COMMON FLAWS IN IMPLEMENTING PAYMENT TERMS ADJUSTMENTS: THE EFFECT OF BENCHMARK CHOICE ON THE ARM S-LENGTH TEST

Transcription

1 13 November 2002 OMMON FLAWS IN IMPLEMENTING PAYMENT TERMS ADJUSTMENTS: THE EFFET OF BENHMARK HOIE ON THE ARM S-LENGTH TEST Published in BNAs Tax Managemen Transfer Priing Repor Vol 11 No 14. by NERA onsulan Nihan Mer-Beydilli NERA Senior Analys Esra Suzme

2 ommon Flaws in Implemening Paymen Terms Adjusmens: The Effe of Benhmark hoie on he Arm s-lengh Tes By Nihan Mer-Beydilli and Esra Suzme * Ideally, esing he arm s-lengh naure of ransaions beween affiliaed eniies relies on ouside evidene from ompanies ha have idenial or similar ransaions wih independen paries. Unforunaely, suffiien ransaional priing daa are ofen no readily available from publi soures. In hese ases, he analysis of arm s-lengh pries relies on publily available profiabiliy daa from omparable ompanies. When using profiabiliy of ouside ompanies, omparabiliy wih respe o erain variables affeing eah firm s profiabiliy and apial sruure beomes an imporan issue. One suh variable is he level of paymen erms. This arile examines he signifiane of seleing differen benhmarks for implemening erms adjusmens. I demonsraes how and when he hoie of benhmark paymen erms -- he days payable and reeivable of he esed pary, he omparables, or some oher norm -- an maerially affe he final es resul. As a general proposiion, he auhors onlude ha he hoie of he benhmark affes he final resul and herefore ha he benhmark should ordinarily be deermined by he arm s-lengh paymen erms of he omparables. Paymen Terms Differenes in apial employed and profiabiliy arise in par due o varianes in he erms of rade wih usomers and suppliers. Paymen erms affe reeivable and payable balanes and, herefore, apial employed. The paymen period represens finaning graned o he buyer in ase of aouns reeivable or obained from he seller in ase of aouns payable. Boh require -- in addiion o he required reurn for he underlying produ or servie -- a separae rae of reurn ha is ypially negoiaed a he margin using ineres raes for shor-erm finaning. Hene, differenes in paymen erms imply differenes in operaing profis due o he finaning graned o usomers or obained from suppliers. If no eliminaed, hese differenes in paymen erms an disor he measuremen of arm s-lengh profis. Transfer priing regulaions agree on he neessiy and appropriaeness of making an adjusmen for erms of rade o improve omparabiliy whenever here are maerial differenes in he level of paymen erms beween he esed pary and he omparable * Nihan Mer-Beydilli is a onsulan and Esra Suzme a Senior Analys a Naional Eonomi Researh Assoiaes, In. The auhors would like o hank Harlow Higinboham for his valuable onribuions and suppor in wriing his arile

3 ompanies. They do no provide lear guidane, however, as o wha he benhmark paymen erms should be. Regs (d)(3)(ii)(7) saes ha if he ime for paymen in a onrolled ransaion differs from ha in an unonrolled ransaion, an adjusmen should be made if suh differene would have a maerial impa on prie. Regs ()(2)(iv) saes, as an example, ha where maerial differenes exis in aouns payable among he omparable ompanies and he esed pary, i is appropriae o adjus he operaing profi of eah pary by an impued ineres harge alulaed on eah pary s aouns payable. This suggess ha aouns payable balanes should be adjused o zero days and he ineres effe assoiaed wih i should be inluded in operaing profis. Similarly, Regs (e), Example (6)(ii), adjuss boh he esed pary and he omparables o zero aouns payable, whereas Regs (e), Example (5), adjuss he omparables o he esed pary s aouns reeivable erms. 1 A he same ime, an updaed Inernal Revenue Servie sudy guide on Advane Priing Agreemens ( A ) argues ha adjusing omparables o he esed pary erms or he esed pary o he omparables erms or boh paries o zero paymen erms should yield he same resuls and ha he A program ypially adjuss he omparables o he esed pary erms. 2 Organizaion for Eonomi ooperaion and Developmen guidelines, on he oher hand, sae ha o make appropriae adjusmens o esablish arm s lengh ondiions (or a range hereof), i is neessary o ompare aribues of hese ransaions or enerprises ha would affe ondiions in arm s lengh dealings, inluding he onraual erms. 3 This wording suggess a preferene for benhmarking he esed pary o he arm s-lengh paymen erms of he omparables raher han he oher way around. As we will demonsrae, he disinion an indeed make a differene. Reen ariles on erms of rade adjusmens fous primarily on alernaive ways o ompue he implied ineres omponen of aouns reeivable and aouns payable. hrisian Sholz and ohers disuss various approahes o breakdown sales or os of sales ino wo basi omponens: 1) he prie paid for he underlying ommodiy and 2) 1 anada s regulaions, irular 87-2R, seion 1.3, require adjusmen o he erms and ondiions of he ransaion ha would have been made beween arm s lengh persons. In onras, seion 3.1(2) of Japan s Transfer Priing irular released in June 2001 reommends adjusing omparable ompanies o he esed pary s paymen erms. (8 Transfer Priing Repor 472, 9/29/99; 10 Transfer Priing Repor 260, 8/8/01) 2 11 Transfer Priing Repor 478, 10/2/02 3 OED Transfer Priing Guidelines for Mulinaional Enerprises and Tax Adminisraions, 1995, paragraph

4 he ineres omponen reeived or paid for he redi graned or obained 4. Then, by eliminaing he ineres omponen ompleely, hey ompue eah firm s profis as if he firm were dealing on a ash basis wih zero paymen erms. The balane shee aouns are adjused aordingly. Alernaive formulaions used o ompue he ineres effe resul in adjused operaing profis ha differ only marginally from eah oher when adjused o he same level of benhmark erms. 5 Wha he auhors do no onsider, however, is he benhmark level iself o whih he erms are adjused. Oher praiioners disuss he signifiane of he hoie of benhmark erms in deermining arm s lengh resuls in onjunion wih he alernaive ways o ompue he implied ineres omponen of aouns payable and reeivable. Vior Miesel and Rohi Verma show ha using exreme values of benhmark erms an maerially affe an arm s lengh es based on he inerquarile range of omparables profi level indiaors (PLIs). 6 Speifially, hey demonsrae ha he ranking of omparables may be reversed based on he hoie of benhmark erms. The remedy hey reommend is o hoose omparables ha have a level of paymen erms similar o ha of he esed pary and hen o use he average of he omparables paymen erms as he benhmark. 7 T So Newlon fouses primarily on he need o adjus operaing profi for differenes in paymen erms in order o measure arm s lengh profis reliably, and he onludes ha as long as he omparables and he esed pary are adjused o a ommon level of paymen erms, he hoie of he ommon paymen erms is a maer of onveniene. 8 Newlon also draws aenion o an implii assumpion: ha he overall rae of reurn on operaing asses is equal o he shor-erm ineres rae when aouns payable are dedued from operaing asses wihou any adjusmens o he operaing profi, as was required by he 1993 emporary U.S. ransfer priing regulaions. The examples he provides adjus aouns payable and aouns reeivable o zero, impliily impuing shor-erm ineres raes on aouns payable and reeivable balanes in heir enirey. an one reliably impue shor-erm ineres raes o aouns reeivable or payable when adjusing omparables and he esed pary o zero paymen erms? Alhough shor-erm ineres raes may be applied a he margin o value inremenal differenes in rade erms, i does no follow ha all aouns payable and aouns reeivable are valued a suh ineres raes. This is anoher reason why, as a general rule, i is bes o minimize 4 See Sholz, hrisian M.; Akerman, Abraham; and Shmi, Volker, Adjusing Profi Level Indiaors for Differen Levels of Working apial, 10 Transfer Priing Repor936, 3/20/ Transfer Priing Repor , 3/20/02. 6 See Miesel, Vior, and Verma, Rohi, Transfer Priing Eonomis: Poenial Errors in Paymen Terms adjusmens, The Inernaional Tax Journal, Summer Miesel and Verma, p Newlon, T. So, Dealing wih Ineres-Free omparables when Applying he omparable Profis Mehod, 3 Transfer Priing Repor533, 11/2/

5 he adjusmens made o he omparables operaing a arm s lengh by adjusing he esed pary o he omparables erms and adjusing only a he margin for differenes among he omparables. Benhmark Terms Maer Muh of he disussion on erms adjusmens has foused on alernaive formulaions used o ompue he ineres effe assoiaed wih paymen erms. However, he hoie of formulaion does no maer muh. 9 Wha does maer is he direion of he adjusmen and he benhmark level of paymen erms. Terms adjusmens an lead o maerially differen implied arge profis for he esed pary depending on wheher he omparable ompanies are adjused o he esed pary erms, or he esed pary is adjused o he omparable ompanies erms, or boh he omparables and he esed pary are adjused o a ommon benhmark level of paymen erms (e.g., zero erms), as illusraed in Table 1. Table 1 Targe Profis under Alernaive Benhmark Payables Terms Aual Tesed Pary as Adjused omparable as Adjused omparable To To Tesed Tesed To Zero To Zero omparable s Pary s Pary Terms Terms Terms Terms Sales OGS Operaing expense Operaing profi Operaing asses Aouns payable apial employed (E) ROE 39.0% 19.2% 15.9% 13.5% 44.8% 33.6% Memo: Days payable Adjused E/OGS 64.2% 28.9% 38.6% 51.1% 43.3% 76.7% Targe Profi alulaion: Adjused E of he esed pary omparables ROE 39.0% 33.6% 44.8% Operaing profi a omparables erms Less: Adjusmen o aual erms Equals: Implied arge profi a aual erms Peren o OGS 14.5% 15.8% 13.0% Noes: 1 A shor-erm ineres rae faor of 6% is used for he ompuaion of adjusmens o os of goods sold (OGS) and operaing profi. 9 See Sholz, Akerman, and Shmi

6 Table 1 presens an example using reurn on apial employed (ROE) as he PLI ha illusraes how he implied arge profi for he esed pary differs depending on he benhmark level of paymen erms used. In his example, he omparable and he esed pary have 45 and 80 days payable, respeively. The omparable is more apial inensive han he esed pary, as indiaed by he respeive apial employed o os of sales raios (64.2 peren versus 28.9 peren). ompuaions of erms-adjused operaing profi and apial employed for he esed pary and he omparable under alernaive benhmark payables erms appear in he op porion of Table 1. For example, in he hird olumn of he able, he esed pary s os of goods sold (OGS) and aouns payable are adjused from 80 days paymen erms o 45 days paymens erms: 10 Adjused aouns payable 45 x Aual aouns payable /80 45 x 20 / Adjused OGS Aual OGS peren x ( ) 89.5 Ineres rae faor x (Adjused aouns payable - Aual aouns payable) Implied Targe Profi The boom porion of Table 1 presens he arge profi alulaion under he alernaive erms adjusmen benhmarks. Implied arge profi is he arm s-lengh profi he esed pary should earn. I is alulaed in wo seps. The firs sep is o ompue he operaing profi of he esed pary a he omparable s rae of reurn: apial employed of he esed pary adjused for differenes in paymen erms is muliplied by he erms-adjused ROE of he independen omparable. The resuling operaing profi represens he arm slengh profi for he esed pary a he benhmark paymen erms of he omparable raher han a is own paymen erms. In he seond sep, he erms adjusmen is reversed by subraing he adjusmen o operaing profi o ompue he arm s-lengh profi for he esed pary ha refles is own aual paymen erms. This eliminaes he profi inremen aribuable solely o he hange in esed pary s apial employed resuling from he erms adjusmen. The resuling implied arge profi represens he arm s lengh reurn ha he esed pary should earn based on ouside evidene from omparables performing similar funions and bearing similar risks. As he illusraive alulaions in Table 1 indiae, he resuling differenes in implied arge profi are maerial, ranging from 13.0 peren o 15.8 peren of OGS depending upon he benhmark seleed for payables erms. The variaion in implied arge profis are aribuable o differenes in he raio of he adjused denominaor of he PLI apial 10 In praie, he OGS adjusmen formula is usually refined by dividing he aouns payable erm by he disoun faor (1+ineres rae*days payable/360), as desribed in Miesel e al. This refinemen does no maerially affe he resuls indiaed in Tables 1-3 or he onlusions of his paper

7 employed in his ase o sales and o os of sales of he esed pary and hose of he omparable ompanies. The implied arge profis would be he same regardless of he benhmark paymen erms only if he raios of adjused denominaor of he PLI o sales and o os of sales of he esed pary and he omparables were idenial. See Appendix A for a mahemaial proof of his proposiion. In praie, he raios of he adjused denominaor of he PLI o sales and o os of sales of he omparable ompanies ofen differ from hose of he esed pary. In he alernaive, praiioners migh onsider seleing omparables ha have he same or similar raios of adjused denominaor of he PLI o sales and o os of sales o hose of he esed pary. The problem wih his approah is ha one migh hereby disard many omparables ha are oherwise suiable and ha provide valuable insighs and daa onerning arm s-lengh priing. Given he diffiulies of finding omparables whose funional and risk profiles are he same as or similar o he esed pary, i may be impraial or unreasonable o eliminae omparables simply on he basis of apial inensiy or similar raios so as o reae a sample of omparables wih raios of adjused denominaor of PLI o sales and o os of sales equal or lose o hose of he esed pary. Aordingly, he hoie of he benhmark paymen erms beomes riial. Adjusing o Zero As disussed in furher deail below, adjusing paymen erms o zero as suggesed by he U.S. regulaions and as praied by many praiioners may no improve omparabiliy beween he esed pary and omparables, and hus may no produe he mos reliable resuls. To demonsrae his, he implied arge profi for he esed pary, is expressed as a funion of he differenes in he adjused apial employed o sales and o os of sales beween he omparables and he esed pary (see Appendix A). The implied arge profi of he esed pary is hen ompued when: (1) boh he esed pary and he omparable ompanies are adjused o zero paymen erms; and (2) he esed pary is adjused o he omparable ompanies paymen erms. Finally, he differene beween he implied arge operaing profi margins, expressed as a markup on oal oss, is examined. 11 This margin differene in implied arge profis is found o be a funion of he exising differene beween he adjused apial employed o os of sales raios of he omparables and he esed pary as well as he differene in he adjused ROE of he omparables due o erms adjusmens, as expressed in he following equaion. (The derivaion of his general equaion is provided in Appendix B.) 11 Essenially equivalen expressions an be derived for operaing profi reurn on sales margins wih eiher aouns reeivable erms adjusmens or aouns payable erms adjusmens; he magniude of he margin differenes (and of he implied disorion due o benhmarking o zero paymen erms) for a given differene in paymen erms is appreiably smaller han wih ROE or reurn on asses as he PLI, bu nonzero in any ase

8 T E, * ( ROE ) where ( TΠ )/ margin differene in arge profi when boh he omparables and he esed pary are adjused o zero paymen erms and when he esed pary is adjused o he omparables, (E /), differene beween he raio of adjused apial employed o os of sales of he omparables and ha of he esed pary, (ROE ) differene beween he aual and adjused ROE of he omparable ompanies when he omparables are adjused o zero paymen erms. When he wo omponens of he righ-hand side of he above equaion he differene beween he raio of adjused apial employed o os of sales of he omparable and ha of he esed pary and he differene beween he aual and erms-adjused PLI of he omparable are nonzero, adjusing boh he esed pary and he omparable o zero paymen erms an poenially lead o maerially differen implied arge profis. The firs variable, i.e., he differene beween he raios of adjused apial employed o os of sales of he omparable and ha of he esed pary, is a funion of omparabiliy beween he omparable and he esed pary. When omparabiliy is poor, i is highly likely ha he raio of adjused apial employed o os of sales of he esed pary and ha of he omparable will be differen, leading o a nonzero value. The seond variable, i.e., he differene beween ROE of he omparable when adjused o zero paymen erms and unadjused ROE, on he oher hand, is a funion of he level of paymen erms of he omparable. This differene is always nonzero. Moreover, he more ha he paymen erms of he omparable diverge from zero, he greaer will be he differene beween he ROE values of he omparable when adjused o differen benhmark erms. This proposiion suggess ha one would obain a differen implied arge profi by adjusing boh he esed pary and he omparables o zero paymen erms han is obained by adjusing he esed pary o omparables paymen erms. Furhermore, as he omparabiliy beween he omparables and he esed pary deerioraes, and as omparables paymen erms diverge from ypially observed levels of paymen erms, he divergene in resuls is amplified. Tables 2 and 3 illusrae his amplifying effe, using he same daa provided in Table

9 Table 2 Margin Differene in Implied Targe Profi under Differen Benhmark Terms Zero Paymen Days vs. omparables Average Paymen Days 1 Differene in Terms-Adjused apial Employed/OGS Tesed Pary omparable Differene Noes: Terms Adjusmen Differene in omparable s ROE Differene in Targe Profi/OGS 60.0% 76.7% 16.7% 5.4% 0.9% 51.1% 76.7% 25.6% 5.4% 1.4% 40.0% 76.7% 36.7% 5.4% 2.0% 30.0% 76.7% 46.7% 5.4% 2.5% 20.0% 76.7% 56.7% 5.4% 3.1% 10.0% 76.7% 66.7% 5.4% 3.6% 1 Values are based on he example provided in Table 1. In Table 2, we assume ha he raio of adjused apial employed o os of sales of he esed pary varies from 10 peren o 60 peren, while ha of he omparable remains onsan assuming a payables inensiy of zero days. The erms adjusmen differene in omparable s ROE is ompued vis-à-vis 45 days paymen erms. Table 2 illusraes how he margin differene grows as he differene beween he raios of adjused apial employed o os of sales of he esed pary and he omparable grows. To illusrae how he margin grows as he omparable s paymen erms diverge from zero, he ompuaions in Table 3 refle payable erms of 45, 90, and 135 days for he omparable. Table 3 Summary -- Margin Differene in Implied Targe Profi under Differen Benhmark Terms - Zero Paymen Days vs. omparables Average Paymen Days Terms-Adjused apial Employed/OGS for he Tesed Pary Differene in Implied Targe Profi/OGS a 45, 90, and 135 Days Payable for he omparable 45 days 90 days 135 days 60.0% 0.9% 2.2% 4.2% 51.1% 1.4% 3.4% 6.6% 40.0% 2.0% 4.9% 9.7% - 8 -

10 30.0% 2.5% 6.2% 12.4% 20.0% 3.1% 7.6% 15.1% 10.0% 3.6% 8.9% 17.8% As he paymen erms of he omparable ompanies diverge from zero (e.g., 45 days, 90 days, 135 days payable, e.), he differene beween implied arge profi margins inreases more han proporionaely beause he differene beween he aual and adjused ROE of he omparables inreases as he benhmark paymen erms inrease. For example, when he omparable ompany has 45 days of payables ousanding and he erms-adjused apial employed o os of sales raio for he esed pary is 40 peren, he differene in implied arge profi margins is 2 peren. This means ha if boh he esed pary and he omparables are adjused o zero paymen erms, he arge profi margin for he esed pary will be 2 peren higher han i would be if he esed pary is adjused o omparables paymen erms. Had he aouns payable of he omparable ompanies been 90 days insead of 45 days, he margin differene in he implied arge profi for he esed pary when adjused o zero days versus he omparable s average erms would have been 4.9 peren. onlusion onrary o he guidane provided by he U.S. regulaions, and onrary o widely adoped erms adjusmen praies, adjusing boh he esed pary and he omparables o zero paymen erms does no always generae he mos reliable resuls. Two faors mus be aken ino aoun when seleing a mehod for adjusing for he varianes beween he paymen erms of he omparables and he esed pary: (1) he degree of omparabiliy beween omparables and he esed pary as measured by he differene beween he raio of he adjused denominaor of he seleed PLI o sales and o os of sales, and (2) he omparables level of paymen erms. When omparabiliy is poor and omparables operae a relaively long paymen erms, adjusing o zero paymen erms may resul in subsanially differen implied arge profis for he esed pary. In hese irumsanes, he auhors sugges adjusing he esed pary o he omparables average erms of rade beause he omparables daa refle an arm s-lengh negoiaion of paymen erms. Adjusing he omparables o a differen level of benhmark erms suh as zero erms disors he arm s-lengh naure of he observed profis of he omparable ompanies if he omparables have differen underlying apial inensiy raios han he esed pary. Moreover, he empirial basis for impuing a shor-run ineres rae of reurn o he enire amoun of a ompany s payable or reeivable balane, insead of simply o inremenal differenes in suh balanes a he margin, is no well esablished and may disor he implied resuls. Aordingly, he mos reliable way o adjus for differenes in paymen erms is o adjus he esed pary s finanials so ha hey refle he average of he omparable ompanies paymen erms

11 PENDIX A Terms adjusmens an be performed by adjusing eiher he omparables o he esed pary s erms or he esed pary o he omparables erms or boh he omparables and he esed pary o ommon benhmark erms e.g. zero paymen erms. These hree approahes generae he same resuls for he implied arge profi of he esed pary as long as he adjused denominaor of he PLI o sales and he adjused denominaor of he PLI o os of sales raios of he omparables and he esed pary are he same. The mahemaial proof of his proposiion is provided below for aouns payable using ROE as PLI, and he parallel proof for aouns reeivable adjusmen is essenially equivalen. ase 1: Boh he omparable and he esed pary are adjused o zero paymen erms When boh he omparable ompany and he esed pary are adjused o zero paymen erms, implied arge profi of he esed pary an be expressed as follows: i [1] ( )(E ) + i E where TΠ implied arge profi of he esed pary operaing profi of he omparable ompany before he erms adjusmen E apial employed of he omparable ompany before he erms adjusmen hange in aouns payable of he omparable when adjused o benhmark erms i shor-erm ineres rae E apial employed of he esed pary before he erms adjusmen hange in aouns payable of he esed pary when adjused o benhmark erms [2] - [3] - where and refer o aouns payable of he omparable ompany and he esed pary before he erms adjusmen, respeively. Subsiuing equaions [2] and [3] in equaion [1], equaion [1] beomes: [1`] ( E + i + )(E + )

12 Assuming omparables and he esed pary s adjused apial employed o os of sales raios are he same, he relaionship beween he omparable ompany and he esed pary an be saed as: [4] E E where omparable s os of sales esed pary s os of sales Subsiuing equaions [2], [3], and [4] in equaion [1`], equaion [1`] simplifies o: [1``] + i ase 2: Tesed pary is adjused o omparable s paymen erms When he esed pary is adjused o omparable ompany s paymen erms, implied arge profi of he esed pary an be expressed as follows: [1] ( )(E ) + i E [2] ( ) Subsiuing equaion [2] in equaion [1], equaion [1] beomes: [1`] ( E )(E + ) + i Assuming he adjused apial employed o os of sales raio of he esed pary and he omparable is he same, he relaionship beween he esed pary and he omparable ompany an be saed as: [3] E E E

13 Subsiuing [3] in equaion [1`], equaion [1`] simplifies o: [1``] + i ase 3: omparable is adjused o esed pary s paymen erms When he omparable ompany is adjused o esed pary s paymen erms, implied arge profi of he esed pary an be expressed as follows: i [1] ( )(E ) E [2] ( ) Subsiuing equaion [2] in equaion [1], equaion [1] beomes: [1`] ( E / / + i + ) E Assuming he adjused apial employed o os of sales raio of he esed pary and he omparable is he same, he relaionship beween he omparable ompany and he esed pary an be saed as: [3] E E Subsiuing equaions [2] and [3] in equaion [1`], equaion [1`] simplifies o: [1``] + i The implied arge profi of he esed pary redues o he same equaion (equaion [1``]) in all ases. The differene beween he adjused apial employed o os of sales raio of he omparable ompany and ha of he esed pary and he adjused ROE of he omparable ompany are he drivers of differen implied arge profis observed

14 depending on he benhmark paymen erms used. To demonsrae his, he implied arge profi expressed in erms of he differene beween he adjused apial employed o os of sales raio of he omparable ompany and ha of he esed pary is derived for he hree ases desribed above. The differene is defined by δ: δ E E ase 1: Boh he omparable and he esed pary are adjused o zero paymen erms i [1] ( )(E ) + i E Adjused apial employed of he esed pary an be expressed as: E [2] E ( δ ) Subsiuing equaion [2] in equaion [1], equaion [1] beomes: [1`] i T i ( ) δ E + i [3] - [4] - Subsiuing equaions [3] and [4] in equaion [1`], equaion [1`] beomes: [1``] + i + i ( ) δ E + The hird erm of equaion [1``] is he adjused ROE of he omparable ompany imes he dela and os of sales of he esed pary. Equaion [1``] hen simplifies o: [1```] + i δ E

15 ase 2: Tesed pary is adjused o omparable s paymen erms [1] ( )(E ) + i E Adjused apial employed of he esed pary an be expressed as: E [2] E ( δ ) Subsiuing equaion [2] in equaion [1], equaion [1] beomes: [1`] T ( ) δ E + i [3] Subsiuing equaion [3] in equaion [1`], equaion [1`] beomes: [1``] + i ( ) δ E The hird erm of equaion [1``] is he adjused ROE of he omparable ompany imes he dela and os of sales of he esed pary. Equaion [1``] hen simplifies o: [1```] + i δ E ase 3: omparable is adjused o esed pary s paymen erms i [1] ( )(E ) E Adjused apial employed of he esed pary an be expressed as: E [2] E ( δ ) Subsiuing equaion [2] in equaion [1], equaion [1] beomes:

16 [1`] i δ ( E i ) [3] Subsiuing equaion [3] in equaion [1`], equaion [1`] beomes: [1``] + i δ ( E i ) The las erm of equaion [1``] is he adjused ROE of he omparable ompany imes he dela and os of sales of he esed pary. Equaion [1``] hen simplifies o: [1```] + i δ E Thus, he implied arge profi of he esed pary redues o he same equaion (equaion [1```]) in all ases

17 PENDIX B The differene beween implied arge profis under ase 1 and ase 2 an be expressed as follows: + i [1] ( ) 1 ( ) 2 i + i δ E + + i + δ E Equaion [1] simplifies o: [1`] δ E E + i + Subsiuing δ in equaion [1`], equaion [1`] an be expressed as: [1`] T E + E + E E + i + The margin differene in implied arge profis under ase 1 and ase 2 an be expressed as a funion of he differene in he raios of adjused apial employed o os of sales of he esed pary and omparable ompanies and he differene in adjused PLI of he omparable ompanies under ase 1 and ase 2. T E [1`] * (ROE )