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. 17-19 GERMAN ECONOMIC ASSOCIATION OF BUSINESS ADMINISTRATION – GEABA
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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. 17-19
GERMAN ECONOMIC ASSOCIATION OF BUSINESS ADMINISTRATION – GEABA
Tax and Managerial Effects of Transfer Pricing on
Capital and Physical Products∗
Oliver M. Duerr† Thomas Rüffi eux‡
March 27, 2017
- Preliminary and Incomplete Draft; please do not cite without author’s permission -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, Flandern-
strasse 101, D-73732 Esslingen, Germany, Tel.: +49 711 397 4312, eMail: [email protected]‡Thomas Rüffi eux, University of Zurich, Chair of Managerial Accounting, Seilergraben 53, CH-8001
Tax and Managerial Effects of Transfer Pricing on Capital and PhysicalProducts
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
1 Introduction
The research on transfer pricing has a long tradition in management accounting. Start-
ing 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 manage-
ment accounting literature Baldenius et al. (2004) were among the first who analytically
analyze the integration of tax and managerial objectives in transfer pricing. Others ex-
tended 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
1See Göx/Schiller (2007) for an extensive overview of analytical transfer pricing models.2See Ernst & Young (2013) survey where intra group financial arrangements and intangible property are
listed second and third on areas of transfer pricing controversy.3See e.g. Grubert (1998, 2003).
3
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 inter-
nally 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 opera-
tive 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
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, kS) that can be reduced by investing capital
kS in cost-saving activities. Accordingly, we assume the following additively separable cost
function C(q, kS) for the seller:
C(q, ks) := C1(q) + C2(kS) · q. (1)
The cost function consists of variable production costs C1(q) and a cost reduction effect
C2(kS) of the investment kS with the following properties:
∂C1(q)
∂q> 0,
∂2C1(q)
∂q2≥ 0, (2)
∂C2(kS)
∂kS< 0,
∂2C2(kS)
∂k2S≥ 0. (3)
4We assume no profit repatriations to the HQ, e.g. via dividend payments, which allows us to neglect
the tax rate of the headquarter.
5
Property (2) implies that the cost function is increasing and convex in the quantity q.
Condition (3) means that an investment kS reduces the cost of production for any given
quantity q at a decreasing marginal rate. The investment of capital kS results in utilization
cost of capital, denoted as IS(kS) which can be different from the pure amount of capital in-
vestment due to additional efforts to integrate new production equipment and organizational
changes. The utilization cost function has the following properties:
∂IS(kS)
∂kS> 0,
∂2IS(kS)
∂k2S≥ 0, (4)
implying that the utilization cost of capital is increasing in kS at an increasing marginal rate.
To keep the model focused on purposes of transfer pricing, we abstract from competi-
tion 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 uncer-
tain and depends on the state of the world θ := (θ1, θ2), represented by two stochastically
independent random state variables θ̃1 and θ̃2.5
Alike the seller, the buyer can invest capital kB in marketing activities that increase rev-
enues. The revenue function R(q, θ, kB) is defined as:
R(q, θ, kB) := (R1(q, θ) +R2(kB)) · q. (5)
Its first part, R1,is the price function and depends on the quantity q and the realization of
the state of the world θ, whereas the second part, R2, represents the additional revenues
from marketing activities. The price function and the marketing revenue function have the
following properties:
∂R1(q, θ)
∂q< 0,
∂2R1(q, θ)
∂q2≤ 0, (6)
∂R2(kB)
∂kB> 0,
∂2R2(kB)
∂k2B≤ 0. (7)
The first property (6) states that the price function, R1, is decreasing and concave in the
quantity q. The second property (7) implies, that R2 is increasing in the amount of capital
invested kB but at a decreasing rate. As for the seller, the investment of capital kB implies
utilization cost IB(kB) that are convex in the amount of capital invested:
∂IB(kB)
∂kB> 0,
∂2IB(kB)
∂k2B≥ 0. (8)
5This setting is akine to Edlin and Reichelstein (1995).
6
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 kB and kS, 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 kB and kS.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, kS)/∂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 τF 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 θ̃1,
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
kB and kS. At date t = 4, subsidiary B observes the realization of θ̃2. 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
6We 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
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
θ̃1 and θ̃2.
The three subsidiaries’after tax profits then unfold as:
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.
7The assumption that both managers observe the realization θ but outsiders do not is akine to Baldenius,
Reichelstein, Sahay (1999) and Edlin and Reichelstein (1996).8We 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
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 kB and kS, 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 θ̃1 and θ̃2 and has to base its decisions on expectations
E[θ̃1] and E[θ̃2]. Therefore the group’s expected profit results as:
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:
∂Eθ[Π(q, kS, kB, θ)]
∂r= τ · kS + (τ + δ) · kB ≥ 0 (14)
∂Eθ[Π(q, kS, kB, 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 kB and kS 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
(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 HQmaximizing the group’s expected profit with respect
to the quantity q and the investment amounts kB and kS are as follows:
∂Eθ[Π(q, kS, kB, θ)]
∂q= (1− τ − δ) · (Eθ[R1(θ, q) + q · ∂R1(θ, q)
∂q] +R2(kB))
+(1− τ) · (−∂C1(q)∂q
− C2(kS)) + δ · t = 0 (16)
∂Eθ[Π(q, kS, kB, θ)]
∂kB= (1− τ − δ) · (∂R2(kB)
∂kB· q − ∂IB(kB)
∂kB) + (r · (τ + δ)− r) = 0 (17)
∂Eθ[Π(q, kS, kB, θ)]
∂kS= (1− τ) · (−∂C2(kS)
∂kS· q − ∂IS(kS)
∂kS) + (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 6= 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
9Already 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
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 kB and kSand 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 kB and kS 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
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 θ̃1 and θ̃2. 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 θ̃1 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 θ̃2.
Observing θ1 and θ2, 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 HQmight 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 ΠB w.r.t. the
quantity q, yielding the optimality condition:
∂ΠB(q, kB, θ)
∂q= R1(q, θ) + q · ∂R1(q, θ)
∂q+R2(kB)− 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 θ1 and θ2, 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 kB.
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
10The 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
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(θ1, θ2, kB, t) depends solely on its marginal return, that in turn is a positive
function of the investment level kB, the product transfer price t as well as the realization of
the state variables θ̃1 and θ̃2.
Quite intuitively, in the prevailing model setting with asymmetric information and dele-
gated investment decisions, both subsidiaries set the investment amounts in order to optimize
their profits, given their information θ1 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 invest-
ment 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:
∂Eθ2[ΠB(q
◦(θ), kB, θ)
]∂kB
= Eθ2 [q◦(θ)] · ∂R2(kB)
∂kB− ∂IB(kB)
∂kB− r = 0, (20)
∂Eθ2[ΠS(q
◦(θ), kS)
]∂kS
= −Eθ2 [q◦(θ)] · ∂C2(kS)
∂kS− ∂IS(kS)
∂kS− r = 0. (21)
The optimal investment amounts k◦B := kB(Eθ2 [q
◦(θ)], r) and k
◦S := kS(Eθ2 [q
◦(θ)], r)
depend on the expected quantity and the capital transfer price. Both subsidiaries know
θ1 but at the time the investment decisions have to be reached the realization of θ̃2 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
Lemma 3: The optimal capital investments kB(Eθ2 [q◦(θ)], r) and kS(Eθ2 [q
◦(θ)], r) are de-
creasing 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 Eθ[Π(q◦(θ), k
◦B, k
◦S, θ)].
To shorten notation we define Vθ(q◦, k
◦B, k
◦S) := Eθ[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:
∂Vθ(q◦, k
◦B, k
◦S)
∂r= Eθ[(τ + δ) · k◦B + τ · k◦S
+(1− τ) · (t− (∂C1(q
◦(θ))
∂q− C2(k
◦
S))) · ∂q∂kB
· ∂kB∂r
+(r − r) · ∂(k◦B + k
◦S)
∂r] = 0, (22)
∂Vθ(q◦, k
◦B, k
◦S)
∂t= Eθ[δ · q
◦(θ) + (1− τ) · (t− (
∂C1(q◦(θ))
∂q− C2(k
◦
S))) · ( ∂q∂kB
· ∂kB∂t
+∂q
∂t)
+(r − r) · ∂(k◦B + k
◦S)
∂t] = 0. (23)
Solving these FOC’s for r and t results in an optimal CTP r◦
:=r(Eθ[q◦(θ), k
◦B, k
◦S, θ])
and an optimal PTP t◦
:= t(Eθ[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
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, ∂kB/∂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/∂kB > 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.
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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 kBthat 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 invest-
ments kB and kS. 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
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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 θ̃ to be a sum of θ̃1 and θ̃2,
where θ̃1 and θ̃2 are uncorrelated, uniformly distributed over an interval [−ξ, ξ] and exhibitan expected value of E[θ̃l] = 0 and a variance of V ar(θ̃l) = 1/12 · (ξ − (−ξ))2, for l ∈ {1, 2}.Further we assume quadratic utilization cost of capital Ii(ki) = γ · k2i , i ∈ {B, S}, where γis a scaling parameter. The revenue function for the buyer is specified as:
R(q, θ1, θ2, kB) = (R1(θ1, θ2, q) +R2(kB)) · q
= (a+ θ1 + θ2 − q + α · kB) · q (24)
and the seller’s cost of production is given by:
C(q, kS) = C1(q) + C2(kS) · q
= (c− α · kS) · q, (25)
where the scaling parameter α represents the investment effi ciency. The profit functions