DISCUSSION PAPER
SERIES IN
ECONOMICS AND
MANAGEMENT
Specific investment and negotiated transfer pricing
in an international transfer pricing model
Oliver M. Dürr & Robert F.
Göx
Discussion Paper No. 10-37
GERMAN ECONOMIC ASSOCIATION OF BUSINESS
ADMINISTRATION – GEABA
Specific investment and negotiated transfer pricing in an
international transfer pricing model∗
Oliver M. Dürr†
Robert F. Göx‡
June 2010
∗
We thank Tim Baldenius, Martin Wallmeier, and participants of the EIASM Workshop on Accounting
and Economics in Vienna for their valuable suggestions and comments.
†
Dr. Oliver Michael Dürr, University of Fribourg, Bd. de Pérolles 90, CH-1700 Fribourg (Switzerland),
Tel.: +41 26 300 8761, Fax +41 26 300 9659, email: olivermichael.duerr@unifr.ch.
‡
Prof.
Dr.
Robert F. Göx, Chair of Managerial Accounting, University of Fribourg, Bd.
de
Pérolles 90, CH-1700 Fribourg (Switzerland), Tel.: +41 26 300 8310/8311, Fax +41 26 300 9659, email:
robert.goex@unifr.ch, web: http://www.unifr.ch/controlling/
1
Abstract
We study the efficiency of the negotiated transfer pricing mechanism proposed by Edlin
and Reichelstein (1995) for solving a bilateral holdup problem in a multinational enterprise.
Our main finding is that the proposed renegotiation procedure will generally not provide
incentives for efficient renegotiations of the initial trade quantity if the same transfer price
is also used for minimizing the global tax bill. Moreover, given that efficient renegotiations
are expected to fail, the divisions will not make efficient investments in the first place.
Nevertheless, we demonstrate that Pareto improving renegotiations are still possible in many
cases but the first-best solution can generally not be attained. Finally, we demonstrate that
the conflict between the two functions of transfer pricing can be solved by the use of different
transfer prices for tax and managerial purposes. Since using a second set of books is costly,
the firm faces a cost-benefit trade-off that can only be solved in the context of a particular
decision problem.
2
1
Introduction
The ongoing globalization of the world economy has significantly increased internal trade
within multinational firms. According to a recent report of the Economist (2004) around 60%
of all global trade takes the form of internal transactions within multinational enterprises.
This trend has also increased global tax competition and the importance of international
tax management for multinational firms. Transfer prices are an important instrument for
managing the global tax liability of multinationals. According to a recent survey conducted
by Ernst & Young (2008) 90 % of the multinational enterprises found transfer pricing fairly
or very important and 39 % of corporate tax directors named transfer pricing as the most
important item on their agendas.
Despite the increased importance of international transfer pricing, the management accounting literature has focused on the managerial aspects of transfer pricing and largely
ignored the tax function of transfer pricing. Starting with Hirshleifer (1956), transfer pricing was primarily analyzed as an internal coordination mechanism enabling the management
of decentralized firms to achieve goal congruence between the firms’ headquarters and the
management of autonomous divisions.
The most important topic in the recent managerial transfer pricing literature was certainly the role of transfer prices in providing incentives for specific investments at the divisional level. In their seminal paper, Edlin and Reichelstein (1995) demonstrate that negotiated transfer pricing can be an efficient mechanism for solving a bilateral holdup problem in
a multidivisional firm and motivate the divisions to make efficient investment decisions. A
number of other papers have subsequently examined the investment incentives provided by
various forms of negotiated and cost-based transfer pricing mechanisms.1 However, except
1
See, for example, Baldenius et al. (1999), Baldenius (2000), Wielenberg (2000), Sahay (2003), or Pfeiffer
3
Johnson (2006) none of the papers has so far analyzed a bilateral hold-up problem in the
context of a multinational enterprise.
In this paper, we aim to close this gap in the literature by analyzing the usefulness of
the negotiated transfer pricing mechanism proposed by Edlin and Reichelstein (1995) for
solving a bilateral holdup problem in a multinational enterprise. The mechanism comprises
3 steps. First, the divisions negotiate a fixed-price contract specifying a transfer quantity
and a lump-sum transfer payment. Second, the divisions make specific investments under
uncertainty that increase the expected value of internal trade. Third, uncertainty resolves
and the divisions renegotiate the initial contract specifying a new transfer quantity and a
new transfer payment. Our main finding is that the proposed renegotiation procedure will
generally not provide incentives for efficient renegotiations of the initial trade quantity if
the same transfer price is also used for minimizing the global tax bill. Moreover, given that
efficient renegotiations are expected to fail, the divisions will not make efficient investments
in the first place.
Intuitively, the negotiated transfer pricing mechanism suffers from the fact that the divisions possess only one instrument for solving two problems. They can either adjust the lump
sum payment in order to minimize the global tax bill or they can adjust it to redistribute
the mutual gains from implementing a new contract. Both objectives can only be achieved
simultaneously when they are coincidentally solved by the same transfer price. Nonetheless,
we demonstrate that Pareto improving renegotiations are still possible in many cases. In
fact, if the intermediate input is transferred at the tax minimizing transfer prices and both
divisions benefit from an increase or a decrease of the transfer quantity, the operating profit
can be improved by adjusting the initial contract. However, since the efficient quantity will
only be achieved incidentally in this case, the divisions’ investment incentives are generally
distorted. We also show that the divisions can benefit from renegotiations if they cannot
et. al. (2008). Recent survey of the incomplete contracting literature are provided by Göx and Schiller
(2007) and Baldenius (2009).
4
agree to adjust the trade quantity at the tax minimizing transfer price. In these cases, there
is always a solution in which the two divisions can benefit from adjusting the transfer price
and the trade quantity, but this solution requires that both variables take inefficient values.
Finally, we demonstrate that the conflict between the two functions of transfer pricing can be
solved by the use of different transfer prices for tax and managerial purposes. Since the use
of two sets of books usually involves additional cost for additional resources, the firm faces
a trade-off between the benefits of a more flexible transfer pricing policy and the additional
cost associated with the use of two sets of books that can only be solved in the context of a
particular decision problem.
Our analysis contributes to the existing transfer pricing literature by exploring the limits
of the negotiated transfer pricing mechanism proposed by Edlin and Reichelstein (1995) in
the context of a multinational enterprise. So far, only Johnson (2006) has analyzed the
problem of providing divisional investment incentives in an international transfer pricing
model. Johnson’s model is not directly comparable to ours. She considers a model in which
two divisions can sequentially invest in an intangible asset and compares the effectiveness of
three transfer pricing methodologies for intangibles: A renegotiated royalty-based transfer
price, a non-negotiable royalty-based transfer price and purely negotiated transfer price. She
finds that a renegotiable royalty-based transfer price provides better investment incentives
than the other two methodologies and in some cases it even motivates first-best investments.
Johnson (2006) also discusses the possibility of decoupling the royalties for tax reporting
and internal purposes and find that decoupling the two transfer prices usually increases the
firm’s after tax profit.2
A number of other papers has analyzed the benefits of separate transfer prices for tax
reporting and managerial purposes. Baldenius et al. (2004) show that firms are better off
by using two sets of books if tax and managerial objectives are conflicting. In a related
paper, Hyde and Choe (2005) analyze the relation between tax and incentive transfer prices
2
See Baldenius (2006) for a detailed discussion of Johnson’s model.
5
and find that the optimal transfer prices with two sets of books are typically related to each
other although they serve different functions. Finally, Dürr and Göx (2011) show that using
one set of books can be an optimal strategy if firms compete in prices in industries with
a small number of competitors. The reason for this result is that the unique tax transfer
price can be used strategically vis-à-vis a competitor even if the internal transfer price is
unobservable. By using a tax transfer price above marginal cost, the firm can credibly signal
to its competitor that its division manager will adopt a less aggressive pricing strategy in
the final product market.
The remainder of our paper is organized as follows. In section two we present the model
and its main assumptions. We also derive the first-best solution of our model. Section three
analyzes the equilibrium strategies of the non-cooperative investment game between the
divisions of the decentralized firm. We first show that efficient renegotiations of the transfer
quantity and global tax minimization can generally not be achieved with the same transfer
pricing mechanism. We also discuss different forms of Pareto improving renegotiations and
show that efficient renegotiations and first-best investment can be achieved if the firm uses
two sets of books. Section four summarizes the main results.
2
Model setup
2.1
Firm organization, technology, and taxation
We consider a decentralized firm consisting of headquarters (HQ) and two divisions, (j =
S, B). Divison S (the ”seller”) produces an intermediate product and supplies it to division B
(the ”buyer”). The buyer processes the intermediate product and sells it in the final product
market. We assume that one unit of the intermediate product is required to produce one
final product unit and that there is no external market for the intermediate product.
The two divisions can make upfront specific investments Ij in order to increase the value
6
of internal trade. For making an investment, division Ij incurs a cost ω(Ij ), where the cost
function ω(Ij ) is twice differentiable and convex in Ij . The cost of the selling division is
given by the function C(q, θ, IS ), where q denotes the quantity of the intermediate product,
θ is a state variable that is unknown at the beginning of the planning horizon, and IS is
the amount of specific investment undertaken by the seller. Likewise, the revenue of the
buying division from selling the final product is defined as R(q, θ, IB ), where IB denotes the
buyer’s specific investment. We assume that the specific investment of the seller reduces her
marginal cost, whereas the specific investment of the buyer increases her marginal revenue.3
For example, the seller might invest in specialized production equipment or the training of
workers. Likewise, the buying division might invest in the training of sales personnel or
marketing activities.
As in Edlin and Reichelstein (1995), we assume that the firm employs a negotiated
transfer pricing mechanism for motivating the divisions to make efficient investment and
production decisions. The mechanism comprises four steps. At date one the two divisions
negotiate a fixed-price contract specifying a transfer quantity q and a lump-sum transfer
payment of T . At date two, the divisions make their investment decisions I ≡ (IS , IB ) and
at date three they learn the actual value of the state variable θ ∈ Θ,where Θ denotes the set
of possible states. At date four, the initial contract is renegotiated, and the parties agree on
an actual trade quantity qb and a monetary transfer Tb . The ratio between a given lump sum
payment T and a transfer quantity q, t = T /q, can be interpreted as a negotiated transfer
price. To rule out that the divisional investment problem can be solved by a complete ex
ante contract, we assume that HQ cannot observe θ and I and that both variables are not
contractible. Figure 1 summarizes the sequence of events.
[please insert Figure 1 about here]
3
More formally, we require that ∂ 2 C(q, θ, IS )/∂q∂IS < 0 and ∂ 2 R(q, θ, IB )/∂q∂IB > 0. See Edlin and
Reichelstein (1995) for an equivalent assumption.
7
The above assumptions are equivalent to the model setup proposed in Edlin and Reichelstein (1995). The novel element of our study is that we allow for potential differences in the
taxation of divisional income. We assume that the firm’s HQ and the selling division are
located in the home country and the buying division is located in a foreign country. The
marginal tax rate in the home country equals τ and the marginal tax rate in the foreign
country equals τ + δ. The differences in marginal tax rates equals δ. To keep the model as
general as possible we do not restrict the sign of δ. If δ is positive, there is a domestic tax
advantage. If δ is negative, the foreign country offers a tax advantage. Since marginal tax
rates in both countries are reasonably restricted to the interval between zero and one, δ can
take values from the interval [−τ ; 1 − τ ].
The existence of international tax differences places additional demands on the firm’s
transfer pricing policy. In fact, if δ > 0 (δ < 0), the firm has an incentive to tax the largest
(smallest) possible part of its world income in the home country. Accordingly, the firm has
an incentive to set a high transfer price in case of a domestic tax advantage and a low transfer
price in case of a foreign tax advantage. In line with the majority of the international transfer
pricing literature and for making our results comparable to those of Edlin and Reichelstein
(1995), we assume for most of the analysis that the firm uses the same transfer price for
tax and managerial purposes. In section 3.4 we also consider the case where the firm uses
different transfer prices for tax and managerial purposes assuming that carrying two sets of
books incurs additional fixed cost of F for the firm.
Tax authorities usually require firms to report the unit transfer price in conformity with
the arm’s length principle. This principle demands that transfer prices are set within an
acceptable range of prices that could be found for similar transactions between independent
parties under comparable circumstances (OECD 2001). This broad definition leaves firms
with substantial leeway in determining their transfer prices because in most cases comparable
transactions are not easily identified. In what follows, we capture the arm’s length constraint
by an interval of admissible transfer prices that is accepted by the tax authorities in both
8
countries. We assume that the negotiated transfer price t must take values from the interval
[s, s], where s (s) denotes the lowest (highest) acceptable unit transfer price from the tax
authorities’ perspective. Since the arm’s length constraint is defined on the basis of a per
unit transfer price, there exists a large set of transfer payments T and transfer quantities
q that are acceptable for tax authorities. Moreover, in order to negotiate a tax conform
transfer price, the divisions can either adjust the transfer quantity, the lump-sum payment
or both variables. This additional degree of flexibility provided by negotiated transfer pricing
should make it easier to satisfy the arm’s length constraints than with any other transfer
pricing method that allows for price adjustments only.
2.2
Benchmark case: Centralized investment and transfer pricing
Before we analyze the decentralized solution of the model presented in section 2.1, we briefly
present the first best solution. The analysis starts with the optimal transfer pricing and
production decisions at date 4. For a given value of the state variable θ and investments
undertaken at stage 2, the operating profit after taxes is given by
M (q, t, θ, I) = α · [R(q, θ, IB ) − C(q, θ, IS )] + δ · [t · q − C(q, θ, IS )],
(1)
where α = 1 − τ − δ, and t is the transfer price set by HQ. The expression in (1) comprises
the difference between revenue and cost after taxes evaluated at the foreign tax rate and
a tax term capturing the impact of the firm’s transfer pricing policy on its global tax bill.
This second term equals zero if the tax rates in both countries are identical (δ = 0), or if the
value of internal transactions equals total cost. Maximizing the contribution margin with
respect to t yields δ · q. For a given production quantity, the sign of this expression depends
on the sign of δ, so that the optimal transfer price can be characterized as follows:
⎧
⎪
⎨
t∗ = ⎪
⎩
s f or δ > 0
s f or δ < 0
9
.
(2)
The optimal transfer pricing policy in (2) is solely determined by tax considerations. In
case of a domestic tax advantage, the firm sets the highest possible transfer price in order
to tax the largest possible part of its global income in the home country. In case of a foreign
tax advantage, the firm sets the lowest acceptable transfer price in order to tax the largest
possible part of its global income in the foreign country. For a given transfer price, the
optimal volume of internal trade is found by maximizing the operating profit in (1) with
respect to q. The resulting optimality condition,
Ã
!
Ã
∂M (q, t, θ, I)
∂R(q, θ, IB ) ∂C(q, θ, IS )
∂C(q, θ, IS )
=α·
−
+δ· t−
∂q
∂q
∂q
∂q
!
= 0,
(3)
shows that the existence of international tax differences usually affects the optimal quantity
decision at date 4. In fact, if we reasonably assume that transfer prices satisfying the arm’s
length constraint must at least equal marginal cost, so that s ≥ ∂C(q, θ, IS )/∂q, the optimal
production quantity of a multinational enterprise is strictly higher (weakly lower) than the
production quantity of a domestic firm if there is a domestic (foreign) tax advantage. Let
q ∗ (θ, I, t) denote the efficient quantity and let M(θ, I) ≡ M(q∗ (θ, I, t∗ ), t∗ , θ, I). At date 2,
the firm maximizes the expected profit after taxes and investment costs,
Γ (I) = Eθ [M(θ, I)] − (1 − τ ) · ω(IS ) − α · ω(IB ),
(4)
with respect to IS and IB . The optimal solutions satisfy
−Eθ
"
#
∂C(q ∗ , θ, IS )
∂ω(IS )
=
∂IS
∂IS
and Eθ
"
#
∂R(q∗ , θ, IB )
∂ω(IB )
=
.
∂IB
∂IB
(5)
That is, the efficient investment levels equate the marginal investment costs with the marginal cost reduction and revenue increase resulting from the respective investment outlay.
Unlike the quantity decision, the optimal investment decision is not directly affected by
tax considerations, so that the decision rule determining the efficient investment levels is
equivalent to the domestic transfer pricing model in Edlin and Reichelstein (1995).4
4
Evidently, the expected marginal cost savings and revenue increase in (5) depend on the expected
quantity determined at stage 4, so that they also affect the investment decision, but this effect works
indirectly and does not affect the structure of the optimal investment decision.
10
3
Decentralized investment and pricing decisions
3.1
Investment efficiency and tax minimization as conflicting objectives
To analyze the usefulness of negotiated transfer pricing in the context of a multinational
enterprise, we first employ the same renegotiation procedure as Edlin and Reichelstein (1995).
As explained in section 2.1, this procedure entails that the two divisions initially agree on
a fixed-price contract specifying a transfer quantity q and a lump-sum transfer payment of
T . After undertaking specific investments and after learning the actual value of the state
variable θ, the initial contract is renegotiated and a new trade quantity qb and a new monetary
transfer Tb are specified.
The renegotiation procedure itself is cooperative in the sense that the division managers
jointly maximize the operating profit at date 4 and distribute the resulting surplus over the
profit resulting from the execution of the initial contract according to a γ-surplus sharing
rule. The allocation rule reflects the parties’ bargaining power and allocates a share γ of the
renegotiation surplus to the seller and a share 1 − γ to the buyer. The renegotiation surplus
is defined as the difference between the maximum operating profit and the profit resulting
from the initial quantity q and the initial transfer price t = T /q
SP = M (θ, I) − M (q, t, θ, I) .
(6)
In order to achieve a mutually beneficial and acceptable renegotiation of the initial contract,
the adjusted lump-sum payment Tb must satisfy the following conditions:
b θ, IS )) = (1 − τ ) · (T − C(q, θ, IS )) + γ · SP
(1 − τ ) · (Tb − C(q,
b θ, IB ) − Tb ) = α · (R(q, θ, IB ) − T ) + (1 − γ) · SP,
α · (R(q,
(7)
(8)
where efficient production requires that qb = q ∗ . The conditions assure that for both divisions
the operating profit under the adjusted contract terms equals the payoff resulting from the
11
original contract plus the division’s share of the renegotiation surplus. It can be seen from
the seller’s participation constraint in (7) that a higher bargaining power of the seller (γ)
is economically equivalent to a higher transfer payment Tb from the buyer to the seller.
Moreover, as Edlin and Reichelstein (1995) show, it is always possible to find a transfer
payment Tb satisfying conditions (8) and (7) as long as transfers are unrestricted.
However, for the multinational enterprise, efficiency does not only require that the divi-
sions agree on the optimal production quantity for a given transfer payment, but also that
the resulting unit transfer price minimizes the companies global tax bill. That is, efficiency
requires that the divisions agree on a new contract specifying a quantity qb = q ∗ (θ, I, t∗ ) and
a tax minimizing transfer payment Tb = T ∗ ≡ t∗ ·q ∗ (θ, I, t∗ ). The following proposition shows
that both objectives can generally not be achieved simultaneously.
Proposition 1: Negotiated transfer pricing is generally insufficient for implementing an
efficient renegotiation of operating profits in the presence of international tax differences.
Proof: see appendix.
The proof of proposition 1 shows that an efficient renegotiation of the initial contract
usually fails because one of the two divisions will be better off if the initial contract is
executed. The reason is that global tax minimization restricts the adjusted transfer payment
Tb under the new contract and thereby makes efficient renegotiation impossible. In fact,
optimal transfer pricing requires that Tb = T ∗ . Since all other variables in the divisions’
participation constraints (7) and (8) are fixed, there exists only one particular distribution
of bargaining powers satisfying equations (7) and (8). This bargaining power equals:
γ ∗ = (1 − τ ) · [T ∗ − C(q ∗ , θ, IS ) − (T − C(q, θ, IS ))]/SP.
(9)
While it cannot be excluded that the distribution of bargaining power between the two divisions actually happens to equal (9), an efficient renegotiation is excluded for all bargaining
powers γ 6= γ ∗ . Intuitively, the firm suffers from the fact that the divisions possess only one
instrument for solving two problems. The divisions can either use Tb to minimize the global
12
tax bill or to redistribute the mutual gains from implementing a new contract. Both problems
can only be solved simultaneously when the distribution of contract gains and losses implied
by the optimal tax transfer T ∗ happens to coincide with the adjusted transfer payment Tb
that solves equations (7) and (8). In addition, we can make the following observation:
Corollary 1: Negotiated transfer pricing is generally insufficient for implementing first
best investment decisions in the presence of international tax differences. Proof: If γ 6= γ ∗ ,
efficient renegotiations fail and q = q. Efficient investments require that q = q ∗ (θ, I, t∗ ) from
(5); a contradiction.
Corollary 1 shows that the failure of efficient renegotiations naturally implies that the
divisions do not have the right incentives to make the first-best investment decisions at
stage two because they anticipate that renegotiations will fail in almost all cases except for
a bargaining power distribution of γ = γ ∗ . However, the fact that efficient renegotiations
are generally impossible does not imply that negotiated transfer pricing does not permit the
divisions to improve their situation as compared to the original contract. In what follows,
we explore the conditions for Pareto improving renegotiations between the two divisions.
3.2
Quantity adjustment with optimal tax transfer price
An efficient renegotiation procedure requires that the divisions set the tax minimizing transfer amount T ∗ and the efficient quantity q ∗ (θ, I, t∗ ). In principle, an adjustment of both
decision variables can lead to a Pareto improving contract adjustment. In what follows we
first analyze the case where the divisions agree to apply the tax minimizing transfer price
b That is, the transfer
and restrict renegotiations to an adjustment of the transfer quantity q.
b where the optimal unit transfer price t∗ is given in (2). This
payment equals Tb = t∗ · q,
situation is economically equivalent to a situation where the firm commits to the use of a
particular unit transfer price vis-à-vis tax authorities. For any given production quantity q,
it would be rational for the firm to set the initial transfer payment equal to T = t∗ · q in
order to minimize the expected tax bill.
13
Given the tax minimizing transfer pricing policy, the two divisions can only renegotiate
the quantity at date 4, but not the transfer price. The divisions realize the following profits
for a given transfer quantity q, state θ and divisional investments IS and IB :
MS (q, t∗ , θ, IS ) = (1 − τ ) · (t∗ · q − C(q, θ, IS ))
(10)
MB (q, t∗ , θ, IB ) = α · (R(q, θ, IB ) − t∗ · q).
(11)
For the selling division a renegotiation of the quantity is favorable if
¯
∂MS (q, t∗ , θ, IS ) ¯¯
∂C(q, θ, IS )
∗
¯
=
t
−
6= 0.
¯
∂q
∂q
q=q
(12)
That is, the marginal cost evaluated at the initial quantity q must be different from the tax
minimizing transfer price t∗ . Whenever the optimal transfer price is higher than marginal
cost, the selling division has an incentive to agree on a transfer quantity qb > q, and if
marginal cost is higher than t∗ , the seller will accept to reduce the transfer quantity. Likewise,
the buying division benefits from adjusting the initially negotiated quantity if its marginal
revenues at date 4 are different from the transfer price
¯
∂R(q, θ, IB )
∂MB (q, t∗ , θ, IB ) ¯¯
¯
− t∗ 6= 0.
=
¯
∂q
∂q
q=q
(13)
As for the supplying division the buying division will benefit from an increase (decrease)
of the original transfer quantity if marginal revenues evaluated at the initial quantity q are
higher (lower) than the tax minimizing transfer price t∗ . However, mutually beneficial renegotiations can only take place if the two conditions in (12) and (13) are satisfied and have
the same sign. In fact, whenever both conditions are positive (negative), the divisions will
agree on an upward (downward) adjustment of the initial transfer quantity during renegotiations. Since the only degree of freedom for adjustments is the transfer quantity, the divisions’
bargaining power play no role in determining the lump sum transfer payment which is obb If
tained as the product of the tax minimizing transfer price t∗ and the adjusted quantity q.
renegotiations take place, division j realizes the following surplus as compared to the initial
contract
b t∗ , θ, Ij ) − Mj (q, t∗ , θ, Ij ) .
SPj = Mj (q,
14
(14)
This surplus is positive, whenever renegotiations are successful. In addition, we can make
the following observation:
Corollary 2: If t = t∗ and renegotiations are beneficial for both divisions but restricted to
the set of quantities {q S , qB } that maximize divisional profits, the divisions will generally not
agree on the efficient transfer quantity q∗ . Proof: Given t = t∗ the divisions would find it
optimal to adjust their quantities so that
∂R(q B , θ, IB )
∂C(q S , θ, IS )
= t∗ and
= t∗ ,
∂q
∂q
(15)
where q B denotes the optimal quantity from the buyer’s perspective and qS denotes the
optimal quantity from the seller’s perspective. As in general q B 6= q S , the efficient quantity
q ∗ is only achieved coincidentally and if the following condition holds
∂C(q S , θ, IS )
∂R(q B , θ, IB )
=
.
∂q
∂q
(16)
More generally, the divisions are free to agree on any quantity q + ex post that increases
the profit of both divisions. Since qB can be smaller or larger than qS , the potential set of
renegotiation quantities q+ is given by the closed interval q + ∈ [min {q S , qB }, max {qS , q B }].
In particular, any quantity q+ from this interval satisfying the condition
R(q+ , θ, IB ) − R(q, θ, IB ) > (q+ − q) · t∗ > C(q+ , θ, IS ) − C(q, θ, IS )
(17)
increases the profit of both divisions. This condition requires that the revenue difference
realized by division B is larger than the incremental transfer payment which, in turn, must
exceed the cost difference incurred by division S. As there are a large number of renegotiation
quantities satisfying condition (17), it cannot be excluded that the divisions agree on the
efficient quantity q + = q ∗ .
However, even if the divisions renegotiate the quantity efficiently for some states, efficient
investment is generally excluded. Let H ⊂ Θ be the set of states for which the divisions
renegotiate and H be its complement. Then, the ex ante expected profits of divisions S and
15
B at date 2 are equal to
ΓS = E θ|θ∈H [MS (q, t∗ , θ, IS )] + E θ|θ∈H [MS (q + , t∗ , θ, IS )] − (1 − τ ) · ω (IS )
(18)
ΓB = E θ|θ∈H [MB (q, t∗ , θ, IB )] + E θ|θ∈H [MB (q+ , t∗ , θ, IB ] − α · ω (IB ) .
(19)
From the expressions in (18) and (19) the two divisions maximize a weighted average of the
operating profit evaluated at the initial quantity and at the renegotiated quantity minus the
investment cost after taxes. Maximizing the expected profit at t = 2 with respect to the
divisional investments yields the following first-order conditions:
"
#
"
#
∂ω(IS )
∂C(q, θ, IS )
∂C(q+ , θ, IS )
−E θ|θ∈H
− E θ|θ∈H
=
∂IS
∂IS
∂IS
"
#
"
#
+
∂R(q, θ, IB )
∂R(q , θ, IB )
∂ω (IB )
E θ|θ∈H
+ E θ|θ∈H
=
.
∂IB
∂IB
∂IB
(20)
(21)
Comparing these conditions with the conditions for efficient investment in (5) shows that
the divisions will generally not invest efficiently because for all states θ ∈ H, no renegotia-
tions take place and q+ is generally not equal to q ∗ . Nonetheless, the divisions’ investment
comes closer to the first-best solution the larger the set of states H for which the divisions
renegotiate the quantity and chose q+ = q ∗ .
3.3
Simultaneous adjustment of quantity and transfer price
If the conditions in (12) and (13) have the opposite sign, renegotiations of the transfer quantity at the tax minimizing transfer price will fail because one of the divisions prefers to
increase the quantity while the other division prefers to decrease it. Under these circumstances, it may be beneficial for both divisions to adjust the transfer price and the transfer
quantity in order to find a Pareto improving contract adjustment. For example, suppose
that
∂R(q, θ, IB )
∂C(q, θ, IS )
>
> t∗
∂q
∂q
(22)
so that the buying division would benefit from increasing the trade quantity at the tax
minimizing transfer price, whereas the selling division would like to reduce the quantity
16
because the transfer price is lower than marginal cost. If the divisions agree to deviate
from the tax minimizing transfer prices, set a transfer price t◦ > t∗ that falls between
marginal revenues and marginal cost and increase the quantity to q◦ > q, both divisions
can realize a higher profit albeit the global tax bill of the firm is no longer minimized. An
adjustment of transfer price and quantity might also be Pareto improving if in the former
case the renegotiated quantity q + is below the efficient quantity q ∗ . If renegotiations take
place, division j realizes the following surplus as compared to the initial contract
SPj = Mj (q◦ , t◦ , θ, Ij ) − Mj (q, t∗ , θ, Ij ) .
(23)
Since the divisions can adjust the quantity and the price, there exists a large set of feasible
contracts that increase the profit of both divisions. The final contract is determined by the
division’s bargaining power. The set of mutually acceptable transfer payments T ◦ = t◦ · q◦
can be obtained by solving the divisions’ participation constraints in (7) and (8) for T ◦ ,
yielding
SP ◦
,
(24)
1−τ
where SP ◦ = M(q◦ , t◦ , θ, I)−M(q, t∗ , θ, I) is the joint renegotiation surplus of both divisions.
T ◦ = t∗ · q + C (q ◦ , θ, IS ) − C (q, θ, IS ) + γ ·
The optimal transfer quantity is found by maximizing SP ◦ with respect to q◦ and subject to
(24). This quantity is generally inefficient because t◦ 6= t∗ and thus q◦ (θ, I, t◦ ) 6= q∗ (θ, I, t∗ ).
Given the optimal renegotiation procedure the ex ante expected profits of divisions S and
B at date 2 become
ΓS = Eθ [MS (q, t∗ , θ, IS ) + γ · SP ◦ ] − (1 − τ ) · ω (IS )
(25)
ΓB = Eθ [MB (q, t∗ , θ, IB ) + (1 − γ) · SP ◦ ] − α · ω (IB ) .
(26)
From the expressions in (25) and (26) the two divisions maximize the status quo profit
plus the divisions’ share of the renegotiation surplus minus investment cost after taxes.
Maximizing the expected profit of division B with respect to IB yields the following firstorder condition:
γ · Eθ
"
#
"
#
∂R(q, θ, IB )
∂R(q ◦ , θ, IB )
∂ω(IB )
+ (1 − γ) · Eθ
=
∂IB
∂IB
∂IB
17
(27)
Comparing this condition with the condition for efficient investment in (5) shows that division
B will generally not invest efficiently because it does not produce the efficient quantity q∗ .
A similar observation can be made for the selling division. We can make the following
observation.
Corollary 3: If the divisions renegotiate the transfer price and the quantity, division j
will generally not invest efficiently even if it was the residual claimant. Proof: Assume that
the buying division is the residual claimant of its own investment return (γ = 0). Comparing
the resulting first order condition from (27) with the condition for efficient investment in (5)
shows that investment is only efficient if by coincidence q ◦ = q ∗ . A similar argument can be
made for division S.
Overall, the results of this sections 3.2 and 3.3 show that Pareto improving renegotiations
are generally possible but the first-best solution is typically not achieved when the negotiated
transfer price is expected to provide efficient investment incentives and to minimize taxes at
the same time.
3.4
Separate transfer prices for tax and managerial purposes
As a potential alternative to the use of a single transfer price for tax and managerial purposes,
the firm might use separate transfer prices for tax reporting and for providing investment
incentives. Baldenius et al. (2004) have shown that decoupling tax and managerial objectives
is generally beneficial because it helps to avoid potential conflicts between the two objectives.
Nonetheless, it seems very likely that a second set of books requires additional resources for
satisfying the increased demands faced by the firm’s accounting department. Apart from
additional administrative consequences it has also been hypothesized that the use of different
transfer prices for tax and managerial purposes increases the likelihood of a tax audit.5 In
both cases, the use of two sets of books is associated with additional cost. Let F be the
5
See e.g. Kant (1988), Smith (2002a) and Smith (2002b).
18
incremental cost of a second set of books, then the potential benefits of using two separate
transfer prices must be higher than these additional cost to justify their use.
In what follows, we assume that the firm uses a unit transfer price denoted s for tax
reporting and a negotiated transfer price for managerial purposes. It should be evident,
that the optimal policy entails a tax transfer price equal to s = t∗ in order to minimize the
global tax bill of the firm, where the optimal transfer prices t∗ is defined in (2). Given this
transfer price, the divisions will renegotiate the initial contract at date 4. Since the adjusted
transfer payment is no longer restricted by tax considerations, we can make the following
observation:
Proposition 2: With two set of books negotiated transfer pricing is sufficient for implementing an efficient renegotiation of operating profits in the presence of international tax
differences. Proof: Since Tb can take any value, the divisions can maximize the renegotiation
surplus and find a side payment that satisfies the participation constraints (7) and (8).
From proposition 2, operating decisions will always be efficient with two sets of books.
That is, the firm sets a tax transfer price s = t∗ and the divisions agree to exchange the
efficient quantity q ∗ (θ, I, t∗ ). Accordingly, the ex ante expected profits of divisions S and B
at date 2 become
ΓS = Eθ [MS (q, t∗ , θ, IS ) + γ · SP ] − (1 − τ ) · ω (IS )
(28)
ΓB = Eθ [MB (q, t∗ , θ, IB ) + (1 − γ) · SP ] − α · ω (IB ) .
(29)
From the expressions in (28) and (29), the two divisions maximize the expected sum of the
status quo profit plus the share of renegotiation surplus minus the investment cost after
taxes. The first order conditions become:
"
#
"
#
∂C(q, θ, IS )
∂C(q ∗ , θ, IS )
∂ω(IS )
−(1 − γ) · Eθ
− γ · Eθ
=
∂IS
∂IS
∂IS
"
#
"
#
∂R(q, θ, IB )
∂R(q ∗ , θ, IB )
∂ω(IB )
+ (1 − γ) · Eθ
=
.
γ · Eθ
∂IB
∂IB
∂IB
19
(30)
(31)
The first order conditions in (30) and (30) are generally different from the first order conditions of HQ in (5). However, as shown by Edlin and Reichelstein (1995), the two conditions
coincide, if the cost and revenue functions satisfy certain separability conditions and the
ex-ante quantity equals the expected from renegotiations q = Eθ [q ∗ ].6
We conclude that the efficiency result derived by Edlin and Reichelstein (1995) generally
prevails in the context of a multinational enterprise if it uses two sets of books. Otherwise
efficient renegotiations for all states are generally impossible and the first-best investment
solution cannot be implemented. However, since carrying two sets of books is associated
with an incremental cost of F , this result does not imply that the net benefit form using
two sets of books is positive. The higher the efficiency loss induced by the use of a single set
of transfer prices for tax and managerial purposes and the lower the incremental cost of a
second set of books, the more likely is it that the firm prefers to use different transfer prices
for tax and managerial purposes
4
Summary
A significant part of the recent managerial transfer pricing literature studies the role of
transfer prices in providing incentives for specific investments at the divisional level. Most
notably, Edlin and Reichelstein (1995) demonstrate that negotiated transfer pricing can be
an efficient mechanism for solving a bilateral holdup problem in a multidivisional firm and
motivate the divisions to make efficient investment decisions. We contribute to the transfer
pricing literature by analyzing the usefulness of negotiated transfer pricing for solving a
bilateral holdup problem in multinational enterprises.
6
In fact, Edlin and Reichelstein (1995) show that (30) and (30) are equivalent with (5) if the revenue
and cost functions take the following forms R(q, θ, IB ) = R1 (IB ) · q + R2 (q, θ) + R3 (θ, IB ) and C(q, θ, IS ) =
C1 (IS ) · q + C2 (q, θ) + C3 (θ, IS ), respectively and the initial quantity equals the expected optimal quantity
q = Eθ [q ∗ ]
20
Our main finding is that the proposed renegotiation procedure will generally not provide
incentives for efficient renegotiations of the initial trade quantity if the same transfer price is
also used for minimizing the global tax bill. Moreover, given that efficient renegotiations are
expected to fail, the divisions will not make efficient investments in the first place. Intuitively,
the negotiated transfer pricing mechanism suffers from the fact that the divisions possess
only one instrument for solving two problems. They can either adjust the lump sum payment
in order to minimize the global tax bill or they can adjust it to redistribute the mutual gains
from implementing a new contract. Both problems can only be solved simultaneously when
they are coincidentally solved by the same transfer price.
Nevertheless, we demonstrate that Pareto improving renegotiations are still possible in
many cases. In fact, if the intermediate input is transferred at the tax minimizing transfer
price and both divisions benefit from an increase or a decrease of the transfer quantity,
the profit can be increased as compared to the initial contract but the quantity will only be
efficient by coincidence. This result stems from the fact, that the optimal quantities from the
perspective of the two divisions are generally different. As the efficient quantity is generally
not achieved, the divisions’ investment incentives are also distorted. We also show that the
divisions can benefit from renegotiations if they have the possibility to adjust both, the trade
quantity and the transfer price. In these cases, there is always a solution in which the two
divisions can benefit from an adjustment of the original contract, but this solution generally
requires that both variables take inefficient values. Finally, we demonstrate that the conflict
between the two functions of transfer pricing can be solved by the use of different transfer
prices for tax and managerial purposes. Since the use of two sets of books usually involves
additional cost for additional resources, the firm faces a trade-off between the benefits of
a more flexible transfer pricing policy and the additional cost associated with the use of
two sets of books. This trade-off can only be solved in the context of a particular decision
problem.
21
Appendix
Proof of Proposition 1: For an initial contract (T , q), the efficient quantity qb =
q ∗ (θ, I, t∗ ) and the tax minimizing transfer payment Tb = T ∗ ≡ t∗ · q∗ (θ, I, t∗ ), the seller
accepts the new contract if the following condition is met:
(1 − τ ) · (∆T − ∆C) ≥ γ · SP
(32)
where ∆T = T ∗ −T , and ∆C = C(q∗ , θ, IS )−C(q, θ, IS ) are the changes in lump sum transfers
and cost induced by the new contract. From the definition in (6) we can rewrite the renegotiation surplus as SP = α · ∆R − (1 − τ ) · ∆C + δ · ∆T, where ∆R = R (q∗ , θ, IB ) − R (q, θ, IB )
is the change in revenues caused by the adoption of the new contract. Substituting this
expression into the buyer’s participation constraint in (8) and rearranging terms indicates
that the buyer will only accept the new contract if the following condition is met
(1 − τ ) · (∆T − ∆C) ≤ γ · SP,
(33)
a contradiction to (32). We conclude that efficient renegotiations will typically fail unless
the distribution of bargaining powers happens to satisfy (32) and (33) with equality.
22
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Figure 1: Time line of events
t=1
q and T
negotiated
t=2
t=3
t=4
Investments
IS and IB
state 
realized
qˆ and Tˆ
25
renegotiated