The Value of Negotiating Cost-Based Transfer Prices

BuR -- Business ResearchOfficial Open Access Journal of VHBVerband der Hochschullehrer für Betriebswirtschaft e.V.Volume 3 | Issue 2 | November 2010 | 113--131

The Value of NegotiatingCost-Based Transfer PricesAnne Chwolka, Department of Management and Economics, Otto-von-Guericke-University Magdeburg, Germany, E-mail: [email protected]

Jan Thomas Martini, Department of Business Administration and Economics, Bielefeld University, Germany, E-mail:[email protected]

Dirk Simons, Department of Accounting, Business School, Mannheim University, Germany, E-mail: [email protected]

AbstractThis paper analyzes the potential of one-step transfer prices based on either variable or full costs forcoordinating decentralized production and quality-improving investment decisions. Transfer pricesbased on variable costs fail to induce investments on the upstream stage. In contrast, transfer pricesbased on full costs provide strong investment incentives for the upstream divisions. However, they failto coordinate the investment decisions. We show that negotiations prevent such coordination failure.In particular, we find that the firm benefits from a higher degree of decentralization so that total profitincreases in the number of parameters being subject to negotiations.

Keywords: transfer pricing, centralized management, decentralized management, investment, productdifferentiation, negotiations

Manuscript received April 30, 2009, accepted by Rainer Niemann (Accounting) May 31, 2010.

1 IntroductionIn the literature, different transfer-pricingschemes are recommended depending on the pur-pose they are intended for. On the one hand, two-step transfer prices consisting of a unit price com-pensating for variable production costs and anup-front lump-sum payment to cover fixed costsare suggested for the purpose of coordinating in-vestment and production activities within divi-sionalized firms (e.g., Drury 2004: 900). On theother hand, the OECD recommends among oth-ers a cost-plus scheme for international taxation(OECD 1999: II-11). Empirically, one-step cost-based transfer pricing prevails in business practice(see Section 2). However, it is well known from theliterature that cost-based types of transfer pricesexhibit significant disadvantages with respect toinvestment incentives in decentralized settings.Taking into consideration that these investmentsconstitute a crucial strategic competitive advan-tage, finding an adequate transfer-pricing policyis an important managerial issue. As an example,consider today’s markets where firms have the op-portunity to attract customers’ attention by prod-uct differentiation. The responsibility for product

improvements and development or for ensuringhigh quality is typically placed not on one but onseveral divisions. Plausibly, improving the qualityof the final product is achieved by joint activities ofthe divisions, meaning that in divisionalized firmscoordination of such kind of activities is necessaryin order to exploit synergistic effects.The goal of our paper is to analyze the invest-ment incentives generated by one-step cost-basedtransfer prices. Our theoretical analysis builds onthe empirical fact that these transfer prices pre-vail in business practice. We start by replicatingthe well-known investment distortions for variablecost-based and full cost-based transfer prices. Cou-pled with the empirically observable dominance ofcost-based transfer prices this is the motivation foranalyzing the potential of negotiations for mitigat-ing the investment incentive problem by varyingthe extent of negotiations.The major innovation of our paper is that we donot only account for interstage but also for in-trastage dependencies of the divisions’ investmentdecisions. This means that we analyze interdepen-dencies across the stages -- as it is commonly donein the literature -- as well as goal conflicts between

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divisions on the same stage. This modificationenables us to analyze interesting coordination is-sues on the upstream stage and to demonstratehow negotiations between the divisions and theextent of delegation influence the performance oftransfer pricing. In doing so, we also resolve thedichotomy of cost-based and negotiated transferprices. Moreover, we do not conceive transfer pric-ing as a separate incentive system which can beoptimized in isolation. Rather, we consider the as-signment of decision rights within the firm alsoas variable. We demonstrate that central manage-ment may reach better coordination by delegatingmore -- rather than fewer -- aspects of the transfer-pricing system, which has important managerialimplications.The remainder of the paper is organized as fol-lows. Section 2 provides a brief literature review.The organizational setting is described in the thirdsection together with the underlying assumptions.Section 4 contains the model results for differ-ent settings. Initially, the first-best solution is de-rived. Subsequently, we demonstrate that noneof the considered schemes is able to induce in-vestments in all of the three divisions. Moreover,transfer pricing based on full costs is prone tosuffer from coordination failure. In this context,introducing negotiations on both the investmentsand the transfer prices is shown to ensure optimalcoordination. The paper concludes with manage-rial implications. Appendices A and B contain theproofs and an example, respectively. Additionalexplanations concerning the negotiations undertransfer pricing based on full costs are provided inAppendix C.

2 Related literatureRelated literature falls into an empirical and atheoretical strand. From an empirical perspec-tive, it can be confirmed that one-step cost-basedtransfer-pricing schemes prevail in business prac-tice. This observation is supported by the surveyof empirical studies in Horngren, Datar, and Fos-ter (2006: 774). It is confirmed and extended byErnst & Young (2001: 19) who document the pre-dominance of cost-based transfer-pricing schemesirrespective of the type of transaction in the con-text of international taxation. It is valid to build onthe findings of Ernst & Young (2001) in our con-text because Ernst & Young (2003: 17) find that

80 percent of 641 multinational parent companiesuse the same transfer price for managerial and taxpurposes. Czechowicz, Choi, and Bavishi (1982:59) find a corresponding share of 84 percent. Fur-thermore, although two-step transfer prices pro-vide more flexibility by allowing for a lump-sumtransfer payment to cover fixed costs, empiricalevidence suggests that the prevalence of two-steptransfer prices is extremely low: According to Tang(1993: 71), only one percent of 143 firms employtwo-step schemes to price national or internationaltransfers. With respect to the question of whethertransfer prices are administered or negotiated, thesurvey by Horngren, Datar, and Foster (2006: 774)seems to document a rather low prevalence of ne-gotiated transfer prices ranging between 11 and26 percent. Yet, Eccles points out a shortcoming ofmany empirical studies which do not consider ne-gotiations given a certain pricing scheme. Accord-ingly, referring to firms that transfer at a profitmarkup based on a given scheme, Eccles (1985:43) states that ’’seventy-two percent of these firmssaid yes’’ when asked ’’if some kind of negotiationwas also involved.’’From a practical as well as a theoretical per-spective, coordination is an important functionof transfer prices, see, e.g., Drury (2004: 883) orGrabski (1985: 35). This becomes evident with theintroduction of relation-specific investments, see,e.g., the seminal papers of Edlin and Reichelstein(1995, 1996) or Holmstrom and Tirole (1991) wherethe hold-up problem is highlighted. Extensionshave been made by Baldenius (2000), Wielen-berg (2000), Anctil and Dutta (1999), and Balde-nius, Reichelstein, and Sahay (1999). All thesepapers focus on freely negotiated transfer prices,i.e., without a given pricing scheme, or on thecomparison of negotiated and cost-based transferprices. Sahay (2003) analyzes additive versus mul-tiplicative markups on costs, whereas Lengsfeld,Pfeiffer, and Schiller (2006) analyze the compara-tive advantages of transfer prices based on actualand standard costs. All these contributions assumeinvestments inducing a reduction of productioncosts or an increase in sales revenue. The consid-ered investments might be called ’’egoistic’’ sinceit is assumed that it is the investing division whichdirectly benefits from the induced returns (see Cheand Hausch 1999, for a similar terminology).Similar to the papers cited above, we considerthe problem of motivating divisional investments

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via transfer prices. We also rely on negotiationsto overcome interest conflicts between the divi-sions. However, we do not distinguish betweencost-based transfer prices on the one hand andnegotiated transfer prices on the other. Instead,we follow an integrated perspective by extend-ing the solution space provided by administeredcost-based transfer prices by inter-divisional ne-gotiations on the specification of the given pricingscheme. Another difference of our setting is thatthe divisions invest knowing the specified trans-fer price and that each investment’s productivitydepends on the other investment levels. Thus, theproblem of coordinating investments has to besolved in the first place instead of a hold-up prob-lem potentially occurring after the investmentshave been made.Only a few other papers have incorporated coop-erative -- instead of egoistic -- investments intotransfer-pricing settings. Our investment setting issimilar to Johnson (2006) or Chwolka and Simons(2003). In contrast to their approaches, we con-centrate on transfer prices instead of sharing rulesand incorporate negotiations. Moreover, analyzingthree divisions enables us to illustrate two differ-ent kinds of coordination problems: On the onehand the coordination among the upstream divi-sions which is typically neglected in the literatureand on the other hand the ’’traditional’’ coordina-tion problem between upstream and downstreamdivisions.The contribution of our paper results from the in-troduction of a second upstream division. Giventhe traditional setting with one upstream and onedownstream division, it seems obvious that thefirm faces an overinvestment problem on the up-stream production stage when transfer prices coverfull costs plus a multiplicative markup. In our ex-tended setting, we not only confirm this intuitionbut show also that an underinvestment problemmay occur as well. More importantly, we showthat ensuring investments and production doesnot only require solving the coordination problembetween the production stages, but also betweenthe divisions on the same stage. Accordingly, we ex-amine how negotiations over the investment levelsinduces coordination on the upstream productionstage. We extend the analysis by demonstratingthat the firm benefits from having the upstreamdivisions not only negotiate investments but alsotransfer prices.

3 Model descriptionWe consider a firm consisting of three investmentcenters Di, i ∈ {1,2,3}, being subordinated toheadquarters, HQ. HQ confines itself to installinga transfer-pricing system -- where transfer pricesdo not necessarily have to be administered -- forcoordinating the investment centers. We assumethat transfer prices have to be defined before anyactivities take place. One justification for this as-sumption are requirements demanded by tax au-thorities or other legal requirements. HQ delegatesany operative decision to the divisions, includingthose referring to the investment levels Ii. All divi-sions have access to external factor markets wherethey procure the required raw materials and goods-- except for the intermediate products which areexclusively traded between the divisions. The up-stream divisions D1 and D2 deliver intermediategoods or services to the downstream division D3and are compensated via transfer-price payments.The downstream division completes the productand sells it to an external market. These generalassumptions are fairly standard and depicted inFigure 1 where ci symbolizes the variable costs perproduction unit accruing in division Di before ac-counting for transfer payments, whereas t1 and t2are the transfer prices at which each product unitof D1 and D2 is valued. Ii denotes the investmentlevel and equals the expected investment costs. x isthe production and sales quantity, and p(·) is theexpected sales price.In the following, we explain the assumptions inmore detail. We assume that divisionalization isgiven. Headquarters is not able to calculate opti-mal investment levels because it lacks informationon productivity parameters. Consequently, HQ del-egates the investment and trade decisions to the di-vision managers. Ex post, HQ can neither verify theinvestment levels nor evaluate their optimality, butcan only observe the corresponding actual costs.However, the investment costs resulting from thechosen investment levels are stochastic.Having a closer look at the divisions, note that fromthe perspective of organizational theory a majoradvantage of decentralization is greater flexibilitywith respect to market demands (see Grabski 1985for reasons in favor of decentralization). This factis incorporated in our model by the assumptionof information asymmetry between headquartersand the divisions. Further, we assume that the

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division managers are interested in their respec-tive divisional profit. This assumption could bejustified by the existence of an according incen-tive system. The investment-center organizationinduces self-interested divisional decisions so thatany formal or informal agreement between thedivisions has to be in the interest of each of thedivisions. Communication between the divisions istherefore of no use unless the resulting agreementis self-enforcing. Note that the three divisions -- incontrast to HQ -- share perfect information as to thetransaction under consideration. This assumptionis motivated by the fact that the operative divisionshave a deeper knowledge of product-specific dataas compared to HQ.The two-stage production process is performed bythe three divisions as depicted in Figure 1. Theintermediate products cannot be sold externally soD1 and D2 are obliged to deliver their products toD3. D3, in turn, has to procure these specific inter-mediate goods from D1 and D2 because they arenot offered on an external market. For analyticalconvenience, all production coefficients are equalto one. The maximal product quantity x > 0 reflectscapacity restrictions, i.e., x ∈ [0, x]. As motivatedlater in the paper, the investments considered heredo not affect capacity.The most important objective of modern firmsrelying on decision decentralization is to handlethe fragmentation of product responsibilities. Thisholds true especially when the competitive ad-vantage is based on product differentiation. Thisproblem is integrated into our model by focusingon quality-improving investments. Note that theterm ’’investment’’ has to be interpreted in a widesense in our paper. We have in mind spendingsthat are able to increase the customers’ willing-ness to pay, which depends on the product-specificbundle of features (Simon 1989: 1). These invest-ments may be spendings for machines producingat a higher quality level, research and develop-ment expenditures implying an improvement of

the product’s functionalities, or organizational ar-rangements speeding up service times and thusincreasing customer satisfaction.The interrelated effects of the divisional invest-ments are reflected by the sales price p whichdepends on the individual investment levels and arandom variable ε. We have

(1) p(I1, I2, I3) = p(I1, I2, I3) + ε

with non-negative investment level Ii chosen byDi, i ∈ {1,2,3}. An example with a specific pricefunction is presented in Appendix B. ε is a randomvariable with mean μ(ε) = 0. Thus, the expectedprice is given by Eε

[p(I1, I2, I3)

]= p(I1, I2, I3). As

argued above, the price is increasing in quality-improving investments. Moreover, we assume thatp is strictly concave and bounded; additionally theinput factors’ contributions to the output cannotbe isolated. Formally, we have

(2)∂p(I1, I2, I3)

∂Ii> 0,

∂2p(I1, I2, I3)∂Ii∂Ij

�= 0 ∀i, j ∈ {1,2,3}.

We assume that the costs resulting from invest-ment level Ii, i ∈ {1,2,3}, are uncertain andamount to Ci(Ii) = Ii + κi ≥ 0, where κ1, κ2, andκ3 are independent random variables with meansμ(κi) = 0. Thus, the expected investment costsare given by Eκi [Ci(Ii)] = Ii. Actual, i.e., realized,investment costs are denoted by Ci.In order to emphasize quality-improving invest-ments we abstract from capacity increases andthus leave the quantity effect on the sales priceout of account. Observe that this is a standardassumption, e.g., in the target-costing literature.In business practice, the quantity effect is negli-gibly small in several environments: For instance,in markets with a high brand loyalty, e.g., luxurygoods or certain food products, the price sensi-tivity is low. Similarly, if the customer has made

Figure 1: Structure of the firm

p(I1,I2, I3)x

HQ

inputs

c3x+I

3

xx

x

c1x+I1

c2x+I2

division D3

division D2 suppliers

customersdivision D1

suppliers

suppliersinputs

inputs

t1x

t2x

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investments in the past, the present buying de-cision might be predetermined. As an exampleconsider software updates. Generally, this phe-nomenon arises whenever accessories have to bebought for non-standardized products.The timing of decisions and actions is as shown inFigure 2. In the first step, HQ chooses a cost-basedtransfer-pricing scheme, i.e., either scheme v basedon variable costs or scheme f based on full costs.Additionally, the parameters determining the cho-sen scheme respectively the extent of delegationare specified. In the next step, the divisions si-multaneously decide on their investment levels Ii,i ∈ {1,2,3}, under perfect information, i.e., eachdivision knows its own as well as the others’ de-cision problems. Subsequently, D3 determines theproduction and sales quantity x. Finally, productunits are manufactured and sold, the sales priceis realized, and the realized investment costs aredetermined, which allows the calculation of totaland divisional profits. We refer to HQ’s decisionmaking as centralized planning which defines theconditions of the subsequent decentralized plan-ning, i.e., investments and production.We assume all managers and HQ to be risk-neutral.The goal of HQ is to maximize expected total, i.e.,firm-wide, profit:

(3)

Π(I1, I2, I3, x)

=

(Eε

[p(I1, I2, I3)

]−3∑

i=1

ci

)x −

3∑i=1

Eκi

[Ci(Ii)

]=

(p(I1, I2, I3)−

3∑i=1

ci

)x −

3∑i=1

Ii.

Observe that the divisional profits sum up tototal profit. Moreover, remember that c3 doesnot account for any transfer prices but symbol-izes the costs per unit for externally procuredinputs as depicted in Figure 1. We assume apositive contribution margin which may be im-

proved by divisional investments. Formally, wehave Π(0,0,0, x) > 0 and ∂Π(0,0,0, x)/∂Ii > 0 forx > 0 and i ∈ {1,2,3}.For the first-best situation, we assume informa-tion symmetry between HQ and the divisions. Inthe second-best situation, we assume that variableas well as realized investment costs are observ-able and contractible so that the transfer-pricingschemes introduced and analyzed in the follow-ing below are feasible. However, HQ is not able toobserve the chosen investment level. This infor-mation asymmetry is the reason for HQ to delegatedecision authority to the divisions and to imple-ment a transfer-pricing system.

4 Model analysisIn this section, we first consider the first-best so-lution. The two following subsections deal withtransfer pricing based on variable and full costs,respectively. They deviate from the first-best situ-ation in that there is information asymmetry be-tween HQ and the divisions. We refer to themas the second-best situation. We start the analy-sis of the second-best situation by replicating thewell-known underinvestment problem for variablecost-based transfer prices and the overinvestmentproblem for full cost-based transfer prices. In par-ticular, the transfer-pricing scheme v is based onvariable costs and induces investment incentivesonly on the downstream production stage. Under-investment occurs under this scheme since bothupstream divisions do not invest. In contrast,scheme f is based on full costs and has the po-tential to create strong investment incentives onthe upstream production stage. Then, however, thetransfer price on its own is insufficient to inducecoordination among the divisions. We show hownegotiations may remedy this defect effectively andmay even align upstream divisions with the firm’sobjective.

Figure 2: Time line

profit generation and allocation

decentralized planning

centralized planning

and investment costs Ci(Ii), sales, accountingproduction, realization of sales price p(I1, I2, I3)

HQ specifies transfer prices t1 and t2

D3 decides upon quantity x

Di determines investment Ii, i ∈ {1,2,3}

(or delegates specification to D1 and D2)

HQ chooses scheme v or f1

2

3

4

5

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4.1 First-best situation

In the first-best situation with information symme-try between HQ and the divisions, HQ is able to de-termine and enforce optimal divisional investmentlevels and the optimal product quantity. Proposi-tion 1 states the first-best solution. All proofs aregiven in Appendix A. In Appendix B we calculatethe first-best solution for an example.

Proposition 1. The first-best quantity is xfb* = x.The first-best investment levels Ifb*

i , i ∈ {1,2,3},are positive and finite.

With the price-quality relation as defined in equa-tion (1) the corporate objective function is givenby (3). The first part of equation (3) representsthe total expected contribution margin per prod-uct unit. By assumption, this margin is positive forany combination of investment levels. Hence, it isoptimal for HQ to set the product quantity to itsmaximum value.

4.2 Transfer prices based on variablecosts (scheme v)

Sections 4.2 and 4.3 reflect the second-best situa-tion where HQ delegates decision authority to thedivisions and confines itself to administering thetransfer-pricing system. As a first step we analyzethe investment incentives of transfer prices basedon variable costs.We assume that transfer prices under scheme vare defined by tv

i = (1 + γi)ci, i ∈ {1,2}, wherethe multiplicative markup factors γi ≥ 0 ensurenon-negative divisional contribution margins onthe upstream production stage. Remember thatall division managers are risk-neutral and seekto maximize their expected divisional profits. Thedivisional objective functions Πv

i read

(4)Πv

i (I1, I2, I3, x) = (tvi − ci)x − Eκi

[Ci(Ii)

]= γicix − Ii

for the upstream divisions Di, i ∈ {1,2}, and

(5)

Πv3(I1, I2, I3, x)

=(Eε

[p(I1, I2, I3)

]−2∑

j=1

(1 + γj)cj − c3

)x

− Eκ3

[C3(I3)

]=(

p(I1, I2, I3) −2∑

j=1

(1 + γj)cj − c3

)x − I3

for the downstream division. Expected profits ofD1 and D2 equal the difference of the transferpayment and the sum of the variable productionand expected investment costs. Divisional expectedprofits in (4) immediately show that the upstreamdivisions have no incentive to invest at all underscheme v replicating the underinvestment effect ofvariable cost-based transfer prices.In contrast to the upstream divisions, D3 receivesthe actual turnover. In addition to its own vari-able production and investment costs, D3 has toaccount for the transfer payments to D1 and D2. Ac-cordingly, it is only optimal for D3 to set a positiveproduct quantity, if its expected contribution mar-gin is non-negative. Moreover, inducing a positiveinvestment on the downstream production stageimplies a non-negative expected profit for D3. Thisrequires sufficiently small markups. We have thefollowing equilibrium in divisional decisions.

Proposition 2. Presume that markup factors γ1and γ2 under scheme v are sufficiently small sothat

(6) (γ1, γ2) ∈{

(γ1, γ2) ∈ R2

+ :

p(0,0,0) −2∑

i=1

(1 + γi)ci − c3 ≥ 0

}

is satisfied. Then, in equilibrium, divisional invest-ments are Iv*

1= Iv*2

= 0, Iv*3

> 0, and the productis marketed, xv* = x.

With respect to the upstream divisions, transferprices based on variable costs seem to be inade-quate for inducing investments. Accordingly, theunderinvestment problem on the upstream pro-duction stage has to be managed by other organi-zational arrangements.

4.3 Transfer prices based on full costs(scheme f )

In this section, we analyze transfer-pricingschemes based on full costs with different organiza-tional embeddings. We start by showing that fullyadministered transfer prices, i.e., without inter-divisional negotiations, may result either in anunderinvestment or an overinvestment problem.For the overinvestment problem, investment in-centives on the upstream production stage are sostrong that further coordination in addition to the

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administered transfer prices is needed. We demon-strate how negotiations on the investment levelssolve the coordination problem. For further im-proving the investment levels we introduce fullynegotiated cost-based transfer prices which allowfor substantial improvements.

4.4 The divisional decision problemswith full cost-based transfer prices

For positive product quantities, transfer pricesbased on full costs tf

i , i ∈ {1,2}, are defined ac-cording to

(7) tfi = (1 + ωi)

(ci +

Ci(Ii)x

)as full cost plus markup. Otherwise, with no sales,transfer prices are zero. ωi symbolizes a multiplica-tive markup factor determining divisional profits.We restrict our analysis to multiplicative markups,because transfer prices with additive markups donot provide sufficiently strong investment incen-tives for the upstream divisions. Note that due tothe uncertainty of the investment costs the trans-fer prices based on full costs are also randomvariables. Accordingly, the risk-neutral divisionmanagers base their investment decisions on theexpected transfer prices tf

i = (1 + ωi)(ci + Ii/x).Calculation of the realized transfer prices requiresthat the accounting system is able to measure therealized investment costs Ci beside the variablecosts ci and the quantity x.In case the product is marketed, x > 0, upstreamdivision Di’s, i ∈ {1,2}, objective function underscheme f reads

(8)

Πfi (I1, I2, I3, x)

=(Eκi

[tf

i

]− ci

)x − Eκi

[Ci(Ii)

]= ωi(cix + Ii),

whereas D3 shows expected profit

(9)

Πf3(I1, I2, I3, x)

=

(Eε

[p(I1, I2, I3)

]−2∑

i=1

Eκi

[tf

i

]− c3

)x

− Eκ3

[C3(I3)

]= p(I1, I2, I3)x

−

(2∑

i=1

(1 + ωi)(

ci +Ii

x

)− c3

)x − I3.

All divisions incur a loss amounting to their corre-sponding expected investment costs Ii, if no pro-duction takes place. Again, the upstream divisions’profits are calculated as transfer payment net ofproduction and investment costs. D3’s profit isdefined as turnover net of transfer payments, pro-duction, and investment costs.D3 chooses quantity

(10) xf (I1, I2, I3)

=

⎧⎪⎪⎨⎪⎪⎩x if p(·)−

2∑i=1

(1+ωi)(

ci +Ii

x

)−c3 ≥ 0

0 otherwise

maximizing its expected contribution margin andthereby its expected divisional profit Πf

3(·). Note

that D3 bases this decision on an expected contri-bution margin that does not only account for allvariable costs but also for the expected upstreaminvestment costs and a markup on all upstreamcosts. This means, in turn, that the expected in-vestment costs of the upstream divisions influencethe production decision whereas its own invest-ment costs are sunk.Under the assumption that production takes place,i.e., xf (I1, I2, I3) = x, differentiating expected di-visional profits with respect to the upstream divi-sions’ investment levels I1 and I2 yields

(11)∂Πf

i (I1, I2, I3, x = x)

∂Ii= ωi ∀i ∈ {1,2}.

Otherwise no division invests in order to avoida loss. Note that the derivatives in (11) suggestan overinvestment problem with respect to theupstream divisions as long as the markup factorsare positive. Loosely speaking, D1 and D2 increasetheir divisional profits by incurring costs. In amore general setting, where the investments wouldreduce the production costs, it would not be clearthat the overinvestment problems of the upstreamdivisions will occur with transfer prices based onfull costs. This would depend on the effect of theinvestments on the sum of variable and investmentcosts, which could be positive or negative, resultingin an over- or underinvestment problem.In the following, we discuss the results of differentorganizational scenarios. We start with adminis-tered transfer prices. Here two scenarios emergedepending on whether inter-divisional negotia-tions on the investment levels are prohibited or

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permitted. In the third scenario, we modify our as-sumption of a fully administered transfer-pricingsystem and allow the upstream divisions to deter-mine both the investment levels and the markupfactors in bilateral negotiations.

4.5 Administered transfer prices withoutnegotiations

In an administered transfer-pricing system a firstalternative for HQ is to choose negative markups.Mathematically, this is a feasible solution, althoughit appears to be uncommon from a business per-spective. With ωi < 0divisions D1 and D2 renounceto any investment, whereas D3’s investment deci-sion is the same as in the case of transfer pricesbased on variable costs with small markup factors.A second alternative for HQ are positive markups.At first glance, expression (11) suggests that forpositive ω1 and ω2 both D1 and D2 have an incen-tive to increase their individual investments un-boundedly. However, excessive upstream invest-ments would imply a negative contribution marginfor D3 due to the corresponding high expectedtransfer payments, i.e., p(I1, I2, I3) −

∑2

i=1(1 +ωi)(ci + Ii/x) − c3 < 0, inducing the downstreamdivision to cease production at date t = 4 accord-ing to (10). This implies negative profits for theupstream divisions amounting to their sunk in-vestment costs. Hence, it is not in the upstreamdivisions’ interest to increase their investments toan arbitrarily high level. Rather, it is optimal foreach upstream division to raise its investment tothe highest level that still induces the downstreamdivision not to cease production. Since both up-stream divisions proceed in this manner, maxi-mum investment levels depend on each other. Thesolution to this problem requires an agreement ofthe upstream divisions on one combination of in-vestment levels ensuring that D3 chooses a positivequantity. In the absence of further coordination itis therefore not obvious which investment levelsthe upstream divisions should choose. Moreover,infinitely many combinations of upstream invest-ments can just be borne by D3.Note that any solution leaving a positive contri-bution margin to D3 is not self-enforcing. Theargument is as follows: Suppose the three divi-sions agree on investment levels leaving a positivecontribution margin for D3. In this case each up-stream division has an incentive to deviate from

the negotiated agreement and to increase its invest-ment beyond the agreed level in order to increaseits respective profit, because with full cost-basedtransfer prices as defined in (7), investment levelsand divisional profits are positively related for D1and D2. Moreover, the upstream divisions can in-crease their investment levels and D3 -- behavingrationally -- does not cease production unless itsexpected contribution margin is negative. But thenthe upstream divisions end up in a similar situa-tion as before the negotiation: Without any furtheragreement they do not know how to coordinateinvestment increases. That is why we restrict ouranalysis to negotiations between the two upstreamdivisions leaving a zero expected contribution mar-gin to D3.To formalize this idea, let If

1,2 : R+ → 2R2+ denotethe set of combinations of upstream investmentsbeing Pareto efficient with respect to upstreamexpected divisional profits for given downstreaminvestment I3. There are two cases for the parame-ter setting: On the one hand, it could be that theredoes not exist any pair of upstream investmentlevels greater than zero such that xf (I1, I2, I3) = xholds for given I3. This is the case, e.g., if themarkup factors ωi are so high that D3’s contribu-tion margin is negative for all positive investmentlevels. Consequently, the upstream divisions wouldnot invest, i.e., If

1,2(I3) ={

(0,0)}

, and earn zeroprofits. On the other hand, there could be at leastone pair of upstream investment levels such thatD3 decides to produce. In this case it is neitherindividually rational for the upstream divisionsto choose zero investments nor a combination ofinvestment levels leaving a positive contributionmargin to D3 since by (8) they increase their ownprofits by appropriately raising their investmentlevels. Hence, any (I1, I2) ∈ If

1,2(I3) solves

(12)(

p (I1, I2, I3) −2∑

i=1

(1 + ωi)ci − c3

)x

−2∑

i=1

(1 + ωi)Ii = 0.

This condition can be derived from (10) and isequivalent to the fact that D3 just earns zero ex-pected contribution margin, if it decides to produceat date t = 4. Put differently, with I(12)

1,2 (I3) ⊂ R2+

denoting the solutions to (12) in (I1, I2) we haveIf1,2(I3) ⊆ I(12)

1,2 (I3).

120


Scrutinizing condition (12), we note that it gener-ally does not single out a unique pair of upstreaminvestments. Refer to the diagram on the left-handside of Figure 3 for an illustration of I(12)

1,2 (I3) forthree different pairs ω, ω′, and ω′′ of positivemarkup factors (ω1, ω2). The corresponding divi-sional profits are depicted in the diagram on theright-hand side of Figure 3. Since we know from (8)that upstream divisional profits are increasing ininvestments, any combination of upstream invest-ments uniquely corresponds to a combination ofupstream divisional profits, and vice versa. Thus,both diagrams of Figure 3 can be derived fromeach other. Moreover, upstream investments be-longing to the Pareto boundary of I(12)

1,2 (I3), denoted

by I(12)1,2 (I3), are also Pareto efficient with respect to

upstream divisional profits. Pareto boundaries areindicated by bold lines in Figure 3. Hence, the setof upstream investments inducing Pareto-efficientupstream divisional profits, given downstream in-vestment I3, is

(13) If1,2(I3) =

{I(12)1,2 (I3) if I(12)

1,2 (I3) �= ∅{(0,0)

}if I(12)1,2 (I3) = ∅

.

If D1 and D2 are able to coordinate their decisions,If1,2 can be interpreted as D1’s and D2’s optimal

joint reactions. Interestingly, the Pareto boundaryI(12)1,2 (I3) may include instances of underinvestment

as well as overinvestment, although D1 and D2have strong incentives to overinvest expressed by(11). Moreover, underinvestment corresponds tohigh markup factors, and vice versa. In Figure 3,parameter setting ω′′ induces upstream invest-ments that are below the first-best levels for bothupstream divisions. The key to this observationare the definitions of upstream profits in (8) and(9): High markup factors on upstream productioncosts imply that even small upstream investmentsconsume D3’s total contribution margin.To summarize, administered transfer prices do notyield a unique combination of upstream invest-ment levels. Even though it is clear that a self-enforcing solution always entails zero investmentof D3, the upstream divisions do not know whichcombination of investment levels they should se-lect from the set of Pareto-efficient investmentcombinations satisfying (12). Hence, in the consid-ered scenario with administered transfer pricesand decentralized operative decision authority,further coordination is necessary.

4.6 Administered transfer prices withnegotiated investments

In the previous section we have shown that ad-ministered transfer prices with positive markupfactors provide strong investment incentives for

Figure 3: Investments I(12)1,2 (I3) and corresponding divisional profits

(Ifb1

(0)Ifb2

(0)

)

(ω1

(c1x + Ifb

1(0)

)ω2

(c2x + Ifb

2(0)

))Πf ,n1,2

ω′

Π1

ωω′

ω′′

Π2

I1 0

0

0

0

(ω′1

(c1x + Ifb

1(0)

)ω′2

(c2x + Ifb

2(0)

))ω′′

ω′

I2

ω

The setting underlying both diagrams is p(I1, I2, I3) = p − θ/∏3

i=1(ai + Ii) with p = 30, θ = 50, a1 = a3 = 1, a2 = 2, x = 1,c1 = c2 = c3 = 1, and I3 = 0. The values of the markup factors are ω ≈ (2,4.31), ω′ ≈ (4,1.57), and ω′′ = (4,4).

121


the upstream divisions. However, as both D1 andD2 want to invest as much as possible such thatproduction is not stopped by D3 administeredtransfer prices are not sufficient to provide ade-quate coordination among all divisions. In this sec-tion, the transfer-pricing system is supplementedwith inter-divisional negotiations on the invest-ment levels. Note that the markup factors are stillassumed positive and remain under the control ofHQ. Refer to Appendix C for additional explana-tions on negotiations under scheme f .The negotiation result is an agreement between theupstream divisions on a pair of investments (I1, I2)satisfying If

1,2(I3), i.e., we assume (I1, I2) ∈ If1,2(I3).

In other words, the upstream divisions agree onone joint reaction to given downstream invest-ment I3 and thereby solve the coordination prob-lem. Note that such an agreement between D1 andD2 does not call for a formal contract, becauseit is in the divisions’ interests to stick to the se-lected equilibrium. Thus, the question to focus onis not enforcement, but coordination. Since anypair of such joint reactions entails zero contribu-tion margin on the downstream production stage,D3 never invests in equilibrium and there is nopoint in the downstream division taking part in thenegotiations. This result is stated in the followingproposition.

Proposition 3. The equilibrium downstreaminvestment under scheme f with given positivemarkup factors and negotiated upstream invest-ments is If *

3= 0.

The main idea of Proposition 3 is that transferprices based on full costs with positive markupsincite the upstream divisions to increase their in-vestments at date t = 3 extracting all of D3’s con-tribution margin at date t = 4. Consequently, D3has no benefit associated to its investment andthus does not invest. Proposition 4 uses this resultto derive the equilibrium production decision.

Proposition 4. The equilibrium product quan-tity under scheme f with given positive markupfactors and negotiated upstream investments is

(14) xf * =

{x if I(12)

1,2 (0) �= ∅0 if I(12)

1,2 (0) = ∅.

The top case of (14) is straightforward because asolution of (12) is equivalent to D3 not incurring

a loss from production. The bottom case accountsfor the case that condition (12) has no solution.On further inspection of this condition, we noticethat its solubility depends on the markup factorswhich are set by HQ: For sufficiently large markupfactors revenue does not cover D3’s productioncosts and the transfer payments, i.e., the left-handside of (12) is negative. As a consequence, D3 ceasesproduction. We get the following existence resultconcerning the markup factors.

Lemma 1. There exist (sufficiently small) posi-tive markup factors such that I(12)

1,2 (I3) �= ∅.The following proposition confirms that it is hence-forth justified to restrict attention to sufficientlysmall markup factors because otherwise HQ wouldnever incur a positive total profit.

Proposition 5. Under scheme f with negoti-ated upstream investments, (sufficiently large)markup factors such that If

1,2(0) = ∅ and I3 = 0are not optimal for HQ.

Moreover, total profit is entirely transferred to theupstream divisions leaving D3with zero profit. For-mally, with (I1, I2) ∈ If

1,2(0) the equilibrium profit

allocation exhibits the property Πfi (I1, I2,0, x) > 0,

i ∈ {1,2}, and Πf3(I1, I2,0, x) = 0.

So far, the optimal upstream investments havebeen conceived as the result of negotiations be-tween D1 and D2. Anticipating the equilibriumdownstream decisions If *

3= 0 and xf * = x, this

bargaining situation can be described by the setΠf ,a1,2⊂R

2+ defined as

(15) Πf ,a1,2 =

{(Πf1(I1, I2,0, x),Πf

2(I1, I2,0, x)

):

(I1, I2) ∈ If1,2(0)

}.

The setΠf ,a1,2 contains all Pareto-efficient profits the

upstream divisions can achieve by their investmentdecisions. Πf ,a

1,2 is indicated by bold lines in the di-agram on the right-hand side of Figure 3. It clearlyshows that Πf ,a

1,2 depends on the markup factors.

Let Ifbi : R+ → R+ denote the first-best investment

of division Di, i ∈ {1,2}, for given I3. Analogousto the computation to derive Proposition 1, weget Ifb

i (0) > 0. Then, we are able to establish thefollowing benchmark for inter-divisional negotia-tions.

122


Lemma 2. There exist positive markup factorssuch that

(Ifb1

(0), Ifb2

(0)) ∈ If

1,2(0).

Lemma 2 asserts that HQ may choose markup fac-tors such that -- from HQ’s perspective -- the mostfavorable combination of upstream investments(Ifb1

(0), Ifb2

(0))

is a feasible and Pareto-efficient re-sult of the negotiations between D1 and D2. InFigure 3 this is the case for settings ω and ω′.Yet, generally the divisions only pick this pointby chance. Theoretically, the parties could applya cooperative solution concept which guaranteesthe agreement on the most favorable combina-tion of upstream investments. In fact, they wouldcome up with this second-best solution if they fol-lowed the utilitarian solution, see Myerson (1981),i.e., if they chose a combination of upstream in-vestments that maximizes the sum of their profitswhich equals total profit. However, if the outcomeof the negotiations followed the well-known Nashbargaining solution as introduced in Nash (1950,1953), the divisions would agree on investmentsthat maximize the product -- instead of the sum --of divisional profits. Actually, it is not clear whetherthe upstream divisions want to implement a coop-erative solution concept. Generally, they are freeto implement any arbitrarily chosen solution, sothat the most favorable combination of upstreaminvestments is not guaranteed. Hence, given thebargaining situation in which HQ administers themarkup factors, it cannot be taken for grantedthat the divisions agree on the first-best upstreaminvestments for I3 = 0.Let us sum up the established results for scheme fwith positive markup factors and negotiated in-vestments: First, in a situation with negotiated in-vestment levels, D3 is left with zero profit becauseany other agreement does not form an equilib-rium in the investment game and is thus not self-enforcing. Second, it is in HQ’s interest to set smallmarkups because a higher total profit is achievedif production takes place. Third, even if the combi-nation of first-best investment levels, given I3 = 0,is a feasible result of inter-divisional negotiations,the upstream divisions agree upon that solutiononly by chance. The reason for this is that negoti-ating the investment levels solely means that boththe generation and the allocation of profits are de-termined in a single step. Thereby, the interests ofthe division managers are typically not in line withHQ when deciding on divisional investments.

The last point is illustrated in the diagram on theright-hand side of Figure 3. The bold lines indicatePareto-efficient profit allocations for D1 and D2 forgiven transfer prices. The thin, negatively slopedline indicates feasible divisional profits if both up-stream divisions stick to their first-best investmentlevels and agree upon the profit allocation sepa-rately. Delegation of the transfer-pricing authorityto D1 and D2 means to make the thin line feasi-ble. Thus, the upstream divisions can agree uponinvestments inducing the second-best profit andnegotiate the profit allocation in a separate step.This situation is analyzed in the following.

4.7 Negotiated transfer prices

We now consider a system of negotiated transferprices under scheme f , i.e., HQ delegates the au-thority of specifying the markup factors ω1 and ω2to the upstream divisions. Again, there is no pointin D3 taking part in the negotiations because, inde-pendently of the (positive) markup factors, this di-vision ends up with zero profit for any equilibriumin the investment game, see expression (12) andProposition 3. The bargaining situation is differentnow: D1 and D2 negotiate on both the markupfactors and their investment levels at the sametime. Let Πf ,n

1,2 denote the set of Pareto-efficientupstream profits resulting from this negotiation.Proposition 6 calculates Πf ,n

1,2.

Proposition 6. Πf ,n1,2 is given by

(16) Πf ,n1,2 =

{(Π1,Π2

) ∈ R2

++ :

Π1 + Π2 = Π(Ifb1

(0), Ifb2

(0),0, x)}

.

The idea of Πf ,n1,2 is that the upstream divisions

choose investments that maximize total profit forI3 = 0 and shift this profit by means of the markupfactors arbitrarily between each other. Consult thediagram on the right-hand side of Figure 3 for anillustration of Πf ,n

1,2. Πf ,n1,2 may be interpreted as the

envelope of all profit combinations that arise ifpositive markup factors are chosen such that first-best investments

(Ifb1

(0), Ifb2

(0))

are a solution ofcondition (12).It is important that it does not matter to HQ inthis bargaining situation on which profit combi-nation the upstream divisions actually agree sinceany combination inΠf ,n

1,2 yields the same (maximal)total profit. Thus, there is no dependency of aggre-

123


gate efficiency on the special negotiation outcome.Furthermore, a comparison of the two bargain-ing situations suggests a remarkable conclusion:It is possible to overcome dysfunctional incentivesrooted in responsibility-center organization by ac-tually reducing the degree of central planning inthe form of delegating the transfer-pricing author-ity.

5 Conclusions and managerialimplications

Transfer prices are a prominent instrument ofcoordination in decentralized firms. This paperfocuses on the performance of simple cost-basedtransfer-pricing schemes, which are prevailing inbusiness practice as to the coordination of invest-ment and production decisions in a decentralizedsetting of team production for inducing quality-improving investments. In addition to the team-production setting, we allow for two divisions onthe upstream production stage. The convergentproduction structure is the driving force of theidentified coordination problems.In a first step, we concentrate on the hypotheti-cal first-best situation where central managementtakes and enforces all decisions in an optimal way.The second step is the analysis of the performanceof different transfer-pricing schemes applied in thecorresponding second-best situation.Transfer prices based on variable costs are able toinduce coordination, but the upstream divisionshave no incentive to invest and the downstreamdivision maximizes total profit given the underin-vestment of the upstream divisions. Accordingly,additional organizational instruments, such as in-vestment committees or mandatory minimal in-vestment levels, are indicated.In contrast to the variable cost-based scheme,transfer prices based on full costs offer strong in-centives for overinvestment on the upstream pro-duction stage under administered transfer priceswith positive markups. Moreover, like in the vari-able cost-based scheme with high markups, theexistence of two divisions on the same produc-tion stage overcharges the coordination capabilityof the transfer price. From an organizational per-spective, investment budgets may mitigate thisproblem but entail new agency problems. Anothersolution approach is to choose negative markupsimplying that the upstream divisions restrain from

any investment activities. With respect to divi-sional investments and total profit, this solution isidentical to the scheme based on variable costs withsmall markups. Therefore, a change of the orga-nizational arrangements seems promising. Allow-ing for negotiations between the upstream divisionmanagers on the investment levels yields a solutionto the overinvestment and coordination problem.Nevertheless, first-best upstream investments canonly be guaranteed if negotiations include boththe investments and the markup factors. Thus, thedelegation of transfer-pricing authority may be aviable option for HQ in order to improve coordi-nation. Even though this paper concentrates onquality-improving investments, there is probablyalso potential to benefit from negotiations in situa-tions where investments bear on production costs.Comparing the different schemes for motivatingquality-improving investments, it holds true thatnegotiations on transfer prices based on full costsalways guarantee at least a total profit as high asadministered transfer prices based on full costswith positive markups and negotiated investmentlevels. Other dominance relations depend on theactual parameter setting. The strength of transferprices based on variable costs is the investmentincentive on the downstream production stage. Theopposite is true for full cost-based transfer pricing.Consequently, the former is the better choice ifthe investments of the downstream division arecritical for the product’s quality compared to thedownstream investments, and vice versa.

Appendix A: ProofsA.1 Proof of Proposition 1

The contribution margin which can be improvedby divisional investments is assumed to be pos-itive, such that the maximal product quantity isoptimal. The objective function is assumed to bestrictly concave in the investment levels. The first-order derivatives of the expected total profit withrespect to a single divisional investment level Ii,i ∈ {1,2,3}, are assumed to be strictly positivewhich yields the positive first-best investmentsIfb*

i > 0, i ∈ {1,2,3}.

124


A.2 Proof of Proposition 2

Inspecting (6) we conclude that

(17) p(I1, I2, I3) −2∑

i=1

(1 + γi)ci − c3 ≥ 0

holds for any combination of (non-negative) in-vestments and thus x = x is an optimal quantitydecision for D3 independent of the divisional in-vestments. As production is guaranteed by (17),any positive investment on the upstream produc-tion stage decreases the upstream divisions’ profitsgiven by (4) so that I1 = I2 = 0 holds in equilib-rium. D3’s individual profit maximization for x = xis characterized by

(18)∂Πv3(0,0,0, x)

∂I3> 0,

such that choosing a strictly positive investmentlevel is optimal for D3.


D3’s objective function for deriving the optimallevel of its investment can be inferred from (9): Itis Πf

3

(I1, I2, I3, xf (I1, I2, I3)

). Let If

3(I1, I2) denote

the optimal downstream investment in reactionto upstream investments (I1, I2) ∈ R

2+. Then, it

is sufficient to show that If3(I1, I2) = 0 holds for

(I1, I2) ∈ If1,2(I3).

Start with the assumption If3(I1, I2) > 0. Sup-

pose first that xf(I1, I2, If

3(I1, I2)

)= 0. Then,

D3’s loss amounts to its investment costs andIf3(I1, I2) > 0 cannot be optimal since If

3(I1, I2) = 0

implies zero profit for D3. Now suppose thatxf(I1, I2, If

3(I1, I2)

)= x. Since (I1, I2) ∈ If

1,2(I3)holds in equilibrium, condition (12) applies andD3 again incurs a loss for every positive invest-ment level. Consequently, If

3(I1, I2) = 0 holds for

(I1, I2) ∈ If1,2(I3).


The assertion uses Proposition 3 and followsfrom (10) and (13). For I(12)

1,2 (0) �= ∅, we have

(I1, I2) ∈ If1,2(0) = I(12)

1,2 (0). Thus, condition (12)is satisfied and therebyxf (I1, I2,0) = x holds for any (I1, I2) ∈ If

1,2(0). Oth-erwise the upstream divisions do not invest accord-ing to (13) and p(0,0,0) −

∑2

i=1(1 + ωi)ci − c3 < 0holds. Referring to (10), this implies xf (0,0,0) = 0which completes the proof.

A.5 Proof of Lemma 1

p(I1, I2, I3) −∑3

i=1 ci > 0 follows from the assump-tion Π(0,0,0, x) > 0 for x > 0. Consequently, theleft-hand side of (12) is positive for I1 = I2 = 0and sufficiently small markup factors ωi. As theprice function p is increasing and bounded in Ii,i ∈ {1,2,3}, by the intermediate-value theoremthere always exists a pair of upstream investments(I1, I2) �= 0 satisfying (12) for any given I3.


Lemma 1 ensures existence of markup factorsωi > 0, i ∈ {1,2}, such that If

1,2(0) �= ∅. Supposesuch markup factors are chosen. Then, by (13) andPropositions 3 and 4, we have positive total profitΠ(I1, I2,0, x) > 0. Otherwise, total profit is zeroaccording to Π(0,0,0,0) = 0.

A.7 Proof of Lemma 2

As Ifbi (0) > 0, i ∈ {1,2}, the markup factors neces-

sarily are such that If1,2(0) = I(12)

1,2 (0). Accordingly,we have to verify that there are markup factors suchthat

(Ifb1

(0), Ifb2

(0)) ∈ I(12)

1,2 (0). First, we check that(Ifb1

(0), Ifb2

(0)) ∈ I(12)

1,2 (0). Evaluating the left-hand

side of (12) for(Ifb1

(0), Ifb2

(0))

yields

(19)(

p(

Ifb1

(0), Ifb1

(0),0)

−2∑

i=1

(1 + ωi)ci − c3

)x

−2∑

i=1

(1 + ωi)Ifbi (0).

Obviously, for sufficiently large markup factors(19) is negative. For ω1 = ω2 = 0 (19) equalsΠ(Ifb1

(0), Ifb2

(0),0, x)

which is positive. Hence, bythe intermediate-value theorem there must bemarkup factors ω1, ω2 > 0 such that condition(12) holds for

(Ifb1

(0), Ifb2

(0)).

Pareto efficiency of(Ifb1

(0), Ifb2

(0))

follows from the

fact thatΠ(Ifb1

(0), Ifb2

(0),0, x)

is maximal for I3 = 0and thus the corresponding profit allocation

(20)(Πf1

((Ifb1

(0), Ifb2

(0),0, x),

Πf2

(Ifb1

(0), Ifb2

(0),0, x))

is Pareto efficient.


First note that the profit combinations in (16) arePareto efficient since the upstream investments are

125


first best given I3 = 0. We then have to verify thatfor each profit combination in (16) there is a pair ofmarkup factors described by Lemma 2 that inducesit. Let Ω ⊂ R

2++ denote the set of pairs of markup

factors described by Lemma 2. We conclude Ω ={(ω1, ω2) ∈ R

2++ : ω2 = a − bω1

}from (19), where

a and b are positive constants. Note that Ω definesa negatively sloped line in R

2++. For each pair of

markup factors (ω1, ω2) ∈ Ω we have upstreamdivisional profits Πf

i

(Ifb1

(0), Ifb2

(0),0, x)

= ωi(cix +

Ifbi (0)

), i ∈ {1,2}, which sum up to the maximal

value Π(Ifb1

(0), Ifb2

(0),0, x). These profit functions

are positive linear transformations of the markupfactors. Hence,

(ω1

(c1x + Ifb

1(0)

), ω2

(c2x + Ifb

2(0)

))is a parametrization of Πf ,n

1,2.

Appendix B: ExampleTo illustrate the general analysis developed in thepaper, this appendix presents analytical and nu-merical results for a specific price function. Herethe interrelated effects of the decentralized in-vestments are reflected by the sales price p whichreciprocally depends on multiplicatively connectedinvestment levels. We have

(21) p(I1, I2, I3) = p −θ

3∏i=1

(ai + Ii)

+ ε

with investment level Ii ≥ 0 and costs Ci(Ii) =Ii + κi ≥ 0, i ∈ {1,2,3}, ai > 0 symbolizing thecapital stock of Di already in place, and constantθ > 0 calibrating the investment effect. ε andκi are independent random variables with meanμ(ε) = μ(κi) = 0. The expected sales price andinvestment costs are given by

(22) Eε[p(I1, I2, I3)

]= p −

θ3∏

i=1(ai + Ii)

=: p(I1, I2, I3) > 0

and

(23) Eκi

[Ci(Ii)

]= Ii =: Ci ≥ 0 ∀i ∈ {1,2,3}.

Even with arbitrarily large investments in all di-visions the supremum p > 0 of the sales pricecannot be reached, as the marginal investment ef-fect decreases with increasing investment levels asdepicted in Figure 4.

Figure 4: Price function

3∏i=1

(ai + Ii)

3∏i=1

ai

p(I1, I2, I3)

00

p −θ3∏

i=1ai

p

Under the assumption (θx)1/4 > max{a1, a2, a3},the first-best investment policy entails positiveinvestment levels in all divisions.

B.1 First-best situation

The first-best investment levels Ifb*i , i ∈ {1,2,3},

are given by

(24) Ifb*i = (θx)1/4 − ai > 0.

Further, the optimal investment levels decreasein initial endowments ai. The optimal solution ischaracterized by (ai + Ii) = (aj + Ij) ∀i, j, whichreflects the decisions’ interdependence. With theinvestment levels according to (24), the maximumtotal profit is given by

(25) Π(

Ifb*1

, Ifb*2

, Ifb*3

, x)

=

(p −

3∑i=1

ci

)x − 4(θx)1/4 +

3∑i=1

ai.

This profit serves as a benchmark measuring or-ganizational efficiency when we take the informa-tional asymmetry into consideration.

B.2 Transfer prices based on variablecosts

With transfer prices based on variable costs andsufficiently small markup factors γ1 and γ2, seeProposition 2, the divisional investments in equi-librium are given by Iv*

1= Iv*2

= 0 and

(26) Iv*3 =

√θx

a1a2− a3 > 0.

126


Interestingly, the level of Iv*3

is independent ofthe specific combinations of markups satisfyingcondition (6). This is due to the absence of anyquantity effects in the price function (1). Observethat the optimality condition for D3’s investmentis the same as in the first-best situation. However,the actual investment level is not first best since D1and D2 do not behave accordingly but renounce toany investments. Summing up, for transfer pricesbased on variable costs with small markup factorsthe optimal investment levels and profits emergeas given in Table 1.

B.3 Transfer prices based on full costs

With transfer prices based on full costs, the markupfactors are ω1 and ω2. Under the assumption thatproduction takes place, i.e., xf (I1, I2, I3) = x, deriv-

ing divisional profits with respect to the divisions’investment levels yields

(27)∂Πf

i (I1, I2, I3, x = x)

∂Ii

=

⎧⎪⎪⎪⎨⎪⎪⎪⎩ωi if i ∈ {1,2}

θx

(a3 + I3)3∏

j=1(aj + Ij)

− 1 if i = 3 .

Consider the case with administered prices with-out negotiations. HQ can choose negative markups,which yields the same optimal investment levelsand total profit as under scheme v which can be in-ferred from comparing Table 2 with Table 1. Table 3summarizes the results for negotiated scheme f .

Table 1: Investments and profits for scheme v

Division Di Investment Iv*i Profit Πv

i

(Iv*1

, Iv*2

, Iv*3

, x)

D1 0 γ1c1x

D2 0 γ2c2x

D3

√θx

a1a2− a3

(p −

2∑i=1

(1 + γi)ci − c3

)x − 2

√θx

a1a2+ a3

Total profit3∑

i=1Πv

i (·) =

(p −

3∑i=1

ci

)x − 2

√θx

a1a2+ a3

Table 2: Investments and profits for administered scheme f (negative markups)

Division Di Investment If *i Profit Πf

i

(If *1

, If *2

, If *3

, x)

D1 0 ω1c1x

D2 0 ω2c2x

D3

√θx

a1a2− a3

(p −

2∑i=1

(1 + ωi)(

ci +Ii

x

)− c3

)x − 2

√θx

a1a2+ a3

Total profit3∑

i=1Π

fi (·) =

(p −

3∑i=1

ci

)x − 2

√θx

a1a2+ a3

Table 3: Investments and profits for negotiated scheme f

Division Di Investment If *i Profit Πf

i

(If *1

, If *2

, If *3

, x)

D1

(θx

a3

)1/3

− a1 ω1

(c1x +

(θx

a3

)1/3

− a1

)

D2

(θx

a3

)1/3

− a2 ω2

(c2x +

(θx

a3

)1/3

− a2

)

D3 0 0

Total profit3∑

i=1Π

fi (·) =

(p −

3∑i=1

ci

)x − 3

(θx

a3

)1/3

+ a1 + a2

127


B.4 Numerical results

In the following, we calculate the profits for dif-ferent parameter settings. The upper bound of thesales price is given by p = 30, the scaling parame-ter θ is set to 50, the variable production costs ofthe divisions are c1 = c2 = c3 = 1 and the (max-imum) sales quantity is x = 3. The capital-stockendowment of division 3 is a3 = 2.5, whereas a1and a2 can be inferred from the column and rowheadings in the tables. All numbers are rounded totwo digits after the decimal point.We give a reading example for Table 4 showingthe model results for the first-best case: Considerthe entries for a1 = a2 = 1. Here, the investmentlevels of D1 and D2 are Ifb

1= Ifb1

≈ 2.50, whereas

D3 only invests Ifb3

≈ 1.00. Divisional profits arenot defined for the first-best case. Total profit isgiven by Π

(Ifb1

, Ifb2

, Ifb3

, x)

≈ 71.50. Obviously, inthe optimum capital stocks after investments areequal in all divisions, meaning the marginal ratesof capital productivity are equal over the threedivisions ex post. Consequently, total profits onlydiffer due to varying investment costs.In Table 5 the results are presented for trans-fer prices based on variable costs (scheme v) withsmall markups. In addition to the parameters men-tioned above, the markups γ1 = γ2 = 0.1 are intro-duced. As stated in the paper, D1 and D2 cannot

Table 4: Numerical example for thefirst-best case

a1

1.0 1.5 2.0 2.5 a2

Ifb1

2.50 2.00 1.50 1.00

Ifb2

2.50 2.50 2.50 2.50

Ifb3

1.00 1.00 1.00 1.001.0

Π(Ifb1

, Ifb2

, Ifb3

, x)71.50 72.00 72.50 73.00

Ifb1

2.50 2.00 1.50 1.00

Ifb2

2.00 2.00 2.00 2.00

Ifb3

1.00 1.00 1.00 1.001.5

Π(Ifb1

, Ifb2

, Ifb3

, x)72.00 72.50 73.00 73.50

Ifb1

2.50 2.00 1.50 1.00

Ifb2

1.50 1.50 1.50 1.50

Ifb3

1.00 1.00 1.00 1.002.0

Π(Ifb1

, Ifb2

, Ifb3

, x)72.50 73.00 73.50 74.00

Ifb1

2.50 2.00 1.50 1.00

Ifb2

1.00 1.00 1.00 1.00

Ifb3

1.00 1.00 1.00 1.002.5

Π(Ifb1

, Ifb2

, Ifb3

, x)73.00 73.50 74.00 74.50

Table 5: Numerical example for scheme v

a1

1.0 1.5 2.0 2.5 a2

Iv*1

0 0 0 0

Iv*2

0 0 0 0

Iv*3

9.75 7.50 6.16 5.25

Πv1

(Iv*1

, Iv*2

, Iv*3

, x)

0.30 0.30 0.30 0.30 1.0

Πv2

(Iv*1

, Iv*2

, Iv*3

, x)

0.30 0.30 0.30 0.30

Πv3

(Iv*1

, Iv*2

, Iv*3

, x)58.41 62.90 65.58 67.41

Π(Iv*1

, Iv*2

, Iv*3

, x)59.01 63.50 66.18 68.01

Iv*1

0 0 0 0

Iv*2

0 0 0 0

Iv*3

7.50 5.66 4.57 3.82

Πv1

(Iv*1

, Iv*2

, Iv*3

, x)

0.30 0.30 0.30 0.30 1.5

Πv2

(Iv*1

, Iv*2

, Iv*3

, x)

0.30 0.30 0.30 0.30

Πv3

(Iv*1

, Iv*2

, Iv*3

, x)62.90 66.57 68.76 70.25

Π(Iv*1

, Iv*2

, Iv*3

, x)63.50 67.17 69.36 70.85

Iv*1

0 0 0 0

Iv*2

0 0 0 0

Iv*3

6.16 4.57 3.62 2.98

Πv1

(Iv*1

, Iv*2

, Iv*3

, x)

0.30 0.30 0.30 0.30 2.0

Πv2

(Iv*1

, Iv*2

, Iv*3

, x)

0.30 0.30 0.30 0.30

Πv3

(Iv*1

, Iv*2

, Iv*3

, x)65.58 68.76 70.65 71.95

Π(Iv*1

, Iv*2

, Iv*3

, x)66.18 69.36 71.25 72.55

Iv*1

0 0 0 0

Iv*2

0 0 0 0

Iv*3

5.25 3.82 2.98 2.40

Πv1

(Iv*1

, Iv*2

, Iv*3

, x)

0.30 0.30 0.30 0.30 2.5

Πv2

(Iv*1

, Iv*2

, Iv*3

, x)

0.30 0.30 0.30 0.30

Πv3

(Iv*1

, Iv*2

, Iv*3

, x)67.41 70.25 71.95 73.10

Π(Iv*1

, Iv*2

, Iv*3

, x)68.01 70.85 72.55 73.70

be motivated to invest. Further -- as no quantityeffects occur -- divisional profits of D1 and D2 re-main stable over all combinations of capital stocks.In contrast, D3 invests less the higher the other di-visions’ capital stocks are, thereby raising its ownprofit.Table 6 exhibits the results for administered trans-fer prices based on full costs (scheme f ) withoutnegotiations over the investment levels. Here theparameters ω1 = ω2 = −0.1 are introduced. Notethat they are negative in order to prevent the co-ordination problem explained in the paper. SinceD1 and D2 still cannot be motivated to invest, totalprofits remain unchanged compared to Table 5.However, due to differing transfer prices the allo-cation of total profit among the divisions alters.Table 7 provides the results for negotiated transferprices based on full costs. Note that in comparisonto scheme f with negative markups inverse invest-

128


ment incentives are induced, i.e., the upstreamdivisions are motivated to invest whereas D3 re-strains from investment. As shown in the paper,D1’s and D2’s decisions leave D3 with zero profit.Furthermore, uncountably many pairs (ω1, ω2) ex-ist which generate the presented investments. Bysetting ω1 = 7 and adjusting ω2 appropriately wearbitrarily choose one of them. The notably highmarkup factors are due to the parameter setting.

Table 6: Numerical example foradministered scheme f (negativemarkups)

a1

1.0 1.5 2.0 2.5 a2

If *1

0 0 0 0

If *2

0 0 0 0

If *3

9.75 7.50 6.16 5.25

Πf1

(If *1

, If *2

, If *3

, x)

−0.30 −0.30 −0.30 −0.30 1.0

Πf2

(If *1

, If *2

, If *3

, x)

−0.30 −0.30 −0.30 −0.30

Πf3

(If *1

, If *2

, If *3

, x)59.61 64.10 66.78 68.61

Π(If *1

, If *2

, If *3

, x)59.01 63.50 66.18 68.01

If *1

0 0 0 0

If *2

0 0 0 0

If *3

7.50 5.66 4.57 3.82

Πf1

(If *1

, If *2

, If *3

, x)

−0.30 −0.30 −0.30 −0.30 1.5

Πf2

(If *1

, If *2

, If *3

, x)

−0.30 −0.30 −0.30 −0.30

Πf3

(If *1

, If *2

, If *3

, x)64.10 67.77 69.96 71.45

Π(If *1

, If *2

, If *3

, x)63.50 67.17 69.36 70.85

If *1

0 0 0 0

If *2

0 0 0 0

If *3

6.16 4.57 3.62 2.98

Πf1

(If *1

, If *2

, If *3

, x)

−0.30 −0.3 −0.30 −0.3 2.0

Πf2

(If *1

, If *2

, If *3

, x)

−0.30 −0.3 −0.30 −0.3

Πf3

(If *1

, If *2

, If *3

, x)66.78 69.96 71.85 73.15

Π(If *1

, If *2

, If *3

, x)66.18 69.36 71.25 72.55

If *1

0 0 0 0

If *2

0 0 0 0

If *3

5.25 3.82 2.98 2.40

Πf1

(If *1

, If *2

, If *3

, x)

−0.30 −0.30 −0.30 −0.30 2.5

Πf2

(If *1

, If *2

, If *3

, x)

−0.30 −0.30 −0.30 −0.30

Πf3

(If *1

, If *2

, If *3

, x)68.61 71.45 73.15 74.30

Π(If *1

, If *2

, If *3

, x)68.01 70.85 72.55 73.70

Table 7: Numerical example for negotiatedscheme f

a1

1.0 1.5 2.0 2.5 a2

ω2 5.05 5.72 6.40 7.08

If *1

2.91 2.41 1.91 1.41

If *2

2.91 2.91 2.91 2.91

If *3

0 0 0 0

Πf1

(If *1

, If *2

, If *3

, x)41.40 37.90 34.40 30.90

1.0

Πf2

(If *1

, If *2

, If *3

, x)29.85 33.85 37.85 41.85

Πf3

(If *1

, If *2

, If *3

, x)

0 0 0 0

Π(If *1

, If *2

, If *3

, x)71.26 71.76 72.26 72.76

ω2 5.61 6.34 7.08 7.82

If *1

2.91 2.41 1.91 1.41

If *2

2.41 2.41 2.41 2.41

If *3

0 0 0 0

Πf1

(If *1

, If *2

, If *3

, x)41.40 37.90 34.40 30.90

1.5

Πf2

(If *1

, If *2

, If *3

, x)30.35 34.35 38.35 42.35

Πf3

(If *1

, If *2

, If *3

, x)

0 0 0 0

Π(If *1

, If *2

, If *3

, x)71.76 72.26 72.76 73.26

ω2 6.28 7.09 7.90 8.72

If *1

2.91 2.41 1.91 1.41

If *2

1.91 1.91 1.91 1.91

If *3

0 0 0 0

Πf1

(If *1

, If *2

, If *3

, x)41.40 37.90 34.40 30.90

2.0

Πf2

(If *1

, If *2

, If *3

, x)30.85 34.85 38.85 42.85

Πf3

(If *1

, If *2

, If *3

, x)

0 0 0 0

Π(If *1

, If *2

, If *3

, x)72.26 72.76 73.26 73.76

ω2 7.10 8.01 8.91 9.82

If *1

2.91 2.41 1.91 1.41

If *2

1.41 1.41 1.41 1.41

If *3

0 0 0 0

Πf1

(If *1

, If *2

, If *3

, x)41.40 37.90 34.40 30.90

2.5

Πf2

(If *1

, If *2

, If *3

, x)31.35 35.35 39.35 43.35

Πf3

(If *1

, If *2

, If *3

, x)

0 0 0 0

Π(If *1

, If *2

, If *3

, x)72.76 73.26 73.76 74.26

Appendix C: Additionalexplanations for Section 4.3This appendix provides further explanations con-cerning the negotiations under transfer pricingbased on full costs presented in Section 4.3. In par-ticular, we first motivate why negotiated transferpricing does not maximize (expected) total profitand then why the downstream division is not con-sidered in the analysis of the negotiations.At first glance, it might be surprising that, as aresult of our analysis, negotiated transfer pric-ing is inefficient with respect to total profit, seePropositions 1 and 6. One might rather expectthat the three divisions agree on maximizing total

129


profit by choosing appropriate investments and di-vide the maximal total profit among themselves bymeans of the transfer prices. While this course ofaction would produce Pareto-efficient (expected)divisional profits, it is only feasible either if in-vestments are contractible or if, given the agreedtransfer prices, it is in each division’s individual in-terest not to deviate from the agreed investments.In our setting, the investment decisions, Ii, are notcontractible; only the investments’ actual costs,Ci, are. Since the investment decision only deter-mines the investment’s expected actual costs, theinvestment decision cannot be inferred from actualinvestment costs. Consequently, it is not feasibleto maximize total profit by contracting the invest-ment decisions themselves or by a forcing contractbased on the associated investment costs. Enforce-ability of an agreement on investments thereforerequires that it is a Nash equilibrium in the non-cooperative investment game arising from the si-multaneous investment choices at date 3. Sincethe downstream division does not invest in equi-librium, see Proposition 3, first-best investmentsas given by Proposition 1 do not form an equilib-rium and transfer pricing based on full costs doesnot achieve first best.In our model, negotiating investment levels forpositive markups basically means that the divi-sions select one out of multiple equilibria in theinvestment game. Each of these equilibria has theproperty that the downstream division’s contribu-tion margin is zero, see expression (12). To see thisrefer to Figure 3 and concentrate on the pair ω ofmarkup factors. Assume that D2 invests Ifb

2(0) and

remember that Figure 3 is based on zero invest-ment for D3. Then, D1’s best reaction to I2 = Ifb

2(0)

and I3 = 0 is I1 = Ifb1

(0). The corresponding profitfor D1 is approximately 7.4. Any higher invest-ment implies that D3 expects a negative contribu-tion margin and thus does not market the product,which leads to a negative profit for D1. Investingless is not optimal for D1 either: For instance, forI1 = Ifb

1(0)/2 the profit for D1 amounts to approx-

imately 4.7, while the corresponding contributionmargin for D3 is positive.Increasing D1’s investment then means higher (ex-pected) revenue for D3 due to the investment’spositive effect on the sales price. Yet, the associ-ated increase of the (expected) transfer payment toD1 is even higher. Thus, increasing I1 lowers D3’s

contribution margin, while D1’s profit increases.D3’s contribution margin is just exhausted andD1’s profit is maximized, when I1 reaches Ifb

1(0).

Equivalent effects govern D1’s optimal reaction toother investment levels chosen by D2 and D3, andalso apply for D2’s optimal investment reaction.Hence, in any equilibrium of the investment game,D3 incurs zero contribution margin. It is there-fore not worthwhile for this division to invest, sothat, in equilibrium, D3 incurs zero profit. Sincethis result holds for any pair of positive markupfactors, there is no effect of D3 taking part in thenegotiations, neither on the investment levels noron the markup factors.

AcknowledgmentsThe authors acknowledge comments received atthe EAA conference in Gothenburg, the confer-ence of the German Operations Research Soci-ety in Karlsruhe, and the conference of the Ger-man Academic Association for Business Research(VHB) in Dresden. Further beneficial recommen-dations have been given by workshop participantsat the Otto-von-Guericke-University Magdeburg.We would like to thank two anonymous refer-ees and Rainer Niemann (the department editor).Their comments helped to significantly clarify thepaper.

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BiographiesAnne Chwolka has held the Chair of Busi-ness Economics and Accounting at the Otto-von-Guericke-University Magdeburg since 2004. Shereceived her Diploma in Managerial Economicsand her Doctoral degree at Bielefeld University,where she also completed her Habilitation. Her re-search interests include decision analysis, internalpricing, risk reporting, and performance measure-ment.

Jan Thomas Martini, MA, Diplom-Kaufmann,Dr., is a postdoctoral research and teaching asso-ciate at the Chair of Management Accounting andOperations Management at Bielefeld University(Germany). He graduated in International Busi-ness at ESC Rennes School of Business (France)and in Business Administration at Bielefeld Uni-versity, from which he also received a doctoraldegree. His research interests include managerialaccounting, in particular transfer pricing, indus-trial services, and the links between managerialaccounting on the one hand and financial account-ing and taxation on the other.

Dirk Simons has been Professor and Chairof Business Administration & Accounting atMannheim University since 2004 and Head ofthe Center of Doctoral Studies in Business Ad-ministration since 2008. He studied Business Ad-ministration and received his Diploma Degree atBielefeld University, where he also received hisdoctorate and achieved his Habilitation. His mainfields of research are theory of accounting andauditing, applied institutional economics, interna-tional accounting, and convergence of managerialand financial accounting.

131

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The Value of Negotiating Cost-Based Transfer Prices

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