The Optimal Timing of the Transfer of Hidden Reserves in the German and Austrian Tax Systems

Transcription

1 The Opimal Timing of he Transfer of Hidden Reserves in he German and Ausrian Tax Sysems A Marke-Based Approach wih Special Aenion o he Term Srucure of Ineres Raes and Ineres Rae Risk November 29, 2001 Manfred Frühwirh Deparmen of Corporae Finance Vienna Universiy of Economics and Business Adminisraion Augasse 2-6, 1090 Vienna, Ausria Manfred.Fruehwirh@wu-wien.ac.a hp:// The auhor would like o express his graiude o Sefan Bogner, Chrisopher Casey and Michaela Schaffhauser-Linzai for valuable remarks and discussions.

2 Absrac In his paper, he opimal iming of hidden reserves ransfers is derived wih special aenion o he erm srucure of ineres raes and ineres rae risk, and using wellknown conceps from he field of finance. The paper presens one model under cerainy and, as a generalizaion of his model, anoher model under ineres rae risk. In boh models, he crierion used for decision-making is he value of he righ o ransfer, which can be inerpreed as he iniial cos of a replicaing/hedging sraegy for ax paymens incurred/saved. In he model under cerainy, he ne presen value concep is used o derive he value of he righ o ransfer. The procedure used in he model under ineres rae risk is a combinaion of flexible planning and he no-arbirage approach common in derivaives pricing. I is shown ha he righ o ransfer hidden reserves wih flexible iming is equivalen o an American-syle conversion opion. In addiion, he impac of erm-srucure volailiy on he value of he righ o ransfer is analyzed. The echnique presened in his paper can also be used o solve oher iming problems resuling from rade-offs beween early and lae ax paymens/ax benefis. Keywords: Earnings Managemen, Timing Opion, Real Opion, Term Srucure of Ineres Raes, Ineres Rae Risk, Risk Managemen 2

3 1 Inroducion This paper deals wih earnings managemen, which is an imporan aspec of accouning. In general, earnings are managed by aking advanage of he righ o choose among various alernaives. Examples of his include he choice of depreciaion mehod and iming/valuaion leeway in connecion wih bad deb provisions or invenory valuaion (e.g., see Francis/Hanna/Vincen (1996), Healy/Wahlen (1999) or Jackson/Piman (2001)). A large number of empirical sudies have been carried ou on he opic of earnings managemen o es various earnings managemen hypoheses involving differen incenives. 1 In addiion, here are empirical sudies on he opimal design of earnings managemen sudies (see Guay/Kohari/Was (1996), McNichols (2000), Barov/Gul/Tsui (2000) or Thomas/Zhang (2000)). In comparison o he large quaniy of empirical lieraure in his field, relaively few heoreical works have been wrien on earnings managemen. Examples of he laer include he work of Trueman/Timan (1988), Hand (1993), Demski/Frimor (1999) and Wagenhofer (1999). This paper deals wih a heoreical model for an earnings managemen problem encounered in German-speaking counries. In his conex, herefore, i is useful o poin ou several differences beween Anglo-American accouning and ha of Germanspeaking counries. 2 Firs of all, crediors' proecion as opposed o a purely informaional funcion of he financial saemens is dominan in German-speaking counries, a fac ha lends grea imporance o he principle of conservaism. Second, here is a link beween commercial law and ax law in German-speaking counries 1 There are, for example, papers which invesigae wheher earnings managemen is performed in order o smooh earnings (Ronen/Sadan (1981)), in order o increase manager compensaion (Healy (1985), Holhausen/Larcker/Sloan (1995), Balsam (1998), Soo (1999), Guidry/Leone/Rock (1999)), in order o reduce ax liabiliies (Boynon/Dobbins/Plesko (1992), Hand (1993), Chen/Daley (1996), Chung (1998), Calegari (2000)), in order o fulfill regulaory requiremens (Moyer (1990), Scholes/Wilson/Wolfson (1990), Collins/Shackelford/Wahlen (1995), Chen/Daley (1996), Kim/Kross (1998)), in order o avoid/delay echnical defauls (Sweeney (1994)) or in order o fulfill managemen's performance forecass or he marke expecaions of analyss (Robb (1998), Kasznik (1999)). In addiion, he connecions beween earnings managemen and akeovers (Easerwood (1997)), CEO changes (Pourciau (1993)), anirus invesigaions (Cahan (1992)), impor relief invesigaions (Jones (1991)), labor union negoiaions (Libery/Zimmerman (1986)), managemen buyous (De Angelo (1988), Perry/Williams (1994)) and equiy offers (Aharony/Lin/Loeb (1993), Teoh/Wong/Rao (1998)) have been examined. 3

4 which is no found in England or he USA, as axable income is calculaed on he basis of commercial earnings (wih several correcions). This means ha he area of earnings managemen ha deals wih minimizing ax liabiliies is aribued grea imporance in German-speaking counries. This specific area of earnings managemen is he focus of his paper. One essenial research area wihin his form of earnings managemen is he analysis of iming decisions in ligh of heir ax effecs. This paper deals wih one such iming decision for German and Ausrian companies by analyzing he ransfer of hidden reserves in paricular. The background o his problem lies in he principle of conservaism and he resuling lower-of-cos-or-marke principle, according o which an asse can no be valued above is acquisiion coss. The lower-of-cos-or-marke principle implies ha an asse's book value can be below is marke value. This circumsance gives rise o he ax-relevan "disclosure" of hidden reserves when he asse is sold. German and Ausrian ax laws ( 6b and 6c of he German Income Tax Ac [EsG] and 12 of he Ausrian Income Tax Ac [EsG]) make i possible for companies o ransfer such hidden reserves (disclosed when an asse is sold) o anoher, newly purchased asse as an expense wihin a cerain period of ime (subsequenly called he "ransfer period" in analogy o he Ausrian ESG), and his sraegy is used frequenly in pracice (see Hilke (2000), S. 122). 3 The purpose of his paper is o deermine he opimal poin in ime for ransfer, wih special aenion o he erm srucure of ineres raes and uncerainy regarding fuure ineres rae evoluion. As regards he opimal ransfer sraegy (wihou referring o he erm srucure of ineres raes or ineres rae risk), for example, Seich (1990) wries ha his is a considerable sraegic opporuniy in accouning policy. However, lieraure on he ransfer of hidden reserves is sparse. Many exbooks (e.g., see Endriss (1998)) implicily assume a fixed ime of ransfer and sugges ransfers o asses wih he longes useful life in order o pospone ax paymens as long as possible. Wimann (1982) as well as Euler (1984) examine he benefis of allocaing 6b 2 For a deailed descripion of differences beween American and German accouning, see Corbridge/Ausin/Lemak (1993). Accouning in oher German-speaking counries is relaively similar o German accouning. 3 Similar possibiliies, albei wih resriced flexibiliy, can be found in R.35 of he German Income Tax Direcives and Ar. 64 of he Swiss Federal Ac on he Direc Federal Tax. Boh of hese legal sources allow - under cerain prerequisies - businesses o ransfer hidden reserves disclosed by he sale of asses ino a subsiue invesmen or o allocae a provision or reserve for replacemen invesmens. 4

5 reserves 4 and he opimal liquidaion sraegy for 6b reserves, bu boh sudies are based on he assumpion ha no ransfer or reinvesmen is iniially planned. Von Rosenberg/Müller (1990) analyze wheher allocaing a 6b reserve makes sense in cases where reinvesmen is no planned / no cerain. In a ceeris paribus analysis, hese auhors demonsrae ha a ransfer becomes more advanageous he laer i is performed ("ime effec"), he longer he useful life of he new asse is ("useful life effec"), and he higher he afer-ax ineres rae is ("ineres rae effec"). In order o decide wheher o allocae a 6b reserve or no, he businessperson's personal risk aiudes have o be aken ino accoun. The opimal ime o liquidae he reserve (i.e., he opimal ime of ransfer) in consideraion of he hree influencing facors (ime, useful life and ineres rae) is no discussed. This paper presens models for he German and Ausrian ax sysems for deermining he opimal ime of ransfer. The approach aken here differs from previous works in he following ways: Firs, he effecs described by von Rosenberg/Müller (1990) are inegraed ino a model in order o deermine he opimal ransfer sraegy. The opimal iming of he ransfer is sraighforward in cases where he invesmen projec wih he longes useful life sars a he laes possible ransfer ime (i.e., a he end of he ransfer period). In such cases, his poin in ime prevails over all earlier daes. (Lae ransfer o an asse wih a long useful life always pospones ax paymens furher ino he fuure han an early ransfer o an asse wih a shor useful life.) In all oher cases, however, a rade-off exiss beween he ime effec and he useful life effec, hus making opimizaion necessary. This paper presens a soluion o his opimizaion problem in a coheren model. The second significan expansion his paper adds o he exising lieraure is ha wellknown mehods from he field of finance are applied in order o solve his iming problem. The replicaing principle used (ax paymens incurred/avoided are replicaed by buying/selling bonds) has he advanage of enabling marke-based decisions, hus making i unnecessary o quanify he businessperson's personal risk aiude. Third, he model under cerainy in his paper is he firs o inegrae he erm srucure of ineres raes ino he ransfer decision. The model under cerainy is hen generalized 4 See below for furher deails on 6b reserves. 5

6 o become a model under ineres rae risk. This sep is appropriae in ligh of he fac ha ineres rae volailiies have increased in recen years, which has also manifesed iself in he growing number of ineres rae derivaives and he increased aenion o ineres rae risk in he relevan lieraure (e.g., see Heah/Jarrow/Moron (1990), Bühler e al. (1999) or Frühwirh (2001)). In paricular, he influence of erm srucure and ineres rae risk on managemen decisions has been he subjec of increased analysis (e.g., see Ingersoll/Ross (1992) or Höger (1995)). The analysis in his paper comes o he following conclusions: In he model under cerainy wih aenion o erm srucure, i is shown ha he opimal ransfer ime generally depends on he iniial erm srucure of ineres raes and on he developmen of he invesmen program over ime. The model under ineres rae risk demonsraes ha he managemen's flexibiliy in iming he ransfer is comparable o an American-syle conversion opion. Premaure ransfer of a hidden reserve can be opimal or sub-opimal, and a flexible ransfer sraegy (i.e., a sochasic ransfer ime) can represen he opimum. The approach used, which is based on opions pricing heory, makes i possible o value he righ o ransfer in consideraion of he flexibiliy wih respec o ransfer imes. In his conex, he influence of ineres rae volailiy on he opimal ransfer sraegy and on he value of he righ o ransfer is also examined. This paper is srucured as follows: Secion 2 briefly describes he relevan legal regulaions in Germany and Ausria. Secion 3 explains he model under cerainy, a base model which is hen supplemened by a generalizaion for he case of ineres rae risk o be found in Secion 4. 2 Legal Regulaions in Germany and Ausria The possibiliy of ransferring hidden reserves in Germany is governed by 6b and 6c of he German ESG. In 6b Paragraph (2), hidden reserves are defined as he amoun by which he sale price of an asse exceeds is book value afer deducion of he selling coss. Under 6b Paragraph (1), hidden reserves from he sale of land, crops along wih he accompanying land (if he crops belong o operaing asses used in agriculure/foresry), and buildings are ransferable. Transfers can be made o land, 6

7 crops along wih he accompanying land, or buildings. The requiremens for such ransfers are lised in Paragraph (4). 6b Paragraph (3) allows companies o allocae an unaxed reserve in he year of hidden reserve disclosure for laer ransfer, unless hey have ransferred he hidden reserve in ha year. In his way, he hidden reserve can be ransferred o asses (described in Paragraph 1) acquired or produced in he ensuing four years. A he ime of ransfer, he unaxed reserve is o be liquidaed. 6b Paragraph (6) says ha, if he hidden reserve is ransferred o a new asse under Paragraph (1) or (3), he amoun of he hidden reserve is o be subraced from he full acquisiion or producion coss for ax purposes. The annual ax depreciaion amoun for he new asse is o be reduced accordingly. In cases where he unaxed reserve sill exiss a he end of he fourh year, he legal consequences are described in wo places: 6b Paragraph (3) dicaes ha a reserve which sill exiss a he end of he fourh year afer is allocaion is o be liquidaed o increase earnings a ha ime. In such cases, 6b Paragraph (7) furher requires ha a premium be added o axable earnings in he amoun of 6% of he liquidaed reserve amoun for each full business year in which he reserve exised. A comparable opporuniy can be found in 12 of he Ausrian EsG. In conras o is German counerpar, his secion does no provide a complee lis of he asses o which hidden reserves can be ransferred. Paragraphs 2 and 3 describe he circumsances under which such ransfers are permissible. For ax purposes, 12 Paragraph (5) sipulaes a reducion of he acquisiion/producion coss of he new asse in a manner similar o German law: Tax depreciaion is calculaed on he basis of acual acquisiion/producion coss reduced by he amoun of he ransferred hidden reserve. Similar o he German law, 12 Paragraph (7) says ha an unaxed reserve can be allocaed in he year of disclosure unless he hidden reserve is ransferred o a new asse in he same business year. Under 12 Paragraph (8), he period for he liquidaion of his unaxed reserve is welve monhs, or in cerain cases 24 monhs, from he disposal of he asse. 7

8 According o 12 Paragraph (8), if he hidden reserve is no ransferred o a new asse by he end of ha period, he unaxed reserve has o be liquidaed wih an increase in profis. In conras o Germany, Ausria does no provide for a premium in cases where he reserve is liquidaed wihou being ransferred o a new asse. 3 Model under Cerainy The objecive of his secion is o develop a base model under cerainy in order o deermine he opimal ransfer ime wih aenion o he erm srucure of ineres raes. This model will hen be expanded o include ineres rae risk in Secion 4. Secion 3.1 describes he srucure of he model. In Secion 3.2, he (ax) paymens relevan o decision-making are deermined on he basis of he model, as is he value of he righ o ransfer he reserve a a given poin in ime. In Secion 3.3, he ne presen value concep is used o idenify he opimal ime of ransfer among all possible ransfer imes. 3.1 Srucure of he Model In his model, a capial marke wihou ransacion coss and wih he possibiliy of shor selling is assumed. On his marke, here are infiniely divisible, credi-risk free, axexemp zero-coupon bonds wih a par value of one currency uni for all mauriies up o he model's horizon τ. The prices of zero-coupon bonds wih various mauriies reflec he ineres raes of differing mauriies and hus he erm srucure of ineres raes. 5 The model assumes a business whose profis are axed a he ax rae s. The annual accouns are closed as of December 31 each year. Taxes are also o be paid on December The assumpions in his paragraph are sandard assumpions in afer-ax bond valuaion as well as aferax capial budgeing, and hey enable afer-ax marke-based valuaion. These assumpions, especially ha which says here are infiniely divisible, credi-risk free, ax-exemp zero-coupon bonds for all mauriies up o he model's horizon, are far less problemaic han hey may seem a firs glance. Even if ax-exemp zero-coupon bonds were non-exisen, hey could be creaed synheically using bonds subjec o axaion wih various mauriies if an arbirage-free, complee marke is assumed (see Seiner/Uhlir (2000), p. 47ff). For furher deails on he esimaion of he afer-ax erm srucure of ineres raes on an incomplee marke, see McCulloch (1975). 8

9 I is assumed ha he business in quesion sold fixed asses in he previous year a a price higher han heir book value for ax purposes, whereby a hidden reserve in he amoun of SR was disclosed. Thus he business' axable earnings rise by he amoun of SR a he end of ha year (ime: 0). If we assume ha he business' axable earnings for ha year (before disclosure of he hidden reserve) are non-negaive, he business' ax liabiliy will increase by SR s due o he disclosure. I is also assumed ha he legal prerequisies for ransferring his hidden reserve are fulfilled. The business hus has he following alernaives a ime 0: 1) The business can pay he axes on he hidden reserve immediaely. In his case, he previously menioned increase in ax liabiliy in he amoun of SR s a ime 0 remains unchanged. 2) The hidden reserve SR can be allocaed o an unaxed "ransfer reserve" a ime 0 in order o ransfer he hidden reserve immediaely or wihin a period of T years. The period T is referred o as he "ransfer period" below. This allocaion o he ransfer reserve reduces axable earnings by SR a ime 0, resuling in ax savings in he amoun of SR s. The decision o ransfer he hidden reserve or a leas o wai unil he nex year o do so is made a he end of each year. The effecs of selecing his Alernaive 2 in he ensuing years depend on wheher or no he hidden reserve is acually ransferred o a new asse wihin he ransfer period, which is described under 2a and 2b. 2a) When he hidden reserve is ransferred o a new asse, he ransfer reserve is liquidaed agains he acquisiion/producion coss of he new asse, which in effec increases fuure ax paymens (furher deails below). 6 Selecing Alernaive 2 herefore allows he business o pospone he increase in ax paymens in he amoun of SR s from ime 0 o he fuure, which brings abou a corresponding ineres gain. 2b) If he hidden reserve is no ransferred wihin he ransfer period, he ransfer reserve is o be liquidaed in is enirey o increase profis, wih a percenage premium of z. This causes an increase in axable earnings a he end of he ransfer period in he amoun of SR (1+z) and hus an increase in ax paymens of 6 This is an abbreviaed descripion which is equivalen o acual enry procedures in is effecs on ax liabiliies. Because his special deducion for ax purposes is no acually depreciaion under commercial law, i mus no reduce he acquisiion/producion coss. For his reason, he hidden reserve ransfer is acually enered ino he books in he form of a "Special iem wih reserve porion" (in Germany) or a "Valuaion reserve" (in Ausria). Furher deails on he enry procedures for such ransfers can be found in Endriss (1998) for Germany and in Wagenhofer (2000) for Ausria. 9

10 SR s (1+z). The ineres gain resuling from posponing he ax paymen is hus couneraced by an increase in ax paymens from SR s o SR s (1+z). In order o shif ax paymens ino he fuure, he business decides for Alernaive 2 a ime 0. 7 A ime 0, he business' invesmen program is already fixed up o he end of he ransfer period. The program consiss of invesmen projecs wih deerminisic invesmen daes and deerminisic useful lives for ax purposes. For he purposes of furher analysis, only hose projecs o which he hidden reserve can be ransferred are relevan. I is assumed ha such a projec exiss a any given poin in ime. 8 In his paper, i is assumed ha he hidden reserve can only be ransferred o depreciable asses. This assumpion is based on he highly resricive legislaion in Ausria and Germany wih regard o ransferring hidden reserves o non-depreciable asses. 9 Due o he ransfer of he hidden reserve, depreciaion on he new asse is reduced, which implies ha ax paymens are shifed ino he fuure. These ax paymens are shifed farher ino he fuure when he hidden reserve is ransferred o asses wih long useful lives han when he hidden reserve is ransferred o asses wih shor useful lives 7 Under Ausrian law, Alernaive 2 is preferable o Alernaive 1 in any case, because - even if he hidden reserve is no ransferred during he ransfer period - no premium is charged and herefore Alernaive 2 will definiely resul in an ineres gain. Under German law, Alernaive 1 may be preferable if he probabiliy of ransfer wihin he ransfer period is very low and hus he probabiliy of paying a premium for non-ransfer in Alernaive 2 is correspondingly high, which could more han compensae for he ineres gain. However, he assumpion ha Alernaive 2 is seleced is necessary even in he German case, because i enables - along wih he following model - a wo-sage procedure for he decision beween an immediae ax paymen for he hidden reserve and he allocaion of a ransfer reserve: In he firs sage, i is assumed ha he hidden reserve is ransferred (Alernaive 2), and he model presened is used o calculae he value of he righ o ransfer based on he opimal ransfer sraegy. In he second sage, i is necessary o check wheher he opimal sraegy in Alernaive 2 prevails over an immediae ax paymen (Alernaive 1). 8 The mehodology described in his paper can likewise be used in he more general case of ineresconingen invesmen daes and/or ineres-coningen useful lives. I is also possible o use a generalizaion in which no invesmen projec is available a cerain imes or in cerain saes. A hese imes/in hese saes, oher paymens would be incurred in comparison o he imes/saes where invesmen projecs are available, and he resuling conversion opion described in Secion 4.2 would become more complex. Inegraing hese generalizaions, however, would increase he complexiy of he model unnecessarily and no yield any essenial addiional resuls. 9 For example, he ransfer of hidden reserves o land in Ausria is only permissible for businesses which calculae heir profis under 5 EsG and when he hidden reserves hemselves arise from he sale of land. In Germany, similarly, he ransfer of hidden reserves o land is only allowed when he profis arise from he sale of land. Inegraing he righ o ransfer hidden reserves o non-depreciable asses ino he model described would require knowledge of he ime of sale for each of hese asses, as he hidden reserves would be disclosed again a he ime of sale. 10

11 (see von Rosenberg/Müller (1990) or Wagenhofer (2000)). Given a fixed ime of ransfer, a raional person would hus ransfer he hidden reserve o he asse wih he longes useful life. The maximum useful life over all asses o which he hidden reserve can be ransferred a ime is deerminisic bu dependen on ; his maximum useful life in years is represened by n(). This ime dependency is based on macroeconomic (business cycle, indusry echnology, ec.) and/or microeconomic (each business' invesmen program will flucuae over ime independenly of macroeconomic facors) changes over ime. For each poin in ime, he following is assumed of he asse wih he maximum useful life: The asse involves acquisiion/producion coss which exceed he amoun of he hidden reserve ha has been disclosed; he asse will be reained unil he end of is useful life for ax purposes; ax depreciaion is exclusively sraigh-line; and each year a full year's depreciaion is claimed. Aside from he possible ransfer of he hidden reserve o his asse, no oher invesmen-relaed ax privileges are claimed, and no wrie-ups or wrie-downs are performed. 10 In summary, a ransfer a ime creaes, in effec, a reducion of he acquisiion/producion coss (for ax purposes) of he new asse by he amoun of SR. The ransfer hus decreases ax depreciaion by SR/n() a he end of each year from o he end of he asse's useful life. I is assumed ha in all ax years afer ime 0 he business' axable earnings are sufficienly high ha he decrease in ax depreciaion increases ax paymens by SR s/n(). 3.2 Value of he Righ o Transfer a Time The value of he ransfer a ime can be calculaed by deermining he ne presen value of he ax paymens which are incurred/avoided in he fuure due o he ransfer a ime. Table 1 gives an overview of he ax paymens incurred/avoided in connecion wih 10 These assumpions rule ou, iner alia, he possibiliy ha he hidden reserve migh have o be ransferred o several asses due o insufficien acquisiion coss in he new asse, as well as he possibiliy ha he ransfer of hidden reserves o a new asse may bring abou addiional hidden reserves in he fuure (when he new asse is sold). In addiion, ineracion among invesmen-relaed ax privileges and/or wrie-ups/wrie-downs on he one hand and he ransfer of he hidden reserve on he oher hand is prevened. All of hese assumpions could be relaxed wihin he framework of he model used, wih he side-effec of increased complexiy. Because no significan addiional conclusions would arise from his increased complexiy, his was no done. 11

12 he allocaion of he ransfer reserve a ime 0 and wih he ransfer of he hidden reserve a ime : Table 1: Tax paymens incurred/avoided by allocaing he ransfer reserve/ransferring he hidden reserve Time poins Procedure Allocaion of ransfer reserve Immediae ax savings Allocaion of ransfer reserve Threa of ax-increasing liquidaion a T if hidden reserve is no ransferred by T Transfer Avoidance of axincreasing liquidaion a T Transfer Reducion of depreciaion amoun during useful life of new asse + SR s 0,+1,...,+n()-1 T - SR s / n() - SR s ( 1+ z) + SR s ( 1+ z) Securing he ransfer opporuniy a ime 0 generaes he following paymens: A ime 0, a ax benefi in he amoun of SR s resuls from he allocaion of he ransfer reserve. However, his implies a ax increase including he premium of SR s ( + z) 1 a he end of he ransfer period in he case of non-ransfer. 11 Because he ransfer opporuniy is assumed o have already been secured (see Secion 3.1), hese paymens are no longer relevan o decision-making. The following paymens are caused by ransfer a ime : The ax increase of SR s ( + z) 1 for non-ransfer a he end of he ransfer period is avoided. The avoidance of his ax increase can be regarded as a cash inflow which compensaes for he cash ouflow in he same amoun menioned in he previous paragraph. The value of he avoided ax increase as of he ime of ransfer can be 11 In his paper, he erm "ax increase" is used o denoe any increase in ax paymens. 12

13 calculaed by muliplying i by he price of a zero-coupon bond wih mauriy T a ime, which is denoed as P,T : ( 1+ z) P T SR s, On he oher hand, he ransfer a ime increases ax paymens in each year of he new asse's useful life by SR s / n(). The value of hese increased ax paymens in each year of he asse's useful life as of he ime of ransfer is SR s RBF,n() /n(), where RBF, n () = + n () j = 1 P, j. Borrowing from an analysis wih a fla erm srucure of ineres raes, RBF,n() is referred o as a "presen value facor for an afer-ax annuiy in advance" as of ime for a mauriy of n() years. The value of he ransfer a is he value of he avoided ax increase a T minus he value of he ax increases caused by he ransfer in each year of he new asse's useful life (each as of he ime of ransfer ): SR s SR s RBF, n() ( 1+ z) P T n() = SR s, 1 RBF n(), n() ( + z) P, T If, as of ime, he value of he ax increase avoided is lower han he value of he ax increases caused by he ransfer, he value of he ransfer a ime will be negaive. In such cases, deciding no o ransfer he hidden reserve a and liquidaing he ransfer reserve o increase profis a he end of he ransfer period is beer, which means ha ax paymens are neiher avoided nor incurred by ransferring a ime. The value of he righ o ransfer a ime is hus 0 insead of he (negaive) value of he ransfer a ime. The value of he righ o ransfer a ime (as of ime ) is generally: V ÜM RBF RBF,n() = 1, 0 = SR s MAX ( 1 + z) P,T, 0. n(),n() () MAX SR s( + z) P,T n() 3.3 Opimal Timing of he Transfer In order o enable a comparison of various ransfer imes, a common poin in ime is necessary as a reference. The reference poin in ime used below is ime 0. The 13

14 valuaion, as of ime 0, of he individual values of he righ o ransfer a ime, V ÜM (), is carried ou using a marke-based approach by muliplying values by he zero-coupon bond prices prevalen a ime 0. The value of he righ o ransfer a ime as of he reference poin 0 is herefore as follows: NPV ÜM TRBF,n() () = VÜM () P0, = SR s MAX ( 1+ z) P0,T, 0 n() where TRBF,n() = P0, RBF,n () = + n () j= 1 P 0, j value facor for a deferred afer-ax annuiy in advance"., which can be regarded as he "presen NPV ÜM () can be inerpreed as he addiional amoun which given he ransfer ime remains for he enerprise/owner a ime 0 if fuure ax paymens (avoided/incurred due o he ransfer a ime ) are shifed o ime 0 by buying/selling zero-coupon bonds a ime 0. The opimal ime for ransfer is hen he ime which maximizes he value of he righ o ransfer a ime as of ime 0, NPV ÜM (). The value of he righ o ransfer a any given poin in ime is hus: max NPV 0 T ÜM TRBF (), 0 n,n() () = max SR s MAX ( + z) P 0 T 1 0,T Equaion 1 This means ha given he maximum useful life as a funcion of, n(), one would end o ransfer laer he more sharply TRBF,n() drops over ime (i.e., when is increased). Addiional saemens on he influence of level or slope of he erm srucure of ineres raes are only possible wih he use of numerical mehods and would require knowledge of he maximum useful life as a funcion of, n(). Example 1: The model horizon is four years saring from December 31, 2000 (=0). In he year 2000, hidden reserves in he amoun of 100,000 were disclosed hrough he sale of fixed asses. Legal regulaions permi he ransfer of hese hidden reserves. The ransfer 14

15 period lass wo years, saring on December 31, No premium is charged for nonransfer wihin he ransfer period. The business' ax rae is 50 %. The following ransfer opporuniies exis: Transfer ime Maximum useful life 12/31/2000 (=0) n(0) = 4 12/31/2001 (=1) n(1) = 4 12/31/2002 (=2) n(2) = 2 The erm srucure of ineres raes as of December 31, 2000 is as follows: j P 0,j The opimal ransfer ime can be calculaed as follows: The value of he ransfer on December 31, 2000 is 50,000 [ ( )/4] = -764, which means ha his can no be an advanageous ime o ransfer. The value of he righ o ransfer on December 31, 2000 is hus 0. The value of he righ o ransfer on December 31, 2001 is 50,000 [ ( )/4] = The value of he righ o ransfer on December 31, 2002 is 50,000 [ ( )/2] = Therefore, in he decision beween December 31, 2001 and December 31, 2002, he useful life effec prevails over he ime effec. The opimal ime for he ransfer is December 31, By posponing he ransfer from December 31, 2000 o December 31, 2001, he business gains 1420 currency unis (CUs). If he erm srucure of ineres raes were subjeced o an upward parallel shif (i.e., if zero-coupon bond prices were shifed downward), wih P 0,1 = , P 0,2 = , P 0,3 = and P 0,4 = , for example, hen December 31, 2002 would be he opimal ime o ransfer he hidden reserve (1594 CUs for ransfer on December 31, 2001 vs CUs for ransfer on December 31, 2002). If he erm srucure of ineres raes were flaer han in he given example e.g., P 0,1 = , P 0,2 = , P 0,3 = and P 0,4 = hen he opimal ransfer ime would likewise be shifed o December 31, 2002 (1299 CUs for ransfer on December 31, 2001 vs CUs for ransfer on December 31, 2002). This gives an example of he influence of he level and slope of he erm srucure of ineres raes on he opimal ime of ransfer. However, 15

16 generalizaions of hese saemens for oher maximum useful lives as a funcion of are no possible. 4 Model under Ineres Rae Risk The objecive of his secion is a generalizaion of he base model described in Secion 3 for he case of ineres rae risk. For his purpose, Secion 4.1 gives a generalizaion of he model's srucure, and Secion 4.2 generalizes he valuaion and opimizaion echnique described in Secion Srucure of he Model In addiion o he securiies described in he base model, a ax-exemp, credi risk-free money-marke accoun exiss. 12 Uncerainy arises from developmen in he prices of zero-coupon bonds wih various mauriies, ha is, from he evoluion of he afer-ax erm srucure. The zero-coupon bond prices follow an arbirary, discree-ime, complee, no-arbirage erm srucure model (for he sake of simpliciy, i is assumed below ha exacly one ineres rae change occurs per year 13 and ha he zero-coupon bonds are always raded on December 31). The erm srucure model can be assembled using any number of facors (sources of uncerainy). Recombining rees (pah-independen models) as well as nonrecombining rees (pah-dependen models) are permissible. Using an arbirary erm srucure model permis, for example, a model in which he erm srucure is subjeced o parallel shifs (see Ho/Lee (1986)), or a model in which shor-erm ineres raes flucuae more drasically han long-erm raes (see Heah/Jarrow/Moron (1990)). Because a complee, no-arbirage erm srucure model is assumed, here is a unique risk-adjused probabiliy measure under which he relaive zero-coupon bond prices 12 This assumpion is redundan because he money-marke accoun can be replicaed by means of revolving invesmens in single-period zero-coupon bonds. Neverheless, i is used as a sandard assumpion in erm srucure models. 13 Because changes in ineres raes during he year are realisic, i appears useful for he purposes of pracical implemenaion o assume several ineres rae changes per year, bu only one ime of ransfer per year. This is possible wihin he framework of he model presened here, bu because he purpose of his paper is o presen he problem as well as an approach o be used as a basis for implemenaion, his is no done. 16

17 (zero-coupon bond prices in relaion o he value of he money-marke accoun) are maringales (see Harrison/Kreps (1979) and Harrison/Pliska (1981)). Figure 1 gives a graphic overview of he evoluion of he erm srucure over he firs wo years when a single-facor model is used. Figure 1: Evoluion of he erm srucure of ineres raes under a single-facor model Term srucure a (2,UU) Term srucure a (0) 1 0,8 0,6 0,4 0, Mauriy T Zero-coupon Bond Price Term srucure a (1,U) 1 0,8 0,6 0,4 0, Mauriy T Term srucure a (1,D) Mauriy T Zero-coupon Bond Price 1 Zero-coupon Bond Price 0,8 0,6 0,4 0,2 1 0,8 0,6 0,4 0, Mauriy T Term srucure a (2,UD) 1 0,8 0,6 0,4 0, Mauriy T Term srucure a (2,DU) 1 0,8 0,6 0,4 0, Mauriy T Term srucure a (2,DD) 1 0,8 0,6 0,4 0, Mauriy T Zero-coupon Bond Price Zero-coupon Bond Price Zero-coupon Bond Price Zero-coupon Bond Price Saring wih node (0) a ime 0, here are wo nodes a ime 1 (1,U) and (1,D) and four nodes a ime 2 (2,UU), (2,UD), (2,DU) and (2,DD) where U sands for an upward movemen and D for a downward movemen in zero-coupon bond prices. 17

18 4.2 The Opimal Transfer Sraegy As in Secion 3.3, he value of he righ o ransfer a ime as of ime 0 is o be calculaed on he basis of V ÜM (), he value of he righ o ransfer a ransfer ime as of ime. In conras o he model under cerainy, i is now also possible o pursue flexible ransfer sraegies using sochasic ransfer imes. To provide an example in coninuaion of Example 1, he ransfer sraegy "If ineres raes drop in he firs year, we will ransfer on December 31, If ineres raes rise in he firs year, we will ransfer on December 31, 2001" represens one possible (sochasic) ransfer ime. Now ha sochasic ransfer imes are also under consideraion, valuaion by simply muliplying by zero-coupon bond prices is no longer possible. For his reason, a more general procedure which unies he advanages of flexible planning and he no-arbirage approach o he valuaion of coningen claims will be presened. The mehodology is comparable o he one used by Ingersoll/Ross (1992) and Höger (1995) for he opimal iming of invesmen projecs and has he advanage of enabling valuaion on he basis of marke prices, hus eliminaing he need for assumpions regarding personal risk aiudes. The procedure is based on he modeling of a no-arbirage, complee marke (see Secion 4.1). On such a marke, any paymen can be replicaed. 14 A ime 0, he paymen mus have he same value as he replicaing porfolio. The value of he replicaing porfolio (as of ime 0) is he expeced value under he risk-adjused probabiliy measure of he paymen's presen value, where he presen value of he paymen is calculaed by dividing he paymen by he value of a ficiious money-marke accoun (e.g., see Pliska (1998)). The value of he righ o ransfer for a given ransfer ime as of ime 0 is hus: 14 This also applies o paymens incurred a a sochasic poin in ime, as long as his poin in ime fulfills he prerequisies of a sopping ime (e.g., Pliska (1998), p. 134f; for prerequisies of a sopping ime, see Lamberon/Lapeyre (1996), p. 17). These prerequisies are fulfilled for he ransfer ime because i is possible a any poin in ime o deermine wheher he hidden reserve is ransferred a. 18

19 NPV ÜM () = E Q VÜM B () = E Q SR s MAX, n() ( 1+ z) P, T n() B RBF,0 Equaion 2 where B represens he value of he money-marke accoun a ime (B 0 = 1) and E Q [.] depics he expeced value under he risk-adjused probabiliy measure. The expression in Equaion 2 can be inerpreed as he amoun which given ransfer ime remains for he business(person) if a self-financing rading sraegy in zerocoupon bonds is used o hedge he ineres rae risk which resuls from he ransfer a ime (and o which boh he ax paymens incurred during he new asse's useful life from on and he ax paymen avoided as of T are subjec). In conras o Secion 3, a dynamic hedging sraegy is generally necessary, i.e., bond ransacions are necessary a all poins in ime. The opimal ransfer ime is ha which maximizes NPV ÜM (). The value (as of ime 0) of he righ o ransfer a any ime is herefore: max NPV 0 T ÜM () = SR s max E 0 T Q MAX,n() ( 1+ z) P (),T n B RBF, 0 Equaion 3 This value corresponds o ha of SR s American-syle opions wih an inrinsic value a of: MAX RBF +, T, 0 n(), n() ( 1 z) P. From he definiion of RBF,n() one can see ha his is he inrinsic value of an American-syle opion o conver an equally weighed bond index ino (1+z) zero- 19

20 coupon bonds wih mauriy T. The bond index is calculaed using a pool of n() zerocoupon bonds wih mauriies from 0 o n()-1. The size of he pool is hus imedependen and depends on he maximum useful life of all asses o which he hidden reserve can be ransferred a. The weighing assigned o each bond in he index is he reciprocal of his useful life. The expression for he inrinsic value can be inerpreed as follows: If ( + z) P, T RBF n,n () () 1 >, hen he opion is in he money, and ransferring a ime is beer han liquidaing he ransfer reserve (wihou a ransfer) a he end of he ransfer period T (which does no necessarily imply ha here is no ransfer ime ha is beer han ). If ( + z) P, T 1 RBF n,n () (), hen he opion is a (=) or ou of (<) he money, and ransferring a is equally advanageous (=) or worse (<) han liquidaing he ransfer reserve a T, meaning ha a premaure ransfer a ime is disadvanageous and he inrinsic value of he opion is 0 (see Secion 3.2). The value of his opion and he opimal exercise ime depend on he iniial erm srucure of ineres raes, he maximum useful life as a funcion of, n(), and on erm srucure dynamics. The opimal ime o ransfer he hidden reserve is idenical o he opimal ime o exercise he American-syle opion. The calculaion of he expeced value in Equaion 3, as well as he idenificaion of he opimal exercise/ransfer ime, is possible using sochasic, dynamic opimizaion. One suiable procedure is backward recursion, in which one begins wih he las possible poin in ime and hen works back in succession o ime 0 (e.g., see Cox/Ross/Rubinsein (1979), Ho/Lee (1986) or Jarrow (1996)). Applying his procedure o he ransfer of hidden reserves, he end of he ransfer period is used as he poin of deparure. A his poin in ime, he value of he opion, V T, corresponds o he inrinsic value a T: V T = MAX RBF RBFT, n( T ),,0 = ( 1+ z) 0 n( T ) T, n( T ) ( 1+ z) PT T n( T ) 20

21 Because z is non-negaive and zero-coupon bond prices (under he plausible assumpion of non-negaive ineres raes) are less han or equal o 1, V T is non-negaive. I herefore makes sense o exercise he opion in any case, a he laes a he end of he ransfer period. 15 The values a arbirary earlier poins in ime ( < T) can be calculaed as follows: The value upon exercise a is RBF VA, = 1, n() ( + z) P, T n() The value a, if exercise is posponed unil afer, is V W, = E Q V B B F where E Q [. F ] is he expeced value condiional on he informaion available a ime (symbolized by F ). (For more informaion on he concep of condiional expecaion, see Duffie (1996), p. 272, for example.) The value of he opion a ime, denoed by V, is he maximum of he wo values: V = MAX[V W,,V A, ] The opion is exercised a (i.e., he hidden reserve is ransferred a ) if V A, V W,. In all oher cases he opion is exercised laer (i.e., he hidden reserve is ransferred laer). 15 This fac also allows analysis in he special case of a ime-consan invesmen program (i.e., he maximum useful life is he same in all business years). Due o he maringale characerisics and he monoony of (discouned) zero-coupon bond prices, he end of he ransfer period is he opimal ime o ransfer in his case. This is also inuiively plausible because he ax increases resuling from he reduced depreciaion in each year of he new asse's useful life (he lengh of which is independen of he ransfer ime because he useful life is consan) can be posponed as far as possible ino he fuure. 21

22 Example 2: Complemening Example 1, his example assumes he following: The money-marke accoun's value as of December 31, 2000 is B 0 = 1. The ime 0 bond prices used in Example 1 are aken as he poin of deparure: j P 0,j On December 31, 2001 (=1) wo saes are possible, one reflecing an upward movemen (U) and he oher reflecing a downward movemen (D) in zero-coupon bond prices. In boh saes, he value of he money-marke accoun is B 1 (U) = B 1 (D) = 1/P 0,1 = Bond prices a hese wo nodes as of =1 are shown in he able below: j P 1,j (D) P 1,j (U) On December 31, 2002 (=2), four saes exis: DD (downward movemens in boh periods), DU (downward movemen hen upward movemen), UD (upward movemen hen downward movemen) and UU (upward movemens in boh periods). The value of he money-marke accoun in saes DD and DU is B 2 (DD) = B 2 (DU) = B 1 (D)/P 1,2 (D) = The value of he money-marke accoun in he saes UD and UU is B 2 (UD) = B 2 (UU) = B 1 (U)/P 1,2 (U) = Bond prices in hese four saes are shown in he able below: j P 2,j (DD) P 2,j (DU) P 2,j (UD) P 2,j (UU) These erm srucure dynamics are idenical o he developmen shown in Figure 1. They correspond o hose in he Ho/Lee (1986) model wih he parameers q=0.6 (riskadjused condiional probabiliy for an upward movemen of zero-coupon bond prices) 22

23 and δ=0.945 (a parameer which is inversely relaed o erm srucure volailiy). The marke is hus complee and arbirage-free. Now o he backward-recursive valuaion of he opion and o he idenificaion of he opimal exercise/ransfer sraegy. Figure 2 shows he individual nodes in his model wih he value of he opion upon exercise (V A, ), he value when exercise is posponed (V W, ), and he value of he opion (V ). Figure 2: Backward-recursive valuaion of he opion (1,U) V A,1 = V W,1 = V 1 = (2,UU) V 2 = (2,UD) V 2 = (0) V A,0 = V W,0 = V 0 = (1,D) V A,1 = V W,1 = V 1 = (2,DU) V 2 = (2,DD) V 2 = Value calculaions are explained in he order in which hey are performed: 23

24 Sep 1: Decision as of December 31, 2002 (=2) A he end of he ransfer period, he value of he opion is he value upon exercise. A node (2,DD), his is: RBF2, V2 = V A,2 = 1 = 1 = The same procedure is o be applied o he remaining hree nodes a =2, resuling in he values shown in Figure 2. Sep 2: Decision as of December 31, 2001 (=1) Node (1,D) is considered firs. The value of he opion if exercised afer =1 is: V E V B F1 = W, 1 = Q 2 = B The value upon exercise a (1,D) is: V RBF = , 4 A, 1 = P1, 2 = The value of he opion a (1,D) is hus Because V W,1 > V A,1, he opimal sraegy a his node is o pospone he exercise of he opion. An analogous procedure is applied o node (1,U): The value of he opion if exercised afer =1 is: = V W, 1 = The value upon exercise a (1,U) is: 24

25 = V A, 1 = The value of he opion is hus Because V A,1 > V W,1, he opimal sraegy a node (1,U) is o exercise he opion. Sep 3: Decision as of December 31, 2000 (=0) The value of he opion if exercised a a laer poin in ime is: V B 1 1 = W, 0 = EQ V1 = B The value of he opion if exercised a =0 is: V A, 0 = P 0, 2 RBF 4 0, = = Thus he value of he opion a =0 is Therefore, he opimal sraegy a =0 is o pospone he ransfer of he hidden reserve. If bond prices rise by he ime =1, hen he hidden reserve should be ransferred. If bond prices fall by he ime =1, i is beer o keep waiing unil =2 and hen ransfer he hidden reserve. According o Equaion 3, he value of he righ o ransfer is 50, = 1445 CUs. This example shows ha even wih a deerminisic invesmen program a flexible (i.e., ineres-coningen) ransfer sraegy can be he opimum. In sae (1,U), he useful life effec prevails over he ime effec, which means ha an earlier ransfer o an asse wih a longer useful life is preferable; in sae (1,D), he opposie is rue. In comparison o Example 1, he value of he righ o ransfer he hidden reserve increases due o ineres rae risk (1445 currency unis as opposed o 1420 CUs). 25

26 When he volailiy parameer δ is changed, he following resuls can be found: δ Opimal Node a which ransfer Value of righ o ransfer ime is carried ou ransfer (in CUs) 1 (Example 1) Deerminisic (=1) (1,U), (1,D) Deerminisic (=1) (1,U), (1,D) Sochasic (=1,=2) (1,U), (2,DU), (2,DD) Sochasic (=1,=2) (1,U), (2,DU), (2,DD) Sochasic (=1,=2) (1,U), (2,DU), (2,DD) 2281 The following is herefore rue: A flexible ransfer sraegy (sochasic ransfer ime) is only opimal once a cerain level of ineres rae volailiy has been exceeded. From his level upward, each increase in ineres rae volailiy leads o an increase in he value of he righ o ransfer. Numerical analyses have also demonsraed such behavior for oher erm srucures a ime 0 and for oher maximum useful lives as a funcion of, n(): When volailiy is close o 0 (i.e., δ is close o 1), a deerminisic ransfer sraegy is always found o be opimal. When ineres rae volailiy rises, here are wo possible scenarios, depending on he erm srucure a ime 0 and he maximum useful life as a funcion of, n(). For some combinaions of iniial erm srucure and n(), he opimal ransfer sraegy remains idenical o he one under cerainy for all volailiy levels and he value of he righ o ransfer is hen independen of ineres rae volailiy. For all oher combinaions, he following is rue: Once a cerain level of volailiy is reached, a flexible ransfer sraegy becomes he opimum and each furher increase in volailiy beyond his level leads o an increase in he value of he righ o ransfer he hidden reserve. In addiion o he hree effecs observed under cerainy (ime effec, useful life effec, ineres rae effec), herefore, he model under ineres rae risk also includes a "volailiy effec" which is definiely ineresing from a axaion policy sandpoin. The connecion beween ineres rae volailiy and he value of he righ o ransfer ("The higher he ineres rae volailiy, he higher he value of he righ o ransfer") is reminiscen of he well-known fac from opion pricing heory ha he value of a European-syle opion rises wih increasing volailiy due o he convexiy of is payoff profile. Wha is remarkable abou his connecion is ha he conversion opion 26

27 described here is American-syle, no European-syle, and ha i is definiely exercised a some poin in ime and is hus de faco a forward conrac, which causes is payoff profile o lose he convexiy inheren o opions. Summary In his paper, he opimal iming of hidden reserves ransfers is derived wih special aenion o he erm srucure of ineres raes and ineres rae risk. The paper presens one model under cerainy and, as a generalizaion of his model, anoher model under ineres rae risk. In boh models, he crierion used for decision-making is he value of he righ o ransfer, which can be inerpreed as he iniial cos of a replicaing/hedging sraegy for ax paymens incurred/avoided. In he model under cerainy, he ne presen value concep is used o derive he value of he righ o ransfer. The procedure used in he model under ineres rae risk is a combinaion of flexible planning and he no-arbirage approach common in derivaives pricing. I is demonsraed ha he righ o ransfer hidden reserves wih flexible iming is equivalen o an American-syle conversion opion (beween zero-coupon bonds mauring a he end of he ransfer period and an equally weighed index composed of zero-coupon bonds wih differen mauriies). In addiion, he impac of erm-srucure volailiy on he value of he righ o ransfer is analyzed. The echnique presened in his paper can also be used o solve oher iming problems resuling from rade-offs beween early and lae ax paymens/ax benefis. References Aharony, J./Lin, C.-J./Loeb, M. P. (1993), Iniial Public Offerings, Accouning Choices, and Earnings Managemen, Conemporary Accouning Research 10 (1), Balsam S. (1998), Discreionary Accouning Choices and CEO Compensaion, Conemporary Accouning Research 15 (3), Barov, E. (1993), The Timing of Asse Sales and Earnings Manipulaion, The Accouning Review 68 (4),

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