Discussion Papers in Economics

Discussion Papes in Economics No. No. 003/0 000/6 Dynamics About of Debt Output and Gowth, the Option Consumption to Extend Debt and Physical Matuity Capital in Two-Secto Models of Endogenous Gowth by by Maco ealdon Fahad Nili Depatment of Economics and elated Studies Univesity of Yok Heslington Yok, YO10 5DD

AOUT DET AND THE OPTION TO EXTEND DET MATUITY by Maco ealdon Depatment of Economics and elated Studies Univesity of Yok YO10 5DD Heslington, Yok Tel: 0044/(0)1904/433750 E-mail: m15@yok.ac.uk ASTACT oth boowes and ceditos often have an implicit option to extend debt matuity as the debto appoaches financial distess. This implicit extension option is associated with the possibility fo debtos and ceditos to enegotiate the debt contact in the hope that extending debt matuity may allow the debto to ovecome tempoay liquidity poblems. This pape analyses and evaluates such extension option in a time independent setting with constant nominal capital stuctue and in a time dependent setting with not constant nominal capital stuctue. The extension option is shown to significantly incease the value of equity and has a non-negligible impact on debt cedit speads. The extension option can also incease the shot-tem cedit speads of outstanding debt and, in this espect, it amelioates the shotcoming typical of stuctual models of cedit isk, i.e. the unde-pediction of shot tem cedit speads. The value of the extension option is vey sensitive to diffeent possible execise 1

policies. Fou such policies ae illustated, encompassing cases in which the debto extots concessions (to extend debt matuity) fom ceditos and cases in which ceditos make self inteested concessions (to extend debt matuity). In geneal, when default is tiggeed by the wothless equity condition, the value of the extension option is much highe than when default is tiggeed by a liquidity shotage. The option to enegotiate debt matuity is of inteest because extending debt matuity can decease debt value even without cutting pomised coupon payment, i.e. without giving up pat of the tax shield associated with coupon payments. Keywods: copoate debt, debt matuity, default baie, enegotiation, cedit speads.

INTODUCTION Fims that appoach financial distess may enegotiate thei debt obligations. Such debt enegotiations can entail extending the oiginal contactual matuity of debt in ode to allow the fim to ovecome tempoay poblems such as a tempoay lack of liquidity. The e-negotiation of debt matuity as the debto appoaches financial distess has been neglected by the debt valuation liteatue that adopts a continuous time finance appoach. Such liteatue has instead concentated on the e-negotiation of contactual coupon payments o of debt pincipal. In this pape the poblem is the valuation of the fim s debt (and equity) when debt holdes and equity holdes may have the ability to extend debt matuity in ode to avoid default and costly assets liquidation. In such case debt holdes and equity holdes have an implicit option to enegotiate and extend debt aveage matuity. The esults of the analysis ae: - the option available to equity holdes to extend the aveage matuity of debt inceases equity value moe than it deceases debt value; such option can mateially incease equity value, while often causing a non negligible incease o decease in the yield equied by debt holdes; - povided debt matuity is extended befoe assets liquidation, the diffeent ational extension option execise policies" do not alte total fim value, but they significantly affect the extension option values; - as in Longstaff (1990), sometimes it is possible fo both equity holdes and debt holdes to benefit fom the extension of debt matuity as the fim appoaches distess; 3

- diffeent default conditions, eithe wothless equity o cash flow shotage, can mateially affect the values of the extension option and imply diffeent incentives fo debt holdes and equity holdes to e-negotiate and extend debt matuity; - the pesence of an implicit extension option can impove the pediction of the stuctual model by inflating shot-tem cedit speads. The analysis of this pape is split into time dependent and time independent settings. In a time independent setting, single debt issues ae continuously efunded as they continuously fall due at matuity. Thus the nominal amount of debt outstanding at any time is constant, which makes the valuation of debt and equity a poblem independent of time. Late, instead, the extension option is analysed in a time dependent setting in which debt is not efunded at matuity, in which the nominal amount of debt outstanding is not constant, in which the default pobability is lowe and in which the extension option is less valuable. Past liteatue Extendible debt was valued by ennan and Schwatz in 1977 and by Ananthanaayanan and Schwatz in 1980, but these two papes assume that debt is default fee. Two othe papes deal with debt that is subject to default isk and whose matuity can be extended by equity holdes o by debt holdes. The fist pape is by Fanks and Toous (1989) and consides the implicit option fo equity holdes to file fo US Code Chapte 11 eoganisation, which entails suspending all payments of coupons and pincipal to debt holdes. Fanks and Toous show that ecognising this implicit option to file fo chapte 11 makes contingent claims models capable of 4

pedicting cedit speads on copoate debt that moe closely appoximate those obseved in the bond maket. The second pape is by Longtaff (1990) and povides closed fom solutions fo a simila option fo equity holdes to extend debt matuity. Longstaff also consides the option fo debt holdes to spontaneously extend debt matuity in ode to avoid costly assets liquidation as the debto defaults. oth Fanks/Toous and Longstaff estict thei attention to a Metonian setting in which default and extension of debt matuity can take place just on the contactually ageed debt matuity date. Instead, this pape consides the case in which default and extension of debt matuity can take place at any time. Cental to this pape is the case in which debt matuity can be enegotiated by equity holdes and debt holdes. In fact the e-negotiation of debt matuity has been neglected by the debt valuation liteatue concened with stategic debt sevice (e.g. Andeson and Sundaesan (1996), Andeson and Sundaesan and Tychon (1996), Mella-aal and Peaudin (1997)). In sections 1 to 3 the analysis of the option to extend debt matuity is caied out in a time independent setting in which default is tiggeed by cash flow shotage o by wothless equity, wheeas in section 4 the same analysis is caied out in a time dependent setting in which default is tiggeed by wothless equity. 1. THE GENEAL MODEL IN A TIME INDEPENDENT SETTING 1.1) esults fom past liteatue Now we intoduce the notation and some esults of past liteatue. These esults ae the basis fo the subsequent analysis of the option to extend debt matuity. 5

Let us assume that equity holdes and debt holdes ae isk neutal and have pefect infomation. is the value of the fim's assets, whose isk neutal pocess is a geometic ownian motion, i.e.: 1) d (-d) dt s dz, whee: s is the volatility of the fim's assets; d is the fim's assets pay-out ate; is the default fee inteest ate, which is assumed constant dz diffeential of a Wiene pocess. In addition, let us assume that: a denotes bankuptcy/liquidation costs popotional to assets value; K is the fixed cost of assets liquidation/bankuptcy, tax is the copoate income tax ate, C is the annual coupon, P is the face value of debt, c C / P, m is the faction of outstanding debt that is etied and substituted with newly issued debt evey yea (in shot m is the debt etiement ate), ff() is the value of the fim's debt when extension of debt matuity is not possible, C() is the value of the fim's bankuptcy costs, e() is the value of the fim's equity, TT() is the value of the tax shield, 6

is the default the baie (i.e. the value of the fim's assets at which default occus). Following Leland (1998) and Eicsson (000), but adding fixed bankuptcy costs (K), it is possible to show that ) ( ) ( ) b K a 1 m P m C m P m C ff 3) ( ) ( ) ( ) [ ] b K a 1 b 1 m mp C j K a j 1 C tax e with 4) ( ) s s m s d - s d - - b 5) s s s d s d j. Total fim value is then equal to 6) ( ) ( ) ( ) j K a j 1 C tax e ff. The impotant aspect is that evey yea a faction m of debt is continuously efunded as it falls due. Then aveage debt matuity is equal to 1/m yeas. 7

1.) When aveage debt matuity can be extended The above esults ae next modified to account fo the possibility that equity holdes and debt holdes enegotiate the debt contact and extend debt aveage matuity by escheduling the payments of debt pincipal. e-negotiation may take place in an infomal wokout o in a fomal bankuptcy poceeding. It is impotant to emak that in what follows it is assumed that all single debt issues compising the fim s total outstanding debt have thei espective time to matuity extended at the same time and by the same popotion. Fo example, if thee ae two outstanding debt issues, one with a esidual life of 1 yea and the othe one of yeas, thei espective esidual lives ae simultaneously extended to yeas and 4 yeas. Equity holdes and debt holdes may want to enegotiate the debt contact and extend debt matuity befoe default o as soon as default takes place, whee default hee means missing a payment that is due to ceditos. y ageeing with ceditos to postpone epayment of debt pincipal, equity holdes may avoid default, insolvency o difficult and costly efunding though issuance of new debt. On the othe hand, also debt holdes may be enticed to enegotiate the debt contact as explained late in section. An impotant assumption undelies all the analysis: equity holdes always keep paying the contactually ageed coupons to debt holdes until debt pincipal is eventually paid back. Let us now assume matuity is extended. Fo now we take denotes the value of the fim's assets at which debt aveage as given, but in section it will be shown how can be detemined. Anyway cannot be lowe than, othewise debt matuity would not be extended and thee would be no diffeence fom the analyses of past liteatue, thus 8

7). On the othe hand, it is hee assumed that 8) < 0, whee 0 denotes the fim's assets value today. Condition 8) does not imply a geat loss in geneality as it will become appaent late. Then 1/ m is debt aveage matuity afte "extension" and 1/ m is debt aveage matuity befoe "extension". The change fom m to m is ievesible, and we can wite: 9) m m 0. Fo simplicity, in all this pape it is assumed that debt aveage matuity can be extended just once. When, debt value befoe "extension", F(), must satisfy 1 10) s F vv ( d) F v F C m (P F) 0, subject to F( ) C m P m and to ( ) f ( ) F, whee debt value afte "extension", f(), must satisfy 1 11) s f vv ( d) f v f C m (P f) 0, subject to f ( ) C m P m and to f ( ) ( 1- a) K, 9

whee denotes the default baie afte debt aveage matuity has been extended. In geneal is lowe than, since by extending debt matuity default is postponed. The solutions to equations 10) and 11) ae espectively 1) ( ) ( ) b h K a 1 m P m C m P m C m P m C m mp C F 13) ( ) ( ) h K a 1 m P m C m P m C f, with b as pe equation 4) and with 14) ( ) s s m s d - s d - - h. Then, the value of equity in the pesence of the "extension option" [E()] is equal to total fim value in the pesence of the extension option, which is given by equation 17) below, minus the value of debt befoe extension, thus: 15) ( ) ( ) ( ) F j K a j 1 C tax E. 10

Instead, the value of equity afte the "extension option" has been execised [E()] is equal to total fim value as pe equation 17) below, minus the value of debt afte extension, thus: 16) ( ) ( ) ( ) f j K a j 1 C tax E. When debt matuity can be extended the above fomulas give the values of debt and equity. 1.3) Modigliani and Mille' s poposition 1 and the option to extend debt matuity Now, since copoate taxes and bankuptcy costs have been assumed, Modigliani - Mille' s poposition 1 cannot hold. This entails that total fim value changes due to the pesence of the "extension option": total fim value would no longe be given by equation 6) but by 17) ( ) ( ) ( ) j K a j 1 C tax E F. This equation is the same as equation 6), but fo the fact that the default baie is now lowe since debt matuity is extended befoe o at default. This means that total fim value is now highe than total fim value as pe 6), because a lowe default baie entails highe expected value of the debt induced tax shield [ ( ) j 1 C tax ( ) ( ) TT ] and lowe expected value of bankuptcy costs [ j K a C ]. 11

Now, since longe debt matuity implies highe total fim value, it is not clea why fims should eve be inteested in an option to extend debt matuity if they could simply choose to issue debt of longe matuity in the fist place. As Leland (1996) puts it, longe-tem debt may not be incentive compatible, in othe wods it is too sensitive to assets substitution o to othe agency costs. Anyhow, copoate debt usually does have finite matuity. Equation 17) also eveals that total fim value does not depend on as long as condition 7 holds. In othe wods, given the pesence of copoate taxes and/o bankuptcy costs, total fim value only depends on "whethe o not" debt matuity is extended not late than default, but not on "when" debt matuity is extended. Late numeical examples will confim this statement. 1.4) The payoff and the values of the option to extend debt matuity The value of debt whose matuity can be extended (F()) can be viewed as the value of debt whose matuity cannot be extended (ff()) plus a position in the option to extend debt matuity: heeafte the value of this (often shot) position is denoted by O(). In the same way the value of equity when debt matuity can be extended (E()) can be thought of as the value of equity when debt matuity cannot be extended (e()) plus a position in the option to extend debt matuity: heeafte the value of this (often long) position is denoted by OE(). 1

At this point we can specify the payoffs fo OE() and O() when it is equity holdes who decide as to the execise of the "extension option" and detemine 18) ( ) max{ E( ) e( ),0 } OE, 19) ( ) F( ) ff ( ) O. : Instead when it is debt holdes who execise the "extension option", which is a possibility as is noticed late on, then 1 : 0) ( ) E( ) e( ) OE, 1) ( ) max{ F( ) ff ( ),0 } O. The above allows to deive the expession fo O() as the diffeence between F() and ff() and the expession fo OE() as the diffeence between E() and e(): ) C m P m C m P m C m P m ( ) ( 1 a) O C m P m - ( 1 a) b K. h b K 1 Clealy these payoffs imply that E[ 1 ] E[ 1 ] with F[ 1 ] f[ 1 ]. 13

3) ( ) ( ) j K a j K a j j C tax O - OE. Equation 3) highlights how OE() is diffeent fom O(). In the jagon of options: the value of the (often long) position in the "extension option" (OE) is diffeent fom the value of the (often shot) position in that same "extension option" (O). This unusual asymmety is again due to the fact that Modigliani and Mille's poposition 1 does not hold, because taxes and bankuptcy costs ae assumed to exist.. CONDITIONS FO EXTENSION OF DET MATUITY AND FO DEFAULT As stated above, given that, when the value of the fim s assets () declines down to, debt aveage matuity is extended. Possible ways to detemine ae now discussed and then possible ways to detemine and ae discussed too..1) The conditions fo debt matuity to be extended As fo, thee ae at least fou possible ways to detemine when debt matuity can be extended..1.1) Take-it-o-leave-it offes 14

Debt matuity can be extended when equity holdes make the following "take-it-oleave-it" hostile offe to debt holdes: "If you, debt holdes, want us, equity holdes, to keep sevicing outstanding debt, you must concede that debt aveage matuity be extended!". This hostile offe is simila in spiit to the take-it-o-leave-it offe assumed by that Andeson and Sundaesan (1996). If equity holdes stopped sevicing debt, debt holdes would need to satisfy thei claim though costly liquidation of the fim's assets. We now assume that equity holdes make thei hostile offe to debt holdes when 1. Then debt holdes will concede an "extension" only if assets ecovey value upon immediate liquidation is lowe than debt value with extended matuity, i.e. 4) f ( ) X( ) 1 whee ( ) ( ) 1 X is the assets ecovey value if default is foced when and 1 1 f is the value of debt with extended matuity. The assumption about assets 1 ecovey is 5) X( ) ( 1 a) K, whee K denotes the fixed costs of assets liquidation and a denotes the popotional costs of liquidation. Fom 4) and 5) the condition fo debt holdes to accept the "take-it-o-leave-it" offe by equity holdes can be estated as 6) ( ) ( 1 a) K f 1 1. Condition 6) implies that all bagaining powe duing e-negotiation of the debt contact lies with equity holdes. Then, equity holdes will want to have debt aveage matuity extended just if the extension option (OE()) is in the money, i.e. if 7) E ( ) E( ) > e( ). 15

Equity holdes may want to optimally choose 1, while making sue that condition 6) is met. This means that equity holdes would detemine 1 as 8) max 1 E, 1 subject to conditions 6) and 7). As it will be appaent late, this often implies that equity holdes choose 1 as the highest value of the fim's assets () at which condition 6) is met. Thus 6) is often a binding constaint. Condition 6) is moe easily met when fixed liquidation costs (K) ae high. The same is not always tue if popotional liquidation costs ae high (i.e. if a is high). Condition 6) is moe easily met also when is low. If is low, also 1 can be low even without violating constaint 7) (i.e. 1 ). Then the lowe 1 implies ( ) the lowe X 1 and condition 6) is moe likely to hold..1.) When also debt holdes gain fom extension of debt matuity Equity holdes and debt holdes can agee to enegotiate the debt contact and to extend debt matuity even if equity holdes do not make the hostile offe implied by condition 6). This is the case when debt holdes (as well as equity holdes) ae bette off by extending matuity, i.e. when the value of debt with longe aveage matuity supasses the value of debt with shote aveage matuity. Then debt matuity would be extended at, whee is detemined as 9) max E, subject to 7) and to 30) ( ) F( ) f. 16

.1.3) Extension of debt matuity upon default Default can take place without being peceded by the extension of debt matuity. This may be the case wheneve equity holdes and debt holdes cannot enegotiate the debt contact, due fo example to the high numbe of ceditos involved o to asymmetic infomation between debto and ceditos. ut, when default takes place, debt holdes may spontaneously concede an extension of debt matuity to avoid immediate and costly assets liquidation. Then debt matuity would be extended at 3, whee 3 would be detemined by the two simultaneous conditions: 31) 3, and again 3. 3) f ( ) ( 1 a) K 3.1.4) Explicit option to extend debt matuity Debt holdes may be unconditionally subjected to the decision of equity holdes as to the extension of debt matuity. This theoetical limit case applies when the debt contact o the bankuptcy code concede an "explicit" option to equity holdes to extend debt matuity at any time. The debt indentue may concede one such option in some issues of extendible debt giving equity holdes the unilateal ight to extend debt matuity. A hypothetical bankuptcy code may concede to equity holdes the ight to voluntay file fo an official eoganisation poceeding that, without the appoval of ceditos, would gant a moatoium to the debto. The moatoium would allow the debto to tempoaily suspend debt payments and thus to stetch the effective matuity of debt. 17

Such extension options ae theoetical limit cases and ae explicit in that they ae povided by the debt contact o by the code. Instead, the pevious extension options ae implicit in that debt matuity is extended though e-negotiation o though a unilateal concession by debt holdes upon default. Anyway, an explicit extension option would allow equity holdes to unilateally decide to extend debt matuity so as to maximise equity value. Equity holdes could then extend debt matuity at whee 4 is such that 33) max E,. 4 4 4, Usually 4 1 since condition 6) is not equied in this case. Fo ealistic paametes 4 is usually an intenal value intenal value, i.e.: 4 0. Equity holdes choose 4 0 when they want to immediately extend debt matuity. This may be the case especially when assets volatility is high. Instead, when the ate of debt coupons is vey high equity holdes would neve want to extend debt matuity (i.e. 4 ) as they would want to minimise the numbe of high coupons to be paid and efinance at cheape inteest ates. Finally, when liquidation costs ae exceptionally high, constaint 6) is not binding so that 4 1. Of couse 1,, 3, 4 all imply ationality and symmetic infomation fo both equity holdes and debt holdes. 1, and 4 can be found by numeical algoithms. Fo 3 also closed fom solutions ae available as becomes appaent next. Equity holdes ae assumed to extend the matuity of all outstanding debt at the same time. 18

.) The default baies Now the ways to detemine the default baies As fo and ae discussed., default befoe debt matuity is extended can take place at diffeent possible values of the fim's assets (), in paticula: - at I when default is tiggeed by a cash flow shotage that makes the fim insolvent; - at E when default is tiggeed by equity becoming wothless. As fo, default afte debt matuity has been extended can again be detemined eithe by a cash flow shotage o by equity becoming wothless. In the fist case default takes place at I, wheeas in the second case default takes place at Then, I would be detemined by the following cash flow shotage condition: 34) d m f ( ) d m [( 1- a) K] C (1- tax) m P I which implies I I I, E. 35) I ( K P) C ( 1 d m ( 1 a) m tax. ) Conditions 34) and 35) ae the same as in Eicsson (000) and state that default occus when the fim becomes insolvent, i.e. when the instantaneous inflows to the fim ae equal to in the instantaneous outflows fom the fim. Condition 34) pesupposes that debt aveage matuity cannot be extended. ut, if debt aveage matuity is extended not late than default, i.e. I, then the default baie becomes 19

36) I ( K P) C ( 1 d m ( 1 a) m tax. ) Finally, when default is tiggeed by wothless equity, equity holdes ae assumed to endogenously detemine the default baie as pe Leland (1998). In this case, and if debt matuity cannot be extended, the default baie is detemined by the following conditions 37) [ E ] 0, E E E 38) [ ] 0 that imply 39) C C m P tax K j b K b m E. ( 1 a j ( 1 a) b) If instead debt matuity is extended befoe default o at default, i.e. E, then 40) E C C m P tax K l b K b m. ( 1 a l ( 1 a) b) In this section the conditions fo debt matuity to be extended and the default baies have been detemined. In the next section such conditions ae discussed with efeence to a base case scenaio in which ealistic aveage paamete values ae assumed. Diffeent conditions fo extension of debt matuity and diffeent default baies ae shown to heavily affect the values of debt, equity and the extension options. 0

3. NUMEICAL ANALYSIS IN A TIME INDEPENDENT SETTING WHEN DEFAULT IS TIGGEED Y CASH FLOW SHOTAGE O Y WOTHLESS EQUITY The following analysis builds on a base case scenaio, which is of inteest since it assumes ealistic aveage paametes. Such paametes ae simila inte alia to those in Fan and Sundaesan (001), Eicsson (000), Leland (1998) and ae displayed in italics in Table I. The significant effect of diffeent default conditions and diffeent policies to extend debt matuity is highlighted. 3.1) ase case scenaio when default is tiggeed by a cash flow shotage (liquidity default) The base case scenaio with liquidity default eveals that I < I < 4 < 0 < ( I 49.8, 4 8.8, 0 100, 13.5) whee 0 denotes the value of the fim's assets today. 1 and 3 ae non existent since condition 6) is neve met when I. The fact that 1 and 3 ae nonexistent means that debt holdes will always choose immediate liquidation athe than extension of debt matuity, even if extending debt matuity would in fact postpone default by loweing the default baie fom I 49.8 to I 44.8. The fact that I < 4 means that, if equity holdes can unilateally decide when to extend debt matuity in an unconstained fashion, they will do so at 4 befoe default. On the othe hand, the fact that 49.8 I < 13.5 eveals that debt holdes may 1

accept an offe to extend debt matuity befoe default when, i.e. when the fim is vey fa fom default. If debt matuity was extended at, then OE() 1.7 and O() 0. In this scenaio, equity holdes may want to have an "explicit option" to unilateally impose an extension of debt matuity to debt holdes. Such explicit option would be optimally execised at 4 8.8, since 4 maximises OE() (and E()) and minimises O() and (F()). esults fo 4 ae displayed in Table I Panel A 3. Total fim value inceases and equity value (E()) ises by some 4.1% (fom 55 to 57.), while debt value (F()) deceases just slightly (fom 50.5 to 50). A slight incease in the annual coupon ate (0.4%) would be enough to compensate debt holdes fo conceding the explicit extension option (i.e. c 6.4% implies ff() F()). This case is an example of the esult that geneally, given taxes and bankuptcy costs, the "extension option" inceases the value of equity well moe than it deceases the value debt. 3.) When assets volatility is low Now assets volatility is assumed to be equal to 10% athe than 0% and all othe things ae equal to the base case scenaio. This new scenaio implies that now: I I 3 < 1 < < 4 < 0 ( 3 I 49.8, 1 5.4, 5.7, 4 63.4, 0 100). So, unlike in the base case scenaio, 1 and exist since condition 5) can be met even when 3 I. The 3 The Panels of Table I ae sepaately epoduced hee below and the entie Table I is displayed also at the end of the pape fo diect compaisons acoss diffeent cases.

eason why condition 6) can now be met is that lowe assets volatility makes debt less isky and moe valuable and hence the value of debt with extended matuity (f()) is now moe likely to be highe than the assets ecovey value (X()). When condition 6) is met, debt holdes will pefe to have debt matuity extended athe than outight assets liquidation. Anyway, since in this case 1 <, debt holdes may accept to have debt matuity extended even if equity holdes do not make the "take-it-o-leave-it" offe mentioned above. In fact, when 5.7 debt of longe matuity (f()) is not less valuable than debt of shote matuity F(). Then, in this scenaio debt holdes ae inteested in spontaneously extending debt matuity at default, i.e. at I 3, in ode to avoid assets liquidation (this case is illustated in Table I Panel ). This impotant point is simila to that of Longtaff (1990), who assumes that, as the fim defaults, debt holdes may pefe to extend debt matuity athe than costly liquidation of the fim's assets. Though the analysis of Longstaff is limited to the classic Metonian setting: a zeo coupon bond is the only debt and default cannot occu befoe debt matuity. So, when I 3 the analysis by Longstaff is being extended to a time independent setting in which the fim has multiple debt issues that ae continuously efunded at matuity and in which default can take place at any time. As in Longstaff, even in this setting debt holdes can pefe extension of debt matuity to liquidation. 3.3) ase case scenaio when default is tiggeed by wothless equity ase case scenaio paametes now imply that: E E 3 < < 1 < 4 < 0 ( E 30.4, E 3 3

35.5, 44.5, 1 50.5, 4 76.5, 0 100). Table I Panels C, D and E illustate this scenaio when debt matuity is extended at 1 o o 3. Thus, unlike when default is tiggeed by a cash flow shotage, when default is tiggeed by wothless equity 3 and 1 exist even with base case scenaio paametes. In fact, when default is tiggeed by wothless equity, default takes place at lowe values of the fim's assets ( E and I E I ) so that condition 6) is moe likely to obtain befoe o at default. In othe wods, as the fim appoaches default, debt holdes ae moe likely to pefe to concede an extension of debt matuity (athe than assets liquidation) when default is tiggeed by wothless equity than when default is tiggeed by a cash flow shotage. Moeove, optimal leveage is highe when the explicit option to extend matuity is pesent as opposed to when such option is absent, and the highe the fim leveage is, the stonge is the incentive fo debt holdes to enegotiate and concede a matuity extension. Figue 1 shows the values of debt and equity, assuming base case scenaio paametes, when debt matuity is extended at 1 50.5. 1 is such that f 1 X 1 and is the highest value of at which condition 6) is met befoe the fim defaults, i.e. befoe the value of equity in the absence of the extension option dops to 0: in this case 1. Debt matuity can be extended only if the ecovey value of assets (X()) is not geate than debt value afte execise of the extension option (f()) and only if equity (e()) has not yet become wothless. 4

Fo this same case, Figue displays the values of OE(, ) and O(, ) 1 1 4 and thei espective payoffs (E()-e(), f()-ff()). efoe "extension" we can see that [ E (, ) e(, )] > OE(, ), so it is clea that OE(, ) 1 1 1 1 is not optimally execised. In fact, equity holdes can extend debt matuity only when condition 6) is met. Figue also shows the case in which, ceteis paibus, debt of extended matuity is a pepetuity so that m moe valuable OE (, ) is and the less valuable (, ) 1 0: the longe the extension is, the O 1 is. Panels C, D and E of Table I show the effect of diffeent execise policies of the extension option with base case paametes and when default is tiggeed by wothless equity. In paticula: OE ( 100, ) 171 and ( 100, ) 1 O 1-0.09; OE ( 100, ) 161 and ( 100, ) O 0; OE ( 100, ) 144 and ( 100, ) ( 100, ) OE 1 3 O 3 0.17. denotes the value of the extension option when debt matuity is extended at 1. It is then clea that equity holdes have an incentive to execise thei bagaining powe by enegotiating debt matuity as soon as condition 6) is met, i.e. at 1, since this inceases the extension option value. On the othe hand ( 100, ) O 1 is negative, which means that the detiment of debt holdes if debt matuity wee extended at 1. 4 (, ) O and OE(, ) 1 extended at 1. 1 denote the option values when debt matuity is 5

If debt matuity was extended at, debt holdes would neithe lose no gain, so the extension option would be wothless fo debt holdes in such case: ( 100, ) O 0. On the othe hand, when matuity is extended at < 44.5, debt holdes too would gain fom an extension of debt matuity and indeed they would gain the most if matuity wee extended just at default, i.e. at E 3. In these cases equity holdes would have to shae with debt holdes the benefit of having debt matuity extended (i.e. the incease in total fim value). Panels C, D and E of Table I show that: (, ) O(, ) OE(, ) O(, ) OE(, ) O(, ) OE 1 1 3 Finally Figue 3 displays how highe assets volatility does not necessaily incease the option values OE (, ) and O (, ). Highe volatility inceases O (, ) 3 when default is fa, moeove it can decease OE (, ) since OE(, ) 3 becomes a locally concave function of as default neas. Highe volatility implies a lowe default baie. Figue 3 shows the values of the extension option, OE(, 3) and O(, 3), in the base case scenaio with default tiggeed by wothless equity and matuity extended just upon default: 3 E, volatility is equal eithe to 10% o to 0%. 3 3 3. 3 3.4 When debt holdes gain fom having debt matuity extended It is hee eminded that is the value of assets at which debt holdes would be indiffeent as whethe to have debt matuity extended o not, because is such that 6

( ) f ( ) F. It may appea supising that equals 44.5 in the base case scenaio when default is tiggeed by wothless equity, given equals 13.5 when default is tiggeed by a cash flow shotage condition (see above). The eason fo this diffeence is that, when default is tiggeed by wothless equity, thee ae in eality two values of the fim's assets that make debt of shote matuity of equal value to debt of longe matuity in this base case scenaio. So thee ae two values fo : one is 44.5 and the othe one is 106.6. Moe pecisely, when > 106.6 debt of longe matuity is moe valuable than debt of shote matuity (f() > F()): this is because when gows, debt becomes safe and the contactual coupon ove-emuneates the isk of default of debt (debt value ises above pa). When this is the case, debt holdes will want to extend debt matuity in ode to get such ove-emuneation fo a longe peiod. In the base case when default is due to a cash flow shotage this happened when > 13.5 athe than when > 106.6. Then, when 44.5 < < 106.6 debt of longe matuity is less valuable than debt of shote matuity (f() < F()): this is because when falls below 106.6, the isk of default inceases in such a way that the contactual coupon unde-emuneates the isk of default of debt. In this case debt holdes will not want to extend debt matuity in ode to limit the peiod in which they ae unde-emuneated. Then again, when < 44.5, debt of longe matuity becomes again moe valuable than debt of shote matuity: this is because longe matuity postpones default by implying a lowe default baie and hence a lowe pobability of default. In the base case when default is due to a cash flow shotage this neve happened since, when < 13.5, debt of shote matuity was always moe valuable than debt of longe matuity, even if debt of shote matuity implied a highe default baie. 7

The above analysis has coveed a time independent setting. The following analysis coves a time dependent setting. 4. A TIME DEPENDENT SETTING The main new assumption in this setting is that debt is not continuously efunded so as to keep the nominal capital stuctue constant and independent of time as in the pevious section. athe, the (continuous) payment of pincipal is funded by assets geneated cash flows and/o by issuance of new equity. Now time is an explicit independent vaiable. In a time dependent setting closed fom solutions fo the values of debt, equity and the option to extend debt matuity ae no longe possible, so explicit finite diffeences ae employed to povide numeical solutions to the elevant valuation equations. 4.1) The model in a time dependent setting Some moe notation befoe poceeding: P(t) is the face value of debt outstanding at time t; c is the annual coupon ate on debt; C(t) is the instantaneous coupon payment at time t, C(t) c P(t); t denotes time; to highlight time dependence the notation changes to () t, t, () t, (, t), E(, t), E(, t), f (, t), ff (, t), F(, t) e ; without loss of geneality today's date is set equal to t 0, e.g. P(0) denotes today s outstanding debt; T is the contactually ageed time at which debt amotisation is completed; () 8

T*(>T) is the time at which debt amotisation is completed afte debt matuity has been extended; M is the ate at which debt pincipal is continuously amotised, so that P(T) P(0) - M T 0; unlike in Appendix, it is hee assumed that P(T) 0, so that debt pincipal is completely paid back by time T. Now the poblem of valuing equity and debt whose matuity can be extended is efomulated in a time dependent setting. efoe debt matuity is extended, when () t 1, debt value befoe extension (F(, t)) must satisfy 41) F s F ( d) F F c [ P( 0) M t] M 0 with t F (,T) 0, with P(T) 0, with ( t), T 0 t 4) F( ) e { M c [ P M t] } dt ( t) f ( ( t), t) F and with, e T ( M c P) e T c M ( T 1) ( M c P) c M. Condition 4) states that, as gows infinitely, debt value appoaches the value of a default fee debt that pomises the same cash flows, i.e. {M c [P - M t}dt in evey small peiod dt. Then t* is the fist time at which eaches ( t) fom above. t* is a andom vaiable that depends on the futue path of. Fo evey 0 t* T, debt value afte the e-negotiation, f(, t), must satisfy 43) [ ] M 0 1 f t s f ( d) f f c P( t *) M ( t t *) with f (,T *) 0, with P(T*) 0, with ( t *) P T * t *, with M, 9

( ) ( 1 a) ( t) K 44) f () t, t and with 45) f, T * e (t t*) [ M c P(t*) c M t t * ]dt t * (, t) ( ) e. ( T * -t *) ( M c P) e ( T * -t *) c M ( ( T * -t *) ) ( M c P) M is such that M < M and is the ate at which debt pincipal is epaid afte debt matuity has been extended. In appendix 1 the poblem is efomulated fo the case in which M 0.Condition 45) states that, as gows infinitely, debt value appoaches the value of a default fee debt that pomises the cash flows equal to [ M c P(t*) c M ( t t *)] dt in evey small peiod dt afte t*. 1 c M Then, as in section, we ae left with the poblem of detemining () t, () t and () t, whee it is again assumed that ( t) ( t) 0 5. Such poblem is solved by valuing the fim s equity, which is done next. Heeafte E(,t) denotes equity value befoe debt matuity has been extended and E(,t) denotes equity value afte debt matuity has been extended. Then: 46) 1 E t s E, ( d) E E d ( 1 tax) c [ P M t] M 0 5 denotes the value of the fim s assets today. 0 30

with E with (, t), with E (,T) P( T) ( ) ( () ) 47) E () t, t E t, t, fo t,0 t T max () t, subject to ( ) ( () ) 48) E () t, t E t, t, () () 48.1) t t, 0 ( ) ( 1 a) ( t) K 49) f () t, t. (since P(T) P(0) M T 0), 50) [ ] M 0 1 E t s E ( d) E E d ( 1 tax) c P( t *) M ( t t *) E, t E,T *, with with ( ), with ( ) ( ) 0 51) E () t, t, ( ) () 0 5) [ E, t ]. t Explicit finite diffeences allow to solve equations 41) to 5) simultaneously. () t is detemined fo evey time t as the highest assets value at which conditions 48) 48.1 and 49) ae all satisfied: these conditions ensue that debt matuity is extended in such a way that equity value, E(), is maximised subject to condition 49) and povided default has not yet taken place. Condition 49) is simila to condition 6) and must hold if the option to extend debt matuity is implicit in the possibility of debt enegotiation. This is the case we focus on below and the matuity extension policy [ () t ] is compaable to 1 in the time dependent setting of the pevious sections. 31

Fo some paamete values, thee is no ( t) satisfying conditions 48), 48.1) and 49); in such case debt matuity cannot be extended and E(,t) is equal to e[,t] as defined below. Conditions 51) and 5) gant that equity value is always non-negative and that it be maximised by the choice of () t 53) OE(, t *) max E[ ( t *), t *] e[ ( t *), t ] 1 e s e ( d) e e d ( 1 tax) c P( 0) M t M t, (, t) e(, T) Max[ ( P( 0) M T ),0] Moeove, upon extension the payoff to debt holdes is: 57) O(, t *) { f [ ( t *), t *] ff [ ( t *), t *]},. Conditions 51) and 5) ae simila to conditions 37), 38) and to condition 17) in Mello and Pasons (199) at page 1891. Assuming it is equity holdes who decide as to the execise of the extension option, the payoff to equity holdes is: with [ ( t *), t *] E ( t ) { *,0} [ *, t *] E, [ *, t *] with ( t ) e denoting the value of equity depived of the extension option. Then e[,t] must satisfy the same equation as E(,t), but the lowe bounday condition is the default condition (since debt matuity cannot be extended befoe default): 54) with e, 55) [ e (, t) ] 0, 56) [, t ] (t) ( ) ( ) 0 e t. and with, [ ] 0 3

[ ] [ ( ) ] with f ( t *), t * F t *, t * and with ( t ) [ *, t *] ff denoting the value of debt in the absence of the "extension option". Then ff[,t] must satisfy the same equation as F(,t), but the lowe bounday condition is the payoff upon default (since debt matuity cannot be extended befoe default): 1 58) ff s ff ( d) ff ff c [ P( 0) M t] M 0 t with ff and with 59) ff (,T) 0 since P(T) 0, with ff ( t), T t ( t) ( 1 a) ( t) K (, t) e t [ M c P(0) c M t] dt, e T ( M c P) e T c M ( T 1) ( M c P) c M. We have fomulated the time dependent model. Next numeical esults with base case paametes ae examined. 4.) ase case scenaio in a time dependent setting when default is tiggeed by wothless equity The base case scenaio paametes assumed in section 3 ae hee employed again 6. Hee again E(,t0) is geate than o equal to E(,t0) fo evey value of the fim s assets (). In fact extending debt matuity inceases equity value by inceasing the value of the tax shield, since moe coupons must be paid if debt matuity is 6 In the pevious time independent settings debt aveage matuity "1/m" was doubled upon execise of the "extension option": similaly in the base case scenaio of this time dependent setting the aveage matuity of debt is doubled at t*, so that M M aveage matuity (T/) is such that T/ (1/m) 5.. Moeove, T is now chosen so that the initial debt 33

extended. Equity value inceases also because equity is hee simila to some sot of compound call option that is continuously execised as debt is continuously seviced: thus extending debt matuity inceases equity value also by inceasing the time value of the equity compound call option. The endogenous default baie dops fom (t), fo t < t*, to (t) fo t > t*. Since E(,t0) is geate than o equal to E(,t0), equity holdes will have an incentive to enegotiate debt matuity as soon as condition 49) is met. If condition 49) is satisfied, debt holdes have incentives to voluntaily concede extensions of debt matuity befoe default. The values of the model paametes detemine whethe o not condition 49) is satisfied. Then, the base case scenaio in this setting eveals that debt both befoe and afte default is moe valuable (F(100, t0) 5.0 and f(100, t0) 5.8) than debt befoe and afte default as pe the base case scenaio of section 3 (espectively F(100) 50.54 and f(100) 50.5 ). This is mainly due to the fact that the pobability of default is now lowe since assets pay-outs ae mainly used to pay back debt pincipal, wheeas in section 3 debt was efunded and a geate shae of assets pay-outs could be destined to be distibuted as dividends athe than to epaying debt pincipal. Since debt is now moe valuable, the extension option is much less valuable fo equity holdes than in the base case of section 3. In fact, the iskie debt is, the moe valuable the extension option fo equity holdes is. The base case scenaio now gives OE(100, t0) 0.08 instead of OE(100) 1.71, and O(100, t0) -0.03 instead of O(100) -0.09. Figue 4 displays the values of the extension option OE(, t0) and O(, t0) assuming base case scenaio paametes in the pesent time dependent setting: due to constaint 49), [E(, t) - e(, t)] > OE(, t0). Unlike in 34

the time independent setting, now nominal outstanding debt is not constant and the time at which debt matuity is extended affects total fim value. An explicit finite diffeences scheme is employed with asset-step 4 and time-step < (1 yea /100). See appendix 3 fo the case in which debt matuity is extended at (t). 4.3) The tem stuctue of cedit speads In a time dependent setting the tem stuctue of cedit speads can be analysed. Figue 5 displays the diffeential cedit speads due to an implicit option to enegotiate and extend debt matuity when bankuptcy costs ae high (K10, a15%) and debt is not amotised (M0). It is inteesting that the implicit extension option causes a significant incease in shot-tem cedit speads (lowe assets values entail a moe accentuated incease). In fact it is pecisely such shot-tem cedit speads that taditional stuctual models, which do not account fo debt e-negotiation, systematically undestate. So, these esults suggest that stuctual models may undestate shot-tem cedit speads because they neglect the pesence of the implicit option to extend debt matuity. ut it may not be appaent why shot-tem cedit speads should incease moe than long-tem cedit speads when an implicit extension option is ecognised. The eason is that, fo high leveage, debt maket value (f(, t)) is below debt face value (P), but as debt matuity appoaches, debt maket value is pulled to pa if the debto is solvent. This means that, when is low, the payoff of the extension option (O(, t*) {f[ (t*), t*] - ff[ (t*), t*]} {F[ (t*), t*] - ff[ (t*), t*]}) inceases as t* appoaches oiginal debt matuity (T): execising late implies a highe option payoff. Thus, as matuity daws nea, O(, t) becomes moe valuable and its pesence implies a highe incease in shot-tem cedit speads. On the othe hand, if it is a few months 35

befoe matuity and is high enough, the implicit extension option is going to expie out of the money as the pobability of the ecovey value of assets dopping below ff[ (t), t] gadually vanishes. So immediately befoe matuity O(, t) is too low to imply any significant incease in cedit speads. These aguments explain the shape in Figue 5 of the incease in the shot-tem cedit speads due to the pesence of an implicit extension option. CONCLUSIONS This pape has focused on the value of debt given an option to enegotiate and/o extend debt matuity befoe default o just at default. The analysis has coveed a time independent setting in which the fim keeps a constant nominal capital stuctue and a time dependent setting in which the fim s nominal capital stuctue is not constant. The main esult in a time independent setting is that an implicit o explicit extension option inceases equity value moe than it deceases debt value. Such option can cause a mateial incease in the value of equity and may also cause a non-negligible incease o decease in the yield equied by debt holdes when the fim is fa fom default. Unde some conditions, equity holdes and debt holdes can both be bette off by enegotiating and extending debt matuity, which extends a pevious esult by Longstaff in a simple Metonian setting. This may often be the case when debt matuity is extended soon befoe o just at default in ode to avoid costly liquidation of the fim's assets. In a time independent setting it has also been shown that diffeent default conditions heavily affect the value of the implicit option to e-negotiate debt matuity and the 36

incentive fo debt holdes to accept e-negotiation: when default is tiggeed by cash flow insolvency the implicit option to extend debt matuity may easily be wothless if debt holdes ae not enticed to accept e-negotiation by the theat of high bankuptcy costs. Finally, in a time dependent setting it has been shown that when the fim does not efund debt with new debt, the pobability of default deceases making debt moe valuable and the extension option less valuable. Moeove, in a time dependent setting the pesence of the implicit extension option boosts the shot-tem cedit speads on the fim s debt thus patially ovecoming the typical poblem of stuctual models pedicting too low shot-tem cedit speads. Futue eseach could extend the above analysis and valuation of extension options to the case in which default fee inteest ates ae stochastic. Futue eseach may also conside: 1. the impact of the option to extend debt matuity on the choice of optimal capital stuctue;. the case in which the extended matuity of debt is endogenously detemined so as to maximise equity value athe than being exogenous as it has been assumed in this pape. 37

APPENDIX I: THE OPTION TO EXTEND MATUITY AND CEDIT SPEADS The pesence of the option to extend debt matuity (O()) implies a change in debt cedit spead (dy), whee 60) C m dy F [ P - F( ) ] ( ) C m ff [ P - ff ( ) ] ( ) and whee F() is debt value (as pe equation 1) when the extension option is pesent and ff() is debt value (as pe equation ) when the extension option is absent. The expessions m [ P - F( ) ] and [ P - ff ( ) ] m denote the cash flows to and fom debt holdes due to continuously olling debt ove. Equity holdes may compensate debt holdes fo the option to enegotiate and extend debt matuity by pomising a highe coupon ( C ) that would make F() ff(). Substituting fo F() and ff() fom equations ) and 1), this gives: 61) C C mp m mp m C C mp m mp m C ( 1 a) m P C m P m m b K ( 1 a) h b K Then oot finding numeical algoithms can easily find C by solving 61). APPENDIX II: ANOTHE CONDITION TO EXTEND MATUITY Debt in the time dependent setting of section 4 is safe and moe valuable than in the pevious time dependent settings, so a coupon ate of 6% (i.e. 1% cedit spead) oveemuneates debt holdes fo the isk of default they bea in the base case. Then debt holdes will want this ove-emuneation to last as long as possible. Then debt holdes 38

will want, at some point, to extend the matuity of debt that pays such geneous coupons. In paticula, they will desie to have matuity extended wheneve [ ] F[ ( t), t] 6) f () t, t. This condition can be satisfied at two points fo evey time t:.1 () t (). t 0. Then, if conditions 48) 48.1) and 49) ae substituted, by the following fo t,0 t T max () t, subject to.1 ( ) ( () ) 48.a) E.1() t, t E.1 t, t, () () 48.1.a).1 t t, 0 ( ) ( 1 a) ( t) K 49.a) f.1() t, t fo t,0.1 t T min () t, subject to. ( ) ( ( ) ) 48.b) E. () t, t E. t, t, () 48.1.b). t, 0 ( ) ( 1 a) ( t) K 49.b) f. () t, t., and if all othe equations ae the same as in the system of equations 41) to 5), we can find the values of equity and debt given that debt matuity is extended as soon as it is advantageous fo both the debto and the ceditos to do so. The values () t ( t).1. make debt holdes indiffeent between holding debt of shote o longe aveage matuity. Then, as in section 3, equity holdes could convincingly popose to debt holdes to have debt matuity extended as soon as ( t) (t () t (). t Though, in section 4 ( t 0).1.1 ) o ( ).1 is about 48 and. t 0 is 39

about 80 as opposed to espectively 44.5 and 106.6 in the time independent setting of section 3 with base case paametes. APPENDIX III: WHEN DET AMOTISATION STOPS Given the time dependent setting of section 4, if M 0 then the continuous amotisation of debt pincipal stops at t t* and all debt pincipal still outstanding mat be epaid at T though a single balloon payment. oth when M M and when M 0 with epayment at T, the aveage matuity of debt still outstanding at time t* is effectively double as long as when M M. When M M the ate at which debt pincipal is amotised is halved, when pincipal is suspended until T. When M 0 the epayment of debt M 0, the conditions fo equation 43) change, since debt holdes eceive P(t*) at T and coupons at a ate c P( t *) dt between t* and T. Hence, condition 45) is substituted by 63) f T t tt* Tt (, t) e c P( t *) dt e P( t *) and the final condition is no longe f (,T *) 0, but 64) f (, T) P( t *) if (T)> P(t*), o 65) (, T) min[ P( t *), ( 1 a) ] Then, if f if (T)< P(t*). M longe E(, T *), but 1 e ( T t *) c P 0 and P(t*) is due at T, the final condition fo equation 50) is no ( ) { ( ) } 66) E, T Max P t *,0. T t ( ) ( ) t * e P( t *) 40

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Figue 1: ase case scenaio with default tiggeed by wothless equity 70.00 60.00 50.00 ff() f() e() E() X() 40.00 alues 30.00 0.00 10.00-1 4 7 10 13 16 19 5 8 31 34 37 40 43 46 49 5 55 58 61 64 67 70 73 76 79 Assets value () 43

Figue : alues of the extension option in the base case scenaio with default tiggeed by wothless equity 1.00 10.00 8.00 OE with m10% O with m10% (E-e) with m10% (f-ff) with m10% OE with m0% O with m0% 6.00 alues 4.00.00-51 56 61 66 71 76 81 86 91 96 101 106 111 116 11 16 131 136 141 146 151 156 161 166 171 176 181 186 191 196 (.00) Assets value () 44

Figue 3: alues of the extension option in the base case scenaio with default tiggeed by wothless equity and matuity extended just upon default 4.00 3.50 OE with s10% OE with s0% O with s10% O with s0% 3.00.50 alues.00 1.50 1.00 0.50-1 7 13 19 5 31 37 43 49 55 61 67 73 79 85 91 97 103 109 115 11 17 133 139 145 151 157 163 169 175 181 187 193 199 Assets value () 45

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Figue 4: alues of the extension option with base case scenaio paametes in the time dependent setting 4.00 OE O E-e f-ff 3.00.00 alues 1.00-56 60 64 68 7 76 80 84 88 9 96 100 104 108 11 116 10 14 18 13 136 140 144 148 15 156 160 164 168 17 176 180 184 188 19 196 00-1.00 -.00 Assets value () 47

Figue 5: Incease in shot tem cedit speads due to the "implicit" extension option 1.0% 1.00% Incease in cedit speads 0.80% 0.60% 0.40% 0.0% 108 10 96 84 0.00% Assets value () 13 144 156 0.5 1.5.5 3.5 4.5-0.0% 168 180 19 Time to debt matuity (yeas) 48

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TALE I: SUMMAY OF THE EFFECTS OF THE PESENCE OF THE EXTENSION OPTION PANEL A: ase case with ievesible extension of debt matuity and cash flow shotage default Input data in italics No extension option Ante extension Post extension a (bankuptcy costs as faction of ) 15% 15% 15% (default isk-fee inteest ate) 5% 5% 5% s (volatility of ) 0% 0% 0% d (assets total payout to secuity holdes) 7.0% 7.0% 7.0% tax (tax ate) 35% 35% 35% K (fixed liquidation costs) 0 0 0 C (annual coupon, which is paid coutinuously) 3.00 3.00 3.00 Coupon ate (c C/P) 6.00% 6.00% 6.00% m (pecentage of P that is efinanced evey yea) 0% 0% 10% P (face value of debt) 50.0 50.0 50.0 0 (today's assets value) 100.0 100.0 100.0 4 (value of asset at which debt matuity is extended) 8.8 I and I (value of assets tiggeing default) 49.8 44.8 44.8 OE (value of the "extension option" fo equity holdes).6 E (value of equity) 55.0 57. 57. O (value of the "extension option" fo debt holdes) -0.53 F (value of debt ante extension) 50.5 50.0 f (value of debt post extension) 48.6 50.1 X(4) (assets ecovey value at 4) 70.4 Cedit spead: [Cm(P-F)]/F- o [Cm(P-f)]/f- 0.74% 1.0% 0.98% PANEL : All as in panel A exept fo assets volatility and 3 athe than 4 s (volatility of ) 10% 10% 10% 3 (value of asset at which debt matuity is extended) 49.8 I and I (value of assets tiggeing default) 49.8 44.8 44.8 OE (value of the "extension option" fo equity holdes) 1.65 E (value of equity) 59.5 61. 60.5 O (value of the "extension option" fo debt holdes) 0.01 F (value of debt ante extension) 51.7 51.7 f (value of debt post extension) 4.8 5.4 X(3) (assets ecovey value at 3) 4.3 Cedit spead: [Cm(P-F)]/F- o [Cm(P-f)]/f- 0.14% 0.14% 0.6% PANEL C: All as in panel A exept fo default when equity is wothless and 1 1 (value of asset at which debt matuity is extended) 50.5 E and E (value of assets tiggeing default) 35.5 30.4 30.4 OE (value of the "extension option" fo equity holdes) 1.71 E (value of equity) 59.7 61.4 61.4 O (value of the "extension option" fo debt holdes) -0.09 F (value of debt ante extension) 50.6 50.5 f (value of debt post extension) 4.9 50.5 X(1) (assets ecovey value at 1) 4.9 Cedit spead: [Cm(P-F)]/F- o [Cm(P-f)]/f- 0.68% 0.7% 0.83% PANEL D: All as in panel A exept fo default when equity is wothless and (value of asset at which debt matuity is extended) 44.5 E and E (value of assets tiggeing default) 35.5 30.4 30.4 OE (value of the "extension option" fo equity holdes) 1.61 E (value of equity) 59.7 61.3 61.4 O (value of the "extension option" fo debt holdes) 0.00 F (value of debt ante extension) 50.6 50.6 f (value of debt post extension) 40.1 50.5 X() (assets ecovey value at ) 37.8 Cedit spead: [Cm(P-F)]/F- o [Cm(P-f)]/f- 0.68% 0.68% 0.83% PANEL E: All as in panel A exept fo default when equity is wothless and 3 3 (value of asset at which debt matuity is extended) 35.5 E and E (value of assets tiggeing default) 35.5 30.4 30.4 OE (value of the "extension option" fo equity holdes) 1.44 E (value of equity) 59.7 61.1 61.4 O (value of the "extension option" fo debt holdes) 0.17 F (value of debt ante extension) 50.6 50.8 f (value of debt post extension) 3.9 50.5 X(3) (assets ecovey value at 3) 30. Cedit spead: [Cm(P-F)]/F- o [Cm(P-f)]/f- 0.68% 0.59% 0.83% Note to Table I: The table shows debt when debt matuity can be extended (a time independent setting). The fim's assets value is nomalised at 100 and the face value 50

of debt is assumed to be equal to 50. Panel A (and in the same way the othe panels) is to be intepeted as follows: if debt aveage matuity is extended at 4 (fom a 5 yeas to a 10 yeas), equity (E()) ises fom 55 to 57. and debt (F()) dops fom 50.5 to 50. Extending debt matuity deceases default baie fom I 49.8 to I 44.8, inceases total fim value and the expected value of the tax shield (fom TT()13 to TT()13.7) and decease the expected value of bankuptcy costs (fom C().9 to C().3). 51