 mil euro, including among ohers abou 48 mil euro of EPC cos, 6 mil euro capialized ineres and 9 mil of VAT under consrucion. GE-Inerbanca and he oher banks of he syndicae organized he loan faciliies in wo ranches: 1. A base faciliy of 41 mil euro wih duraion of 15 years and a grace period of 3 years a he beginning of he operaional phase where only ineres paymen was due. 2. A VAT loan of abou 9 mil euro, o be repaid during he operaional phase using he cash corresponding o he VAT on Energy and seam sales. Duraion: consrucion period plus 2 year repaymen. The wo faciliies were supplemened by he ypical projec finance securiy package discussed in Secion 2.2. Minimum DSCR was se a 1.4x wih a DSCR riggering defaul (maerial breach) a 1.05x. 6.4 Risk Analysis Resuls The financial model developed o value he ransacion was made available o he auhors by one of he sponsors of he projec. The model was developed by he Mandaed ead Arranger Bank and realisically simulaes he invesmen's financial performance over is life span reproducing he SPV income saemen, cash flow saemen, and balance shee hrough a complex doveail of Excel workshees. All valuaion crieria used by sponsors and lenders for decision-making are esimaed by he model ha also provides informaion abou he occurrence of covenan breach. We use he financial model and he daa of he Bonollo Energia case o perform a series of numerical experimens o invesigae he condiions under which covenans impac he ransacion and he exen of his impac. Each experimen is a risk analysis performed in accordance wih he procedure presened in Secion 4, 19