GERMAN ECONOMIC ASSOCIATION OF BUSINESS ADMINISTRATION GEABA DISCUSSION PAPER SERIES IN ECONOMICS AND MANAGEMENT

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1 DISCUSSION PAPER SERIES IN ECONOMICS AND MANAGEMENT Tax and Managerial Effects of Transfer Pricing on Capital and Physical Products Oliver Duerr, Thomas Rüffieux Discussion Paper No GERMAN ECONOMIC ASSOCIATION OF BUSINESS ADMINISTRATION GEABA

2 Tax and Managerial Effects of Transfer Pricing on Capital and Physical Products Oliver M. Duerr Thomas Rüffi eux March 27, Preliminary and Incomplete Draft; please do not cite without author s permission - We thank Robert F. Goex and seminar participants at the University of Zurich for valuable comments and suggestions. Dr. Oliver M. Duerr, Esslingen University of Applied Sciences, Department of Management, Flandernstrasse 101, D Esslingen, Germany, Tel.: , oliver.duerr@hs-esslingen.de Thomas Rüffi eux, University of Zurich, Chair of Managerial Accounting, Seilergraben 53, CH-8001 Zurich, Switzerland, Tel.: , thomas.rueffi eux@business.uzh.ch. 1

3 Tax and Managerial Effects of Transfer Pricing on Capital and Physical Products Abstract We study the interrelation between product and capital transfer prices and their effects on the optimal decision authority in multinational companies in an analytical transfer pricing model. We find that in the case of centralized decisions both transfer prices only serve as tax shifting devices and are independent of each other. In contrast, if operating decisions are delegated to better informed subsidiaries, product and capital transfer prices are interdependent and cannot be set independently. Because both transfer prices induce negative coordination effects, either on the quantity or the capital invested, the interrelation between the product and the capital transfer price is negative. We further show that, despite this interrelation of transfer prices, the decentralized case can be an optimal structure of the multinational company (MNC) due to the asymmetric information structure. Keywords: Transfer Pricing, Multinationals, Capital Transfer Pricing 2

4 1 Introduction The research on transfer pricing has a long tradition in management accounting. Starting with Hirshleifer (1956), the research focus was on internal coordination. Despite other extensions (e.g. asymmetric information (Wagenhofer (1994)), specific investments (Edlin and Reichelstein (1995)) and strategic interactions (Goex (2000))), tax saving issues have attracted a lot of attention during the last decade. 1 The global transfer pricing report by Ernst&Young (2013) for example shows that two-thirds of companies identify tax issues (especially tax risk management) as their top priority in transfer pricing. In the management accounting literature Baldenius et al. (2004) were among the first who analytically analyze the integration of tax and managerial objectives in transfer pricing. Others extended the model with tax, and managerial objectives by adding specific investments (Duerr and Goex (2013)), strategic interactions (Duerr and Goex (2011)) or intangibles (Johnson (2006)). What has been largely ignored so far in the management accounting literature is the analysis of transfer prices for physical products and for capital in an integrated analytical model. This is notably astonishing because according to the global transfer pricing report by Ernst&Young (2013) transfer pricing on capital is rated the second most important area for MNCs. 2 However, research on capital transfer prices is widely discussed in the public finance literature. The studies on capital transfer prices in this literature stream mostly assume centralized MNCs and focus on welfare effects and taxation issues, instead of optimal transfer pricing issues. 3 Our study thus contributes to the transfer pricing literature in management accounting in the following ways. We integrate transfer pricing for physical goods and for capital in a single model. As far as we know, our model is the first that integrates both transfer prices in a single model setting. We compare centralized and decentralized decisions, the effects on optimal transfer pricing and the interaction between physical and capital transfer prices. We find the following results. First, we show that in the case of centralized investment and quantity transfer decisions, the transfer prices for capital and for products can be set 1 See Göx/Schiller (2007) for an extensive overview of analytical transfer pricing models. 2 See Ernst & Young (2013) survey where intra group financial arrangements and intangible property are listed second and third on areas of transfer pricing controversy. 3 See e.g. Grubert (1998, 2003). 3

5 independently of each other. Further we find that the transfer prices only serve the tax minimizing function. Second, we find in the case of decentralized investment and quantity transfer decisions, that capital and product transfer prices are interdependent and cannot be set independently of each other. Therefore a MNC has to be aware of the interdependencies and has to take the mutual effects into account when setting the optimal transfer prices. The model is based on a multinational corporation who uses a transfer price for internally supplied intermediate goods and a second transfer price for capital provided to its subsidiaries. In addition to a standard analytical transfer pricing model we allow the operative subsidiaries to make capital investments under asymmetric demand information. In the centralized case the MNC s headquarter (HQ) takes all decisions, i.e. it determines transfer prices, investments and quantity transferred. Our analysis reveals that in this setting, the optimal capital and product transfer prices are set independently of each other. The transfer prices have no coordinative function and solely serve the purpose of tax minimization. We also find that optimal investments are larger in the presence of taxes than without taxes because interest payments on the capital investments are tax deductible. A similar effect results for the quantity that also increases (decreases) in the product transfer price for a higher (lower) tax rate in the buyer s country. In the case of decentralized quantity and investment decisions, we find that transfer prices have additional coordinative effects on quantities and investments. Because transfer prices reflect the buyer s marginal costs of the internally supplied product or capital, higher transfer prices have direct negative effects on quantities and investments. The investments affect marginal returns and costs and thus also have an indirect effect on the quantity decision. Therefore, in the decentralized case, the optimal product and capital transfer prices are interdependent of each other. In fact, we find that both transfer prices are negatively related to each other. The intuition of this result is that the sequential decisions on investments and quantities both have an impact on each other s marginal returns and costs. A lower quantity, induced by an increase in the product transfer price, leads to a decrease in marginal investment returns and thus to a lower capital transfer price. Lower investments, induced by an increase in the capital transfer price, in turn decrease marginal returns of the quantity and thus lead to a lower product transfer price. However, we show that despite those negative coordination effects the decentralization of investment and quantity decisions can be optimal for a MNC. This result is due to the asymmetry of demand information between the HQ and the subsidiaries and the resulting trade-off between the coordination and tax effect on 4

6 the one side and an information effect on the other side. The remainder of the article is organized as follows. In Section 2, we present the basic model. Section 3 characterizes the benchmark case where all decisions are taken centrally by the headquarter. Section 4 discusses the decentralized planning case where the decisions about the quantity and capital investments are delegated to the operative subsidiaries. In section 5, a parametric example supports our findings. Section 6 concludes. 2 Model setup We consider a MNC that consists of a HQ and three legally separate subsidiaries: a seller (subsidiary S), a buyer (subsidiary B) and an internal financing company (subsidiary F ). The subsidiaries are located in different tax jurisdictions with potentially different tax rates. 4 Subsidiary S produces an intermediate product that is supplied to subsidiary B who processes it into a final product and sells it at a price p on the product market. For means of simplicity, we assume one unit q of the intermediate product is transformed into one unit of the final product. In exchange for each unit q of the intermediate product the buyer pays the seller a product transfer price (PTP) t. Producing q units of the intermediate product, the seller incurs production cost C(q, k S ) that can be reduced by investing capital k S in cost-saving activities. Accordingly, we assume the following additively separable cost function C(q, k S ) for the seller: C(q, k s ) := C 1 (q) + C 2 (k S ) q. (1) The cost function consists of variable production costs C 1 (q) and a cost reduction effect C 2 (k S ) of the investment k S with the following properties: C 1 (q) > 0, 2 C 1 (q) 0, q q 2 (2) C 2 (k S ) < 0, 2 C 2 (k S ) 0. k S ks 2 (3) 4 We assume no profit repatriations to the HQ, e.g. via dividend payments, which allows us to neglect the tax rate of the headquarter. 5

7 Property (2) implies that the cost function is increasing and convex in the quantity q. Condition (3) means that an investment k S reduces the cost of production for any given quantity q at a decreasing marginal rate. The investment of capital k S results in utilization cost of capital, denoted as I S (k S ) which can be different from the pure amount of capital investment due to additional efforts to integrate new production equipment and organizational changes. The utilization cost function has the following properties: I S (k S ) k S > 0, 2 I S (k S ) k 2 S 0, (4) implying that the utilization cost of capital is increasing in k S at an increasing marginal rate. To keep the model focused on purposes of transfer pricing, we abstract from competition on the final product market and assume the subsidiary B to be a monopolist, facing a decreasing price function in the quantity q. The demand on the product market is uncertain and depends on the state of the world θ := (θ 1, θ 2 ), represented by two stochastically independent random state variables θ 1 and θ 2. 5 Alike the seller, the buyer can invest capital k B in marketing activities that increase revenues. The revenue function R(q, θ, k B ) is defined as: R(q, θ, k B ) := (R 1 (q, θ) + R 2 (k B )) q. (5) Its first part, R 1,is the price function and depends on the quantity q and the realization of the state of the world θ, whereas the second part, R 2, represents the additional revenues from marketing activities. The price function and the marketing revenue function have the following properties: R 1 (q, θ) < 0, 2 R 1 (q, θ) 0, q q 2 (6) R 2 (k B ) > 0, 2 R 2 (k B ) 0. k B kb 2 (7) The first property (6) states that the price function, R 1, is decreasing and concave in the quantity q. The second property (7) implies, that R 2 is increasing in the amount of capital invested k B but at a decreasing rate. As for the seller, the investment of capital k B implies utilization cost I B (k B ) that are convex in the amount of capital invested: I B (k B ) k B > 0, 2 I B (k B ) k 2 B 5 This setting is akine to Edlin and Reichelstein (1995). 0. (8) 6

8 The financial subsidiary s scope of business is to provide capital to subsidiaries B and S to fund their investments. Subsidiary F serves solely as an internal capital provider without any decision-making authority. In exchange for capital k B and k S, subsidiaries B and S have to pay the financing company an interest rate of r [r; _ r] per unit of capital, referred to as capital transfer price (CTP). The lower bound r represents the interest rate at which subsidiary F can raise funds from the global capital market, the upper bound _ r is the maximum rate accepted by the tax authorities. Further we assume the lower bound of the capital transfer price to be constant and independent of k B and k S. 6 Likewise, we define an acceptable range for the product transfer price t [t, t], such that t lies between marginal production cost t = C(q, k S )/ q and the market price per unit of the final product t = p. Due to the MNC s possibility to raise funds from the global capital market, it faces few restrictions for its financing subsidiary s location. In order to benefit from tax savings, the company has a vested reason to place subsidiary F in a country where the tax rate on interest income is as low as possible. In contrast, the MNC might face more legal, political and organizational restrictions for the location of its HQ. This finally makes a legally separate and delocated financing subsidiary plausible and allows us to set the financing company s tax rate τ F equal to zero. We define the effective tax rate for subsidiary S as τ 0 and the one for subsidiary B as τ + δ 0, with δ [ τ; 1 τ]. The timeline of events and the information structure about the realization of the state of the world θ is as follows: [Please insert figure 1 about here] The timeline starts with the HQ s decision on the capital and the product transfer price, r and t. At date t = 2, subsidiaries B and S observe the realization of the state variable θ 1, that gives them better, though not precise information about the product demand. Based on that private information, they decide in t = 3 on the optimal amounts of capital investments k B and k S. At date t = 4, subsidiary B observes the realization of θ 2. Thus, subsidiary B has full information about the product demand and decides at date t = 5 about the optimal quantity ordered from subsidiary S. At the last stage, the transfer of q units of the 6 We abstract from the case where the amount of capital raised influences the interest rate and assume the group s overall financing conditions on the global capital market to be independent of the concrete amount of capital raised. 7

9 intermediate product takes place and the payments are settled. As it is usually the case in product transfer pricing literature, we assume that communication of the realizations of the state variables to the headquarter is limited such that the HQ cannot write any contract on their realization. 7 Therefore, the HQ can base its decisions solely on its expectation about θ1 and θ 2. The three subsidiaries after tax profits then unfold as: Π B (q, k B, θ) = (1 τ δ) ((R 1 (θ, q) + R 2 (k B )) q t q I B (k B ) r k B ) (9) Π S (q, k S ) = (1 τ) (t q C 1 (q) C 2 (k S ) q I S (k S ) r k S ) (10) Π F (k S, k B ) = (r r) (k B + k S ) (11) The buyer s after tax profit Π B (q, k B, θ) consists of revenue R(q, θ, k B ) minus the transfer payment to the seller, minus the utilization cost of the invested capital and the interest paid to subsidiary F. For means of simplicity we assume that interest payments are fully tax deductible. 8 Accordingly, the seller s after tax profit, Π S (q, k S ), is calculated as the buyer s transfer payment minus the production cost, minus the utilization cost of the invested capital k S and the interest paid to subsidiary F. Subsequently, the financing subsidiary s profit Π F (k S, k B ) consists of the difference between the interest r paid on funds raised on the global capital market and the interest r gained from capital provided to subsidiaries B and S. The MNC s after tax profit Π(q, k S, k B, θ) results as the sum of the three subsidiaries after tax profits: Π(q, k S, k B, θ) = (1 τ δ) ((R 1 (θ, q) + R 2 (k B )) q t q I B (k B ) r k B ) +(1 τ) (t q C 1 (q) C 2 (k S ) q I S (k S ) r k S ) +(r r) (k B + k S ) (12) In the following section we analyze the centralized planning case as a benchmark, where the HQ takes the decisions about transfer prices, investments and the quantity transferred. 7 The assumption that both managers observe the realization θ but outsiders do not is akine to Baldenius, Reichelstein, Sahay (1999) and Edlin and Reichelstein (1996). 8 We do not consider so-called thin capitalization rules used in some countries that disallow firms to deduct interest payments from taxable profit under certain circumstances. 8

10 3 Centralized planning (benchmark case) As benchmark, we analyze a setting of centralized planning where the headquarter takes all decisions, i.e. the HQ determines the quantity q transferred between B and S, the subsidiaries capital investments k B and k S, the product transfer price t and the capital transfer price r. The HQ, unlike the managers of subsidiaries B and S, cannot observe the realizations of the state variables θ 1 and θ 2 and has to base its decisions on expectations E[ θ 1 ] and E[ θ 2 ]. Therefore the group s expected profit results as: E θ [Π(q, k S, k B, θ)] = (1 τ δ) (E θ [R 1 (θ, q) q] + R 2 (k B ) q I B (k B )) +(1 τ) ( C 1 (q) C 2 (k S ) q I S (k S )) +δ t q + (r τ r) k S + (r (τ + δ) r) k B (13) Because the HQ takes all decisions based on the same information the decision process can be modeled as a simultaneous optimization problem. Maximizing the group s expected profit to the capital and product transfer price yields the following optimality conditions: E θ [Π(q, k S, k B, θ)] r = τ k S + (τ + δ) k B 0 (14) E θ [Π(q, k S, k B, θ)] t = δ q. (15) Inspecting the above conditions (14) and (15) we derive our first proposition: Proposition 1: In the centralized case, the optimal CTP and the optimal PTP are set independently of each other. The optimal CTP is set at the upper bound of the admissible interval, r = r, and the optimal PTP is set at the upper (lower) bound t = t ( t = t) for a positive (negative) tax rate difference δ > 0 ( δ < 0). If the tax rate difference between subsidiaries B and S is zero, δ = 0, the optimal PTP has no effect on the expected profit and can be set arbitrarily between t and t. Proof: Results directly from the FOC s (14) and (15). Condition (14) is positive for all levels of capital investments k B and k S and represents the group s tax benefit from shifting profits to the financing subsidiary that has the lowest tax rate within the group. The similar argument holds for the product transfer price. Condition 9

11 (15) is positive or negative, depending on the tax rate difference δ between the subsidiaries B and S. If the tax rate difference is δ > 0 (δ < 0), condition (15) is positive (negative) and the optimal PTP is set at the highest (lowest) admissible level what results in optimal profit shifting. Because all decisions are taken by the HQ there is no coordinative function for the transfer prices. Therefore they can be set independently of each other and have only a tax optimization function. The optimality conditions for the HQ maximizing the group s expected profit with respect to the quantity q and the investment amounts k B and k S are as follows: E θ [Π(q, k S, k B, θ)] q = (1 τ δ) (E θ [R 1 (θ, q) + q R 1(θ, q) ] + R 2 (k B )) q +(1 τ) ( C 1(q) C 2 (k S )) + δ t = 0 (16) q E θ [Π(q, k S, k B, θ)] k B = (1 τ δ) ( R 2(k B ) k B q I B(k B ) k B ) + (r (τ + δ) r) = 0 (17) E θ [Π(q, k S, k B, θ)] k S = (1 τ) ( C 2(k S ) k S q I S(k S ) k S ) + (r τ r) = 0. (18) Inspecting the conditions (16), (17), and (18) we state the following lemma 1: Lemma 1: The optimal quantity increases (decreases) in the product transfer price if the tax rate difference is positive (negative) and the optimal investments increase in the capital transfer price. If we assume no tax rate difference, δ = 0, condition (16) reveals that the optimal quantity transferred would equate expected marginal cost of production with expected marginal revenues. This result is consistent with findings from traditional product transfer pricing literature for the case of centralized decisions in absence of taxes. 9 If indeed subsidiary B and S exhibit different tax rates, δ 0, then according to condition (16) the optimal quantity increases (decreases) in the PTP if the tax rate difference is positive (negative). This effect is due to the fact that the product transfer price is tax deductible for the buying subsidiary. Therefore a positive tax rate difference δ > 0, acts like a tax subsidy 9 Already Hirshleifer (1956) and Schmalenbach (1908/1909) show that in the absence of an external market and specific investments, the optimal transfer price is set to the marginal cost of production. 10

12 and makes the transfer of a higher quantity favorable. The same logic applies to a negative tax rate difference δ < 0. Inspecting the two conditions (17) and (18) reveal that in absence of tax rate differences between the operating subsidiaries B and S and the financing subsidiary F, that is τ = 0 and δ = 0, the optimal investment levels would equate the expected marginal returns with expected marginal investment costs. In the case of a tax rate difference, the optimal investment amounts increase in the capital transfer price r. Like for the product transfer price, the effect is due to a tax saving effect. The capital transfer price paid to the financing subsidiary is tax deductible for the investing subsidiaries and thus makes higher investments more favorable because of the lower taxes that have to be paid. Since we assumed a tax rate of zero for the financing subsidiary, this effect is always positive. The key element for these two effects of the product and capital transfer price is that all decisions are taken centrally. This means that the two transfer prices only have a tax shifting function but are not vital to coordinate optimal decisions. In conclusion, since both transfer prices are solely used for profit shifting and the investments and the quantity are set by the HQ, the two transfer prices can be set independent of each other. The effect of a CTP on the optimal quantity q, the optimal investment levels k B and k S and the product transfer price t for the case where δ > 0 is depicted in figure 2. [Please insert figure 2 about here] Figure 2 particularly highlights the aforementioned observation from lemma 1 that an increase of the CTP r leads to higher optimal investments k B and k S due to profit shifting. The increase in investments from a higher CTP is eventually limited by the upper bound r, the maximum rate accepted by the tax authority. Higher investments in turn reduce marginal cost of production and increase marginal revenues and thus lead to a higher quantity transferred. Since the PTP t serves solely as a means to shift profits, t is set at the highest level because of the assumed positive tax rate difference δ and is independent of the level of the CTP r. Concisely, in the centralized setting, the two types of transfer prices only serve to minimize tax payments and do not intervene with each other. In the following section we analyze the effects on the optimal solutions in the case of decentralized quantity and investment decisions. 11

13 4 Decentralized quantity and investment decisions In the decentralized case, the HQ assigns the investment decisions to the subsidiaries B and S and provides the buyer with the authority to set the quantity transferred. The motivation to delegate these decisions is based on the assumption that the HQ cannot observe the realization of the state variables θ 1 and θ 2. The subsidiaries indeed benefit from private information and sequentially learn the realization of the state variables. In t = 2, both subsidiaries observe the realization of the state variable θ 1 before, in t = 3, they have to decide about their respective capital investments. After the investment decision, subsidiary B receives additional private information about the realization of the state variable θ 2. Observing θ 1 and θ 2, subsidiary B learns the true demand in the product market. Since the subsidiaries of a MNC generally face multiple projects where in turn each project might request a wide range of investment decisions it seems reasonable to assume that an elaborated communication of all private information to the HQ might not be feasible or simply too costly. In such a setting, the delegation of investment decisions from the headquarter to the better informed subsidiaries may finally increase investment and process effi ciency. 10 In order to solve the optimization problem for the sequential decision structure, we apply backward induction. At the last stage subsidiary B maximizes its profit Π B w.r.t. the quantity q, yielding the optimality condition: Π B (q, k B, θ) q = R 1 (q, θ) + q R 1(q, θ) q + R 2 (k B ) t = 0. (19) Comparing condition (19) to the optimality condition in the centralized case (16) we observe two differences from delegating the quantity decision to subsidiary B. First, condition (19) is based on the realization of θ, respectively θ 1 and θ 2, instead of its expectation. Second, the optimality condition (19) implies that the quantity decision now also depends on the product transfer price t. We state these observations in the following lemma. Lemma 2: In the case of decentralized quantity decision the optimal quantity q is decreasing in the product transfer price t and increasing in the amount of invested capital k B. We face the traditional coordination problem. The optimal quantity under decentralized versus centralized planning is of equal amount if the product transfer price t is set to marginal 10 The assumption of asymmetric information that arises from too costly or impossible communication of all local information to the central management has already been mentioned in Kaplan & Atkinson (1998, p. 291) as one major reason to decentralize decisions. 12

14 cost. If t exceeds marginal cost, the optimal quantity in the decentralized setting is lower than in the centralized case. On the one hand, this effect stems from a higher t inducing higher marginal costs for subsidiary B. On the other hand, unlike the HQ in the benchmark case, subsidiary B does not internalize the group s benefit from tax savings by shifting profits to the lowest taxed subsidiary. Instead, subsidiary B bases its decision about the quantity q only on its own profit and neglects the other subsidiaries profits as well as the overall benefit for the MNC. Consequently, subsidiary B s decision on the optimal quantity q (θ) := q(θ 1, θ 2, k B, t) depends solely on its marginal return, that in turn is a positive function of the investment level k B, the product transfer price t as well as the realization of the state variables θ 1 and θ 2. Quite intuitively, in the prevailing model setting with asymmetric information and delegated investment decisions, both subsidiaries set the investment amounts in order to optimize their profits, given their information θ 1 about the demand in the product market. In the centralized case where the headquarter lacks this private information and bases its decisions on expectations, the HQ is more likely to prescribe ineffi cient investment amounts. In that respect, the delegation of the investment decisions to the subsidiaries may increase investment effi ciency but lead to divisional instead of overall profit maximization. The respective optimality conditions of the subsidiaries w.r.t. the capital investments in the decentralized case are as follows: E θ2 [ ΠB (q (θ), k B, θ) ] k B = E θ2 [q (θ)] R 2(k B ) k B I B(k B ) k B r = 0, (20) E θ2 [ ΠS (q (θ), k S ) ] k S = E θ2 [q (θ)] C 2(k S ) k S I S(k S ) k S r = 0. (21) The optimal investment amounts k B := k B(E θ2 [q (θ)], r) and k S := k S(E θ2 [q (θ)], r) depend on the expected quantity and the capital transfer price. Both subsidiaries know θ 1 but at the time the investment decisions have to be reached the realization of θ 2 is still unknown. Therefore, subsidiaries B and S have to base their investment decisions on expectations about the true demand. Considering the optimality conditions (20) and (21), the capital transfer price r represents additional marginal investment costs to divisions B and S. Thus a higher capital transfer price makes capital investments more costly and will in turn reduce the subsidiaries investment incentives. We summarize this effect in the following lemma 3. 13

15 Lemma 3: The optimal capital investments k B (E θ2 [q (θ)], r) and k S (E θ2 [q (θ)], r) are decreasing in the capital transfer price r. This is in contrast to the optimality conditions (17) and (18) in the centralized decision case. In the benchmark the HQ prescribes the investment amounts and the group benefits from a higher CTP due to profit shifting, respectively tax savings. In the decentralized setting, the subsidiaries first care about their divisional profits and indeed neglect the group s tax benefits and the effects on the other subsidiaries profits when deciding about their respective capital investments. Consequently, in the decentralized planning case, the effect of r on the optimal investments is negative and is in the opposite direction compared to the centralized setting. In the final step of the optimization process, the HQ sets the capital transfer price r as well as the product transfer price t to maximize the group s expected profit E θ [Π(q (θ), k B, k S, θ)]. To shorten notation we define V θ (q, k B, k S ) := E θ[π(q (θ), k B, k S, θ)]. Maximizing the group s expected profit w.r.t. the capital and product transfer price, yields the following optimality conditions: V θ (q, k B, k S ) r = E θ [(τ + δ) k B + τ k S +(1 τ) (t ( C 1(q (θ)) q C 2 (k S))) q k B k B r +(r r) (k B + k S ) ] = 0, (22) r V θ (q, k B, k S ) t = E θ [δ q (θ) + (1 τ) (t ( C 1(q (θ)) q C 2 (k S))) ( q k B k B t + q t ) +(r r) (k B + k S ) ] = 0. (23) t Solving these FOC s for r and t results in an optimal CTP r :=r(e θ [q (θ), k B, k S, θ]) and an optimal PTP t := t(e θ [q (θ), k B, k S, θ]) being functions of the expectations about the optimal quantity, the optimal investment amounts and the realization of the state of the world. Inspecting the optimality conditions (22) and (23) we observe that the optimal transfer prices are influenced by three distinct effects. 14

16 The optimal capital and product transfer prices r and t balance a tax effect with two negative coordination effects on the optimal quantity and the optimal capital investments. The first term in the optimality conditions (22) and (23) represents the tax effect. This effect is due to the transfer prices serving as means to shift profits. With respect to the capital transfer price, the profit is always shifted to the financing subsidiary and the tax effect is unambiguously positive. For the product transfer price, the tax effect depends on the tax rate difference δ between the subsidiaries B and S and can either be positive or negative. The second term we refer to as quantity coordination effect. For the capital transfer price, this effect is negative. Lemma 3 states that a higher capital transfer price reduces the capital investment, k B / r < 0, since the capital transfer price r represents additional costs to the subsidiaries. Lemma 2 states that a higher capital investment increases the quantity, q/ k B > 0. Therefore, the second term in condition (22) is strictly negative. For the product transfer price, this effect is also negative as Lemma 2 states that a higher product transfer price decreases the quantity, q/ t < 0. Finally, we observe a third effect that we refer to as investment coordination effect. As aforementioned, with respect to the capital transfer price, Lemma 3 states that a higher capital transfer price reduces investment incentives. However, for the product transfer price we face an indirect effect on the optimal capital investments that arises from the decision about the optimal quantity. Condition (19) shows that a higher product transfer price decreases the optimal quantity and thus decreases marginal investment returns what finally decreases optimal investments. Comparing the optimality conditions in the decentralized setting (22) and (23) to the conditions in the centralized case (14) and (15), the first term that is related to the direct tax effect is similar. The two additional effects, the quantity and investment coordination effects, result from delegating the quantity and investment decisions to the subsidiaries. While the coordination of quantity and investment decisions is not necessary in the centralized setting, a trade-off results in the decentralized case. The headquarter has to balance the positive tax effect from higher transfer prices with the negative effects on the investment decisions and the quantity decision. Because the subsidiaries B and S maximize their respective profits and not the group s profit, they face an increase in their marginal costs (intermediate product and capital) but they do not internalize the tax benefits for the whole MNC from profit shifting. Compared to the centralized setting, the two additional effects are thus weakly negative and the resulting optimal product and capital transfer prices in the decentralized setting are weakly lower than in the centralized case. 15

17 In addition, the optimality conditions (22) and (23) show that the CTP and PTP are no longer independent of each other. We summarize this interrelation between the two transfer prices in proposition 2. Proposition 2: The optimal CTP and PTP negatively relate to each other, i.e. the optimal CTP is decreasing in the optimal PTP and vice versa. Proof: The second term of condition (22), we referred to as quantity coordination effect, is negative in r and is scaled by the difference between t and the marginal cost. Therefore, a higher product transfer price t intensifies the negative quantity coordination effect of r. The proof for the PTP is similar. The third term in condition (23) represents the investment coordination effect of the optimal product transfer price. This effect is negative in t and is scaled by the difference between the capital transfer price and the interest paid on the capital market. A higher capital transfer price r thus intensifies the negative investment coordination effect of t. The intuition for the interaction between the two transfer prices is straight forward. The optimal capital transfer price internalizes the negative effect on the optimal investment k B that results in a lower quantity. This effect is scaled by the difference between the product transfer price and the marginal cost. If the product transfer price is equal to the marginal cost, the quantity coordination effect is zero. A higher product transfer price results in a higher quantity coordination effect that intensifies the negative effect on the capital transfer price. The intuition for the product transfer price is akin. The optimal product transfer price internalizes the effect on the quantity and the resulting indirect effect on the capital investments k B and k S. This effect is scaled by the difference between the capital transfer price and marginal cost of capital. If the capital transfer price is equal to the marginal cost of capital, the investment effect is zero. A higher capital transfer price results in a higher investment coordination effect that intensifies the negative effect on the product transfer price. Figure 3 illustrates these effects of r on the optimal investment amounts, the optimal quantity transferred and the PTP, again for the case δ > 0. [Please insert figure 3 about here] To sum up, in the case of decentralized quantity and investment decisions, implementing a capital transfer price benefits the group from saving taxes via profit shifting, but leads 16

18 to lower investments, distorted managerial decisions, a negative effect on the PTP and its respective tax savings. 5 A parametric example In this section we provide a parametric example to illustrate the relations between the two transfer prices, the impact of different tax rates and consequences of the decision to centralize or decentralize. For means of simplicity we assume the random state variable θ to be a sum of θ 1 and θ 2, where θ 1 and θ 2 are uncorrelated, uniformly distributed over an interval [ ξ, ξ] and exhibit an expected value of E[ θ l ] = 0 and a variance of V ar( θ l ) = 1/12 (ξ ( ξ)) 2, for l {1, 2}. Further we assume quadratic utilization cost of capital I i (k i ) = γ ki 2, i {B, S}, where γ is a scaling parameter. The revenue function for the buyer is specified as: R(q, θ 1, θ 2, k B ) = (R 1 (θ 1, θ 2, q) + R 2 (k B )) q = (a + θ 1 + θ 2 q + α k B ) q (24) and the seller s cost of production is given by: C(q, k S ) = C 1 (q) + C 2 (k S ) q = (c α k S ) q, (25) where the scaling parameter α represents the investment effi ciency. The profit functions of buyer B and seller S then unfold as: Π B (q, k B, θ 1, θ 2, t, r) = (1 τ δ) (R(q, θ 1, θ 2, k B ) t q I B (k B ) r k B ) = (1 τ δ) ((a + θ q + α k B t) q γ kb 2 r k B ),(26) Π S (q, k S, t, r) = (1 τ) (t q C(q, k S ) I S (k S ) r k S ) = (1 τ) ((t c + α ks) q γ ks 2 r k S ). (27) The profit function of the financial subsidiary F remains as in the general model and the MNC s profit function is simply the sum of the three subsidiaries profit functions. 17

19 5.1 The centralized case In the centralized setting, the HQ sets the following optimal quantity q according to condition (16) as: q = 1 2 (a + α k B + δ t + (1 τ) (α ks c) ). (28) (1 τ δ) The parametric representation of the optimal quantity q supports lemma 1. The optimal quantity increases (decreases) in the product transfer price if the tax rate difference δ is positive (negative). Because the HQ takes its decisions based on the expectation about the state variable θ, the quantity decision is not affected by the realization of θ. Further, from equation (??) we observe that the decision about the optimal quantity depends also on the capital investments. Plugging the parametric functions into the optimality conditions (17) and (18), yields the following conditions on the optimal capital investments: 11 E θ [Π(q, k B, k S, θ)] k B = (1 τ δ) (α q 2 γ kb) + (τ + δ) r r = 0, (29) E θ [Π(q, k B, k S, θ)] k S = (1 τ) (α q 2 γ ks) + τ r r = 0. (30) Inspecting the above conditions (29) and (30), we find that the optimal capital investments increase in the capital transfer price r what supports lemma 1. As mentioned above, this effect results from a higher capital transfer price shifting taxes to the lowest taxed subsidiary F. This finally makes higher investments more attractive for the MNC. In this setting, the HQ also takes the decisions about the optimal transfer prices. The resulting optimality conditions are identical to the benchmark case (see (14) and (15)). These two conditions, (14) and (15), accede proposition 1. The two transfer prices can be set independently of each other. The optimal capital transfer price is set at the upper bound of the admissible interval r and the optimal product transfer at the upper or lower level of the admissible interval, depending on the tax rate difference δ. 11 One could solve these equations for the optimal investment amounts being aware that q is in turn a function of k B and k S. We forego this step due to the more intuitive representation of the interdependences out of the FOC. 18

20 5.2 The decentralized case In the decentralized setting the optimal quantity is denoted by q. The subsidiary B chooses the optimal quantity according to the optimality condition (19). Using the parameterization we derive the following optimal quantity: q (θ) = 1 2 (a + α k B t + θ 1 + θ 1 ). (31) Comparing the optimal quantity q to the one in the centralized case (28), we find that the optimal quantity q does not depend on the tax rates. Because subsidiary B does not internalize the group s tax benefits of profit shifting, the tax rate differences are not relevant for the subsidiary s quantity decision. Further, as stated in lemma 2, the optimal quantity q decreases in the product transfer price t since a higher PTP represents higher costs to the buyer. As a consequence of subsidiary B s private information about the final demand, the realization of the state variable θ directly affects the buyer s decision about the optimal quantity q (θ). Finally, the optimal quantity increases in subsidiary B s capital investment k B because it increases the product s marginal revenues. Applying the parametric specifications to the optimality conditions (20) and (21) yields: [ E θ2 ΠB (q (θ), k B, θ) ] = α E θ2 [q (θ)] 2 γ k B r = 0, (32) k B [ E θ2 ΠS (q (θ), k S ) ] = α E θ2 [q (θ)] 2 γ k S r = 0. (33) k S Solving the optimality conditions yields the following optimal investment amounts: k B = k S = α (a t + θ 1 ) 2 r 4 γ α 2. (34) While in the centralized setting the optimal investments depend on the tax rates, they do not rely on tax issues in the decentralized case. In that respect, the parametric example shows that the subsidiaries do not internalize the opportunity to shift profits. In the decentralized case, the capital transfer price represents additional cost to subsidiaries B and S and leads to a decrease in the optimal investment amounts. Because the subsidiaries observe the realization of θ 1 their decision about the respective investments is directly affected by 19

21 θ 1. Another difference to the centralized case is the dependence of the decentralized capital investment decisions on the product transfer price. Compared to the centralized case, where the PTP has no effect on the optimal quantity, in the decentralized setting, the product transfer price influences the subsidiaries s capital investment decisions through the expectation about the optimal quantity. Finally, the decisions about the optimal transfer prices remain to the HQ. Solving the respective conditions (22) and (23) and taking the parametric specifications into account, we get the following optimality conditions w.r.t. the capital and product transfer price: V θ (q, k B, k S ) r = (2 τ + δ) α (a t ) 2 r 4 γ α 2 +(1 τ) E θ [(t (c α α (a )) ] t ) 2 r q k B 4 γ α 2 k B r 4 4 γ α 2 (r r) = 0, (35) V θ (q, k B, k S ) t = δ ( 2 γ (a t ) r ) 4 γ α 2 +(1 τ) E θ [(t (c α α (a )) ( t ) 2 r )] q k B 4 γ α 2 k B t + q t 2 α 4 γ α 2 (r r) = 0. (36) As mentioned in the main part about the decentralized case, there are three effects that influence the decisions on the optimal transfer prices. The parametric representations of the optimality conditions for the two transfer prices (35) and (36) exhibit these three distinct effects. The tax effect is represented on the first line of the two optimality conditions (35) and (36). For the CTP r, this effect is always positive, because a higher capital transfer shifts more profits to the lowest taxed subsidiary F. In contrast, in the optimality condition for the PTP (36), the direction of the tax effect depends on the tax rate difference δ between B and S and can therefore be positive or negative. The terms on the second line of the conditions (35) and (36) represent the quantity coordination effects. As states in lemma 3, a higher CTP implies higher costs for the subsidiaries B and S and thus reduces the optimal capital investment ( k B / r < 0). Further, as stated in lemma 2, the effect of a higher capital investment increases the optimal quantity ordered ( q/ k B > 0). This implies that the 20

22 quantity coordination effect for the optimal CTP is unambiguously negative - as long as the PTP exceeds marginal cost of production. If the PTP is identical to marginal production cost, the effect becomes zero as in the standard transfer pricing model. Considering lemma 2 and lemma 3 and the fact, that q/ t < 0, the argumentation for the product transfer price is similar. Finally, the third line in the conditions (35) and (36) represent the investment coordination effect. This effect is always negative because the investment amount is decreasing in both transfer prices. 5.3 Some comparative statics In order to analyze the effects of a variation in the tax rate difference and the uncertainty about the state of the world, we conduct a numerical example with the following specifications: τ = 0.2, δ [ 0.15, 0.15], θ 1 [ 10, 10], θ 2 [ 10, 10], t = 70, r = 0.25, r = 0, a = 100, c = 50, α = 0.05, γ = Solving the optimality conditions for the decision variables derived in the sections 5.2 and 5.3 for the centralized and decentralized case, we get the following results: [Please insert table 1 about here] First, we analyze the results for the centralized case. According to proposition 1 the two transfer prices just have a tax saving function and are set at the bounds of the admissible intervals. Because the financing subsidiary has a tax rate of zero, the capital transfer price is set at the upper bound. The optimal product transfer price depends on the tax rate difference δ between the subsidiaries and is set at the lower bound that is equal to marginal cost for δ < 0 and at the upper bound for δ > 0. Both transfer prices are independent of each other and only react to tax rate differences. The optimal quantity increases in the product transfer price when the tax rate difference becomes positive. This effect is stated in lemma 1 and is due to tax shifting opportunities once the PTP is above marginal cost. Because the CTP does not vary in the centralized case with δ, the increase in the investments comes from the higher quantity that increases 21

23 marginal returns of the investments. Finally, the expected profit is decreasing in the tax rate difference because the tax rate for subsidiary B is increasing what reduces after-tax profits. Second, we analyze the results for the decentralized case. For a higher (less negative) tax rate difference δ, higher investments become more favorable for the MNC because of tax shifting opportunities. Higher investments are thus stimulated by a lower CTP. Because the PTP is already set at marginal cost it can be decreased only marginally to the lower marginal cost that are induced by higher investments. Increasing the tax rate difference further to positive levels has two effects. First, the PTP increases due to the tax saving effect of profit shifting between subsidiaries B and S. Second, the CTP further decreases as the coordination effects become more negative in the higher PTP. These negatively interacting effects between the transfer prices is described in proposition 2. The effects on the optimal quantity and the optimal investments are stated in lemmas 2 and 3. The optimal quantity is decreasing in the PTP as it represents additional cost to the buyer. This in turn decreases marginal returns of the investments and leads to reduced optimal investment levels. Finally, the expected profit is decreasing in higher tax rates like in the centralized case. What is different is that the profit for a negative or zero tax rate difference is higher in the decentralized case than with centralized decisions. This effect appears because of the information asymmetry between the HQ and the subsidiaries. The HQ can base the quantity and the investment decision only on expected information whereas the subsidiaries have partial information at the date of the investment decision and full information at the date of the quantity decision. Therefore, the numerical example shows that despite of negative coordination effects in the decentralized setting, the decentralization of decisions can be beneficial in the case of asymmetric information between the HQ and the subsidiaries. We summarize the effects of the tax rate differences δ < 0, δ = 0 and δ > 0 on the optimal transfer prices in the following table 2: [Please insert table 2 about here] A graphical representation of the dependence of the HQ s decisions about the transfer prices on the tax rate difference δ and ultimately of the interaction between those three effects is depicted in figure 4. [Please insert figure 4 about here] 22

24 The figure on the left hand side shows the positive interdependence between the tax rate difference δ and the product transfer price. The higher the tax rate difference between the subsidiaries B and S, the higher the profit shifting opportunity and thus the higher the PTP. The PTP is however increasing in δ at a decreasing marginal rate due to the amplifying negative quantity and investment coordination effects. In case of a tax rate difference of δ 0, the PTP is set to marginal cost of production because the tax effect and the quantity and investment coordination effect are all three negative. Since the PTP and CTP interact negatively, the effect for the capital transfer price is in the opposite direction. While the tax effect of the CTP is positive for all tax rate differences, the investment coordination effect is negative for all δ and the quantity coordination effect on r is zero for δ 0 and negative for positive tax rate differences. However, the positive tax effect decreases in δ due to a higher tax rate difference increasing the PTP that in turn reduces the buyer s capital investment and the quantity ordered. Hence, the increasing negative investment and quantity coordination effects push the CTP further down. If we assume an upper border r for the acceptable range of the CTP we would get a cap at the accepted upper range of r, preventing the capital transfer price to be set above that threshold when the tax rate difference becomes low. The values for the capital and product transfer prices in table 1 also support proposition 2 and show the negative mutual interdependence between the two transfer prices. Recall, for a tax rate difference δ > 0, the group benefits from a higher product transfer price due to the opportunity to shift profits from subsidiary B to subsidiary S. As mentioned in lemma 2, this however reduces the quantity ordered by subsidiary B (increases the negative quantity coordination effect) because a higher PTP means higher cost to the buyer that in turn decreases the quantity ordered. A lower quantity ordered in fact decreases also the marginal investment returns of subsidiary B (increases the negative investment coordination effect) and we face decreasing optimal investments out of the amplification through the two negative effects. As a consequence of lower capital investments, the positive tax effect decreases and the quantity coordination effect gets even more negative that in turn leads to a lower CTP. For a tax rate difference of δ 0, the optimal PTP is always set to marginal cost of production since subsidiary B faces a lower tax rate than subsidiary S, inducing the MNC to keep the buyer s profits within division B. Further, as mentioned above, increasing the capital transfer price means, for all tax rate differences, higher investment cost to the subsidiaries B and S and thus lower optimal capital investments (higher negative investment coordination effect). That in turn reduces 23