The Value of Negotiating Cost-Based Transfer Prices

Transcription

1 Volume ssue November The Value of Negotatng Cost-Based Transfer Prces Anne Chwolka, Department of Management and Economcs, Otto-von-Guercke-Unversty Magdeburg, Germany, E-mal: Jan Thomas Martn, Department of Busness Admnstraton and Economcs, Belefeld Unversty, Germany, E-mal: Drk Smons, Department of Accountng, Busness School, Mannhem Unversty, Germany, E-mal: Abstract Ths paper analyzes the potental of one-step transfer prces based on ether varable or full costs for coordnatng decentralzed producton and qualty-mprovng nvestment decsons. Transfer prces based on varable costs fal to nduce nvestments on the upstream stage. n contrast, transfer prces based on full costs provde strong nvestment ncentves for the upstream dvsons. However, they fal to coordnate the nvestment decsons. We show that negotatons prevent such coordnaton falure. n partcular, we fnd that the frm benefts from a hgher degree of decentralzaton so that total proft ncreases n the number of parameters beng subject to negotatons. Keywords: transfer prcng, centralzed management, decentralzed management, nvestment, product dfferentaton, negotatons Manuscrpt receved Aprl 0, 009, accepted by Raner Nemann Accountng) May, 00. ntroducton n the lterature, dfferent transfer-prcng schemes are recommended dependng on the purpose they are ntended for. On the one hand, twostep transfer prces consstng of a unt prce compensatng for varable producton costs and an up-front lump-sum payment to cover fxed costs are suggested for the purpose of coordnatng nvestment and producton actvtes wthn dvsonalzed frms e.g., Drury 004: 900). On the other hand, the OECD recommends among others a cost-plus scheme for nternatonal taxaton OECD 999: -). Emprcally, one-step costbased transfer prcng prevals n busness practce see Secton ). However, t s well known from the lterature that cost-based types of transfer prces exhbt sgnfcant dsadvantages wth respect to nvestment ncentves n decentralzed settngs. Takng nto consderaton that these nvestments consttute a crucal strategc compettve advantage, fndng an adequate transfer-prcng polcy s an mportant manageral ssue. As an example, consder today s markets where frms have the opportunty to attract customers attenton by product dfferentaton. The responsblty for product mprovements and development or for ensurng hgh qualty s typcally placed not on one but on several dvsons. Plausbly, mprovng the qualty of the fnal product s acheved by jont actvtes of the dvsons, meanng that n dvsonalzed frms coordnaton of such knd of actvtes s necessary n order to explot synergstc effects. The goal of our paper s to analyze the nvestment ncentves generated by one-step cost-based transfer prces. Our theoretcal analyss bulds on the emprcal fact that these transfer prces preval n busness practce. We start by replcatng the well-known nvestment dstortons for varable cost-based and full cost-based transfer prces. Coupled wth the emprcally observable domnance of cost-based transfer prces ths s the motvaton for analyzng the potental of negotatons for mtgatng the nvestment ncentve problem by varyng the extent of negotatons. The major nnovaton of our paper s that we do not only account for nterstage but also for ntrastage dependences of the dvsons nvestment decsons. Ths means that we analyze nterdependences across the stages -- as t s commonly done n the lterature -- as well as goal conflcts between

2 Volume ssue November dvsons on the same stage. Ths modfcaton enables us to analyze nterestng coordnaton ssues on the upstream stage and to demonstrate how negotatons between the dvsons and the extent of delegaton nfluence the performance of transfer prcng. n dong so, we also resolve the dchotomy of cost-based and negotated transfer prces. Moreover, we do not conceve transfer prcng as a separate ncentve system whch can be optmzed n solaton. Rather, we consder the assgnment of decson rghts wthn the frm also as varable. We demonstrate that central management may reach better coordnaton by delegatng more -- rather than fewer -- aspects of the transferprcng system, whch has mportant manageral mplcatons. The remander of the paper s organzed as follows. Secton provdes a bref lterature revew. The organzatonal settng s descrbed n the thrd secton together wth the underlyng assumptons. Secton 4 contans the model results for dfferent settngs. ntally, the frst-best soluton s derved. Subsequently, we demonstrate that none of the consdered schemes s able to nduce nvestments n all of the three dvsons. Moreover, transfer prcng based on full costs s prone to suffer from coordnaton falure. n ths context, ntroducng negotatons on both the nvestments and the transfer prces s shown to ensure optmal coordnaton. The paper concludes wth manageral mplcatons. Appendces A and B contan the proofs and an example, respectvely. Addtonal explanatons concernng the negotatons under transfer prcng based on full costs are provded n Appendx C. Related lterature Related lterature falls nto an emprcal and a theoretcal strand. From an emprcal perspectve, t can be confrmed that one-step cost-based transfer-prcng schemes preval n busness practce. Ths observaton s supported by the survey of emprcal studes n Horngren, Datar, and Foster 006: 774). t s confrmed and extended by Ernst & Young 00: 9) who document the predomnance of cost-based transfer-prcng schemes rrespectve of the type of transacton n the context of nternatonal taxaton. t s vald to buld on the fndngs of Ernst & Young 00) n our context because Ernst & Young 00: 7) fnd that 80 percent of 64 multnatonal parent companes use the same transfer prce for manageral and tax purposes. Czechowcz, Cho, and Bavsh 98: 59) fnd a correspondng share of 84 percent. Furthermore, although two-step transfer prces provde more flexblty by allowng for a lump-sum transfer payment to cover fxed costs, emprcal evdence suggests that the prevalence of two-step transfer prces s extremely low: Accordng to Tang 99: 7), only one percent of 4 frms employ two-step schemes to prce natonal or nternatonal transfers. Wth respect to the queston of whether transfer prces are admnstered or negotated, the survey by Horngren, Datar, and Foster 006: 774) seems to document a rather low prevalence of negotated transfer prces rangng between and 6 percent. Yet, Eccles ponts out a shortcomng of many emprcal studes whch do not consder negotatons gven a certan prcng scheme. Accordngly, referrng to frms that transfer at a proft markup based on a gven scheme, Eccles 985: 4) states that seventy-two percent of these frms sad yes when asked f some knd of negotaton was also nvolved. From a practcal as well as a theoretcal perspectve, coordnaton s an mportant functon of transfer prces, see, e.g., Drury 004: 88) or Grabsk 985: 5). Ths becomes evdent wth the ntroducton of relaton-specfc nvestments, see, e.g., the semnal papers of Edln and Rechelsten 995, 996) or Holmstrom and Trole 99) where the hold-up problem s hghlghted. Extensons have been made by Baldenus 000), Welenberg 000), Anctl and Dutta 999), and Baldenus, Rechelsten, and Sahay 999). All these papers focus on freely negotated transfer prces,.e., wthout a gven prcng scheme, or on the comparson of negotated and cost-based transfer prces. Sahay 00) analyzes addtve versus multplcatve markups on costs, whereas Lengsfeld, Pfeffer, and Schller 006) analyze the comparatve advantages of transfer prces based on actual and standard costs. All these contrbutons assume nvestments nducng a reducton of producton costs or an ncrease n sales revenue. The consdered nvestments mght be called egostc snce t s assumed that t s the nvestng dvson whch drectly benefts from the nduced returns see Che and Hausch 999, for a smlar termnology). Smlar to the papers cted above, we consder the problem of motvatng dvsonal nvestments 4

3 Volume ssue November va transfer prces. We also rely on negotatons to overcome nterest conflcts between the dvsons. However, we do not dstngush between cost-based transfer prces on the one hand and negotated transfer prces on the other. nstead, we follow an ntegrated perspectve by extendng the soluton space provded by admnstered cost-based transfer prces by nter-dvsonal negotatons on the specfcaton of the gven prcng scheme. Another dfference of our settng s that the dvsons nvest knowng the specfed transfer prce and that each nvestment s productvty depends on the other nvestment levels. Thus, the problem of coordnatng nvestments has to be solved n the frst place nstead of a hold-up problem potentally occurrng after the nvestments have been made. Only a few other papers have ncorporated cooperatve -- nstead of egostc -- nvestments nto transfer-prcng settngs. Our nvestment settng s smlar to Johnson 006) or Chwolka and Smons 00). n contrast to ther approaches, we concentrate on transfer prces nstead of sharng rules and ncorporate negotatons. Moreover, analyzng three dvsons enables us to llustrate two dfferent knds of coordnaton problems: On the one hand the coordnaton among the upstream dvsons whch s typcally neglected n the lterature and on the other hand the tradtonal coordnaton problem between upstream and downstream dvsons. The contrbuton of our paper results from the ntroducton of a second upstream dvson. Gven the tradtonal settng wth one upstream and one downstream dvson, t seems obvous that the frm faces an overnvestment problem on the upstream producton stage when transfer prces cover full costs plus a multplcatve markup. n our extended settng, we not only confrm ths ntuton but show also that an undernvestment problem may occur as well. More mportantly, we show that ensurng nvestments and producton does not only requre solvng the coordnaton problem between the producton stages, but also between the dvsons on the same stage. Accordngly, we examne how negotatons over the nvestment levels nduces coordnaton on the upstream producton stage. We extend the analyss by demonstratng that the frm benefts from havng the upstream dvsons not only negotate nvestments but also transfer prces. Model descrpton We consder a frm consstng of three nvestment centers D, {,, }, beng subordnated to headquarters, HQ. HQ confnes tself to nstallng a transfer-prcng system -- where transfer prces do not necessarly have to be admnstered -- for coordnatng the nvestment centers. We assume that transfer prces have to be defned before any actvtes take place. One justfcaton for ths assumpton are requrements demanded by tax authortes or other legal requrements. HQ delegates any operatve decson to the dvsons, ncludng those referrng to the nvestment levels. All dvsons have access to external factor markets where they procure the requred raw materals and goods -- except for the ntermedate products whch are exclusvely traded between the dvsons. The upstream dvsons D and D delver ntermedate goods or servces to the downstream dvson D and are compensated va transfer-prce payments. The downstream dvson completes the product and sells t to an external market. These general assumptons are farly standard and depcted n Fgure where c symbolzes the varable costs per producton unt accrung n dvson D before accountng for transfer payments, whereas t and t are the transfer prces at whch each product unt of D and D s valued. denotes the nvestment level and equals the expected nvestment costs. x s the producton and sales quantty, and p ) s the expected sales prce. n the followng, we explan the assumptons n more detal. We assume that dvsonalzaton s gven. Headquarters s not able to calculate optmal nvestment levels because t lacks nformaton on productvty parameters. Consequently, HQ delegates the nvestment and trade decsons to the dvson managers. Ex post, HQ can nether verfy the nvestment levels nor evaluate ther optmalty, but can only observe the correspondng actual costs. However, the nvestment costs resultng from the chosen nvestment levels are stochastc. Havng a closer look at the dvsons, note that from the perspectve of organzatonal theory a major advantage of decentralzaton s greater flexblty wth respect to market demands see Grabsk 985 for reasons n favor of decentralzaton). Ths fact s ncorporated n our model by the assumpton of nformaton asymmetry between headquarters and the dvsons. Further, we assume that the 5

4 Volume ssue November dvson managers are nterested n ther respectve dvsonal proft. Ths assumpton could be justfed by the exstence of an accordng ncentve system. The nvestment-center organzaton nduces self-nterested dvsonal decsons so that any formal or nformal agreement between the dvsons has to be n the nterest of each of the dvsons. Communcaton between the dvsons s therefore of no use unless the resultng agreement s self-enforcng. Note that the three dvsons -- n contrast to HQ -- share perfect nformaton as to the transacton under consderaton. Ths assumpton s motvated by the fact that the operatve dvsons have a deeper knowledge of product-specfc data as compared to HQ. The two-stage producton process s performed by the three dvsons as depcted n Fgure. The ntermedate products cannot be sold externally so D and D are oblged to delver ther products to D. D, n turn, has to procure these specfc ntermedate goods from D and D because they are not offered on an external market. For analytcal convenence, all producton coeffcents are equal to one. The maxmal product quantty x >0 reflects capacty restrctons,.e., x [0, x]. As motvated later n the paper, the nvestments consdered here do not affect capacty. The most mportant objectve of modern frms relyng on decson decentralzaton s to handle the fragmentaton of product responsbltes. Ths holds true especally when the compettve advantage s based on product dfferentaton. Ths problem s ntegrated nto our model by focusng on qualty-mprovng nvestments. Note that the term nvestment has to be nterpreted n a wde sense n our paper. We have n mnd spendngs that are able to ncrease the customers wllngness to pay, whch depends on the product-specfc bundle of features Smon 989: ). These nvestments may be spendngs for machnes producng at a hgher qualty level, research and development expendtures mplyng an mprovement of the product s functonaltes, or organzatonal arrangements speedng up servce tmes and thus ncreasng customer satsfacton. The nterrelated effects of the dvsonal nvestments are reflected by the sales prce p whch depends on the ndvdual nvestment levels and a random varable ε. We have ) p,, )=p,, )+ε wth non-negatve nvestment level chosen by D, {,, }. An example wth a specfc prce functon s presented n Appendx B. ε s a random varable wth mean με) = 0. Thus, the expected prce s gven by E ε [ p,, ) ] = p,, ). As argued above, the prce s ncreasng n qualtymprovng nvestments. Moreover, we assume that p s strctly concave and bounded; addtonally the nput factors contrbutons to the output cannot be solated. Formally, we have ) p,, ) > 0, p,, ) j 0, j {,, }. We assume that the costs resultng from nvestment level, {,, }, are uncertan and amount to C )= + κ 0, where κ, κ, and κ are ndependent random varables wth means μκ ) = 0. Thus, the expected nvestment costs are gven by E κ [ C )] =. Actual,.e., realzed, nvestment costs are denoted by C. n order to emphasze qualty-mprovng nvestments we abstract from capacty ncreases and thus leave the quantty effect on the sales prce out of account. Observe that ths s a standard assumpton, e.g., n the target-costng lterature. n busness practce, the quantty effect s neglgbly small n several envronments: For nstance, n markets wth a hgh brand loyalty, e.g., luxury goods or certan food products, the prce senstvty s low. Smlarly, f the customer has made Fgure : Structure of the frm c x+ supplers dvson D nputs supplers tx dvson D c x+ dvson D nputs x x t x HQ p,, )x x c x+ nputs customers supplers 6

5 Volume ssue November nvestments n the past, the present buyng decson mght be predetermned. As an example consder software updates. Generally, ths phenomenon arses whenever accessores have to be bought for non-standardzed products. The tmng of decsons and actons s as shown n Fgure. n the frst step, HQ chooses a cost-based transfer-prcng scheme,.e., ether scheme v based on varable costs or scheme f based on full costs. Addtonally, the parameters determnng the chosen scheme respectvely the extent of delegaton are specfed. n the next step, the dvsons smultaneously decde on ther nvestment levels, {,, }, under perfect nformaton,.e., each dvson knows ts own as well as the others decson problems. Subsequently, D determnes the producton and sales quantty x. Fnally, product unts are manufactured and sold, the sales prce s realzed, and the realzed nvestment costs are determned, whch allows the calculaton of total and dvsonal profts. We refer to HQ s decson makng as centralzed plannng whch defnes the condtons of the subsequent decentralzed plannng,.e., nvestments and producton. We assume all managers and HQ to be rsk-neutral. The goal of HQ s to maxmze expected total,.e., frm-wde, proft: ) Π,,, x) = = E ε [ p,, ) ] p,, ) c )x = c )x = E κ [ C ) ] =. = Observe that the dvsonal profts sum up to total proft. Moreover, remember that c does not account for any transfer prces but symbolzes the costs per unt for externally procured nputs as depcted n Fgure. We assume a postve contrbuton margn whch may be mproved by dvsonal nvestments. Formally, we have Π0, 0, 0, x) > 0 and Π0, 0, 0, x)/ > 0 for x>0 and {,, }. For the frst-best stuaton, we assume nformaton symmetry between HQ and the dvsons. n the second-best stuaton, we assume that varable as well as realzed nvestment costs are observable and contractble so that the transfer-prcng schemes ntroduced and analyzed n the followng below are feasble. However, HQ s not able to observe the chosen nvestment level. Ths nformaton asymmetry s the reason for HQ to delegate decson authorty to the dvsons and to mplement a transfer-prcng system. 4 Model analyss n ths secton, we frst consder the frst-best soluton. The two followng subsectons deal wth transfer prcng based on varable and full costs, respectvely. They devate from the frst-best stuaton n that there s nformaton asymmetry between HQ and the dvsons. We refer to them as the second-best stuaton. We start the analyss of the second-best stuaton by replcatng the well-known undernvestment problem for varable cost-based transfer prces and the overnvestment problem for full cost-based transfer prces. n partcular, the transfer-prcng scheme v s based on varable costs and nduces nvestment ncentves only on the downstream producton stage. Undernvestment occurs under ths scheme snce both upstream dvsons do not nvest. n contrast, scheme f s based on full costs and has the potental to create strong nvestment ncentves on the upstream producton stage. Then, however, the transfer prce on ts own s nsuffcent to nduce coordnaton among the dvsons. We show how negotatons may remedy ths defect effectvely and may even algn upstream dvsons wth the frm s objectve. Fgure : Tme lne centralzed plannng decentralzed plannng proft generaton and allocaton 4 5 HQ chooses scheme v or f HQ specfes transfer prces t and t or delegates specfcaton to D and D ) D determnes nvestment, {,, } D decdes upon quantty x producton, realzaton and nvestment costs C of sales prce p,, ) ), sales, accountng 7

6 Volume ssue November Frst-best stuaton n the frst-best stuaton wth nformaton symmetry between HQ and the dvsons, HQ s able to determne and enforce optmal dvsonal nvestment levels and the optmal product quantty. Proposton states the frst-best soluton. All proofs are gven n Appendx A. n Appendx B we calculate the frst-best soluton for an example. Proposton. The frst-best quantty s x fb* = x. The frst-best nvestment levels *, {,, }, are postve and fnte. Wth the prce-qualty relaton as defned n equaton ) the corporate objectve functon s gven by ). The frst part of equaton ) represents the total expected contrbuton margn per product unt. By assumpton, ths margn s postve for any combnaton of nvestment levels. Hence, t s optmal for HQ to set the product quantty to ts maxmum value. 4. Transfer prces based on varable costs scheme v) Sectons 4. and 4. reflect the second-best stuaton where HQ delegates decson authorty to the dvsons and confnes tself to admnsterng the transfer-prcng system. As a frst step we analyze the nvestment ncentves of transfer prces based on varable costs. We assume that transfer prces under scheme v are defned by t v = + γ )c, {, }, where the multplcatve markup factors γ 0 ensure non-negatve dvsonal contrbuton margns on the upstream producton stage. Remember that all dvson managers are rsk-neutral and seek to maxmze ther expected dvsonal profts. The dvsonal objectve functons Π v read 4) Π v,,, x) =t v c )x E κ [ C ) ] = γ c x for the upstream dvsons D, {, }, and 5) Π v,,, x) = E ε [ p,, ) ] + γ j )c j c )x j= E κ [ C ) ] = p,, ) + γ j )c j c )x j= for the downstream dvson. Expected profts of D and D equal the dfference of the transfer payment and the sum of the varable producton and expected nvestment costs. Dvsonal expected profts n 4) mmedately show that the upstream dvsons have no ncentve to nvest at all under scheme v replcatng the undernvestment effect of varable cost-based transfer prces. n contrast to the upstream dvsons, D receves the actual turnover. n addton to ts own varable producton and nvestment costs, D has to account for the transfer payments to D and D.Accordngly, t s only optmal for D to set a postve product quantty, f ts expected contrbuton margn s non-negatve. Moreover, nducng a postve nvestment on the downstream producton stage mples a non-negatve expected proft for D. Ths requres suffcently small markups. We have the followng equlbrum n dvsonal decsons. Proposton. Presume that markup factors γ and γ under scheme v are suffcently small so that { 6) γ, γ ) γ, γ ) R + : p0, 0, 0) } + γ )c c 0 s satsfed. Then, n equlbrum, dvsonal nvestments are = = 0, > 0, and the product s marketed, x = x. Wth respect to the upstream dvsons, transfer prces based on varable costs seem to be nadequate for nducng nvestments. Accordngly, the undernvestment problem on the upstream producton stage has to be managed by other organzatonal arrangements. 4. Transfer prces based on full costs scheme f ) n ths secton, we analyze transfer-prcng schemes based on full costs wth dfferent organzatonal embeddngs. We start by showng that fully admnstered transfer prces,.e., wthout nterdvsonal negotatons, may result ether n an undernvestment or an overnvestment problem. For the overnvestment problem, nvestment ncentves on the upstream producton stage are so strong that further coordnaton n addton to the = 8

7 Volume ssue November admnstered transfer prces s needed. We demonstrate how negotatons on the nvestment levels solve the coordnaton problem. For further mprovng the nvestment levels we ntroduce fully negotated cost-based transfer prces whch allow for substantal mprovements. 4.4 The dvsonal decson problems wth full cost-based transfer prces For postve product quanttes, transfer prces based on full costs t f, {, }, are defned accordng to 7) t f = + ω ) c + C ) ) x as full cost plus markup. Otherwse, wth no sales, transfer prces are zero. ω symbolzes a multplcatve markup factor determnng dvsonal profts. We restrct our analyss to multplcatve markups, because transfer prces wth addtve markups do not provde suffcently strong nvestment ncentves for the upstream dvsons. Note that due to the uncertanty of the nvestment costs the transfer prces based on full costs are also random varables. Accordngly, the rsk-neutral dvson managers base ther nvestment decsons on the expected transfer prces t f = + ω )c + /x). Calculaton of the realzed transfer prces requres that the accountng system s able to measure the realzed nvestment costs C besde the varable costs c and the quantty x. n case the product s marketed, x>0, upstream dvson D s, {, }, objectve functon under scheme f reads 8) Π f,,, x) = E κ [ t f ] c )x E κ [ C ) ] = ω c x + ), whereas D shows expected proft 9) Π f,,, x) = E ε [ p,, ) ] ) E κ [ t f ] c x = E κ [ C ) ] = p,, )x + ω ) c + ) ) c x. x = All dvsons ncur a loss amountng to ther correspondng expected nvestment costs,fnoproducton takes place. Agan, the upstream dvsons profts are calculated as transfer payment net of producton and nvestment costs. D s proft s defned as turnover net of transfer payments, producton, and nvestment costs. D chooses quantty 0) x f,, ) x f p ) +ω ) = = 0 otherwse c + x ) c 0 maxmzng ts expected contrbuton margn and thereby ts expected dvsonal proft Π f ). Note that D bases ths decson on an expected contrbuton margn that does not only account for all varable costs but also for the expected upstream nvestment costs and a markup on all upstream costs. Ths means, n turn, that the expected nvestment costs of the upstream dvsons nfluence the producton decson whereas ts own nvestment costs are sunk. Under the assumpton that producton takes place,.e., x f,, )= x, dfferentatng expected dvsonal profts wth respect to the upstream dvsons nvestment levels and yelds ) Π f,,, x = x) = ω {, }. Otherwse no dvson nvests n order to avod a loss. Note that the dervatves n ) suggest an overnvestment problem wth respect to the upstream dvsons as long as the markup factors are postve. Loosely speakng, D and D ncrease ther dvsonal profts by ncurrng costs. n a more general settng, where the nvestments would reduce the producton costs, t would not be clear that the overnvestment problems of the upstream dvsons wll occur wth transfer prces based on full costs. Ths would depend on the effect of the nvestments on the sum of varable and nvestment costs, whch could be postve or negatve, resultng n an over- or undernvestment problem. n the followng, we dscuss the results of dfferent organzatonal scenaros. We start wth admnstered transfer prces. Here two scenaros emerge dependng on whether nter-dvsonal negotatons on the nvestment levels are prohbted or 9

8 Volume ssue November permtted. n the thrd scenaro, we modfy our assumpton of a fully admnstered transfer-prcng system and allow the upstream dvsons to determne both the nvestment levels and the markup factors n blateral negotatons. 4.5 Admnstered transfer prces wthout negotatons n an admnstered transfer-prcng system a frst alternatve for HQ s to choose negatve markups. Mathematcally, ths s a feasble soluton, although t appears to be uncommon from a busness perspectve. Wth ω < 0 dvsons D and D renounce to any nvestment, whereas D s nvestment decson s the same as n the case of transfer prces based on varable costs wth small markup factors. A second alternatve for HQ are postve markups. At frst glance, expresson ) suggests that for postve ω and ω both D and D have an ncentve to ncrease ther ndvdual nvestments unboundedly. However, excessve upstream nvestments would mply a negatve contrbuton margn for D due to the correspondng hgh expected transfer payments,.e., p,, ) = + ω )c + / x) c < 0, nducng the downstream dvson to cease producton at date t = 4 accordng to 0). Ths mples negatve profts for the upstream dvsons amountng to ther sunk nvestment costs. Hence, t s not n the upstream dvsons nterest to ncrease ther nvestments to an arbtrarly hgh level. Rather, t s optmal for each upstream dvson to rase ts nvestment to the hghest level that stll nduces the downstream dvson not to cease producton. Snce both upstream dvsons proceed n ths manner, maxmum nvestment levels depend on each other. The soluton to ths problem requres an agreement of the upstream dvsons on one combnaton of nvestment levels ensurng that D chooses a postve quantty. n the absence of further coordnaton t s therefore not obvous whch nvestment levels the upstream dvsons should choose. Moreover, nfntely many combnatons of upstream nvestments can just be borne by D. Note that any soluton leavng a postve contrbuton margn to D s not self-enforcng. The argument s as follows: Suppose the three dvsons agree on nvestment levels leavng a postve contrbuton margn for D. n ths case each upstream dvson has an ncentve to devate from the negotated agreement and to ncrease ts nvestment beyond the agreed level n order to ncrease ts respectve proft, because wth full cost-based transfer prces as defned n 7), nvestment levels and dvsonal profts are postvely related for D and D. Moreover, the upstream dvsons can ncrease ther nvestment levels and D -- behavng ratonally -- does not cease producton unless ts expected contrbuton margn s negatve. But then the upstream dvsons end up n a smlar stuaton as before the negotaton: Wthout any further agreement they do not know how to coordnate nvestment ncreases. That s why we restrct our analyss to negotatons between the two upstream dvsons leavng a zero expected contrbuton margn to D. To formalze ths dea, let f, : R + R + denote the set of combnatons of upstream nvestments beng Pareto effcent wth respect to upstream expected dvsonal profts for gven downstream nvestment. There are two cases for the parameter settng: On the one hand, t could be that there does not exst any par of upstream nvestment levels greater than zero such that x f,, )= x holds for gven. Ths s the case, e.g., f the markup factors ω are so hgh that D s contrbuton margn s negatve for all postve nvestment levels. Consequently, the upstream dvsons would not nvest,.e., f, )= { 0, 0) }, and earn zero profts. On the other hand, there could be at least one par of upstream nvestment levels such that D decdes to produce. n ths case t s nether ndvdually ratonal for the upstream dvsons to choose zero nvestments nor a combnaton of nvestment levels leavng a postve contrbuton margn to D snce by 8) they ncrease ther own profts by approprately rasng ther nvestment levels. Hence, any, ) f, ) solves ) p,, ) + ω )c c ) x = + ω ) = 0. Ths condton can be derved from 0) and s equvalent to the fact that D just earns zero expected contrbuton margn, f t decdes to produce at date t = 4. Put dfferently, wth ), ) R + denotng the solutons to ) n, )wehave f, ) ), ). = 0

9 Volume ssue November Scrutnzng condton ), we note that t generally does not sngle out a unque par of upstream nvestments. Refer to the dagram on the left-hand sde of Fgure for an llustraton of ), ) for three dfferent pars ω, ω, and ω of postve markup factors ω, ω ). The correspondng dvsonal profts are depcted n the dagram on the rght-hand sde of Fgure. Snce we know from 8) that upstream dvsonal profts are ncreasng n nvestments, any combnaton of upstream nvestments unquely corresponds to a combnaton of upstream dvsonal profts, and vce versa. Thus, both dagrams of Fgure can be derved from each other. Moreover, upstream nvestments belongng to the Pareto boundary of ), ), denoted by Î ), ), are also Pareto effcent wth respect to upstream dvsonal profts. Pareto boundares are ndcated by bold lnes n Fgure. Hence, the set of upstream nvestments nducng Pareto-effcent upstream dvsonal profts, gven downstream nvestment,s ) f, )= {Î), ) f Î ), ) { } 0, 0) f Î ), )=. f D and D are able to coordnate ther decsons, f, can be nterpreted as D s and D s optmal jont reactons. nterestngly, the Pareto boundary Î ), ) may nclude nstances of undernvestment as well as overnvestment, although D and D have strong ncentves to overnvest expressed by ). Moreover, undernvestment corresponds to hgh markup factors, and vce versa. n Fgure, parameter settng ω nduces upstream nvestments that are below the frst-best levels for both upstream dvsons. The key to ths observaton are the defntons of upstream profts n 8) and 9): Hgh markup factors on upstream producton costs mply that even small upstream nvestments consume D s total contrbuton margn. To summarze, admnstered transfer prces do not yeld a unque combnaton of upstream nvestment levels. Even though t s clear that a selfenforcng soluton always entals zero nvestment of D, the upstream dvsons do not know whch combnaton of nvestment levels they should select from the set of Pareto-effcent nvestment combnatons satsfyng ). Hence, n the consdered scenaro wth admnstered transfer prces and decentralzed operatve decson authorty, further coordnaton s necessary. 4.6 Admnstered transfer prces wth negotated nvestments n the prevous secton we have shown that admnstered transfer prces wth postve markup factors provde strong nvestment ncentves for Fgure : nvestments ), ) and correspondng dvsonal profts Π ω Π f,n, ω ω ) ω c x + 0)) ω c x + 0)) 0 0 ω ) 0) 0) ω 0 0 ω ) ω ω c x + 0)) ω c x + 0)) Π The settng underlyng both dagrams s p,, )= p θ/ = a + ) wth p = 0,θ= 50,a = a =,a =, x =, c = c = c =, and = 0. The values of the markup factors are ω, 4.),ω 4,.57), and ω =4, 4).

10 Volume ssue November the upstream dvsons. However, as both D and D want to nvest as much as possble such that producton s not stopped by D admnstered transfer prces are not suffcent to provde adequate coordnaton among all dvsons. n ths secton, the transfer-prcng system s supplemented wth nter-dvsonal negotatons on the nvestment levels. Note that the markup factors are stll assumed postve and reman under the control of HQ. Refer to Appendx C for addtonal explanatons on negotatons under scheme f. The negotaton result s an agreement between the upstream dvsons on a par of nvestments, ) satsfyng f, ),.e., we assume, ) f, ). n other words, the upstream dvsons agree on one jont reacton to gven downstream nvestment and thereby solve the coordnaton problem. Note that such an agreement between D and D does not call for a formal contract, because t s n the dvsons nterests to stck to the selected equlbrum. Thus, the queston to focus on s not enforcement, but coordnaton. Snce any par of such jont reactons entals zero contrbuton margn on the downstream producton stage, D never nvests n equlbrum and there s no pont n the downstream dvson takng part n the negotatons. Ths result s stated n the followng proposton. Proposton. The equlbrum downstream nvestment under scheme f wth gven postve markup factors and negotated upstream nvestments s = 0. The man dea of Proposton s that transfer prces based on full costs wth postve markups ncte the upstream dvsons to ncrease ther nvestments at date t = extractng all of D s contrbuton margn at date t = 4. Consequently, D has no beneft assocated to ts nvestment and thus does not nvest. Proposton 4 uses ths result to derve the equlbrum producton decson. Proposton 4. The equlbrum product quantty under scheme f wth gven postve markup factors and negotated upstream nvestments s 4) x = { x fî ), 0). 0 f Î ), 0) = The top case of 4) s straghtforward because a soluton of ) s equvalent to D not ncurrng a loss from producton. The bottom case accounts for the case that condton ) has no soluton. On further nspecton of ths condton, we notce that ts solublty depends on the markup factors whch are set by HQ: For suffcently large markup factors revenue does not cover D s producton costs and the transfer payments,.e., the left-hand sde of ) s negatve. As a consequence, D ceases producton. We get the followng exstence result concernng the markup factors. Lemma. There exst suffcently small) postve markup factors such that ), ). The followng proposton confrms that t s henceforth justfed to restrct attenton to suffcently small markup factors because otherwse HQ would never ncur a postve total proft. Proposton 5. Under scheme f wth negotated upstream nvestments, suffcently large) markup factors such that f, 0) = and = 0 are not optmal for HQ. Moreover, total proft s entrely transferred to the upstream dvsons leavng D wth zero proft. Formally, wth, ) f, 0) the equlbrum proft allocaton exhbts the property Π f,, 0, x) > 0, {, }, and Π f,, 0, x) =0. So far, the optmal upstream nvestments have been conceved as the result of negotatons between D and D. Antcpatng the equlbrum downstream decsons = 0 and x = x, ths barganng stuaton can be descrbed by the set Π f,a, R + defned as 5) Π f,a, = { Π f,, 0, x), Π f,, 0, x) ) :, ) f, 0) }. The set Π f,a, contans all Pareto-effcent profts the upstream dvsons can acheve by ther nvestment decsons. Π f,a, s ndcated by bold lnes n the dagram on the rght-hand sde of Fgure. t clearly shows that Π f,a, depends on the markup factors. Let : R + R + denote the frst-best nvestment of dvson D, {, }, for gven. Analogous to the computaton to derve Proposton, we get 0) > 0. Then, we are able to establsh the followng benchmark for nter-dvsonal negotatons.

11 Volume ssue November Lemma. There exst postve markup factors such that 0), fb 0)) f, 0). Lemma asserts that HQ may choose markup factors such that -- from HQ s perspectve -- the most favorable combnaton of upstream nvestments fb 0), fb 0)) s a feasble and Pareto-effcent result of the negotatons between D and D.n Fgure ths s the case for settngs ω and ω. Yet, generally the dvsons only pck ths pont by chance. Theoretcally, the partes could apply a cooperatve soluton concept whch guarantees the agreement on the most favorable combnaton of upstream nvestments. n fact, they would come up wth ths second-best soluton f they followed the utltaran soluton, see Myerson 98),.e., f they chose a combnaton of upstream nvestments that maxmzes the sum of ther profts whch equals total proft. However, f the outcome of the negotatons followed the well-known Nash barganng soluton as ntroduced n Nash 950, 95), the dvsons would agree on nvestments that maxmze the product -- nstead of the sum -- of dvsonal profts. Actually, t s not clear whether the upstream dvsons want to mplement a cooperatve soluton concept. Generally, they are free to mplement any arbtrarly chosen soluton, so that the most favorable combnaton of upstream nvestments s not guaranteed. Hence, gven the barganng stuaton n whch HQ admnsters the markup factors, t cannot be taken for granted that the dvsons agree on the frst-best upstream nvestments for = 0. Let us sum up the establshed results for scheme f wth postve markup factors and negotated nvestments: Frst, n a stuaton wth negotated nvestment levels, D s left wth zero proft because any other agreement does not form an equlbrum n the nvestment game and s thus not selfenforcng. Second, t s n HQ s nterest to set small markups because a hgher total proft s acheved f producton takes place. Thrd, even f the combnaton of frst-best nvestment levels, gven = 0, s a feasble result of nter-dvsonal negotatons, the upstream dvsons agree upon that soluton only by chance. The reason for ths s that negotatng the nvestment levels solely means that both the generaton and the allocaton of profts are determned n a sngle step. Thereby, the nterests of the dvson managers are typcally not n lne wth HQ when decdng on dvsonal nvestments. The last pont s llustrated n the dagram on the rght-hand sde of Fgure. The bold lnes ndcate Pareto-effcent proft allocatons for D and D for gven transfer prces. The thn, negatvely sloped lne ndcates feasble dvsonal profts f both upstream dvsons stck to ther frst-best nvestment levels and agree upon the proft allocaton separately. Delegaton of the transfer-prcng authorty to D and D means to make the thn lne feasble. Thus, the upstream dvsons can agree upon nvestments nducng the second-best proft and negotate the proft allocaton n a separate step. Ths stuaton s analyzed n the followng. 4.7 Negotated transfer prces We now consder a system of negotated transfer prces under scheme f,.e., HQ delegates the authorty of specfyng the markup factors ω and ω to the upstream dvsons. Agan, there s no pont n D takng part n the negotatons because, ndependently of the postve) markup factors, ths dvson ends up wth zero proft for any equlbrum n the nvestment game, see expresson ) and Proposton. The barganng stuaton s dfferent now: D and D negotate on both the markup factors and ther nvestment levels at the same tme. Let Π f,n, denote the set of Pareto-effcent upstream profts resultng from ths negotaton. Proposton 6 calculates Π f,n,. Proposton 6. Π f,n, s gven by 6) Π f,n, = { Π, Π ) R ++ : Π + Π = Π 0), fb 0), 0, x)}. The dea of Π f,n, s that the upstream dvsons choose nvestments that maxmze total proft for = 0 and shft ths proft by means of the markup factors arbtrarly between each other. Consult the dagram on the rght-hand sde of Fgure for an llustraton of Π f,n,n,. Πf, may be nterpreted as the envelope of all proft combnatons that arse f postve markup factors are chosen such that frstbest nvestments 0), fb 0)) are a soluton of condton ). t s mportant that t does not matter to HQ n ths barganng stuaton on whch proft combnaton the upstream dvsons actually agree snce any combnaton n Π f,n, yelds the same maxmal) total proft. Thus, there s no dependency of aggre-

12 Volume ssue November gate effcency on the specal negotaton outcome. Furthermore, a comparson of the two barganng stuatons suggests a remarkable concluson: t s possble to overcome dysfunctonal ncentves rooted n responsblty-center organzaton by actually reducng the degree of central plannng n the form of delegatng the transfer-prcng authorty. 5 Conclusons and manageral mplcatons Transfer prces are a promnent nstrument of coordnaton n decentralzed frms. Ths paper focuses on the performance of smple cost-based transfer-prcng schemes, whch are prevalng n busness practce as to the coordnaton of nvestment and producton decsons n a decentralzed settng of team producton for nducng qualtymprovng nvestments. n addton to the teamproducton settng, we allow for two dvsons on the upstream producton stage. The convergent producton structure s the drvng force of the dentfed coordnaton problems. n a frst step, we concentrate on the hypothetcal frst-best stuaton where central management takes and enforces all decsons n an optmal way. The second step s the analyss of the performance of dfferent transfer-prcng schemes appled n the correspondng second-best stuaton. Transfer prces based on varable costs are able to nduce coordnaton, but the upstream dvsons have no ncentve to nvest and the downstream dvson maxmzes total proft gven the undernvestment of the upstream dvsons. Accordngly, addtonal organzatonal nstruments, such as nvestment commttees or mandatory mnmal nvestment levels, are ndcated. n contrast to the varable cost-based scheme, transfer prces based on full costs offer strong ncentves for overnvestment on the upstream producton stage under admnstered transfer prces wth postve markups. Moreover, lke n the varable cost-based scheme wth hgh markups, the exstence of two dvsons on the same producton stage overcharges the coordnaton capablty of the transfer prce. From an organzatonal perspectve, nvestment budgets may mtgate ths problem but ental new agency problems. Another soluton approach s to choose negatve markups mplyng that the upstream dvsons restran from any nvestment actvtes. Wth respect to dvsonal nvestments and total proft, ths soluton s dentcal to the scheme based on varable costs wth small markups. Therefore, a change of the organzatonal arrangements seems promsng. Allowng for negotatons between the upstream dvson managers on the nvestment levels yelds a soluton to the overnvestment and coordnaton problem. Nevertheless, frst-best upstream nvestments can only be guaranteed f negotatons nclude both the nvestments and the markup factors. Thus, the delegaton of transfer-prcng authorty may be a vable opton for HQ n order to mprove coordnaton. Even though ths paper concentrates on qualty-mprovng nvestments, there s probably also potental to beneft from negotatons n stuatons where nvestments bear on producton costs. Comparng the dfferent schemes for motvatng qualty-mprovng nvestments, t holds true that negotatons on transfer prces based on full costs always guarantee at least a total proft as hgh as admnstered transfer prces based on full costs wth postve markups and negotated nvestment levels. Other domnance relatons depend on the actual parameter settng. The strength of transfer prces based on varable costs s the nvestment ncentve on the downstream producton stage. The opposte s true for full cost-based transfer prcng. Consequently, the former s the better choce f the nvestments of the downstream dvson are crtcal for the product s qualty compared to the downstream nvestments, and vce versa. Appendx A: Proofs A. Proof of Proposton The contrbuton margn whch can be mproved by dvsonal nvestments s assumed to be postve, such that the maxmal product quantty s optmal. The objectve functon s assumed to be strctly concave n the nvestment levels. The frstorder dervatves of the expected total proft wth respect to a sngle dvsonal nvestment level, {,, }, are assumed to be strctly postve whch yelds the postve frst-best nvestments * > 0, {,, }. 4

13 Volume ssue November A. Proof of Proposton nspectng 6) we conclude that 7) p,, ) + γ )c c 0 = holds for any combnaton of non-negatve) nvestments and thus x = x s an optmal quantty decson for D ndependent of the dvsonal nvestments. As producton s guaranteed by 7), any postve nvestment on the upstream producton stage decreases the upstream dvsons profts gven by 4) so that = = 0 holds n equlbrum. D s ndvdual proft maxmzaton for x = x s characterzed by Π v 0, 0, 0, x) 8) > 0, such that choosng a strctly postve nvestment level s optmal for D. A. Proof of Proposton D s objectve functon for dervng the optmal level of ts nvestment can be nferred from 9): t s Π f,,, x f,, ) ).Let f, ) denote the optmal downstream nvestment n reacton to upstream nvestments, ) R +. Then, t s suffcent to show that f, )=0holds for, ) f, ). Start wth the assumpton f, ) > 0. Suppose frst that x f,, f, ) ) = 0. Then, D s loss amounts to ts nvestment costs and f, ) > 0 cannot be optmal snce f, )=0 mples zero proft for D. Now suppose that x f,, f, ) ) = x. Snce, ) f, ) holds n equlbrum, condton ) apples and D agan ncurs a loss for every postve nvestment level. Consequently, f, )=0 holds for, ) f, ). A.4 Proof of Proposton 4 The asserton uses Proposton and follows from 0) and ). For Î ), 0), we have, ) f, 0) =Î), 0). Thus, condton ) s satsfed and thereby x f,, 0) = x holds for any, ) f, 0). Otherwse the upstream dvsons do not nvest accordng to ) and p0, 0, 0) = + ω )c c < 0 holds. Referrng to 0), ths mples x f 0, 0, 0) =0 whch completes the proof. A.5 Proof of Lemma p,, ) = c > 0 follows from the assumpton Π0, 0, 0, x) > 0 for x>0. Consequently, the left-hand sde of ) s postve for = = 0 and suffcently small markup factors ω.asthe prce functon p s ncreasng and bounded n, {,, }, by the ntermedate-value theorem there always exsts a par of upstream nvestments, ) 0 satsfyng ) for any gven. A.6 Proof of Proposton 5 Lemma ensures exstence of markup factors ω > 0, {, }, such that f, 0). Suppose such markup factors are chosen. Then, by ) and Propostons and 4, we have postve total proft Π,, 0, x) > 0. Otherwse, total proft s zero accordng to Π0, 0, 0, 0) = 0. A.7 Proof of Lemma As 0) > 0, {, }, the markup factors necessarly are such that f, 0) =Î), 0). Accordngly, we have to verfy that there are markup factors such that 0), fb 0)) Î ), 0). Frst, we check that fb 0), fb 0)) ), 0). Evaluatng the left-hand sde of ) for 0), fb 0)) yelds ) 9) p 0), fb 0), 0 + ω )c c ) x = = + ω ) 0). Obvously, for suffcently large markup factors 9) s negatve. For ω = ω = 0 9) equals Π 0), fb 0), 0, x) whch s postve. Hence, by the ntermedate-value theorem there must be markup factors ω, ω > 0 such that condton ) holds for 0), fb 0)). Pareto effcency of 0), fb 0)) follows from the fact that Π 0), fb 0), 0, x) s maxmal for = 0 and thus the correspondng proft allocaton 0) fb 0), fb 0), 0, x), fb 0), 0, x)) s Pareto effcent. Π f 0), fb A.8 Proof of Proposton 6 Frst note that the proft combnatons n 6) are Pareto effcent snce the upstream nvestments are 5

14 Volume ssue November frst best gven = 0. We then have to verfy that for each proft combnaton n 6) there s a par of markup factors descrbed by Lemma that nduces t. Let Ω R ++ denote the set of pars of markup { factors descrbed by Lemma. } We conclude Ω = ω, ω ) R ++ : ω = a bω from 9), where a and b are postve constants. Note that Ω defnes a negatvely sloped lne n R ++. For each par of markup factors ω, ω ) Ω we have upstream dvsonal profts fb 0), fb 0), 0, x) = ω c x + 0) ), {, }, whch sum up to the maxmal value Π 0), fb 0), 0, x). These proft functons are postve lnear transformatons of the markup factors. Hence, ω c x + 0)), ω c x + 0))) s a parametrzaton of Π f,n,. Appendx B: Example To llustrate the general analyss developed n the paper, ths appendx presents analytcal and numercal results for a specfc prce functon. Here the nterrelated effects of the decentralzed nvestments are reflected by the sales prce p whch recprocally depends on multplcatvely connected nvestment levels. We have θ ) p,, )= p + ε a + ) = wth nvestment level 0 and costs C ) = + κ 0, {,, }, a > 0 symbolzng the captal stock of D already n place, and constant θ > 0 calbratng the nvestment effect. ε and κ are ndependent random varables wth mean με) = μκ ) =0. The expected sales prce and nvestment costs are gven by ) E ε [ p,, ) ] θ = p =: p,, ) > 0 a + ) and = ) E κ [ C ) ] = =: C 0 {,, }. Even wth arbtrarly large nvestments n all dvsons the supremum p >0 of the sales prce cannot be reached, as the margnal nvestment effect decreases wth ncreasng nvestment levels as depcted n Fgure 4. Fgure 4: Prce functon p,, ) p p θ a = 0 0 a = a + ) Under the assumpton ) /4 > max{a, a, a }, the frst-best nvestment polcy entals postve nvestment levels n all dvsons. B. Frst-best stuaton The frst-best nvestment levels *, {,, }, are gven by 4) * =) /4 a > 0. Further, the optmal nvestment levels decrease n ntal endowments a. The optmal soluton s characterzed by a + ) = a j + j ), j, whch reflects the decsons nterdependence. Wth the nvestment levels accordng to 4), the maxmum total proft s gven by ) 5) Π *, fb*, fb*, x ) = p c x 4) /4 + a. = Ths proft serves as a benchmark measurng organzatonal effcency when we take the nformatonal asymmetry nto consderaton. B. Transfer prces based on varable costs Wth transfer prces based on varable costs and suffcently small markup factors γ and γ, see Proposton, the dvsonal nvestments n equlbrum are gven by = = 0 and 6) = a a a > 0. = = 6