Optimal Negotiated Transfer Pricing and Its Implications for
International Transfer Pricing of Intangibles
Peter C. Dawson
Stephen M. Miller
University of Nevada, Las Vegas
University of Connecticut
Working Paper 2009-06R
January 2009, Revised January 2014
365 Fairfield Way, Unit 1063
Storrs, CT 06269-1063
Phone: (860) 486-3022
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This working paper is indexed on RePEc, http://repec.org
Published in revised form as: Dawson, P.C. and Miller, S.M. (2011) ‘Optimal negotiated transfer pricing and its
implications for international transfer pricing of intangibles’, Int. J. Intellectual Property Management, Vol. 4, No.
4, pp.239–269.
Optimal Negotiated Transfer Pricing and Its Implications
for International Transfer Pricing of Intangibles
Peter C. Dawson
Independent
petercdawson@yahoo.com
and
Stephen M. Miller
College of Business
University of Nevada, Las Vegas
4505 Maryland Parkway
Las Vegas, Nevada, USA 89154-6005
stephen.miller@unlv.edu
September 19, 2011
Abstract:
Intangibles exhibit zero marginal licensing cost, including cross-border intra-firm licensing of
intangibles within a MNC. A MNC may not realize the full profit potential of licensing
intangibles intra-firm, however, under suboptimal negotiated transfer pricing schemes. Our
negotiated transfer pricing bargaining structure unlocks this potential by producing an optimal
transfer price and larger optimal intra-firm licensed quantity. Increased licensing of intangibles
intra-firm across borders produces a greater potential tax savings/consolidated after-tax profit
gain per unit of transfer price adjustment, creating a context where MNCs feel a greater
imperative or incentive to move beyond legal tax avoidance toward evasion.
Key Words: Negotiated transfer pricing, licensing intangibles, arm’s length royalty,
decentralized decision-making, multinational corporations, international trade,
intra-firm trade.
JEL Codes: F10, F23; H26; L24; O34.
1.
Introduction
Thirty to 60 percent of international trade occurs through intra-firm trade between related or
controlled divisions of multinational corporations (MNCs) (Guttman 1999; Stanley 2001;
Diewert, Alterman, and Eden 2005) at prices, called “transfer prices” (TPs), that are determined
within a MNC rather than at arm’s length in an external market. The extent of internal MNC
trade creates a substantial opportunity for MNCs to adjust TPs to shift profit earned in high-tax
countries to related corporate entities or divisions in low-tax or tax-haven countries. This
opportunity, coupled with a MNC’s fiduciary imperative to maximize world-wide after-tax
profit, raises governmental concerns about abusive transfer pricing (TPing) practices. In an
unpublished federally-funded study of U.S. Customs data, Pak and Zdanowicz (2002) report
dramatic over-invoicing of U.S. imports and under-invoicing of U.S. exports, creating an
estimated aggregate $53.1 billion loss in U.S. federal tax revenue in 2001 (Diewert, Alterman,
and Eden 2005, p. 4; Dorgman 2002). Eden (2003) concludes “empirical evidence for transfer
pricing manipulation exists but is not overwhelming” (p. 7), while Diewert, Alterman, and Eden
(2004) argue that, in general, the empirical literature on the extent of TPing manipulation proves
“mixed” (p. 3).
This paper develops an optimal negotiated transfer pricing bargaining structure, and
examines the strength of incentives for TPing abuse for tangible versus intangible intra-firm
trade from an economic perspective. Under negotiated transfer pricing (NTPing), a concern is the
ability of a MNC to create goal congruence without sacrificing division autonomy (Hansen and
Kimbrell 1991; Chalos and Haka 1990). Although
negotiation may foster greater divisional autonomy for
performance evaluation and better integration of divisional and
firm profit objectives[,] …these negotiation advantages may be
outweighed by bargainer practices such as nontruthful revelation of
2
cost and revenue information (DeJong et al., 1989) and
opportunistic behavior by a dominant division (Burton and Obel,
1988). These drawbacks may lead to non-Pareto outcomes for the
firm as well as divisional inequities (Ravenscroft, Haka and Chalos
1993, p. 415; italics original).
With our alternative, workable bargaining structure, which evaluates division management
performance independently of the negotiated transfer price (NTP) for income tax purposes,
autonomous divisions face sufficient incentives to select the firm-wide optimal TP (on the arm’s
length boundary) as well as the optimal quantity of tangible intra-firm trade. For tangible intrafirm trade, MNCs avoid taxes, but, given identifiable (near) comparable uncontrolled prices, they
do not necessarily face powerful incentives to evade taxes. For licensed intangible transfers
under NTPing, however, the nature of intangibles creates a larger optimal profit shift for a given
tax-rate differential, which strengthens incentives for TPing abuse. Coupled with the typical
absence of publicly-available information on (near) comparable uncontrolled license
transactions, an intangible’s arm’s length range, therefore, provides an imperfect guideline, a
context where incentives for abuse are more likely to materialize.
2.
The Core Synthesis Model
We develop a core synthesis model to create a common framework within which to review the
relevant core papers’ analyses and results. The MNC owns two divisions, one operating in the
domestic country (country 1) and the other operating in a foreign country (country 2) (Hirshleifer
1956, 1964; Horst 1971; Bond 1980). Division 2’s operations constitute a wholly-owned and
controlled subsidiary of the parent company, incorporated under the laws of country 2. By
convention, intra-firm trade flows from division 1 to division 2, reflecting a MNC’s vertical or
horizontal integration strategy. Top management maximizes the MNC’s global after-tax profit,
subject to regulatory constraints and internal management control limitations. The MNC’s
3
domestic currency-denominated global after-tax profit is
 E  1  t  Π
dc
Π MNC
  1  t1  Π1dc  1
2
fc
2
,
(1)
where Π1dc is the domestic currency value of division 1’s before-tax profit, Π2fc is the foreign
currency value of division 2’s before-tax profit, t1 and t2 are country 1’s and 2’s effective
corporate income tax rates, E is the nominal exchange rate defined as foreign currency per
domestic currency (which is not assumed to equal 1), and there is no import tariff (Bond 1980).
Furthermore,
Π1dc  P1dc X 11  P12dc X 12  C1dc  X 1  , and
(2)
Π 2fc  P2 fcY2  γ2fc Y2   P12fc X 12 ,
(3)
where division 1 produces good 1, X 1 , that sells in country 1, X 11 , and also sells it
internationally intra-firm to division 2, X 12 , at a per-unit domestic currency TP of P12dc
( X 1  X 11  X 12 ). Division 1 incurs a domestic currency cost of producing good 1, C1dc . Division
2 uses X 12 as an input in the production of good 2, Y2 , for sale in country 2. Division 2 incurs a
foreign currency production cost, γ2fc .1 Division 2 uses X 12 as a variable resource input in its
production of good 2, which leads to P12fc X 12 intra-firm input costs (in addition to the variable
labor/input costs already included in γ2fc ). Division 2’s before-tax profit, Π2fc , enters top
management’s profit-maximizing objective function as Π2dc ( Π2dc 
Π2fc
E
).
By convention, division 2 uses one unit of X 12 to produce one unit of Y2 (i.e.,
1
If division 2 resells good 1 in country 2 as good 2, division 2’s output is X 2 , and γ2fc equals division 2’s cost of
processing good 1 for resale as good 2.
4
Y2  f  X 12   X 12 ).2 Division 2 faces a perfectly competitive output market (i.e., P2 fc  P2 fc ), a
strategic simplification that does not change the qualitative results (Bond 1980, pp. 193-194). No
outside market for the intermediate good exists (i.e., X 11  0 ), an assumption relevant to a TPing
analysis for the typical MNC.3 Therefore, the core synthesis model (in domestic currency) is
Π MNC   1  t1  Π1   1  t2  Π 2 ,
(1')
Π1  P12 X 12  C1  X 12  , and
(2')
Π2 
Π2fc
E
 P2 X 12  γ2  X 12   P12 X 12 .
(3')
The intra-firm quantity traded depends on the TP (i.e., X 12  X 12  P12  ), which allows division
managements, under decentralized decision making (DDM), to choose their respective quantities
supplied and demanded (i.e.,
dP12
dX 12s *
 C1''  0 , and
dP12
dX 12d *
  γ''2  0 ).4 The internal market
supply and demand curves are illustrated in Figure 1.5
[Figure 1 about here]
Under centralized decision making (CDM), X 12  X 12  X 120 , since top management determines
the quantity of intra-firm trade.
2
Relaxing this assumption does not alter the quality of the results (Bond 1980, p. 196).
3
Spicer (1988) argues that, for idiosyncratic intermediate goods or for significant transaction-specific human and/or
physical capital, internal trade may best promote the interests of the firm. From a broader perspective, a vertical
integration strategy involves less MNC use of external markets, if any, to source certain inputs (Eccles 1985, p. 79).
Vertical integration reflects anticipated synergistic benefits of integration, including cost savings or productivity
enhancements from sourcing from a related or controlled division. Furthermore, MNCs that do not face an external
market, and therefore do not face an easily discernible comparable uncontrolled market price, maintain more
flexibility to adjust their TP.
4
See Appendix A for these derivations.
Figure 1 reflects Hirshleifer’s (1956; 1964) model, except his analysis assumes C1'' '  0 and γ '2''  0 . To simplify,
we assume linear marginal cost functions. The superscript “0” refers to internal equilibrium.
5
5
3.
Centralized Decision Making: The Modified Horst (1971) Solution
In Horst (1971), the MNC faces an import tariff or duty, d 2 , in country 2 on the value of intrafirm trade, and is horizontally integrated (i.e., division 2 resells X 12 as its final good 2, which is
now X 2 instead of Y2 ). Division 2 produces part of X 2 itself (i.e., X 22 ) with a production cost
of C22 , does not incur a processing cost for the portion of good 2 that it imports from division 1
( γ2  0 ), and sells good 2 in an imperfectly competitive output market. Therefore,
Π 2  P2 X 2  C22  X 22    1  d 2  P12 X 12 ,
(4)
where P2  P2  X 2  and X 2  X 22  X 12 . An imperfectly competitive external market for the
intra-firm good exists; division 1 sells the intra-firm good to unrelated parties in country 1 as
good 1, X 11 , where P1  P1  X 11  . Therefore,
Π1  P1 X 11  P12 X 12  C1  X 1  .
(5)
Equations (1'), (4), and (5) represent Horst’s (1971) original model, which assumes CDM since
the quantity of intra-firm trade, X 12 , does not depend on the TP, P12 . Several possible scenarios
can underlie a CDM assumption, including: (i) The MNC operates as a traditional neoclassical
firm, or “black box,” with no explicit decision-makers or agency relationships, and the “firm”
chooses the TP and the quantity of intra-firm trade to maximize Π MNC ; (ii) an owner-operated
MNC faces no principal-agent problems, since the owner makes all operating divisions, and the
owner chooses both the TP and quantity of intra-firm trade to maximize Π MNC ; or (iii) a MNC’s
top management implements a perfect management control system (MCS) that corrects all
principal-agent problems, such that division managements choose the TP and the quantity of
intra-firm trade that maximize Π MNC . Given the benefits of decentralization, the typical MNC
6
delegates decision-making authority/responsibility to division managements in different
countries, such that an agency relationship between top management and division managements
exists. For comparison purposes, scenario (iii) best characterizes the CDM assumption.
Substitute equations (4) and (5) into equation (1') to produce
Π MNC  Z  P12 X 12  t2  t1    1  t2  d 2  ,
(6)
where Z   1  t1   P1 X 11  C1    1  t2   P2 X 2  C22  . The first-order condition for an optimum
yields
dΠ MNC
Horst
dΠ MNC
(1971)
dP12
dP12
 X 12  t2  t1    1  t2  d 2   0 .
concludes
that
when
 t2  t1 
exceeds
(7)
(falls
below)
( 1  t2 )  d 2 ,
 0   0  and the firm raises (lowers) the TP to the highest (lowest) allowable level.
When the home (foreign) country imposes a high enough tax rate (import tariff rate), the firm
can “take a beating” on the import duty (home country corporate tax bill) to avoid a relatively
high tax bill in country 1 (high import tariff in country 2).
The MNC abides by TPing regulations.6 According to Eden (1985), Horst (1971)
assumes that the arm’s length price lies in the P1 to C1' range, since “he expected tax and tariff
authorities to impose MC1 as an effective lower bound and P1 as an upper bound to P12 ” (p. 19).
Booth and Jensen (1977) note that the TP is arbitrary and indeterminate when top management’s
profit-maximizing objective is unconstrained, such as by an arm’s length constraint (p. 434).
Schjelderup and Sørgard (1997), when modeling Horst (1971), (implicitly) impose an internal
6
Under U.S. TPing regulations in §1.482, a firm must report “arm’s length” income, which conforms to the “arm’s
length standard” (§1.482-1(b)(1)).
7
profit constraint to ensure a determinate solution (pp. 278-279).7 Since a MNC cannot deduct
losses earned in one country on its tax return in another country, the MNC does not adjust the TP
to earn a loss in its high-tax division. Rather, the TP adjusts only until the high-tax division earns
zero profit. Booth and Jensen (1977) show that the TP becomes determinate when top
management, in general, constrains itself to meet minimum profit levels in each country.
Under the assumptions of our simplified core model, we obtain a modified Horst (1971)
CDM solution that retains the substance of the relative tax effect, which is
dΠ MNC
dP12
 X 12  t2  t1    0 .
(8)
When t2  t1 ( t2  t1 ), the MNC chooses the highest (lowest) allowable TP to maximize Π MNC ,
given its optimal choice of X 120 , where the arm’s length range implicitly constrains the TP.8
4.
Decentralized Decision Making: Centralized Transfer Pricing
In Bond’s (1980) decentralized MNC, top management chooses the TP (under DDM with
centralized transfer pricing, CTPing) and division managements choose the quantity of intra-firm
trade (and division output). Bond’s (1980) model contains equations (1'), (2'), and (3') of the core
model. Given the centralized TP set by top management, each division responds by choosing its
optimal quantity of the intra-firm good. The divisions maximize as follows:
Division 1:
Division 2:
Max
1  t1  Π1
s
X 12
Max
 1  t2  Π 2
d
X 12

1  t1   P12  C1'   0 ; and
(9)

1  t2   P2  γ'2  P12   0 .
(10)
P12
P12
7
Schjelderup and Sørgard (1997) consider a MNC’s transfer pricing under DDM with centralized transfer pricing
(CTPing), where division 2 faces oligopolistic competition in its final goods market in country 2.
8
Under U.S. TPing regulations, the arm’s length TP must fall within the interquartile range of prices determined
under the best TPing method (§1.482-1(e)).
8
Top management chooses the TP to maximize Π MNC , given known division supply and demand
curves.9 Bond (1980) calculates top management’s first-order condition, and evaluates it at the
equilibrium TP, P120 :
dΠ MNC
dP12
0
P12  P12
 X 120 (t2  t1 ) .
(11)
He concludes that when t2  t1 ( t2  t1 ), top management raises (lowers) the TP from P120 to
maximize Π MNC . Bond’s (1980) decentralized analysis raises the possibility of a TP within,
rather than on, the arm’s length boundary, which produces an interior solution. Top management,
constrained by its internal MCS and the associated production incentives, adjusts the TP by less
than the maximum allowed by tax law.
We extend Bond (1980) to allow the TP to take any value within, or on, the arm’s length
constraint (i.e., it can differ from P120 ).10 Like Bond (1980), profit-maximizing division
managements under DDM react to changes in the centrally-determined TP by adjusting their
respective intra-firm quantities supplied and demanded. The direction of the quantity’s response
to changes in the TP depends on whether the MNC operates along division 1’s supply curve or
division 2’s demand curve. Given the significance of international intra-firm trade, we assume
that top management hires a competent consultant to determine the arm’s length range (if not
already known) and, therefore, can and does select a TP on, or within, the arm’s length
9
In Hirshleifer (1956; 1964), perfect information would allow a neutral umpire to choose the internal equilibrium
TP, P120 , without an iterative process (refer later to the discussion of Hirshleifer’s (1956; 1964) analysis).
10
In our model, we assume a generalized arm’s length constraint with a lower bound that does not necessarily equal
to the selling division’s (i.e., division 1’s) marginal production cost for the intermediate intra-firm good. By contrast,
Göx and Schiller (2007) assume a more restrictive arm’s length constraint with the lower bound equal to the selling
division’s marginal cost (p. 690). They conclude an interior solution for the transfer price within the arm’s length
boundaries, which reflects “the tension between managerial and tax incentives” (pp. 690-692). They do not
acknowledge Bond (1980).
9
boundary.
Top management’s first-order condition for profit maximization implicitly defines the
optimal TP. The total differential of the first-order condition generates the comparative static
results as follows:
 P12*  P12  C1  X 12  X 12

; and
 t1
CC
'

'
(14)

'
P2  γ'2  P12 X 12
 X 12
 P12*

,
 t2
CC
where
(15)
2
2 ''
'
'
'
CC   t1  1  X 12
C1''    t2  1  X 12
γ2   2 X 12
 t2  t1   0 .11






When
the
MNC
operates along the supply (demand) curve, division 1’s (2’s) first-order condition for division




profit maximization, P12  C1'  0 ( P2  γ'2  P12  0 ), holds. The following tax conditions also
hold when the MNC operates along the supply (demand) curve: t1  t2 ( t1  t2 ).12 The slope of
'
the supply (demand) curve is assumed to be positive (negative); X 12
 X 12s '  0 (  X 12d '  0 ). In
internal equilibrium, the MNC operates at the intersection of division 1’s supply curve and
division 2’s demand curve, satisfying each division’s first-order condition as well as the tax
condition that t1  t2 . When t1  t2 , the comparative static results, which correspond to Bond’s
(1980) conclusion, reduce to
 P12*
 t1

X 12
CC
 0 and
 P12*
 t2

 X 12
CC
0.
(16)
When t1  t2 , the MNC operates along the internal supply curve, and the comparative static
11
See Appendix A for a derivation of the sign of CC.
12
See Appendix A for a derivation of the tax conditions.
10
results reduce to


'
P2  γ'2  P12 X 12
 X 12
 P12* X 12
 P12*

0.

 0 and
CC
 t1
CC
 t2
(17)
When t1  t2 , the MNC operates along the internal demand curve, and the comparative static
results reduce to
'
'
 P12*  X 12
 P12*  P12  C1  X 12  X 12

0.

 0 and
 t2
CC
CC
 t1
(18)
We conclude, more generally, that whether t1  t2 or t1  t2 the sign of equation (14) is always
negative and the sign of equation (15) is always positive.13 The signs of the comparative static
results do not depend on differences in organization structure (i.e., CDM versus DDM). Their
magnitudes probably differ, however, because a decentralized MNC’s top management may not
select the highest or lowest TP allowed by tax law.
Baldenius et al. (2004) extend Hirshleifer’s (1956) domestic-firm model to the MNC,
where a MNC’s divisions face different tax rates, effectively reproducing Bond’s (1980) analysis
and interior solution for the transfer price.14 “The optimal single transfer price balances the
conflicting goals of tax minimization and efficient resource allocation” (Baldenius et al. (2004),
p. 592). Like Bond (1980), they assume DDM with CTPing. In addition, they consider the cases
where (i) division 1 sells the intermediate intra-firm good to the outside market, and (ii) the
MNC “decouples” the transfer price for “managerial performance evaluation purposes” from that
used for “tax reporting purposes” (p. 593). Their analysis assumes no outside market for the
13
Dawson (1999) shows that the qualitative results hold for general functional-form supply and demand curves (pp.
97-100, 108).
14
Baldenius et al. (2004) do not acknowledge Bond (1980).
11
intra-firm good.15 In their model, however, the decoupling assumption is trivial, because they
assume that no principal-agent problem exists between top management and division
managements:
Throughout this paper, we take it as given that divisional managers
seek to maximize the after-tax income of their divisions. While this
specification appears quite descriptive, it is ad hoc within our
model. In effect, we suppress moral hazard problems that generate
an explicit conflict between divisional managers and the overall
corporate objective. In future research it would be desirable to
embed our framework into an explicit principal-agent model…
(Baldenius et al. 2004, p. 594; italics original).
At this point, we question the validity of their results under their decoupling (and inter-company
discounts) assumption(s).16 Baldenius et al.’s (2004) results assume that division managements
respond to the CTP by adjusting their respective division’s intra-firm quantities, such that lessthan-optimal intra-firm trade occurs. Since they assume that no principal-agent problems exist
between top management (representing corporate objectives) and division managements,
division managements always choose the firm-wide optimal intra-firm quantity regardless of the
transfer price. Under CTPing, top management sets the transfer price on the arm’s length
boundary to minimize taxes, while division managements set the optimal intra-firm quantity:
both choices maximize the corporate after-tax profit objective. When correctly applied,
Baldenius et al.’s (2004) assumption of no principal-agent problems (or, equivalently, that a
15
Baldenius et al.’s (2004) outside intra-firm goods market case does not materially differ from the case without an
outside market, since they effectively decouple the transfer price in the form of internal discounts. Internal discounts
eliminate the link between the outside market price and the internal transfer price for performance evaluation
purposes. They agree: “the use of so-called intracompany discounts leaves flexibility for calculating internal transfer
prices that differ from … external arm’s length prices” (p. 600; italics original).
16
Baldenius et al (2004) state, “For both cost- and market-based transfer pricing, we conclude that an internal
transfer price set equal to the arm’s length price will generally result in inefficiently low intracompany transfers. The
optimal cost-based transfer price is a weighted average of the pre-tax unit cost and the most favorable arm’s length
price. When the intermediate product is sold to external parties, we find that internal transfers should be subjected to
intracompany discounts, relative to the market price that also serves as the arm’s length price” (p. 608).
12
perfect MCS alleviates incongruent objectives) would produce the modified Horst (1971)
solution. Achieving the optimal solution does not require a decoupling of the transfer price from
division management performance evaluations. Without a principal-agent problem, division
managements always select the optimal intra-firm quantity of trade at any CTP that is set, for tax
purposes, to meet the arm’s length standard.
5.
Optimal Negotiated Transfer Pricing
CTPing presumes that top management possesses perfect (or at least very good) information
about its divisions (i.e., it knows each division’s reaction function) so that it can choose the
optimal TP and quantity of intra-firm trade (Hansen and Kimbrell 1991, p. 84). Adopting a
decentralized corporate structure copes with the agency costs associated with “impacted
information” (Williamson 1975) at the division level. As Hansen and Kimbrell (1991) note, top
management’s “limited and untimely access to local information and cognitive limitations are
key reasons why firms decentralize!” (p. 84).17 Furthermore, NTPing is common practice
(Vaysman 1998; Emmanuel and Mehafdi 1994; Chalos and Haka 1990; Eccles 1985; Price
Waterhouse 1984; Tang, Walter, and Raymond 1979; Wu and Sharp 1979; Vancil 1978).
Therefore, we relax the CTPing assumption. The existing literature concludes that no TP
resolves the conflict between goal congruence and division autonomy (e.g., Hansen and Kimbrell
1991, p. 79). We show that, under a tractable bargaining structure, a firm-wide optimal solution,
which we refer to as the modified Horst (1971) CDM solution, can occur.
17
Göx and Schiller (2007) suggest that the standard economic model of transfer pricing, which ties to Hirshleifer
(1956), “does not provide a convincing theory of decentralization because coordinating a divisionalized firm by
means of transfer pricing offers no visible advantage over a centralized organization with mandated trade” (p. 692).
That is, should top management possess the local division information necessary to select the “right” transfer price,
it should select the optimal transfer price under CTPing and “simply instruct the divisions to implement the optimal
production policy instead of coordinating their activities by a transfer pricing mechanism. In other words, the model
does not provide a sufficient theoretical explanation for a decentralized organization” (p. 674). On the contrary,
Hirshleifer (1956, 1964) assumes that top management lacks complete local division information.
13
The Domestic Divisionalized Firm Facing Equal Tax Rates
Hirshleifer (1956; 1964) modeled a domestic divisionalized firm facing an identical corporate
profit tax rate in each state or region where it operates. Therefore, in equation (1'), t1  t2 . Under
DDM, division managements choose the TP through negotiation (i.e., NTPing) and the quantity
of intra-firm trade (and division output).18 Under Hirshleifer’s (1956; 1964) assumption of equal
tax rates, P120 equals the domestic firm’s profit-maximizing TP, where, at P120 , the following
maximizing conditions (Hirshleifer 1964, p. 31) hold:
1.
Division 1: P12  C1' ,
2.
Division 2: P12  P2  γ'2 , and
3.
Firm-wide: X 12s  X 12d  X 12 .19
No guarantee exists that autonomous divisions will choose the optimal NTP and intra-firm
quantity of P120 and X 120 , however. Division managements may exploit their internal
(monopolistic or monopsonistic) market power. To overcome potentially dysfunctional effects,
Hirshleifer (1956, 1964) suggests a “neutral umpire” (or “auctioneer”) to facilitate the TP
negotiations through an iterative process. Even though a neutral umpire aims to minimize the
exercise of internal market power, rational divisions possess an incentive to misinform the
neutral umpire “in the hopes of achieving a more favorable price” (Hirshleifer 1964, p. 32).
Under conditions of imperfect information, top management chooses a TPing rule, or bargaining
18
Some papers mischaracterize Hirshleifer (1956) as assuming CTPing (e.g., Baldenius 2008, p. 225).
19
At P120 , we encounter “marginal cost pricing for the intermediate product”, since the TP equals division 1’s
marginal cost, C1' , which Hirshleifer (1956) clarifies by noting “the sum of the divisional marginal costs equal to
price (in the perfectly competitive case) or marginal revenue (in the imperfectly competitive case) in the final
14
structure (e.g., a neutral umpire), that intends to lead autonomous divisions to choose P120 (and,
thus, X 120 ).
Hansen and Kimbrell (1991) analyze a domestic divisionalized firm’s ability to achieve
an efficient level of intra-firm trade under NTPing. Unlike Hirshleifer (1956; 1964), they assume
top management has complete information about division operations, but, because it “does not
possess the cognitive capability to process the information on a timely and accurate basis” (p.
82), it delegates authority over operating decisions to division managements. Division managers
know division 1’s marginal cost function (i.e., internal supply curve) and division 2’s net
marginal revenue function (i.e., internal demand curve)20, know that a potential joint benefit
exists through cooperation in the negotiations (p. 87), and know how to process the relevant
information efficiently and effectively. “The difference between the optimal profits and the
achieved profits of the two divisions is a [potential] joint benefit” (p. 85). Hansen and Kimbrell
(1991) conclude that rational division managers, who “possess sufficient information” (p. 81),
will select the firm-wide optimal intra-firm quantity of trade (and final output) without “any
intervention of the central authority” (p. 81). Weak rationality ensures that, not only do they
cooperate when they expect to earn a higher division profit (and a higher performance-based
compensation payment) than they would without cooperation, they cooperate even when they
expect to earn exactly what they would without cooperation.21 Hansen and Kimbrell (1991) do
not form a conclusion or make an assumption with respect to how the NTP is determined within
market” (p. 175) (i.e., C1'  γ'2  P2 ). Also, division 2’s marginal cost, γ'2 , equals division 2’s net marginal revenue,
P2  P12 .
20
Knowledge of the internal supply and demand curves gives division managements the capability, although not
necessarily the incentive, to choose the optimal quantity of intra-firm trade.
21
In other words, the “concession limits” define the bounds of the “negotiation set” (p. 86).
15
the negotiation set. Implicit in their analysis, we believe, is the assumption that the TP will be
selected in a fair manner. The TP provides “the mechanism used to assign the cooperative gain to
each division” (p. 87), meaning that it is used for both performance evaluation and tax reporting
purposes. Since tax rates are equal for the domestic divisions, the TP allocates the joint gain in
division profit without adversely affecting—through adverse intra-firm trade/production
incentives—the firm’s overall after-tax profit.
Vaysman (1998) extends Hansen and Kimbrell (1991) to include private division
information and a bargaining structure that includes top management intervention to select the
TP (i.e., CTPing) should a negotiation impasse occur at (or before) the end of the negotiation
period. The TP calculates division profits for financial, tax reporting, and performance
evaluation purposes. Divisions earn at least their reservation division profit (and,
correspondingly, managers receive at least their reservation performance-based compensation) to
ensure that they do produce and conduct intra-firm trade. Presumably, these reservation levels
are their conflict payoffs—the division profit they would earn without cooperation. Assuming
incentive compatibility, Vaysman’s (1998) upper bound on profits is quantitatively equivalent to
the profits earned by a MNC with the modified Horst (1971) result.22
We question the content of Vaysman’s (1998) private division information assumption
because, although division managers possess private information not known to other division
managers, they do know the other division’s relevant information. That is, each knows division
1’s supply curve and division 2’s demand curve, which is the information needed to select the
22
A “centralized decision-making scenario [is] used to compute the upper bound on profits” (p. 373) by
hypothesizing an “incentive-compatible direct-revelation mechanism” (p. 355), which is characterized by division
managers truthfully reporting all private information to top management (pp. 355, 356).
16
optimal quantity of intra-firm trade, X 120 .23 Vaysman’s (1998) “asymmetric information”
assumption (p. 354, footnote 2) may not differ from Hansen and Kimbrell’s (1991) information
assumption. We also question the assumption of “extensive-form negotiations” (p. 372) “over the
transfer price” (p. 358) where the “manufacturing manager is induced to reveal all private
information before bargaining begins” (p. 372).24 It may be redundant, since, by prior
assumption, each division already knows the relevant cost and revenue information.
Further, we question Vaysman’s (1998) assumption that centralized intervention in the
event of a negotiation impasse is necessary to guarantee cooperation. If, as Hansen and Kimbrell
(1991) assume, division managers are weakly rational, then division managers (weakly) prefer to
cooperate even when they expect to earn their conflict payoff. With Vaysman’s (1998)
assumption that negotiation impasse leads to no intra-firm trade, no final good production, and
no division profit (and probably a loss), Hansen and Kimbrell’s (1991) weak rationality becomes
strict rationality. That is, when faced with zero performance-based compensation, division
managers would strictly prefer to cooperate and receive at least some performance-based
reward.25 Impasse in Vaysman’s (1998) analysis leads to no production/sales, which can also
lead to layoffs and/or division shut down, bringing a manager’s base compensation to zero as
well, further supporting a strict preference for cooperation and production. Alternatively, when
negotiation impasse interrupts intra-firm trade, a vertically integrated MNC can allow division 2
to source inputs from the outside market (to fulfill its final good sales orders), and, therefore,
23
Vaysman (1998) assumes that “The firm’s accounting system records realizations of costs and revenues” (p. 353)
and “makes them available to all parties” (p. 354).
24
Vaysman (1998) uses “a particular extensive-form scenario … to analyze the process of manager’s negotiation
over the transfer price” (pp. 357-358) because the “Accounting literature does not provide empirical evidence on the
exact nature of bargaining that takes place in negotiated transfer-pricing arrangements” (p. 358). He adopts “the
buyer-offer extensive form to represent the bargaining that takes place over the transfer price” (p. 359).
17
division 2’s supplier-switching costs can make it strictly preferable to cooperate when it expects
to earn its conflict payoff. Moreover, Vaysman (1998) rules out the need for central intervention
to guarantee cooperation by making the explicit assumption that “whenever an agent is
indifferent between various actions, the agent selects the action preferred by HQ” (p. 354).
Hansen and Kimbrell (1991) and Vaysman (1998) do not include how the perceived
fairness of the negotiated TP can affect a domestic divisionalized firm’s overall profit. In their
analyses, the TP does not affect the firm’s overall (before- or after-tax) profit, so the TP can
divide the joint profit gain (if any) without distortion. But, what determines the NTP? Is the
process fair? “[M]anagers believe they are being treated fairly when they receive rewards that
they believe are commensurate with their contribution to the company” (Eccles 1985, p. 270). If
(as we assume below) bargaining outcomes predominantly reflect relative bargaining abilities or
positions, no guarantee exists that both division managers will view the NTP as fair. Division 1’s
(2’s) management responds to an unfairly low (high) NTP by reducing the intra-firm quantity
supplied (demanded), thereby reducing the intra-firm quantity and final good output below their
firm-wide optimal levels.26 Including fairness considerations could undermine resource
efficiency.27
In Hansen and Kimbrell (1991) and Vaysman (1998), divisions first cooperate in their
negotiations to select the optimal firm-wide quantity of intra-firm trade, X 120 . The NTP then
25
We implicitly assume that each division expects to be profitable under a production scenario, so that performancebased compensation is relevant.
26
Although not specifically modeled in our basic analysis, division 1 (division 2) could reduce the quality of the
intra-firm product (its marketing efforts or expenditures) if division managers view the negotiated TP as unfairly
low (high), which would contribute to a lower division 2 sales volume. Vaysman’s (1998) productivity parameter, zi,
which is a shift parameter, could capture these effects.
27
Kachelmedier and Towry (2002) consider the issue of fairness. They conclude “…expectations of fairness-based
price concessions do not survive actual negotiations when participants negotiate over a computer network with no
18
allocates the joint gain in combined division profit (if any) given X 120 . This sequence may not be
rational, however. Assuming that top management wants to alleviate dysfunctional negotiation
behavior, we characterize DDM by the delegation to division managements’ the authority to
choose the intra-firm quantity and TP, and to determine the sequence in which they select those
variables. Division managers do not agree to select the intra-firm quantity first. Given the
binding and enforceable nature of the negotiation agreement, the relatively weaker-bargaining
division management cannot renege on its intra-firm quantity agreement in the event of an unfair
NTP. For example, if division 2 experiences a relatively weaker-bargaining position, the NTP
will exceed the equilibrium TP, and, therefore, it will pay more than what it views as a fair price
for the intra-firm good. As such, it will maximize its division profit, given the unfairly high NTP,
by selecting a quantity of the intra-firm good demanded up along its internal demand curve, a
lower quantity than equilibrium. Since it stands to receive the greatest share of the cooperative
gain, the relatively stronger bargaining division will not challenge the decision sequence of TP
followed by intra-firm quantity because it will not want to forgo the opportunity of a joint gain.
In a dynamic, period-after-period bargaining game, this rational behavior should become more
evident in subsequent periods, given an unfair outcome in the first period.
The MNC Facing Unequal Tax Rates
Halperin and Srinidhi (1991) extend Hansen and Kimbrell (1991) to the international case with
different tax rates. Like Hansen and Kimbrell (1991) and Vaysman (1998), they assume
divisions know each other’s cost and revenue information. Halperin and Srinidhi (1991) consider
the case of an explicit endogenous arm’s length constraint, either determined by the Resale Price
Method or Cost-Plus Method, which the MNC could adjust through a change in its intra-firm
communication other than bids, asks, and acceptances. …outcomes reflect fairness-based price concessions when
19
quantity (and output). This extension is beyond the scope of this paper, however. We assume an
(implicit) exogenous arm’s length constraint. Halperin and Srinidhi’s (1991) scenario with no
arm’s length constraint, however, is relevant here.
Under an implicit arm’s length constraint with an exogenous upper and lower bound,
Halperin and Srinidhi’s (1991) no arm’s length constraint case is as follows. Division managers
cooperate to select the equilibrium quantity of intra-firm trade, X 120 , based on complete
knowledge of cost and revenue functions, binding and enforceable agreements, and preferences
that are unresponsive to the process of negotiation (presumably, an unfair negotiation process
does not change preferences). The NTP allocates the joint gain (if any) in combined division
profit. Complete knowledge of each division’s reaction function gives division managements the
ability, but not necessarily the incentive, to cooperate and select the optimal intra-firm quantity
and TP. The NTP depends on division managers’ relative negotiating strengths, so there is no
guarantee that the NTP will fall on the upper or lower arm’s length boundary. Since the NTP
determines both taxes and bonuses paid, the MNC cannot maximize total after-tax profits. In
other words, the finding in Halperin and Srinidhi (1991) does not achieve the modified Horst
(1971) CDM result.
Halperin and Srinidhi’s (1991) decentralized MNC may not achieve resource efficiency
(i.e., internal equilibrium) either. Like Hansen and Kimbrell (1991) and Vaysman (1998),
Halperin and Srinidhi (1991) do not incorporate the disincentive effects created by a perceived
unfair NTP that reflects bargaining abilities rather than divisions’ relative contributions or valueadded to the firm. Not only will a MNC’s after-tax profits fall below the modified Horst (1971)
profit due to a NTP determined by bargaining power (and, therefore, not necessarily on the arm's
participants negotiate in a face-to-face setting with unrestricted communication.” (571).
20
length boundary), but also a perceived unfair NTP can reduce the quantity of intra-firm trade too.
A suboptimal NTP simultaneously reflects unequal bargaining positions and the associated
unfairness to one division’s management.
An Alternative Approach
Our NTPing model builds upon the strengths of Hansen and Kimbrell (1991), Vaysman (1998),
and Halperin and Srinidhi (1991). We consider a decentralized MNC’s ability and incentives to
achieve the modified Horst (1971) solution assuming (1) the existence of private division
information between division managements, (2) a recognition by divisions that a positive-sum
game exists, (3) the NTP reflects relative bargaining abilities (Halperin and Srinidhi 1991), (4)
unfair NTPs can adversely affect a division manager’s incentives, and (5) the NTP does not
allocate the joint gain in division profit. Our material departures from Hansen and Kimbrell
(1991), Vaysman (1998), and Halperin and Srinidhi (1991) include assumptions (1), (4), and (5).
The MNC faces different effective international tax rates, division management
performance-based compensation depends on division profit (where division manager utility
directly relates to compensation), division managements have private information about their
respective division’s operations and market (including private information about their costs and
revenue functions), divisions play a positive-sum game in their negotiations, and a negotiation
impasse at (or before) the end of the bargaining period triggers a default TP (e.g., last period’s
NTP) or a centrally-determined TP (i.e., CTPing). Under DDM, division managers retain the
authority to reduce their quantity of intra-firm trade should they face an unfavorable NTP.
Under the conventional assumption that taxable income and performance evaluation
depend on the NTP, Hansen and Kimbrell’s (1991) decentralized domestic firm achieves an
optimal firm-wide quantity of intra-firm trade. Under the same assumption, Halperin and
21
Srinidhi’s (1991) MNC’s NTP minimizes the MNC’s global tax payments and divides the joint
gain in combined division profit, probably leading to a sub-optimal NTP, because no guarantee
exists that a NTP based on relative bargaining positions will fall on the upper or lower arm’s
length boundary. By contrast, the NTP is not a sharing mechanism for the joint gain (or loss) in
our bargaining structure, so it does not affect division profit and performance-based
compensation. The optimal NTP only minimizes the MNC’s global tax liability (subject to an
exogenous arm’s length constraint). When relative bargaining power determines the NTP, it can
adversely affect manager morale, effort, and productivity.28 Solutions to this agency-cost
problem include, for example, Choi and Day’s (1998) conclusion that top management can
address the tradeoff between tax avoidance and management incentives by using incentive
compensation based on multiple performance measures. In our NTPing model, division
management performance evaluation depends on division performance evaluation profit, which
is not calculated using the NTP. This removes the NTP as a source of agency costs and suboptimality. In a bargaining structure that separates the NTP and performance evaluation
decisions, the modified Horst (1971) CDM solution obtains. Other agency costs may remain
(e.g., agency costs associated with how the firm allocates the joint gain between divisions), but
they do not reflect the NTP. The form of the allocation mechanism, which division managements
may or may not view as fair, is not critical to our analysis.29
28
When top management cannot observe division managements’ behavior and effort perfectly and division
managements receive their reward based on division profit, top management’s task of coordination within the firm
proves more complicated because its “desire to use the TP to minimize the MNC’s global tax liabilities may
encourage slack effort by its subsidiaries’ managers” (Donnenfeld and Prusa 1995, p. 231). “[I]f a [transfer pricing]
method is chosen to give an advantage for tax purposes, then the use of the results of subsidiary operations for
performance evaluation of managers may yield unfair results, causing managerial conflict and morale problems.
This potential conflict between the transfer pricing method chosen and a fair performance evaluation is a primary
concern in the MNC” (Borkowski 1992, p. 174)
29
Baldenius (2008) considers the domestic divisionalized firm’s investment disincentives that may associate with
top management’s cooperative gain allocation mechanism. Ex ante division investment in relationship-specific
22
Private Information
We assume private division information between division managements (and between divisions
and top management) concerning each division’s respective cost and revenue functions, reaction
(supply and demand) functions, and other relevant operating information and markets. Divisions
may truthfully share this private information with each other, if faced with adequate incentives to
do so. Division managements possess common knowledge and publicly-available information,
including information publicly-available within the MNC (e.g., their negotiations generate a
positive-sum). Division managements exhibit bounded rationality, but exercise due diligence
when making management decisions to operate their divisions competently.
Bargaining Structure
Top management implements the following bargaining structure, which motivates division
managements to negotiate the TP and quantity of intra-firm trade (and the sequence in which
they are negotiated) to maximize the combined after-tax division profit and, thus, the joint gain
in after-tax division profit. Division managements also negotiate a split of the joint gain (or loss).
The motivation to cooperate to maximize the joint after-tax division profit reflects a combination
of assumptions: (1) Performance evaluation depends on division profit, (2) performance
evaluation does not depend on the NTP30; (3) division managements are rational; (4) division
managements negotiate the TP and quantity of intra-firm trade (as well as the sequence of their
decisions); (5) division managements know that negotiations take place in a positive-sum
investments may prove suboptimal, creating underinvestment or a “hold-up problem.” That is, division
managements expect that they will share the cooperative gain from future transfer price negotiations based on an
unfair mechanism (e.g., relative bargaining positions rather than each division management’s relative contribution to
the cooperative gain). In contrast, we assume that the previous periods’ investments and the resulting effects are
exogenous (i.e., implicit in the ceteris paribus assumption).
30
In Baldenius et al.’s (2004) terminology, the transfer price for division management performance evaluation is
“decoupled” from the transfer price reported to the tax authorities for income tax purposes.
23
game;31 (6) the length of the bargaining period is limited; and (7) negotiation impasse triggers
the use of CTPing or a default TP.
Optimal NTPing
Assumption 2 ensures that the NTP does not cause agency costs that relate to the fairness of the
NTP. Under these seven assumptions, cooperation dominates a negotiation impasse and a
cooperative solution obtains. If a negotiation impasse triggers CTPing, top management chooses
a non-equilibrium TP (i.e., P12Cent  P120 ) inside the arm’s length boundary, which leads
autonomous division managements to select a sub-optimal, non-equilibrium quantity of intrafirm trade (i.e., X 12Cent  X 120 ) (Bond 1980; our analysis above).32 With cooperation, division
managements negotiate a TP, P12Neg , at either the upper or lower arm’s length boundary (a
boundary solution), since this maximizes the joint gain in after-tax division profit that they share,
ceteris paribus. They choose the highest (lowest) allowable NTP when t1  t2 ( t1  t2 ), ceteris
paribus, which equals the upper (lower) arm’s length boundary.33 They also choose X 12Neg  X 120
because it maximizes the joint gain in after-tax division profit that they share, ceteris paribus.
31
Hansen and Kimbrell (1991) suggest three reasons why division managements know that negotiations are
positive-sum: “(1) the role of a central authority in supplying information; (2) the expectation that a responsible
divisional manager will gather information about his operating environment; and, (3) open communication which
will likely lead to an exchange of information that, in turn, will lead to a mutual recognition of a joint benefit (in
support of this notion, well documented examples of collusion among competing firms in open markets must be
considered)” (p. 96).
32
If last period’s NTP is the default for negotiation impasse, and it happens to equal this period’s equilibrium TP,
the divisions will achieve an internal equilibrium quantity. The internal equilibrium TP is not the optimal TP (it is
neither on the upper nor lower arm’s length boundary). If last period’s NTP happens to equal this period’s optimal
TP (i.e., on the upper or lower arm’s length boundary), the quantity of intra-firm trade will be less than optimal.
33
Since we do not assume identical firms and/or identical tangible products, the exogenous arm's length range that
depends on data for comparables does not necessarily relate, in a predictable manner, to the subject MNC's internal
equilibrium TP (or the cost and revenue functions that underlie it). The arm's length range probably straddles the
subject MNC's internal equilibrium TP in many cases, assuming a fairly good set of comparable companies and/or
comparable products are used to estimate the arm's length range (e.g., see the horizontal dashed lines in Figure 2).
The quality of our results is unaffected by this assumption.
24
Complete Information Not Required
Although each division management possesses private information, the existence and knowledge
of the positive-sum game (reinforced by a strictly inferior negotiation impasse profit) produces
the incentive for division managements to cooperate and share relevant information truthfully,
information that allows them to select the equilibrium intra-firm quantity of trade and a NTP on
the arm’s length boundary. Notice that, unlike Hirshleifer (1956; 1964), Hansen and Kimbrell
(1991), Halperin and Srinidhi (1991), and Vaysman (1998), an optimum result in our model does
not depend on complete information between division managements. Under incomplete or
private information, division managements, in pursuit of their economic self-interest, cooperate
and truthfully reveal to each other their respective reaction functions, other relevant operating
and market information, and share TPing studies prepared by outside experts (if not already
shared).
Dikolli and Vaysman’s (2006) analysis, which relates to the information assumption,
extends Vaysman (1996; 1998) by modeling TPing in a domestic divisionalized firm in the
perfect versus imperfect information technology (IT) cases. In the perfect IT case, (i) division
managers communicate all local knowledge to top management costlessly and instantaneously
and (ii) top management completely understands and acts upon this information costlessly and
instantaneously (p. 208),34 while, implicitly, (iii) division managements have a costless and
instantaneous ability to learn all relevant local information and to articulate that information
effectively and efficiently.35 In the imperfect IT case, division managers cannot “freely and
instantaneously transfer all local information to HQ” (p. 209). Imperfect, or “coarse,” IT is
34
Implicit is top management has the ability to fully absorb and process all information reported to it costlessly and
instantaneously.
25
defined as the “limitations of the firm’s formal and informal information systems when
transferring local divisional knowledge to top managers” (p. 204), or the limitations of the
“knowledge-transfer systems” (p. 205). They explain that
In any large firm, local managers have private information—
superior knowledge of local conditions, business processes, and
potential cash flows. Other parties in the firm rely on local
managers’ reports, but there are two important problems with this.
First, a local manager may distort information; if truthful reports
are desired, top management must provide appropriate incentives.
Second, transferring local knowledge may be costly—it may be
difficult or impossible for the local manager to fully describe the
precise links between local information, the multitude of local
decisions, all of the available information, and the potential cash
flows. And it may be difficult or impossible for other parties in the
firm to quickly understand and act upon the local manager’s
reports (p. 204).
We reasonably presume that improved knowledge transfer technology would facilitate the
transfer of a greater quantity of information, reflecting the size of a particular information set of
a given quality. Their model focuses on the “size of the reporting set” (p. 210). The quality of
information conveyed or transferred to top management depends on division managements’
human capital (i.e., the ability of division managements to learn and to articulate a given set of
local information to top management).
We question the relevance of coarse IT. Even if communication technologies and
information reporting systems become perfect, Dikolli and Vaysman’s (2006) human capital
assumptions (ii) and (iii), reflecting human nature and natural limitations, are probably irrelevant
in the near future. The quality component of managerial human capital will not likely approach
perfection. That is, the limitations in (ii) and (iii) continue to exist under perfect IT. Furthermore,
in the international context, the informational constraints within the decentralized firm are
35
They say, “…in the extreme ‘perfect-IT’ case, it is possible for the local manager to quickly and costlessly report
26
greater. Dikolli and Vaysman (2006) appear to agree.36 Therefore, we question the
meaningfulness of their analysis in both the domestic and international cases.
Nevertheless, if our analysis is correct, the effect of improved IT may not affect the
modified Horst (1971) solution. Recall that we do not require complete information to obtain the
optimal modified Horst (1971) solution in our model.
Allocation of the Joint Gain
Bargaining outcomes probably reflect each party’s relative bargaining power (Chalos and Haka
1990; Chatterjee and Samuelson 1987; Abdel-Khalik and Lusk 1974; and Dupuch and Drake
1964). Thus, division managements’ relative bargaining strength or position determines the
allocation of the joint gain. This assumption is not critical to our analysis, however. To consider
fairness, top management could, as part of its authority to determine management compensation,
calculate each division’s share of the joint gain using the known37 internal equilibrium TP, P120 .
Nevertheless, the NTP remains on the upper or lower arm’s length boundary because that price
(along with X 120 ) maximizes the combined after-tax division profit, and thus the joint gain (if
any) in combined after-tax division profit that divisions share. Autonomous divisions divide the
joint gain (loss) using another method, not involving the NTP. For performance evaluation
purposes, top management enters into its division management compensation software a measure
on everything of local economic relevance” to top management (p. 204).
36
“…firms with the following characteristics are more likely to prefer negotiated transfer pricing: (i) understanding
divisional operations requires specialized education or training; (ii) divisional operations are physically located far
from the headquarters; (iii) divisional operations are quickly-changing environments requiring rapid responses; (iv)
lack of sophisticated enterprise-resource-planning (ERP) systems; and (v) large firm size” (p. 228).
37
This assumes that top management knows division managers’ revealed costs/revenues through the MNC’s
accounting system. In that case, division managers could not successfully misinform top management.
27
of division profit that adjusts for the negotiated allocation of the joint gain (loss).38 If divisions
view the negotiated split as unfair, this will not change the fact that a NTP on the arm’s length
boundary is optimal for (unequally-positioned) bargainers in our model.
Tax Law Compliance
Compliance with tax law requires that the decentralized MNC choose the NTP on, or within, the
arm’s length boundary, but not outside it. By selecting a NTP on the arm’s length boundary, the
MNC’s global tax burden is legally minimized (i.e., tax avoidance) while not evading its tax
responsibility. The MNC reports each division’s before-tax (i.e., taxable) arm’s length profit on
its tax return in each country (and/or on a consolidated tax return) using the NTP.
6.
Licensing Intangible Assets Intra-Firm
MNC intra-firm transfers of intangible assets are extensive. Such transfers, arguably, constitute
the most important aspect of MNCs’ internal trade, because "Wealth and growth in today's
economy are driven primarily by intangible (intellectual) assets" (Lev 2001, p. 1) (i.e., much of
the market value of modern firms comes from the use of intangible assets). Nonetheless, “little
research addresses transfer pricing for intangibles” (Johnson 2006, pp. 339-340). To our
knowledge, four papers directly analyze the economics of TPing for international intra-firm
transfers of intangible assets: Horst (1973), Halperin and Srinidhi (1996), Boos (2003), and
38
A MNC may use the same TP for performance evaluation and tax purposes because of the resources needed to
implement a dual set of accounting books and the increased likelihood of a (or scrutiny in an existing) tax audit
(Czechowicz et al. 1982, p. 61). With our bargaining structure, a second set of accounting books is not needed (See
Appendix B). Baldenius et al. (2004) agree that using a different price for performance evaluation risks “…the
possibility that multiple transfer prices” (p. 592) may lead the tax authorities “…to subpoena internal records in case
of transfer-pricing disputes [, where] Discrepancies between transfer prices used internally and those used for tax
purposes could then become evidence in legal proceedings with the tax authorities” (p. 598). To alleviate this
possibility, Baldenius et al. (2004) assume that “…the firm has identified a range of allowable arm’s length prices
…. [that would be successfully] justified to the tax authorities as based on an acceptable transfer-pricing method and
a supporting set of data on comparables” (pp. 594-595). This is consistent with our model’s assumption that the
MNC determines the arm’s length range, which is exogenous, and the MNC does not set its transfer price outside
that range.
28
Johnson (2006).39
The Nature of Intangibles
An intangible asset transfer can involve a license grant of the right to its use, or its outright sale
and transfer of ownership. We focus on the license of division 1’s intangible asset(s) intra-firm to
division 2. Intra-firm licensing of intangibles reflects a centralized ownership strategy, where
both legal and beneficial ownership lies with one company in a controlled group (as opposed to a
joint, or distributed, ownership strategy, where one company holds legal ownership but both
companies share beneficial ownership) (Adams and Godshaw 2002). A licensing strategy
provides the greatest opportunity for a MNC to shift profits, because when several companies
within a controlled group legally own separate intangibles (or separate baskets or blocks of
intangibles), “exploitation within the group is by way of a myriad of cross-licenses between
operating companies” (Adams and Godshaw 2002, p. 77). In addition, the number and total
(dollar) value of cross-licensed intangibles makes the TPing analysis complex and burdensome
for tax authorities to audit, thereby creating a lower probability of a tax audit or an irrefutable tax
adjustment in an audit.
Lev (2001) notes that intangible assets incorporate partial excludability and nonrivalry.
By their very nature (i.e., many are knowledge-based assets), the mere possession of an
intangible asset does not necessarily exclude third parties from also possessing and using it.
Methods exist to exclude third parties from using one’s intangible asset, most notably
enforceable legal protection afforded by patents and property rights. Many firms adopt informal
39
In related work, Kopits (1976) estimates the loss in tax revenues generated by abusive TPing practices with
respect to intra-firm royalties and license fees by U.S. firms operating, through direct investment, in several
industrialized and less developed host countries using 1968 data. Also, Grace and Berg (1990) examine cost sharing
of R&D expenses within the MNC to shift profit.
29
measures to protect their intellectual property and intangible assets, such as keeping them a trade
secret, making it difficult for competitors to extract usable information through reverse
engineering, and requiring employee confidentiality agreements. Still, such means erect
imperfect barriers to free use. Expecting an unduly rapid dissemination of proprietary
intangibles, firms also seek to create competitive advantages through lead time, the learning
curve, and marketing strategies. These strategies foster company and brand loyalty to create
barriers to the effective marketing and sale of third-party products that use their intangible assets.
Intangible assets also are nonrival in consumption. Nonrival intangible assets entail a
zero or negligible marginal cost of producing each additional unit, however measured, of the
intangible (Di Tommaso, Paci and Schweitzer 2004). Once division 1 incurs the fixed (or sunk)
R&D cost of creating an intangible asset, the intangible exists and the right to its use can transfer
to division 2 with zero (or negligible) marginal production cost to division 1 (Lev 2001). The
size of the R&D investment that creates the intangible does not affect the marginal cost and,
therefore, does not affect the NTP and intra-firm quantity of trade.
Literature Review
Horst (1973) considers a transfer of a tangible product that embodies division 1’s intangible
asset. In the ordinary course of business, however, division 1 does not transfer to division 2 the
right to exploit commercially the intangible asset, except, as is customary in the sale of a
product, to identify the product feature, trademark, or trade name to market and sell the product.
No intra-firm royalty payment is applicable under the arm’s length standard, since rights to the
intangible asset do not transfer to division 2 (Reilly and Schweihs 1998, p. 472).40 By contrast,
40
Typically, for tangible products with product differentiation created by a valuable intangible feature, the
wholesale price exceeds that of non-differentiated substitute goods. The final 1993 U.S. TPing regulations in
30
this section considers intra-firm licensing. Although Horst (1973) focuses on different issues, he
recognizes “the ‘public good’ nature of technology” (p. 81).
Halperin and Srinidhi (1996) analyze how TP determination under three U.S. TPing
methods for intangibles influences a MNC’s ability to achieve resource efficiency.41 They
assume CDM, however, while our analysis assumes DDM.
Boos (2003) analyzes a MNC’s international TPing for intra-firm licensed intangibles
under the assumptions of CDM and complete information. Boos (2003) concludes that we cannot
determine the unconstrained intra-firm royalty rate, but the MNC chooses the highest (lowest)
allowable royalty rate when t1  t 2 ( t1  t 2 ), which is the modified Horst (1971) CDM result.
Boos (2003) assumes, however, positive marginal costs for producing each unit of a public good
intangible, including a cost-influencing intangible (such as a new process technology, pp. 44-46)
and a demand-influencing intangible (such as a new product technology or a marketing
intangible, pp. 49-50).42 The nature of public good intangibles, however, typically involves zero
marginal cost.
Johnson (2006) considers TPing for intangibles under DDM, focusing on the effects of
different internal TPing policies on the efficiency of each division’s R&D investment decision.
§1.482-3(f) “include an express statement that imbedded intangibles will not be considered a transfer of the
intangible if the controlled purchaser does not acquire any rights to exploit the intangible, other than the right to
resell the tangible property under normal commercial practices” (Mogle 2001, p. 8-22).
41
Under §1.482.4(a), the calculation of an arm’s length royalty for intangibles may use one or more of four TPing
methods: The Comparable Uncontrolled Transaction method (§1.482-4(c)), the Comparable Profits method (§1.4825), the Profit Split method (§1.482-6), or unspecified methods (§1.482-4(d)).
42
In Boos (2003), the variable cost of producing a new process technology is V(T): “The costs of producing the
technology T are V(T) where δV/δT  0 , δ 2 V/δ  2  0 ” (p. 45). The variable cost of producing a new product
technology or a marketing intangible is V(M) (p. 49). Boos simplifies by assuming “trademark M as [the] reference
intangible for both [a] technology and marketing intangible” (p. 49). Presumably, comparable to a new process
technology, δV/δ M  0 (pp. 49-50).
31
Johnson (2006), however, focuses on the intra-firm sale of intangibles rather than their intra-firm
license.43
Intra-Firm Licensing of Intangible Assets
This section considers the relative strength of a MNC’s incentives to choose a TP for intangibles
outside the arm’s length boundary. An important part of this analysis involves the nature of
intangibles. For any given intra-firm quantity of an intangible asset licensed to division 2,
division 1’s marginal cost of supplying the intangible asset under license equals zero. This
assumption, combined with our NTPing bargaining structure, produces an extraordinary result. A
MNC earns a higher after-tax profit licensing its intangible(s) intra-firm because, not only do
divisions negotiate a TP on the arm's length boundary, they negotiate the equilibrium quantity of
intra-firm trade at a much larger quantity than for a commensurate quantity of tangibles.
With intra-firm goods or service trade, P12 equals the price-per-unit of the intra-firm
good or service, X 12 , that division 2 uses in its production and sale of the final good, Y2 . When
intra-firm trade involves a licensed intangible asset, P12 equals the royalty-per-unit of the intrafirm intangible asset, X 12 , used by division 2 in its production and sale of the final good, Y2 .
Since, in practice, it is difficult to measure the quantity, X 12 , of the licensor’s intangible asset
actually used by the licensee, the typical royalty links to the quantity of the final good sold, Y2 .
Further, to better reflect the marginal increase in market power or profitability enjoyed by the
licensee through its use of the licensor’s intangible asset, typically the royalty base equals the
43
Johnson (2006) assumes that the intra-firm intangible transfer reassigns ownership, as indicated by various
references to the seller and buyer (rather than to a licensor and licensee) and to the initial and final owner. Johnson
assumes that the purchase price takes the form of a royalty rate because U.S. tax law favors using a royalty rate for
transfers of intangibles (p. 345, footnote 13). Presumably, she refers to §1.482-4(f)(1).
32
licensee’s sales revenue, P2 Y2 . We assume that the royalty applies to 100 percent of division 2’s
sales revenue, P2 Y2 (which accrues separately from its sales of other products). Without the
license, division 2 would not produce or generate sales receipts for the specific final good.44 The
total royalty payment per period, R , equals the royalty rate, r12 , times the royalty base, P2 Y2 :


R  r12  P2 Y2 . The royalty-per-unit of the final good sold by division 2 equals r12 P2 , which
also equals the TP (i.e., P12  r12 P2 ). By convention, we assume that each unit of the final good is
produced using one unit of the intangible: Y2  f X12   X12 . Thus, the royalty-per-unit, r12 P2 ,
reverts back to the royalty-per-unit of the intangible asset used by division 2, X 12 . With
P12  r12 P2 , equations (2’) and (3’) become
Π1  r12 P2 X 12  C1  X 12  and
(2'')
Π2  P2 X 12  γ2  X 12   r12 P2 X 12 ,
(3'')
where X12  X12 r12  P2   X12 r12 ; P2   X12 r12  .
Due to the nonrival nature of an intangible asset, division 1’s marginal cost of producing
additional units of the intangible asset under license, however measured, equals zero (i.e.,
C1'  0 ) and remains zero at every quantity of the intangible asset licensed (i.e., C1''  0 ). Figure 2
illustrates this with a horizontal internal supply curve for the intangible asset that is located on
the quantity axis. The intangible asset’s past and ongoing R&D costs, as well as any maintenance
44
If the intangible is a design or new product technology, the new product feature may make an existing product
more useful to, and therefore in higher demand by, consumers than the existing product without the new feature. As
an improved product feature on an existing product that replaces the old product feature (as in the case assumed
here), division 2 would pay a royalty based on the new product’s sales revenue. It can also continue to sell the
product without the new feature, for which it would not pay a royalty. P2 Y2 then equals division 2’s incremental
sales revenue above its sales of the product without the licensed intangible.
33
costs (such as annual patent fees), remain fixed and do not vary in relation to the quantity of the
intangible asset licensed (or in relation to the royalty base, licensee sales revenue).
Division 1’s supply curve, which reflects its marginal cost, intersects the demand curve at
a TP of zero (refer to  r12 P2  in Figure 2). At this TP (and the implied royalty rate, r120  0 ), the
0
0
, is significantly larger than will
optimal quantity of intangible asset licensed intra-firm, X12
occur with a positive-sloped supply curve. The tax authorities still constrain the TP to lie within
a positive arm’s length range (e.g., as illustrated by the two horizontal dashed lines in Figure 2),
t1  t 2
-tosuch that CTPing will produce an inefficient quantity of intra-firm trade within the X12
t1  t 2
X12
range (in Figure 2). Under the MNC’s optimal internal TPing policy, NTPing, our
bargaining structure creates sufficient incentives for division managements to agree to a NTP at
either the upper or lower arm’s length boundary, and to select the optimal quantity of intra-firm
0
trade, X12
. Comparing intra-firm intangible licensing with tangible intra-firm trade, the lawful
MNC shifts a larger before-tax profit from one country to another for a given change in its TP,
ceteris paribus. For example, regarding a change in the NTP from the upper to the lower arm’s
length boundary (i.e., a switch of country 1’s tax rate from lower to higher than country 2’s), the
value of the profit shift to division 2 equals the area ACDF in Figure 2, while the value of the
profit shift for tangible goods trade equals area ABEF.45 For intangible asset licenses, the larger
(dollar) profit shift for a given (dollar) TP adjustment (or for a given tax rate differential) gives
tax authorities in high-tax countries good reason for concern about the potential for TPing
45
By contrast, if the bargaining structure requires using the NTP for both tax returns and performance evaluations,
relative division bargaining (or market) power will likely lead to a NTP within the arm’s length boundaries, which
will lead decentralized division managements to select a lower-than-equilibrium quantity of intra-firm trade under
license, at the point where the NTP intersects division 2’s demand curve (in this example).
34
abuses. If we adopt the conventional assumption that the NTP facilitates both tax reporting and
performance evaluation, the MNC would not obtain the potential benefits arising from an
intangible's zero marginal cost. With performance evaluation separated from the NTP, however,
autonomous divisions choose both an optimal NTP and intra-firm quantity. A licensed
intangible's zero marginal cost becomes markedly more relevant to MNCs when they have the
ability to achieve the modified Horst (1971) outcome, an ability provided by our bargaining
structure.
[Figure 2 about here]
When a MNC perceives the arm’s length range to be a guideline, rather than a strict
constraint, it estimates the probability of a tax audit (or a tax adjustment in an audit) along with
the potential tax savings when deciding if, or by how much, to violate the arm’s length constraint
(Kant 1988). In theory, our (implicit) arm’s length constraint is fixed but, in practice, it may
appear to include soft boundaries. The probability of audit (or tax adjustment in an audit) relates
inversely with the inexact nature of arm’s length TP determination (as well as the disinclination
of tax enforcement). Given the inexact nature of the valuation and determination of the arm’s
length TP for intangibles, more room exists to adjust the TP than for tangible goods trade, which
affords a wider arm’s length range in practice. Practitioners know that the relative abundance of
comparable uncontrolled transactions makes the determination of the arm’s length range for
tangible goods fairly concrete, and also know that the relative lack of comparable uncontrolled
license agreements for licensed intangibles makes the estimated arm’s length range for
intangibles inherently less reliable and, thus, subject to greater challenge and compromise (which
allows more flexible arm’s length range boundaries). In general, less reliable arm’s length price
estimates cause taxpayers to perceive a lower probability of audit (or adjustment when audited)
35
for a given deviation from the soft arm’s length range. And, for given incentives to practice
TPing abuse, a weaker arm’s length constraint increases the likelihood of abuse, ceteris paribus.
Our NTPing analysis shows that MNCs experience a greater incentive to violate the
arm’s length range when transferring intangible assets intra-firm under license. For a given tax
rate change (or tax rate differential across borders), the larger quantity (or value) of intra-firm
trade for intangibles raises the potential tax savings for each (dollar) TP deviation outside the
arm’s length range, strengthening the incentive and potential for TP abuse.46 A perceived weaker
arm’s length constraint will release that potential. Tax authorities may desire to audit a greater
number of intra-firm intangible asset transactions, and to invest greater resources to train tax
audit specialists to identify and audit TPing abuses associated with controlled intra-firm
intangibles transactions.
When applying our model in practice, the binding arm’s length constraint assumption
may be relaxed somewhat for intangibles. In practice, the type of intra-firm transfer (i.e., tangible
or intangible) can affect the nature of the arm’s length range. With tangible products, the
availability of comparable (or near-comparable) uncontrolled transactions and prices, as well as
the more visible and understandable link between the price of tangible products and their
underlying determinants, make the estimation of the arm’s length range relatively transparent.
Practitioners hired by MNCs cannot easily move the arm’s length constraint, using alternative
TPing methods or applying a given TPing method in a different way, or select a TP outside a
given arm’s length range. With intra-firm intangible licenses, a reliable arm’s length range for
the royalty rate proves more difficult to estimate, due to the typical lack of access to privately
kept comparable (or near-comparable) license agreements, the lack of comparability (or near-
46
Governments also experience a greater incentive to engage in tax competition.
36
comparability) of publicly-available license agreements (due to the inherently diverse nature of
proprietary intangible assets, or intangible asset differentiation), and the less visible and
understandable link between the price of intangible transfers and its fundamental determinants.
Subjectivity plays a larger part in royalty-rate determination and less agreement exists about the
arm’s length range, such that in practice the arm’s length range that tax authorities estimate
provides a guideline and not necessarily a binding arm’s length constraint. Not only are
practitioners more willing to move the arm’s length range based on the less precise nature and
lower reliability of estimating the arm’s length range for intangibles, MNCs probably are more
willing to take a chance on selecting a TP outside a given (guideline) arm’s length range.
7.
Summary
Under our NTPing bargaining structure, the modified Horst (1971) CDM outcome emerges
irrespective of an equitable or inequitable joint profit gain allocation mechanism. Even under an
allocation mechanism that depends on bargaining power where the divisions wield extremely
unequal bargaining powers, the relatively stronger-bargaining division management faces an
incentive to offer a concession that makes the relatively weaker-bargaining division’s
performance evaluation profit at least as much as its non-cooperative performance evaluation
profit. Our bargaining structure, including a separation of performance evaluation from the NTP
decision, provides that incentive. By unlinking the NTP decision from the division management
compensation equation, even under incomplete information a decentralized MNC can achieve
the higher after-tax profits equivalent to the modified Horst (1971) CDM outcome. The
separation of performance evaluation from the NTP decision creates the incentive to select the
firm-wide optimal solution (i.e., a NTP on the upper or lower arm’s length boundary, and the
equilibrium intra-firm quantity). In their negotiations, division managers face sufficient
37
economic incentives to truthfully share cost and revenue information, giving them the ability to
make firm-wide optimal decisions. Had we adopted Hansen and Kimbrell’s (1991) and
Vaysman’s (1998) assumption that the firm evaluates division management performance based
on the same division profit used for tax reporting, the modified Horst (1971) solution would not
obtain. When the NTP depends on relative bargaining positions, no guarantee exists that the NTP
will lie on the arm’s length boundary. Further, in contrast to Halperin and Srinidhi (1991),
resource efficiency (i.e., an equilibrium intra-firm quantity) would not necessarily occur either,
since fairness comes into play when the NTP depends on bargaining abilities rather than a
division’s actual economic contribution to the MNC’s after-tax profit. The relatively weakerbargaining division, whose quantity decision would be binding, would maximize its division
profit by selecting a lower-than-equilibrium quantity of intra-firm trade, given an unfair NTP.
Should the MNC adopt a fairer mechanism to allocate the joint gain (e.g., one that will produce
an allocation consistent with the equilibrium TP), the modified Horst (1971) result would not
occur because the NTP—being determined by relative bargaining ability—would not necessarily
lie on the arm’s length boundary.
For intra-firm licensing of intangibles under our bargaining structure, we find a greater
incentive for MNCs to practice abusive TPing for intangibles than for a commensurate quantity
or value of tangibles (as well as a greater incentive for governments to engage in tax
competition). When zero marginal cost associates with supplying/licensing additional units of an
intangible, the optimal (i.e., internal equilibrium) quantity of intangible intra-firm trade exceeds
that for tangible intra-firm trade, ceteris paribus. Therefore, for a given national tax rate
differential, MNCs confront a larger potential tax savings for each unit of TP adjustment,
creating a stronger incentive to select a NTP outside the arm’s length boundary. This incentive,
38
coupled with the inexact nature of valuing intangibles and their arm’s length TPs (royalties),
implies that, in practice, TPing abuse for intangible transfers probably exceeds that for tangible
transfers by a significant amount. Therefore, TPing for intangibles is expected to be a prominent
issue for tax authorities, which becomes all the more important as a large portion of international
trade occurs through intra-firm transfers, with an increasing portion involving intangible assets.
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Williamson, Oliver. 1975. Markets and Hierarchies: Analysis and Antitrust Implications. New
York: The Free Press.
Wu, Frederick H., and Douglas Sharp. 1979. An Empirical Study of Transfer Pricing Practice.
The International Journal of Accounting 14: 71-99.
Appendix A:
Division Reaction Functions: Division 1’s and 2’s first-order conditions are
dΠ1
dX 12s
 P12  C1'  0 and
dΠ2
dX 12d
 P2  γ'2  P12  0 .
(A1)
The total differential of these first-order conditions provide the slope of division 1’s supply and
division 2’s demand curve:
X 12s ' 
dX 12s
X 12d ' 
dX 12d
d P2
d P2
 1
 0 , or
''
1
C
 1
''
2
γ
d P2
 0 , or
dX 12s
d P2
 C1''  0 , and
dX 12d
  γ''2  0 ,
(A2)
where C1''  0 and γ''2  0 .
43
Centralized Transfer Pricing (CTPing) Comparative Statics: The total differential of top
management’s first-order condition is
 [AA] dt1  [BB] dt2  [CC] dP12  0 .
(A3)
Solving produces
dP12*
dP* BB
AA

and 12 
,
dt2 CC
dt1 CC
(A4)

'
AA   P12  C1'  X 12
 X 12  ,
where


'
 X 12  ,
BB   P2  γ'2  P12 X 12





and


'
'
CC   1  t1  2 X 12
  X 12
 C1''   P12  C1'  X 12''  1  t2  2 X 12'   X 12'  γ''2  P2  γ'2  P12 X 12'' .
2
2
Given the assumption of profit-maximization, the second-order condition holds (i.e., CC  0 ).
''
With linear supply and demand curves, CC must be negative: With X 12s ''  X 12d ''  X 12
0,
2
2
'
'
'
CC   2 X 12
t2  t1   C1''  X 12
t1  1  γ''2  X 12


 t2  1 . With increasing marginal costs (i.e.,



γ''2  0 , C1''  0 ), 0  t1  1 , 0  t2  1 and t1  t2 ( t1  t2 ) when the MNC operates along the X 12d
( X 12s ) curve, CC  0 .
Tax Conditions: When operating along division 1’s supply curve, top management’s first-order
condition is
 X 12
P  γ  P  X
2
'
2
12
'
12
 X 12
Given 0  t1  1 and 0  t2  1 ,


 1  t2  .
1  t1 
 1  t2   0 ,
1  t1 
(A5)


'
which means  P2  γ'2  P12 X 12
 X 12   0 . We



'
 0 when the MNC operates along the supply curve, which
also know P2  γ'2  P12  0 and X12
44
means
P  γ  P  X
'
2
2
12
'
12
 X 12 . Therefore,
1  t2   1 , and
1  t1 
t1  t2 . When the MNC operates
along division 2’s demand curve, top management’s first-order condition is
'
  P12  C1'  X 12
 X 12 
 X 12
We know
1  t2   0 , which means
1  t1 

 1  t2  .
1  t1 
'
 P12  C1'  X 12
 X 12   0 . We also know  P12  C1'   0 and

'
X12
 0 when the MNC operates along the demand curve, which means
Therefore,
(A6)
P
12
'
 C1'  X 12
 X 12 .
1  t2   1 , and t  t .
1
2
1  t1 
Appendix B:
Bonuses and Taxable Income: The joint gain in division after-tax profit is
JG
  1  t1   1C   1  t2   2C    1  t1   1NC   1  t2   2NC  ,
 MNC
1  t  
where
1
1  t  
1
NC
1
C
1
(B1)
CAT
  1  t2   2C    MNC
(C is cooperative; CAT is cooperative after-tax) and
NCAT
  1  t2   2NC    MNC
(NC is non-cooperative; NCAT is non-cooperative after-
tax). The cooperative solution is P12Neg  P12UB or P12LB , and X 12Neg  X 120 . The non-cooperative
solution is P12LB  P12CTP  P12UB , P12CTP  P120 , and X 12CTP  X 120 . Top management calculates
division management bonuses, without discrimination, using the same function f as follows:
B1  f   1PE  and B2  f   2PE  .
(B2)
 1PE and  2PE are performance evaluation profits, which equal
JG
JG
 1PE   1  t1   1NC   MNC
 and  2PE  1  t2   2NC  1     MNC
 . (B3)
45
 1    equals division 1’s (division 2’s) negotiated share of the joint gain 0    1 , and
 1NC and  2NC equal the non-cooperative before-tax and before-bonus profits. Division
managers communicate to top management the negotiated allocation of the joint gain,  , which
top management enters into its management compensation software to calculate management
bonuses. Division management bonuses, B1 and B2 , do not feedback to cause an adjustment to
 1C ,  1NC ,  1NC , or  2NC , which are fixed at the end of the accounting period. Therefore,
performance evaluation profits,  1PE and  2PE , are also fixed at the end of the accounting
period, once the negotiated profit split,  , is determined and fixed through negotiation. Top
management calculates division before-tax (i.e., taxable) profits for its financial statements and
income tax returns as follows:
 1CFin   1C  B1 and  2CFin   2C  B2 .
(B4)
Division managements’ base salaries already appear in operating expenses that are used to
calculate  1C ,  1NC ,  1NC , and  2NC . The MNC’s after-tax financial profit is
CFin
  1  t1   1C  B1    1  t2   2C  B2  .47
 MNC
47
(B5)
NCFin
 1NCFin   1NC  B1 ,  2NCFin   2NC  B2 , and  MNC
  1  t1   1NC  B1    1  t2   2NC  B2  .
46
Figure 1:
Hirshleifer (1956; 1964)
($)
C1'  γ '2
P2

s
C1' X12
Curve
P120


d
P2  γ '2 X12
Curve

γ '2
0
X12
Figure 2:
(Quantity)
TPing for Intangibles
γ '2
($)
P2
A
B
C
F
E
D
r12 P2 0
t1  t 2
X12
r12 P2 *t  t  r12UB P2
r12 P2 *t  t  r12LB P2
1
1
2
2
t1  t 2
X12
0
X12
(Quantity)

s
C1' X12
Curve


d
P2  γ '2 X12
Curve

Possible Arm’s Length Range
47