Credit Ratings, Collateral, and Loan Characteristics: Implications for Yield*

Transcription

1 Kose John New York University Anthony W. Lynch New York University nd Ntionl Bureu of Economic Reserch Mnju Puri Stnford University nd Ntionl Bureu of Economic Reserch Credit Rtings, Collterl, nd Lon Chrcteristics: Implictions for Yield* I. Introduction Collterl is n importnt prt of more thn 70% of ll commercil nd industril lons mde in the United Sttes (see Berger nd Udell 1990), but the cdemic literture ddressing its role is smll. Ceteris pribus, collterl decreses the riskiness of given lon, since it gives the lender specific clim on n sset without reducing her generl clim ginst the borrower. However, using lrge dt set on secured nd unsecured lons, this rticle finds tht yields on collterlized debt issues re higher thn on generl debt issues fter controlling for credit rting. An explntion for this puzzling result is proposed tht recognizes the effect of gency problems between mngers nd clim holders, nd imperfections in the rting process. We then test number of the model s predictions con- * We would like to thnk Allen Berger, Robert Goldstein, Edith Hotchkiss, Eli Ofek, Avri Rvid, Greg Udell, Dvid Yermck, prticipnts t severl seminrs nd conferences, nd especilly n nonymous referee for useful discussions nd comments. We lso would like to thnk Amr Gnde nd Jynthi Sunder for help in collecting nd orgnizing the dt nd Edwrd Altmn for severl helpful discussions on the rtings process. This rticle studies how collterl ffects bond yields. Using lrge dt set of public bonds, we document tht collterlized debt hs higher yield thn generl debt, fter controlling for credit rting. Our model of gency problems between mngers nd clim holders explins this puzzling result by recognizing imperfections in the rting process. We test the model s implictions. Consistent with our model nd in results new to the literture, we find the yield differentil between secured nd unsecured debt, fter controlling for credit rting, is lrger for low credit rting, nonmortgge ssets, longer mturity, nd with proxies for lower levels of monitoring. (Journl of Business, 2003, vol. 76, no. 3) 2003 by The University of Chicgo. All rights reserved /2003/ $

2 372 Journl of Business cerning the bility of lon nd collterl chrcteristics to explin cross-sectionl vrition in yields nd find tht they re supported in the dt. In prticulr, we find tht the yield differentil between secured nd unsecured debt, fter controlling for credit rting, is lrger for low credit rting, nonmortgge ssets, longer mturity, nd with proxies for lower levels of monitoring. Jensen nd Meckling (1976) rgue tht corporte insiders owning only frction of the firm s equity hve incentives to consume perquisites beyond optiml levels. The sme intuition continues to pply when some of the debt is collterlized. We model scenrio in which the corporte insiders own frction of the equity of the firm. The firm hs generl nd collterlized debt, nd the collterlized sset hs less voltile vlue thn the remining ssets of the firm. Our theoreticl nlysis shows tht the resulting gency problems ffect the vlue of the collterlized ssets more thn the generl ssets. We then show tht if credit rting fils to fully reflect the impct of gency problems on credit qulity, then secured debt hs higher yields fter controlling for credit rting thn unsecured debt. The model is then used to generte some dditionl implictions for the yield differentil between secured nd unsecured debt issues fter controlling for credit rting. The gol is to identify importnt collterl nd lon chrcteristics tht cn ffect yield. First, the nture of the collterl cn be importnt since there re some ssets whose vlues re difficult to erode for exmple, lnd nd buildings. Hence, we expect the yield differentil for mortgges reltive to unsecured issues to be smll but expect yield differentils for nonmortgge secured issues reltive to unsecured issues to be higher. Second, we show tht the yield differentil between secured nd generl debt is incresing in the probbility of defult, which cn be proxied by credit rting. Third, the yield differentil is shown to be n incresing function of the voltility of the generl sset vlue, which cn be proxied by debt mturity. Fourth, the yield differentil is lso shown to be decresing function of monitoring intensity. Proxies for monitoring intensity re developed: for exmple, monitoring intensity is likely to be lower for new thn sesoned issues nd higher in the presence of debt covennts. We gther lrge dt set from Securities Dt Corportion (SDC), on ll fixed-rte, stright debt public issues mde in the period Jnury 1, 1993, to Mrch 31, We exmine the yield differentil between secured nd unsecured debt fter controlling for credit rting both on n ggregte level nd on disggregte level, bsed on lon nd collterl chrcteristics. Consistent with our story, we find tht the yield differentil between secured nd unsecured debt, fter controlling for credit rting, is positive. We then use the implictions of our model to help guide us in investigting how yields re ffected by collterl nd lon chrcteristics. These include the nture of collterl, credit rting, mturity, whether new or sesoned issue, nd the presence of covennts. Our empiricl results cn be summrized s follows. After controlling for

3 Implictions for Yield 373 credit rting, (i) the yield differentil between secured nd unsecured debt is positive. (ii) The yield differentil between secured nd unsecured debt is lrgely driven by nonmortgge secured ssets nd is robust to controlling for cross-firm differences in risk. Mortgged ssets, such s lnd nd buildings, do not exhibit yield differentil s compred to unsecured debt. (iii) The yield differentil between secured nd unsecured debt is higher for low creditrted issues s compred to high credit-rted issues. (iv) The yield differentil between secured nd unsecured debt is higher for long mturity issues s compred to short mturity issues. (v) The yield differentil between secured nd unsecured debt is higher for new issues s compred to sesoned issues. (vi) Finlly, the presence of covennts is found to reduce the yield on collterlized debt more thn on unsecured debt, prticulrly for low credit-rted issues. We believe tht ours is the first empiricl investigtion of how the nture of collterl nd issue chrcteristics cn ffect yields, fter controlling for credit rting. The six results put together re consistent with our gency-cost explntion for the higher yields on collterlized debt fter controlling for credit rting. While there my be lternte explntions tht could explin some of the individul results, it is difficult to find n lterntive explntion tht is consistent with ll six findings. Further, our results suggest tht, even fter tking credit rting into ccount, the nture of collterl, issue chrcteristics, nd the level of monitoring intensity, mong other things, re importnt determinnts of yield. The rest of the rticle is orgnized s follows. Section II hs literture review. Section III describes the dt nd gives discussion of the credit rting process. Section IV contins the theoreticl model, while Section V exmines nd presents the empiricl results. Section VI concludes. II. Literture Review Much of the theoreticl literture on the role of the collterl hs focused on the scenrio where there is privte informtion bout risk known only to borrowers. Further, the collterl is outside collterl where the owners pledge ssets not owned by the firm. In n environment where lenders re not s well informed s borrowers regrding their defult risk, it my be optiml for lenders to rtion credit (see, e.g., Jffee nd Russell 1976; Stiglitz nd Weiss 1981). However, Bester (1985) nd Besnko nd Thkor (1987) show tht, when borrower risk is privte informtion, collterl my mitigte the credit rtioning problem. A number of ppers hve elborted on the role of collterl in the presence of informtion symmetry (see, e.g., Chn nd Knts 1985; Besnko nd Thkor 1987b; nd Chn nd Thkor 1987). The common prediction of these models is tht lower-risk borrowers pledge more collterl. This prediction seems to be t vrince with the conventionl wisdom in the bnking community, which ssocites the use of collterl with observbly risky borrowers. As prt of the prelon credit nlysis, com-

4 374 Journl of Business mercil lenders ssess the riskiness of the prospective borrowers nd require the observbly risky borrowers to pledge more collterl (Morsmn 1986; Hempel, Colemn, nd Simonson 1986). This prediction is lso t odds with the smll mount of empiricl work ddressing the issue of collterliztion nd its effect on lon qulity. Orgler (1970) compiled dtbse on individul lons from bnk exmintion files nd distinguished good from bd lons on the bsis of whether the lons were eventully criticized by the bnk exminers. He regressed good/bd dummy vrible on secured/unsecured dummy vrible nd severl control vribles nd found secured lons to be riskier. Hester (1979), using dt from 1972 survey, regressed secured/unsecured dummy vrible on six ccounting proxies for risk nd found tht riskier borrowers pledge collterl. Berger nd Udell (1990) use the Federl Reserve s Survey of Terms of Bnk Lending dt nd document positive reltionship between collterl nd risk. Klpper (1999) investigtes the use of ccounts receivble nd inventory s collterl by lrger firms, while Crey, Post, nd Shrpe (1998) find tht commercil finnce compnies who specilize in sset-bsed lending (collterlized lending) tend to lend to riskier firms thn do commercil bnks. Finlly, Berger nd Udell (1995) exmine inside collterl in smll business lines of credit in the United Sttes, while Hrhoff nd Korting (1998) exmine collterl use in smll business lending in Germny. Both ppers find positive reltion between collterl nd risk in the context of smll business lons. The only theoreticl pper to obtin positive reltion between borrower risk nd collterl pledged is by Boot, Thkor, nd Udell (1991), who exmine collterl in the presence of both morl hzrd nd dverse selection. In contrst to our rticle, Boot et l. (1991) focus on outside rther thn inside collterl. Severl ppers hve considered the effects of morl hzrd lone in the presence of inside collterl. Smith nd Wrner (1979) rgue tht inside collterl my be useful in solving the sset-substitution problem (e.g., rised in Jensen nd Meckling 1976). Stulz nd Johnson (1985) nlyze the role of secured debt in solving Myers s (1977) underinvestment problem. More generlly, Jmes (1988) shows tht the underinvestment problem cn be solved by rnge of securities with pyoff chrcteristics similr to secured debt. However, none of these ppers study how gency problems ffect the yields of secured lons reltive to unsecured lons. The emphsis of most of the prior work both theoreticl nd empiricl hs been on the reltion between the use of collterl nd lon riskiness. Little ttention hs been pid to differences between secured nd unsecured debt yields fter controlling for credit rting. In prticulr, the ppers to dte do not exmine how the nture of the collterl posted nd the ssocited lon chrcteristics cn ffect yields. Further, none of these ppers provide ny guidnce on the importnt chrcteristics tht one should investigte in the first plce. To begin, we first sk whether collterl ffects the yields of bonds, fter

5 Implictions for Yield 375 tking credit rting into ccount. For this purpose we put together lrge dt set of public debt issues, described below. III. Dt Description We strt out with ll fixed-rte, stright debt public issues mde in the period Jnury 1, 1993, to Mrch 31, This dt re gthered from Securities Dt Corportion. We use the U.S. domestic public new issues dtbse of SDC, which SDC compiles from regultory filings, news sources, compny press releses, nd prospectuses. In creting our smple we exclude issues in the finncil industry (SIC code 6), s debt issues in this industry hve often involved securitiztion of ssets such s pckging of credit crd receivbles s the underlying collterl for debt issues. We lso exclude ll issues where the debt is gurnteed either by the government or by n ffilited compny. Our finl smple consists of 1,327 issues. We wnt to control for the issue s credit rting nd would expect tht higher credit-rted issues hve lower yield spreds thn lower credit-rted issues. It is lso importnt to control for other vribles tht my influence yield, such s size of the issue, purpose of the issue, reputtion of the underwriter, mturity, nd term structure of risk-free (tresury) yields. We now discuss the vribles likely to influence yield spreds nd then define how they re used in this rticle. Size of n issue is importnt, s lrger issues re likely to be ssocited with less uncertinty, to be more liquid, nd to hve more public informtion vilble bout them thn smller offerings. Hence, we would expect lrger issues to hve lower yields. A new debt issue is potentilly ssocited with greter uncertinty thn sesoned issue nd should result in reltively higher spreds. The purpose of the issue or the use of the funds rised cn lso potentilly ffect yield spred. In prticulr, if the purpose of the issue is to refinnce existing bnk debt, this cn increse yield spreds. Mturity cn lso potentilly ffect yield spreds. There is more informtion vilble bout exchnge-listed firms, nd one would expect debt issues of such firms to hve lower yield spreds. Underwriter reputtion is lso potentilly importnt, nd one would expect high reputtion of the underwriter to reduce yield spreds. Informtion on these vribles ws obtined from SDC s new issue dtbse. The vribles used re defined below. Appendix B detils how ech vrible ws constructed from the SDC new issue dtbse. Appendix C gives summry sttistics. BPS: The bsis point spred over the tresury rte of comprble mturity. CREDIT RATING: A set of seven credit-rting dummy vribles, CR0 CR6, tht correspond to Moody s C C, B1 B3, B1 B3, B1 B3, A1 A3, A1 A3, nd A ctegories. MATURITY: Three dummy vribles re constructed bsed on the mturity of the debt issue. LOWMAT, MEDMAT, nd HIMAT: LOWMAT is one if the security m-

6 376 Journl of Business tures in less thn 5 yers, MEDMAT is one if it mtures between 5 nd 15 yers, nd HIMAT is one if the mturity is greter thn 15 yers. All dummy vribles re zero otherwise. LN(AMOUNT): The nturl log of the issue mount in millions of dollrs. SECURED: A dummy vrible tht tkes the vlue of one if the issue is secured, zero otherwise. PRESTIGIOUS: A dummy vrible creted bsed on mrket shre rnk of dollr volume of underwritings of debt issues. PRESTIGIOUS is dummy vrible tht is one if the underwriter is one of the top five underwriters, bsed on mrket shre, zero otherwise. REF BK DEBT: A dummy vrible tht tkes the vlue of one if the purpose of the issue is to refinnce bnk debt, zero otherwise. NEW ISSUE: A dummy vrible tht is one if the debt issue is new one, zero otherwise. In order to construct this vrible we serched the SDC dtbse to check if the firm hd debt issue in the lst 20 yers. If it did, then we tke the issue to be sesoned issue; if not, then we tke it to be new issue. EXCHANGE: A dummy vrible tht tkes the vlue of one if the firm is listed on n exchnge, zero otherwise. INDUSTRY: A number of industry dummy vribles re constructed bsed on one-digit SIC codes. All industries sve for finncil firms re included in the smple nd dummy vrible constructed for ech one. A. Does Credit Rting Cpture It All? We now regress the yield premium of the bond on credit rting s well s the other vribles described bove. We find tht credit rtings do indeed ply very mjor role in determining yields. 1 The credit-rting dummies re highly significnt both economiclly nd sttisticlly. Hence, the higher the credit rting, the better the prices (nd the lower the yields). Thus, for exmple, if the credit rting is C C, it increses yield by 544 bsis points, wheres if the credit rting is B1 B3, it increses yields by 58 bsis points only. An interesting finding, however, is tht other vribles mtter in determining yields, even fter controlling for credit rting. Tble 1 shows us tht other vribles tht re significnt re collterl, mturity, purpose, nd whether it is new issue. Clerly, credit rting is not sufficient sttistic for determining yields. Further, collterl increses yield (lowers price) by 11 bsis points, fter controlling for credit rting. This is n interesting but puzzling result. There is little in the prior theoreticl or empiricl literture to guide us on this finding. One possible explntion tht we present is tht there re imperfections in the rting process. These imperfections imprt bises in rtings whose mgnitudes depend on 1. The importnce of credit rtings for investors is intuitive nd consistent with prior literture, e.g., Crbbe nd Post (1993) nd Gnde et l. (1997).

7 Implictions for Yield 377 TABLE 1 Effect of Secured on Full Dt Vrible Coefficient t-rtio Constnt * CR * CR * CR * CR * CR * CR LOWMAT * HIMAT * LN(AMOUNT) SECURED * PRESTIGIOUS REF BK DEBT *** NEW ISSUE * EXCHANGE Observtions 1,327 2 Adjusted R.86 Note. The tble gives the OLS estimtes of the following eqution: BPS p b0 bcr CREDIT RATING bmat MATURITY ba LN(AMOUNT) b SECURED b PRESTIGIOUS b S P R REF BK DEBT bn NEW ISSUE bi INDUSTRY be EXCHANGE. The dependent vrible for bsis point spred (BPS) is the premium of the ex nte yield of security over the ex nte yield of tresury of comprble mturity in bsis points. The independent vribles re s follows: CR (CREDIT RATING): set of credit rting dummy vribles CR0 CR6 tht correspond to C C, B1 B3, B1 B3, B1 B3, A1 A3, A1 A3, A; MATURITY: dummy vribles constructed bsed on the mturity of debt issue; LOWMAT: vlue of one if the security mtures in less thn 5 yers; HIMAT: vlue of one if the mturity is greter thn 15 yers; LN(AMOUNT): nturl log of the issue mount in millions of dollrs; SECURED: dummy vrible tht tkes the vlue of one if the issue is secured; PRESTIGIOUS: dummy vrible tht is one if the underwriter is rnked in the top five of underwriters bsed on mrket shre; REF BK DEBT: dummy vrible tht tkes the vlue of one if the purpose of the issue is to refinnce bnk debt; NEW ISSUE: dummy vrible tht is one if the debt issue is new one; EXCHANGE: dummy vrible tht tkes the vlue of one if the firm is listed on n exchnge. All dummy vribles re zero otherwise. INDUSTRY dummy vribles re not reported in the tble. The t-rtios re computed using White heteroskedsticitycorrected stndrd errors (White 1980). * Significnt t the 1% level. *** Significnt t the 10% level. lon chrcteristics like the nture of the collterl. In prticulr, the bis is shown to depend on whether the issue is collterlized or not. An lterntive explntion is risk story tht relies on rtings imperfectly correcting for risk differences between collterlized nd uncollterlized issues. This risk story recognizes tht collterlized debt issues re riskier empiriclly nd rgues tht the resulting higher men yield trnsltes into higher men for rtingdjusted yield becuse of the corseness of the rtings bins. 2 In the empiricl 2. We thnk the referee for suggesting this lterntive story. Although the risk story does not hold for ny rbitrry distribution for the yields on collterlized nd uncollterlized debt issues, such result cn hold for quite resonble distributionl ssumptions for the yields on the two types of issues. Consequently, it provides n importnt lterntive to our story tht we subject to creful empiricl testing in Sec. V.

8 378 Journl of Business testing, we develop tests to scertin whether there is role for our story fter controlling for cross-firm differences in risk. We lso present rnge of tests tht llow us to distinguish between the two stories. Since our story relies on imperfections in the rting process, we next go through the criteri for determining credit rting nd sk whether omissions by the rting gencies cn crete bises in rtings cross collterlized nd uncollterlized debt issues. More generlly, we re interested in how these bises vry s function of the nture of collterl nd ssocited lon chrcteristics. Answering this question is importnt, since it estblishes bsis for empiricl testing. B. The Credit Rting Process Our empiricl results bout collterl suggest tht despite Moody s clims, their credit rtings my not provide unbised ssessments of expected recovery rtes. As consequence, it would be useful to document in more detil the process used by Moody s to determine their credit rtings. For this purpose we went through the documenttion provided by Moody s (see, e.g., Moody s Investors Services Web site) nd lso hd detiled discussions with personnel ctully involved in doing the credit rtings s well s cdemic experts who guide nd consult for the credit rting gencies (such s Edwrd Altmn). Moody s clims to use n expected loss frmework for ssigning rtings. Moreover, Moody s uses the prctice of notching to mke rting distinctions mong different libilities of firm. In the investment-grde sector, Moody s first ssigns rting to firm s most importnt libility clss, its senior unsecured debt. In the specultive grde sector, the first step is to ssign senior implied rting, which is the rting tht would be ssigned if the firm hd single clss of debt. The second step in ech cse is to decide how to rte the firm s vrious debt instruments in reltion to this initil rting. Moody s notching guidelines for implementing the second step depend on whether the firm is specultive grde or investment grde. For investmentgrde firms, Moody s typiclly pplies the sme notching guidelines to ll firms with little regrd to firm-specific informtion bout expected recovery rtes cross the firm s issues. In prticulr, secured debt is generlly rted one notch bove the firm s senior unsecured debt rting, while subordinted debt, including junior nd senior subordinted debt, is rted one notch below. For specultive-grde firms, Moody s nlyses ech firm s cpitl structure nd bond covennts nd then uses expected loss s frmework to determine notching djustments. The result is often lrge differences in notching for reltive seniority from one firm to nother. While Moody s ttempts to ssign rtings on the bsis of expected loss, there re severl resons to believe tht in prctice Moody s rtings my not be unbised mesures of expected loss. First, with investment-grde firms, Moody s itself cknowledges tht its rule-of-thumb guidelines for notching re likely to led to undernotching of subordinted issues for firms in the

9 Implictions for Yield 379 highest (A nd A) rtings clsses (see Priority of Clim Stnding Committee nd Rtings Symbols nd Definitions Stnding Committee 2000). Second, with specultive-grde firms, Moody s nlysts hve discretion to notch bsed on firm-specific informtion bout reltive recovery rtes. This discretion could be employed in mnner tht imprts bises s function of whether the issue is collterlized or not. For exmple, while clsses of debt re broken down into secured nd unsecured, Moody s nlysts my fil to consider the kind of security pledged when notching secured issues. Moreover, Moody s itself lso recognizes tht ssigning rtings is inherently subjective process: There is no one size fits ll solution. The notching debte must be dynmic nlysis tht considers corporte governnce, collterl vlue, structure, nd size of the issue in reltion to totl cpitliztion.... The lck of specific rule set recognizes tht evlution of credit qulity nd expected loss is more n rt thn rigid science (Rown 1999, pp. 1, 6; Cntor nd Fons 1999). In summry, our discussion of Moody s rting process suggests tht its rtings do not fully ccount for some importnt issues tht cn rise becuse of collterl. In prticulr, if the kind of ssets being collterlized is not tken into ccount, credit rtings will not reflect ny incrementl impct on sset vlues rising from mngeril incentives for the differentil cre of certin kinds of collterlized nd uncollterlized ssets. Under this scenrio, the prt of the yield differentil between certin kinds of collterlized nd uncollterlized debt tht is not cptured by credit rting cn be explined by exmining crefully mngeril incentives to mintin the ssets of the firm. More generlly, the inherent subjectivity of the notching process, prticulrly for specultive-grde issues, suggests tht Moody s my systemticlly fil to fully incorporte mngeril incentives for perquisite consumption when ssigning rtings. In the next section, we present model to study how mngeril incentives to mintin these ssets ffect the yield differentil between collterlized nd uncollterlized debt. IV. The Model We first explin why mngers typiclly hve n incentive to consume more perquisites out of the secured thn the unsecured ssets. 3 We then nlyze how this pttern of consumption or neglect by mngers cn increse the yield of collterlized debt more thn the yield of uncollterlized debt. Finlly, the model is extended to show tht these results hold more generlly. 3. Although we explicitly model incentives for perquisites consumption, their interprettion is quite brod. They include not just incentives for mngeril perk consumption but lso incentives to underinvest in ny discretionry mngeril ctivities tht preserve the vlue of the ssets. Mngeril effort nd other resources expended to mintin sset vlue re often discretionry. For exmple, the dequcy of the insurnce on the ssets nd the frequency nd qulity of periodic mintennce re often not contrctully stipulted nd re thus under the discretion of the mnger. We show tht mngers expend less effort nd resources in mintining the vlue of the secured ssets thn the unsecured ssets.

10 380 Journl of Business This generl model llows us to identify the collterl nd lon chrcteristics tht hve systemtic impct on expected pyoffs nd ssocited yields. Jensen nd Meckling (1976) rgue tht when corporte insiders own only frction of the equity of the firm, they hve incentives to consume perquisites beyond optiml levels. Similr intuition would pply to when the ssets of the firm re collterlized, cusing them to hve incentives to cre less bout these ssets, which cn be reflected either in reducing the mintennce of the ssets or in incresed mngeril perk consumption from such ssets. Collterliztion of some ssets lters the structure of mngeril ownership in these ssets compred to tht in the remining uncollterlized ssets. This in turn leds to mngeril incentives to consume more perquisites out of the secured thn the unsecured ssets. A. Why Mngers Consume More from the Secured Thn the Unsecured Assets We first show tht mngers typiclly consume (or neglect) more the secured sset s compred to the unsecured sset. In the next section we then show how such neglect, or perk consumption, trnsltes into differentil yields. We use simple model tht forms the bsis for our theory. Consider firm with two ssets, C nd U, nd three clims on these ssets: n equity clim nd two debt clims. The first debt clim, debt U, hs promised pyment of F nd hs generl clim to both the ssets of the firm. The second debt clim, debt C, is collterlized on sset C nd lso hs promised pyment equl to F. Debt C s clim to sset C rnks before tht of debt U, but if sset C is not sufficiently vluble to pyoff F, the unpid blnce of debt C rnks eqully with debt U s clim on sset U. The equity clim receives ny residul fter the two debt clims hve been pid off. While the model in this section trets the firm s cpitl structure s exogenous, Section IVD endogenizes the decision to collterlize portion of the debt nd shows tht the lest risky ssets will be used s the collterl. The firm hs two possible sttes, good (G) nd bd (B). Defult is only n issue in the bd stte, whose probbility of occurring is f B. Once in the bd stte, there is f R chnce tht the firm leves the bd stte nd enters the recovery stte (R). Let v C be the vlue of the collterlized sset in the bd stte nd v U be the vlue of the uncollterlized sset in the bd stte both normlized by the promised pyment F. We tke v C to be one, for simplicity, nd v U to be less thn one to insure tht the firm is in defult in the bd stte. In the bsence of ny neglect by the mnger, the pyoffs on the secured nd unsecured debt re one nd v U, respectively. If the firm enters the recovery stte, the vlue of the uncollterlized sset increses by fctor of l U, where lu k 1, while the vlue of the collterlized sset increses by fctor of l C, where l C is set equl to one. These vlues for l U nd l C cpture the notion tht recovery is good for the firm nd tht, typiclly, collterlized ssets re the lest risky ssets of the firm.

11 Implictions for Yield 381 Turning to the mnger, she holds of the firm s equity nd hs utility function u(.) tht is incresing nd concve in its rgument. Given n sset vlue of Ai nd frction fi consumed from sset i, the mnger receives utility in dollr terms of Au( i f i). It is ssumed tht this utility specifiction holds for both the collterlized nd uncollterlized ssets. This prmeteriztion mens tht the mnger s utility is proportionl to the sset s vlue: doubling the sset vlue therefore doubles the dollr vlue of consumption. Further, the dollr vlue of the sset being consumed is importnt, rther thn the number of ssets from which the mnger consumes, hence, the mnger consumes the sme dollr mount from hundred dollrs worth of ssets, irrespective of whether it is one sset or two ssets. For this subsection, we 1 2 tke the utility function to be qudrtic: u( f i) p fi fi. In the next section 2 we show how the results hold in more generl setting. The mnger s objective function (normlized by dividing through by F ) cn be written s u( f ) vu( f ) fmx [0, (1 f ) v (1 f )l 2], (1) C U U R C U U U where fc nd fu re the mnger s choice vribles nd re defined s bove. The first two terms re the dollr utilities from consuming out of the collterlized nd uncollterlized ssets, respectively, while the third term is the expected pyoff from the mnger s equity holding. Note tht the probbility of entering the bd stte (f B) hs no effect on the mnger s consumption decisions, since these re mde only fter the firm hs rrived in the bd stte. The mnger s optiml consumption choice cn be chrcterized s follows: nd fc p 1 f R (2) fu p 1 frl U (3) for v sufficiently lrge. 4 U Since lu 1 1, these first-order conditions immeditely imply tht the mn- ger consumes greter frction of the collterlized thn the uncollterlized sset. To see the intuition for why, consider reducing the vlue of either sset in the bd stte by 1%. This reduces the generl sset s vlue by l U % in the recovery stte but the collterlized sset s vlue by only 1%. Since collterlized ssets tend to be the lest risky ssets, the greter voltility of the generl sset s vlue mens greter reduction in its recovery-stte vlue. Hence, since the mnger gets of the equity tht hs positive vlue in the recovery stte, she hs greter incentive to consume from the secured thn the unsecured sset. Further, the vlue of the unsecured sset in the bd stte (v! 1) is less thn tht for the secured sset (v p 1), which mkes the dollr U 4. If vu is sufficiently smll, the mnger is better off consuming everything, i.e., fc p fu p 1. C

12 382 Journl of Business vlue of the consumption from the generl ssets even smller reltive to tht from the secured ssets. 5 Another wy to see the intuition is in terms of the fmilir risk-shifting strtegy in the presence of risky debt (which cn rise even if there is no chnge in the totl net present vlue of the ssets). Shifting certin mount, sy D, of perk consumption from the uncollterlized sset to the collterlized sset is tntmount to n incrementl investment of D in the riskier, uncollterlized sset. If the consumption frctions from the two ssets were the sme, this shift would leve the utility from the perk consumption unchnged. At the sme time, the induced greter investment in the riskier generl sset cuses equity vlue to be higher. This leds to n optimum involving higher perk consumption from the collterlized sset. B. How Neglect (or Perk Consumption) Cn Increse the Yield of Collterlized Debt More Thn the Yield of Uncollterlized Debt The previous section shows tht the mnger hs incentives to consume more from the secured thn the unsecured ssets. This section chrcterizes how such perk consumption (or neglect) by the mnger ffects the yields on the secured nd unsecured debt. Even though we use perk consumption for concreteness, the nlysis cn pply more brodly to gency problems such s underinvestment in the mintennce (mngeril neglect) of the collterlized ssets. Collterlized debt hs senior clim on the collterl nd so must recover more in the event of defult. As result, collterlized debt should hve higher prices (lower yields) thn uncollterlized debt. However, when we exmine the impct of gency problems, we re exmining their incrementl impct on the yield of collterlized debt reltive to their incrementl impct on the yield of uncollterlized debt. In wht follows below we show tht the erosion in sset vlues cused by gency problems cn result in lrger yield increse for collterlized thn for generl debt. As expected, this is prticulrly true when the mnger consumes more from the secured thn from the generl ssets, s ws estblished in the previous subsection. In ddition, the reduction in the collterlized sset s vlue s result of gency problems forces the collterlized debt holder to recover from the generl pool tht typiclly hs lower recovery rte. The result cn be lrger increse in the collterlized debt yield thn in the generl debt yield. We use the model from the previous section to mke these ides more concrete, treting the bd (B) stte s the firm s only defult stte. Note tht we focus on pyoff, but since pyoff is inversely relted to yield holding expected bond return constnt, our results re eqully pplicble to yield. 5. Our results cn be generlized to setting where the voltility of the collterlized sset is higher or lower thn the uncollterlized sset nd the mngeril compenstion structure is endogenized to include frction of the uncollterlized debt in ddition to the equity. This structure of mngeril compenstion cn be shown to be optiml in the presence of risk-shifting incentives in vriety of settings (see John, Sunders, nd Senbet 1999).

13 Implictions for Yield 383 Recll tht in the bsence of ny neglect by the mnger, the pyoffs on the secured nd unsecured debt in the bd stte re one nd v U, respectively. Now suppose the mnger consumes kc from the collterlized sset nd ku from the uncollterlized sset, where ech is expressed s frction of the promised pyment F. Note tht in terms of the terminology of the previous section, ki p fa/f i i. The vlues of sset C nd U re now (1 k C) nd (vu k U), nd the collterlized sset is no longer sufficient to meet the collterlized debt obligtion. Insted, k C of the promised pyment on the collterlized debt flls into the generl pool. The uncollterlized sset is shred between the two debt holders pro rt bsed on promised pyment, so the collterlized debt receives k C/[k C 1] of the vlue of the uncollterlized sset. The pyoff on the collterlized debt becomes k C (1 k ) (v k ), (4) C U U 1 k C where the first term is the pyoff from the collterlized sset while the second term is the pyoff from the generl pool. The pyoff for the generl debt cn be obtined similrly: 1 (vu k U). (5) 1 k C The pyoff on the collterlized debt must exceed tht on the generl debt, nd this follows esily from equtions (4) nd (5). We re interested in the reduction in pyoff on ech type of debt due to perk consumption. In prticulr, we wnt to compre the reduction for collterlized debt to tht for generl debt since this drives the yield differentil between secured nd unsecured debt fter controlling for credit rting. We refer to this comprison s the incrementl pyoff differentil in the bd stte. Subtrcting the reduction in pyoff for collterlized debt from tht for uncollterlized debt gives { [ ]} { [ ]} kc kc 1 (1 k C) (vu k U) vu (vu k U), (6) 1 k 1 k C where the first term is the reduction in the pyoff on the collterlized debt nd the second term is the reduction in the pyoff on the uncollterlized debt. Rerrnging eqution (6), we obtin 2k (1 v ) (1 k )(k k ) C U C C U, (7) 1 k C which is esy to evlute. First note tht eqution (7) is decresing in both vu nd ku. This mens tht the incrementl pyoff differentil is decresing in the vlue of the generl ssets in the bd stte nd in the extent of perk consumption (s frction of promised pyment) out of the generl ssets. C

14 384 Journl of Business The impliction is tht the differentil is more likely to be positive when either of these is smll. We would like to more fully chrcterize the {v U, k U, k C} combintions tht cuse this differentil to be positive. Since this differentil is decresing in ku, we cn define k U(v U, k C) to be the ku vlue tht mkes eqution (7) equl to zero, given vu nd kc. Setting eqution (7) equl to zero nd rerrnging gives the following expression: k C(1 2vU k C) k U(v U, k C) p. (8) 1 k C Given vu nd kc, ny ku vlue less thn k U(v U, k C) results in positive in- crementl pyoff differentil. Thus, k U(v U, k C) must be positive for there to exist vlues of k U tht result in positive incrementl pyoff differentil. From eqution (8), it follows tht kc 2vU 1 is equivlent to k U(v U, k C) 1 0. Thus, if perk consumption from the collterlized sset (k C) is sufficiently lrge reltive to the vlue of the generl sset (v U), then the incrementl pyoff differentil cn be positive for rnge of ku vlues from zero to k U(v U, k C). For exmple, if the recovery rte on the generl ssets is 76% of the fce vlue of the generl debt nd the perk consumption from the collterlized sset is 90% of the fce vlue of the collterlized debt, then so long s the perk consumption from the generl ssets is less thn 0.9(1 2 # )/(1 0.9) p 3.42, the incrementl pyoff differentil is positive. Since the perk consumption from the generl ssets cn be no more thn 0.76 (the vlue of the generl ssets), the impliction is tht the differentil is positive for ny level of perk consumption from the generl ssets. This nlysis cn lso be used to illustrte number of other results bout the impct of gency problems on collterlized nd uncollterlized debt yields. For exmple, how might yields be ffected by recovery rtes in the event of defult? The lrger reduction in expected pyoff for collterlized thn uncollterlized debt yields depends crucilly on the generl pool hving low recovery rte. Consistent with this intuition, we used eqution (7) to show tht the incrementl pyoff differentil becomes smller s the vlue of the uncollterlized sset in the bd stte increses. The nture of the collterlized sset cn be importnt. Some collterlized ssets hve vlues tht re lrgely unffected by mngeril ctions nd inctions, including neglect. For exmple, lnd nd buildings my be ffected very little by mngeril inction or neglect nd re reltively insensitive to gency problems. We cn exmine the cse in which the mnger finds it so difficult to consume from the collterlized sset tht the chosen of consumption is zero (kc p 0). From eqution (7) we see tht the incrementl pyoff differentil is nonpositive when kc p 0. Thus, s expected, the incre- mentl pyoff differentil is negtive when it is difficult to consume perks from the collterlized sset. Is there differentil effect for lower qulity debt issues? We sw bove

15 Implictions for Yield 385 tht the optiml perk consumption choices in the bd stte re unffected by the firm s probbility of entering the bd stte. However, the bsolute vlue of the incrementl pyoff differentil is incresing in this probbility. Thus, the incrementl pyoff differentil is lrger for lower qulity debt issues. Finlly, if gency problems re importnt, monitoring should help in limiting these problems. In the next section, we superimpose monitoring technology similr to tht in Rjn nd Winton (1995). As result of the monitoring in plce, there is probbility g tht the mnger s consumption in the bd stte is detected. However, s g increses, the likelihood of zero consumption by the mnger increses, nd the bsolute vlue of the incrementl pyoff differentil decreses. Thus, greter monitoring cuses gency problems to hve smller impct on debt yields. C. The Generl Model This subsection shows tht gency problems induce the mnger to consume more from secured thn the unsecured ssets in such wy tht incrementl pyoff differentils re generlly positive. This is done by extending the nlysis bove to generl utility function with fewer restrictions on the sset vlues in the bd stte ( vc nd vu) nd on the growth in sset vlues going from the bd to the recovery sttes ( lc nd lu). Insted of vc p 1 nd v U! 1, we only restrict vc to be less thn or equl to one nd vu to be less thn or equl to (2 v C). The ltter restriction insures tht the firm will be in defult if the firm stys in the bd stte. The former restriction llows the firm to defult on the secured debt in the bd stte even in the bsence of ny vlue destruction. 6 We llow l C to be greter thn one but mintin the ssumption tht l C lu, since this cptures the ide tht the collterlized ssets re the lest risky ssets of the firm. In ddition, we superimpose monitoring technology s described in the previous subsection, with intensity prmeter g. With this technology, detection occurs with probbility g nd results in the mnger returning ny stolen sset vlue to the firm. Finlly, we cn introduce prmeter y tht mesures the ese with which the mnger consumes from the collterlized sset. When y is set equl to one, the mnger finds it eqully esy to consume from the collterlized nd uncollterlized ssets. On the other hnd, vlue for y of zero implies tht the mnger bers n infinite cost by consuming out of the collterlized sset. In wht follows, y is set equl to one except when ssessing how the nture of the collterl ffects the incrementl pyoff differentil. The mnger s objective function (normlized by dividing through by F) 6. The yield effects tht we focus on would be meliorted if the sset vlues were lrger frctions of the debt fce vlues so tht recovery rtes in defult were closer to one. However, on the flip side, we know tht firms do defult nd tht recovery rtes re usully less thn one, even for secured debt issues. So the effects tht we focus on re likely to hve some impct empiriclly.

16 386 Journl of Business cn be written s (1 g){v yu( f ) vu( f ) f mx [0, v (1 f )k C C U U R C C C v (1 f )k 2]} { V( f, f;v), (9) U U U C U U where fc nd fu re the mnger s choice vribles nd re defined s bove. Since g only enters this function through the sclr multiple (1 g), the solution is invrint to g, just s it is invrint to the probbility of entering the bd stte (f B). The mnger s optiml consumption is completely chrcterized in ppendix A, Section I, nd is generliztion of optiml consumption formuls in equtions (2) nd (3). Since we cre bout the incrementl impct of mngeril self-interest on the expected pyoffs on debt C nd debt U, we define D d( f C, f U) to be [P(0, d 0) P( d f C, f U)] for d p C nd U. Thus, D d( f C, f U) mesures the incrementl impct of perk consumption on the expected pyoff on debt d s frction of its promised pyment. Our prticulr interest is the differentil between D C( f C, f U) nd D U( f C, f U), nd so we define p( f C, f U) to be the incrementl pyoff differentil. Section III of ppendix A provides dditionl intuition for why this vrible is proxied by the difference in yield (fter controlling for credit rting) between secured nd unsecured debt. First, letting ( f C, f U) be the mnger s optiml consumption nd p { p( f C, f U), we wnt to show tht the mnger endogenously chooses (f C, f U) in such wy tht p cn be positive for v U sufficiently smll. The following proposition estblishes this result. 7 Proposition 1. Incrementl pyoff differentil for collterlized versus 0 0 uncollterlized debt. There exists v such tht p 1 0 ny for v! v. This result is consistent with the notion tht the mnger s vlue-reducing ctivities force collterlized clim holders with n otherwise high recovery rte into the generl pool tht hs low recovery rte in the bd stte. Our second result concerns the nture of the collterlized ssets. For some ssets mngeril perk consumption is difficult, or neglect (inction) hs little impct. Setting the prmeter y to zero implies tht the collterlized sset is difficult to consume from nd tht the chosen consumption level is zero. The following proposition shows tht the incrementl pyoff differentil is negtive when y p 0. Proposition 2. Incrementl pyoff differentil when it is difficult to consume from the collterlized sset. When y p 0, f p 0, nd so p 0. Thus, when the collterlized debt is secured on n sset whose vlue is difficult to destroy, gency problems reduce the expected pyoff on generl debt more thn the pyoff on the collterlized debt. This result is intuitive 7. An expression for p(f C, f U) cn be obtined from its definition nd eqq. (A4) nd (A5) in pp. A, Sec. II. It is generliztion of eq. (6). All propositions follow lmost immeditely from this expression. C U

17 Implictions for Yield 387 since the incrementl effect of gency problems on collterlized debt recovery rtes will be low if the vlue of tht sset is unffected by the mnger s selfinterested behvior. Our next result concerns the probbility of rriving in the bd stte nd its effect on debt yields. Incresing this probbility mgnifies the impct of gency problems on collterlized nd uncollterlized debt yields. As consequence, ny incrementl pyoff differentil is lso mgnified by n increse in this probbility. The following proposition estblishes this result. Proposition 3. Incrementl pyoff differentil s function of the defult probbility: dfp F 1 0. df B Thus, positive incrementl pyoff differentil is incresing in the probbility of rriving in the bd stte (defult probbility), while negtive differentil becomes more negtive. Next, we exmine the effect of chnging the vlue of the uncollterlized sset in the bd stte. This vlue is likely to be importnt since it determines the recovery rte for the generl debt pool. In prticulr, lower generl sset vlue reduces the recovery rte for the generl pool tht mkes the collterlized debt s recovery rte more sensitive to mngeril ctions tht reduce the collterlized sset s vlue. This is cptured in the following proposition. Proposition 4 Incrementl pyoff differentil s function of the recovery rte for the generl debt: (dp /dv )! 0. Hence, ny fctor tht reduces the generl debt s recovery rte in the bd stte will result in higher differentil pyoffs for collterlized nd uncollterlized debt. Exmples include lower expected pyoff nd higher voltility for the unsecured sset. Finlly, higher monitoring intensity (g) would be expected to reduce the bsolute mgnitude of ny incrementl pyoff differentil (Fp F). The reson is s follows. Insofr s the level of monitoring increses, the likelihood tht the mnger s consumption is detected lso increses, which leds to decrese in the incrementl pyoff differentil. Turning to second result, the impct of monitoring on the incrementl pyoff differentil is incresing in the likelihood of entering the bd stte. If entering the bd stte is high probbility event, the impct of perquisite consumption on expected pyoffs is high. Consequently, vrying the monitoring intensity hs lrge effect on expected debt pyoffs. The following proposition confirms these two intuitions. Proposition 5. Effect of monitoring intensity on the incrementl pyoff differentil: U dfp F )! 0. dg

18 388 Journl of Business dfp F d F[ ] dg F b) 1 0. df B On slightly different dimension, monitoring intensity lso ffects the extent to which gency problems reduce the collterlized debt s expected pyoff, D C( f C, f U). Proposition 6. Effect of monitoring intensity on the incrementl pyoff to the collterlized debt: d D C( f C, f U) )! 0. dg F F d D ( f, f ) C C U dg d [ ] b) 1 0. df B The size of the reduction in the expected pyoff is decresing in monitoring intensity. Further, the impct of monitoring on D C( f C, f U) is incresing in the likelihood of entering the bd stte. The resons for these results re similr to those given bove to explin the nlogous results in proposition 5. The next subsection explins how bnkruptcy costs cn explin both why firms use collterlized debt nd why they use their less risky ssets s the collterl. D. Bnkruptcy Costs s Motivtion for Using Collterlized Debt In the model of the previous subsection, we tke the existence of collterlized debt s given nd exmine the incentive effects of such debt nd its implictions for yields. In this section, we endogenize the mngement s decision to collterlize subset of the ssets nd the nture (risk chrcteristics) of the collterl chosen, bsed on simple chrcteriztion of the bnkruptcy costs fcing the firm. While mny fctors influence firm s decision to use collterl, bnkruptcy costs re likely to be one of the most importnt. 8 Consider bnkruptcy cost function per dollr of fce vlue tht is concve function of the loss rte. Concve bnkruptcy costs follow nturlly from number of plusible ssumptions bout the destruction of sset vlue in finncil distress. One ssumption tht is prticulrly simple nd ppeling cn be described s follows. Fixed legl fees per dollr of fce vlue re incurred upon defult of debt issue. In ddition, constnt frction of sset vlue is destroyed during the bnkruptcy process. Severl theoreticl nd empiricl ppers (see, e.g., Mello nd Prsons 1992; Lelnd 1998; nd Prrino, Poteshmn, nd Weisbch 2001) chrcterize bnkruptcy costs s fixed frction 8. Boot et l. (1991) endogenize the use of outside collterl in model with morl hzrd nd dverse selection, while number of ppers hve elborted on the role of collterl in the presence of informtion symmetry (see, e.g., Chn nd Knts 1985; Besnko nd Thkor 1987b; nd Chn nd Thkor 1987).

19 Implictions for Yield 389 of sset vlue in defult. Lelnd (1998) exmines cpitl structure in the presence of gency nd bnkruptcy costs nd models the bnkruptcy cost s fixed frction of sset vlue. Mello nd Prsons (1992) exmine gency costs of debt in frmework tht llows n sset s vlue in defult to be given frction of its first best vlue. Recently, Prrino et l. (2001) use such model of bnkruptcy costs in their clibrtion of the gency costs ssocited with investment decision mking. This simple ssumption cuses the cost function per dollr of fce vlue to be strictly concve t zero loss rte. While the cost function is liner elsewhere, the function s concvity t zero loss rte is enough for the nlysis below to go through. However, the sfe sset s vlue must exceed the collterlized debt s fce vlue with positive probbility in the firm s defult stte. More elborte ssumptions cn produce bnkruptcy cost function tht is strictly concve everywhere. 9 For simplicity, the following nlysis ssumes tht the cost function is strictly concve everywhere. Further, defult only occurs in the bd stte, nd the firm either issues generl nd secured debt ech with the sme fce vlue (F) or issues generl debt with fce vlue of 2F. Finlly, the nlysis in this subsection bstrcts from gency cost considertions by exogenously specifying sset vlues in the defult stte. 10 We demonstrte tht the use of secured debt in the presence of defultstte differences in coverge rtes cross the two ssets (s frction of F) leds to reduction in expected bnkruptcy costs. Secured debt concentrtes losses in the unsecured debt, leding to lower bnkruptcy costs becuse of the concve cost function. Moreover, bnkruptcy costs re minimized by using the sset with the lower defult-stte coverge rte s the collterl for the secured debt. The resoning is s follows: for given verge loss rte over ll the firm s debt, the benefit of collterlizing prticulr frction of the debt is incresing in the difference between the verge loss rtes cross the two clsses of debt. Since the loss rte for collterlized debt is lwys higher thn the coverge rte of the collterl, the loss-rte difference is mximized by using the sset with the higher coverge rte in the defult stte s the 9. For exmple, the vlue destruction ssocited with defult, expressed s percentge of sset vlue, is ssumed to be incresing nd concve in the loss rte. Such n ssumption is plusible since monitoring of third prties is likely to be declining in the loss rte. Letting denote the loss rte per dollr of fce vlue, the sset vlue vilble to be destroyed per dollr of fce vlue is (1 ). Suppose first tht vlue destruction s frction of sset vlue vilble is n incresing liner function of the loss rte : b, where b 1 0. So vlue destruction per dollr of fce vlue s function of the loss rte is given by D( ) p b (1 ). It is esy to see tht D(.) is concve function. More generlly, suppose tht vlue destruction s frction of sset vlue vilble is n incresing function of the loss rte : b( ). So vlue destruction per dollr of fce vlue s function of the loss rte is now given by D( ) p b( )(1 ). It is esy to show tht D ( ) p 2b ( ) b ( )(1 ). Thus, more generlly, the function D(.) is concve so long s b(.) is incresing nd not too convex. 10. We could esily extend the nlysis to llow gency problems nd bnkruptcy costs to coexist. The effects of concve bnkruptcy costs on the collterl decision s well s the incentive effects of the debt structure with collterl would be the sme s those developed in the section.

20 390 Journl of Business collterl. This condition is equivlent to sying tht the less risky sset is used s collterl. These results provide rtionle for the use of collterlized debt nd for using the firm s less voltile ssets s the collterl. More formlly, let B(.) be the bnkruptcy cost function per dollr of fce vlue tht is concve function of the loss rte on the issue in the defult stte. An issue with fce vlue of ˆF nd loss rte of incurs totl bnkruptcy costs in the bd stte of ˆFB( ). The firm hs two ssets, one nd two, with vlues vf 1 nd vf 2, respectively, in the defult stte. Let v1 1 v2 nd ssume v1 v 2! 2, so defult occurs in the bd stte. If the firm issues generl debt with fce vlue of 2F, the bnkruptcy cost incurred by the firm in the defult stte is given by ( ) ( ) 2 (v1 v 2) v1 v2 B 2F p B 1 2F p B( G)2F, (10) 2 2 where G is the debt loss rte when only generl debt is issued. If the firm issues collterlized nd uncollterlized debt ech with fce vlue of F, the totl bnkruptcy cost incurred by the firm in the defult stte is given by 1 v C ( C U 2 v ) C 1 ( U ) C U 2 vc B 1 v v F B 1 v F p B( )F B( )F, (11) where v C is the collterlized sset vlue in the defult stte s frction of F, v U is the uncollterlized sset vlue in the defult stte s frction of F, C is the debt loss rte for the collterlized debt, nd U is the debt loss rte for the uncollterlized debt. Note tht by construction, since the sset vlues re given, weighted verge of the debt loss rtes in eqution (11) must equl the loss rte for the generl debt in eqution (10). The weights re bsed on fce vlues, so here the weights re 0.5 for ech debt clss: F F 1 1 G p C U p C U. (12) 2F 2F 2 2 This result holds irrespective of whether sset 1 or sset 2 is the collterlized sset. By Jensen s inequlity, it follows tht 1 1 B( G)F 1 B( C)F B( U)F, (13) 2 2 so long s C ( U. Thus, we hve the first result tht the use of collterlized debt reduces bnkruptcy costs. The second result follows from noting tht for fixed G, the bnkruptcy cost dvntge of collterlized debt is incresing in F U CF. Since the loss rte on the collterlized debt must be greter thn tht on the uncollterlized debt, bnkruptcy costs re minimized by