Transfer Pricing, Vertical Integration and Production Externalities:
Implications on Profits and the Arm’s Length Principle*
Yaron Lahav†
ABSTRACT
According to transfer pricing regulations, multinational enterprises should price their
intercompany transactions as if they are dealing with unrelated companies (i.e., at arm’s length).
This paper shows that when externalities exist in the production processes of related parties,
arm’s length pricing may result in profit shifting, which contradicts transfer pricing regulations.
This paper presents a model of production with externalities that shows how externalities affect
transfer prices and in what way they are detrimental to the arm’s length principle. The paper
then analyzes the effects of externality and the sensitivity of profit shifting to differences in taxes
across jurisdictions.
JEL Classification: F15, F23, H83, K34, L23, M41
Keywords: Arm’s Length, Externalities, Multinaltional Enterprises, Profit
Shifting, Transfer Pricing, Vertical Integration.
I wish to thank Reuven Avi-Yonah, Zvika Afik, Kimberly Clausing and Michael Durst for their
helpful comments. All errors and misinterpretations are solely mine.
† Department of Business Administration, Guilford Glazer Faculty of Management, Ben-Gurion
University of the Negev, P.O. Box 653 Beer Sheva 84105 Israel. Phone: 972-8-6479738. email:
ylahav@som.bgu.ac.il.
*
1
1. Introduction
Transfer pricing is the practice of setting a price that multinational enterprises
(MNEs) use for their intercompany transactions. When two (or more) related companies
are involved in the buying and selling of goods or services, it is important to accurately
price these transactions for several reasons: first, transfer pricing determines the profits
of each entity. Second, improper pricing may interfere with the proper evaluation of
managers and decision makers in the MNE. Finally, every MNE should address certain
tax issues related to transfer pricing. For instance, when a MNE owns two subsidiaries
located in different countries with different tax rates, it has an incentive to determine
its transfer pricing with the goal of shifting its profits to the subsidiary residing in the
country with the lower tax rate. In many countries, however, this practice is constrained
by regulations.
With the exception of a few outliers, transfer pricing regulations are similar across
tax jurisdictions and are based on the arm’s length principle. Accordingly, related
parties should price their intercompany transactions as if they were dealing with
unrelated companies. When two related parties trade in a generic product, it is
sufficient for the MNE to show that the intercompany price determined for their trade is
the price that the MNE would have used in its dealings with an unrelated company. If
the tax authority is convinced by the MNE’s explanation, the latter is thus considered to
be in compliance with transfer pricing regulations. Alternatively, if the product is not
generic and the two parties to the trade represent the sole buyer or seller of that product
(e.g., permission to use intangible assets or trading an intermediate product that is
unique to the production process of the MNE’s final products), the MNE should show
that the transfer price is determined such that each entity earns a normal profit
compared to similar, unrelated entities that engage in the same transactions and
operate in the same business environment.
2
Externalities exist when economic decisions (either to manufacture or consume) are
affected by some activity that is not priced by the market. An example of a production
externality is pollution. A plant spewing pollutants into its surrounding environment
may harm the manufacturing abilities of neighboring plants, thereby reducing their
profits. Although the polluting plant is responsible for an environmental cost (i.e.,
reduction of overall production), it does not bear the actual costs of its activity. The
neighboring plants, meanwhile, do not perceive this externality, instead taking the
pollution as a given. In economic theory, externalities prevent markets from achieving
efficiency. Researchers address several ways to correct the inefficiency, which include
imposing taxes, controlling the quantities produced and consumed or controlling the
externality itself, allowing ownership on the source of externality, integrating the
market, etc.1
Production externalities are common by-products of the business integration of two
or more companies, which is usually accompanied by a change in the production process
or the use of technology. These changes are part of attempts by managers to increase
overall efficiency. In such a case, it is reasonable that the profitability level of one
company (or more) increases at the expense of the other(s).
In this paper, I show that while the profitability of two companies may be affected by
production externalities, the effect may also have consequences for profit shifting for tax
purposes when applying the arm’s length principle if the companies are related. In fact,
I show that if production externalities exist between two related parties that do not
reside in the same country, then the companies may not be in compliance with transfer
pricing regulations. When externalities are present, it is possible that if the company
were using a profit-based method to document its transfer pricing, it would, in fact,
1
These cases and more are discussed in the classic literature and can be found in textbooks on
resource economics. See for example hartwick and Olewiler (1997), P. 194.
3
generate a profit shift that contradicts the essence of the arm’s length principle. I
present a fairly simple model to show this process and analyze the effects externalities
have on MNE compliance with transfer pricing regulations.
This paper is not the first to tackle the objectivity of the arm’s length approach.
Halperin and Srinidhi (1987, 1991, 1996) show that the transfer pricing methods
specified under U.S. regulations can affect the MNE’s resource allocation. Smith (2002)
shows that the arm’s length principle can affect the investment choices of the MNE.
Stevenson and Cabell (2002) argue that subsidiaries have different cost structures than
third parties because of the unique way the MNE allocates costs among its subsidiaries.
Comparing a subsidiary to a third party, therefore, often produces biased results.2 The
five papers cited above illustrate how MNEs can manipulate their cost allocations or
even their levels of investment for tax purposes. However, this paper shows that the
transfer price can become distorted despite MNE wishes to comply with transfer pricing
regulations and to avoid “legal” manipulations. The profit shift occurs because of an
economic environment that the MNE cannot control and in most cases is not even aware
of.
Section 2 presents some of the relevant features of transfer pricing rules together
with analysis. In section 3 I present a simple model of externalities in production to
emphasize their effects on profit shifting. Section 4 discusses externalities caused by
vertical integration in the absence of taxes, section 5 introduces taxes, and Section 6 is a
summary.
2
This opinion regarding the inability to compare related to unrelated parties is also stated by tax
experts. See for example Langbein (1986), Avi-Yonah (1995, 2010, 2011), Clausing et al (2009)
and Avi-Yonah and Benshalom (2012). However, thus far, to the best of my knowledge, there in
no theoretical model that explains this inability.
4
2. Transfer Pricing Regulations (in a nutshell)
As mentioned, countries determine their own regulations, but in general these
regulations comprise the same principles and specify essentially the same methods
around the world. The Internal Revenue Services (IRS) implements the Treasury
regulation section 1.482 (Treas. Reg. 482). The Organisation for Economic Co-operation
and Development (OECD) publishes its own transfer pricing guidelines for MNEs and
tax administrations (OECD Guidelines) that are adopted by its member countries, who
can add modest modifications. Each MNE is required to document its transfer pricing
transactions annually. Highly factual, this documentation should include a detailed
description of the MNE, its business structure, risk analysis and economic analysis,
which together determine whether the MNE’s intercompany transactions are conducted
at arm’s length.
Transfer pricing regulations specify several methods that MNEs can use to
document intercompany transactions. These methods can be divided into two categories:
price-based and profit-based. The former can be used if a market price exists for the
same (or similar) product or service and that product or service is being traded by
unrelated companies. Included among the price-based methods are the comparable
uncontrolled price (CUP) and the comparable uncontrolled transaction (CUT) methods.
According to the first, a MNE should show that the product it sells to related parties
(the tested transaction) is priced similarly to a comparable product sold to unrelated
parties. The CUT effectively applies the same procedure to services.3
In the absence of a similar transaction with unrelated parties, profit-based methods
are used. An economic analysis from a profit-based approach compares the profitability
level of the transaction or (at least) of one party to the transaction (the tested party) to
3
The CUT is specified in the Treas. Regs. 482 only and not in the OECD Guidelines.
5
the profitability level of similar unrelated transactions or companies. To obtain a
favorable comparison, the tested party should engage in routine activities only and
should not own any valuable intangibles. According to the cost plus method, a mark-up
on direct costs associated with producing the product should be similar to the mark-up
on direct costs of similar products produced and sold to unrelated parties. Using the
resale price method (RPM), the profit margin on a product sold to related parties should
be similar to that earned on the same product sold to unrelated parties. 4 The most
common method is the comparable profit method5 (CPM), in which the profitability level
of the tested party is compared to a range of profitability levels of similar, unrelated
companies involved in the same activities and operating in the same business
environment as the tested party.
To compare profitability levels, profit level indicators (PLIs) have been defined by
regulators. The first PLI is the operating margin (OM), measured by dividing the
revenue into the operating profit. The second, the net cost plus (NCP) ratio, is the
quotient of profit divided by total cost (cost of goods sold and operating expenses). The
third, the return on assets, is calculated by dividing operating profit by operating assets
(total assets, net of intangible assets and depreciation). The last indicator for comparing
profitability levels is the return on operating expenses (also known as the Berry Ratio,
or BR), calculated by dividing gross profit by operating expenses.
4
Naturally, the cost plus method is used when the tested party is a manufacturer, and the RPM
is used when the tested party is a distributor.
5
The CPM is essentially the transactional net margin method (TNMM) specified in the OECD
Guidelines with several differences that are negligible in terms of the analysis provided in this
paper. Throughout this paper (unless otherwise mentioned) the use of CPM also implies the
TNMM if the tax authority implements the OECD Guidelines.
6
The last profit-based method – the profit split method (PSM) – is used mainly when
the two companies to the transaction own valuable intangibles or for some other reason
they cannot be compared to other, unrelated companies. In addition, transfer pricing
regulations permit the use of any other unspecified method, provided it is shown to have
more credible results.
3. A Model of Externalities in Production
In this section I use a simple model of externalities in production to illustrate the
effect of externalities on methods of transfer pricing analysis. It consists of two
companies, M and D, which are (for now) unrelated. Company M produces an
intermediate good m, used as input in the production of d, the final good produced by
company D. To manufacture m, the company uses one input, x. For simplicity, m is the
only input used to produce the product d. Companies M and D reside in different tax
jurisdictions.
The production functions of both m and d exhibit diminishing return to scale and
implement the Inada conditions,6 but they cannot be observed by each other. Also, the
use of x in the production process of m generates externality in the production of d (e.g.
as a negative externality, x is a pollutant that adversely affect the production of d).
Nevertheless, company D cannot control the level of x, and therefore, takes it as given:7
𝑚 = 𝑚(𝑥)
𝑑 = 𝑑(𝑚, 𝑥) = 𝑑(𝑚|𝑥)
The marginal production of both x and m is positive and decreasing and the marginal
effect of x on d is constant:
6
7
See Inada, 1963.
Company D’s inability to influence the externality level is because it is unaware of the
production process used by company M.
7
𝜕𝑚 𝜕𝑑
,
𝜕𝑥 𝜕𝑚
𝜕2 𝑚 𝜕2 𝑑
,
𝜕𝑥 2 𝜕𝑚2
> 0,
< 0,
𝜕𝑑
𝜕𝑥
= 𝑒̅
(1)
The value 𝑒̅ determines the type of externality (i.e., positive if 𝑒̅ > 0 or negative if 𝑒̅ < 0).
The prices of x, m and d (𝑃𝑥 , 𝑃𝑚 , 𝑃𝑑 ) are determined competitively (𝑃𝑚 is determined via
negotiations between the companies). In this benchmark case (referred to as the “no
relation” condition), the pre-tax profit of each company is:8
𝜋𝑀 = 𝑃𝑚 ∙ 𝑚(𝑥) − 𝑃𝑥 ∙ 𝑥
(2)
𝜋𝐷 = 𝑃𝑑 ∙ 𝑑(𝑚|𝑥) − 𝑃𝑚 ∙ 𝑚
(3)
Note that the price 𝑃𝑚 is the arm’s length price. As unrelated entities, the two
companies determine the level of inputs that maximize their profits given market prices.
The first order conditions are:
𝑃𝑚∗ ∙
𝜕𝑚(𝑥 ∗ )
𝜕𝑥
𝑃𝑑 ∙
𝜕𝑑(𝑚∗ |𝑥 ∗ )
𝜕𝑚
(4)
= 𝑃𝑥
(5)
= 𝑃𝑚∗
where 𝑥 ∗ and 𝑚∗ are the equilibrium quantities of x and m, respectively, and 𝑃𝑚∗ is the
negotiated price of the intermediate good. Combining equations 4 and 5 provides the
equilibrium path of the “no relation” condition:
𝜕𝑑
𝑃𝑑 ∙ 𝜕𝑚 ∙
𝜕𝑚
𝜕𝑥
(6)
= 𝑃𝑥
The derived quantities and prices determine the profitability levels ( 𝛽 𝑀 and 𝛽 𝐷 ,
henceforth “operating margin”) of both companies as follows:
𝛽𝑀 =
8
∗ ∙𝑚(𝑥 ∗ )−𝑃 ∙𝑥 ∗
𝑃𝑚
𝑥
∗ ∙𝑚(𝑥 ∗ )
𝑃𝑚
(7)
When the two companies are unrelated, it is sufficient to maximize pre-tax profit to determine
the value of the choice variables.
8
𝛽𝐷 =
∗ ∙𝑚∗
𝑃𝑑 ∙𝑑(𝑚∗ |𝑥 ∗ )−𝑃𝑚
𝑃𝑑 ∙𝑑(𝑚∗ |𝑥 ∗ )
(8)
Assume now that these two, previously unrelated companies become part of an
MNE. The owner of this new MNE is interested in complying with transfer pricing
regulations. This can be done either by using the arm’s length price 𝑃𝑚∗ as the transfer
price (using the CUP method) or by maintaining the arm’s length operating margin of
one of the entities (using the CPM). In both cases, the profit function of the new MNE is:
(9)
𝜋𝑀𝑁𝐸 = (1 − 𝑡 𝐷 )[𝑃𝑑 ∙ 𝑑 − 𝑃𝑚 ∙ 𝑚] + (1 − 𝑡 𝑀 )[𝑃𝑚 ∙ 𝑚 − 𝑃𝑥 ∙ 𝑥]
where 𝑡 𝑀 and 𝑡 𝐷 are the corporate tax rates of jurisdictions M and D, respectively. The
MNE then maximizes equation 9, incorporating at least one constraint determined by
the chosen transfer pricing method. For simplicity, assume first that taxes in both
jurisdictions are equal (an assumption that will be relaxed later on), a condition referred
to as the “relation, equal taxes” condition. In this case, the MNE maximizes:
𝜋𝑀𝑁𝐸 = (1 − 𝑡)(𝑃𝑑 ∙ 𝑑 − 𝑃𝑥 ∙ 𝑥)
(10)
where t is the corporate tax rate. As the two companies are now related, the owner of
the MNE can now observe the two production functions and no longer regards the level
of x as given in the production process of d. Furthermore, the transfer price (the price of
m) does not affect the MNE’s profit. To illustrate, I first examine the effect of
externalities on the level of input without incorporating compliance with transfer
pricing regulations. In this case, the first-order condition with respect to the input x is:
𝜕𝑑
𝑃𝑑 ∙ 𝜕𝑚 ∙
𝜕𝑚
𝜕𝑥
+ 𝑃𝑑 ∙ 𝑒̅ = 𝑃𝑥
(11)
Intuitively, equation 11 states that the marginal cost of one unit of x equals the
marginal contribution of the same unit to revenues. However, the contribution of x to
MNE revenues is entered twice. First, it directly increases the revenues (first term on
9
the left side), and second, it indirectly decreases (increases) the revenues of the MNE by
increasing the negative (positive) externality (second term on the left side).
To compare the equilibrium quantities under the “relation, no taxes” and “no
relation” conditions, I compare equations 6 and 11. If the externality is negative, the
second term on the left side of equation 11 is negative. This means that the first term on
the left side of equation 11 is now larger relative to the left term of equation 6 (“no
relation”), implying that the marginal productions of both x and m are higher. The
higher marginal productions of x and m mean (according to equation 1) that the MNE
chooses levels of x and m lower than would have been chosen by the two unrelated
entities M and D. The specific level of x chosen by the MNE is defined as 𝑥̂ where 𝑥̂ < 𝑥 ∗.
If, on the other hand, the externality was positive, then we would obtain 𝑥̂ > 𝑥 ∗.
A graphic description of a negative externality is depicted in Fig. 1. The left-hand
side of equation 6 (the “no relation” condition) is defined as Ψ(x), and the left-hand side of
̂ (x) . The difference
equation 11 (the “relation, equal taxes” condition) is defined as Ψ
between the two functions stems from the existence of a negative externality. As both
equations 11 and 6 show, the equilibrium level of input x is determined by the
interception of each function with the input price, 𝑃𝑥 . A positive externality, therefore,
will imply that 𝑥̂ > 𝑥 ∗ .
Lemma 1 describes the connection between externalities and transfer pricing.
Lemma 1. When two related entities trade an intermediate product, if the seller’s
production process generates an externality affecting the production process of the buyer
and taxes are identical across jurisdictions, then profit maximization shifts the profit as
follows:
(i)
If the externality is negative, the pre-tax profit of the seller (buyer) decreases
(increases).
10
(ii)
If the externality is positive, the pre-tax profit of the seller (buyer) will increase
(decrease).
(iii)
In any case, the pre-tax profit of the MNE will be higher after the merger.
Proving lemma 1,9 notice that because the MNE has chosen to change the level of
input compared to the allocations by the unrelated companies M and D, its profit is now
higher because the production level 𝑥 ∗ is still within the production set of the MNE. It
can still choose the level of input 𝑥 ∗ and stay on the same profit level. Using the same
logic, related entity M chooses a different input level than the unrelated company M,
although there is no change in the production technology or in the market prices of
inputs and output. The input level of related entity M as imposed by the MNE is
possible for the unrelated company M, which has decided (as unrelated) to purchase
different amounts to maximize its profits. It implies that the profit of the related entity
M is lower than that of the unrelated company M. Combining the two explanations, the
related company D must earn a higher profit than the unrelated company D. The
difference between companies D and M (both change levels of production) is that
company D faces a change in the production process via a reduction in x.
In this model, the companies do not own any fixed assets or bear any operating
expenses. This means that if the MNE wishes to use the CPM, it can only use the
operating margin as the PLI. To comply with transfer pricing regulations, the MNE
should therefore either use the market price of the intermediate good or preserve the
pre-merger operating margins of the two entities. In either case, the MNE’s only
instrument is the transfer price. Proposition 1 states that if the MNE wishes (or is
9
The proof is for part i, where the externality is negative. The same proof can be used for the
case of positive externality in part ii. In both cases, total profit is higher, as stated in part iii.
11
required) to use a profitability method, then there is no transfer price that can equalize
the profit margins of the related entities with that of their unrelated counterparts.
Proposition 1. When two entities in a profit-maximizing MNE trade an intermediate
product, if taxes are equal across jurisdictions and externalities exist, then there is no
transfer price that the parties can adopt that will ensure both parties achieve profit
margins equal to those of comparable, unrelated entities.
The proof is in appendix A. The importance of proposition 1 is emphasized by an
explanation about the nature of most related transactions, especially those that involve
tangible goods, documented under transfer pricing regulations. In such cases, when the
analytical method used is the CPM, the tested party to the transaction is usually the
entity responsible for routine activities and that does not own valuable intangibles. The
rationale behind this is that only such companies earn normal returns on their expenses
and therefore, only they can be compared to other benchmark companies. Following the
same rationale, the second party to the transaction, i.e., the one that owns valuable
intangibles (and that probably also engages in other activities that cannot be segmented
out from the financial reports) should earn, in addition to its normal profit, some extra
mark-up for the risks it bears (e.g., research and development or other services such as
central management, information technology, marketing, patenting and other activities)
as the owner of the intangibles. Because the extra mark-up cannot be accurately
measured, it is assumed to be residual profit, after the normal profit of the tested party
was allocated based on economic analysis. Moreover, proposition 1 shows that part of
this residual profit should not be attributed to intangible assets, as it is a result of
externalities (if they exist). The failure to account for this portion of the residual profit is
in fact profit shifting, which contradicts the essence of transfer pricing regulations.
But there is more to it than that. As the proof in appendix A shows, when the
externalities are negative and the production level is reduced as a result of the merger,
12
the profit margin of entity M increases, but according to Lemma 1, its operating profit
decreases. If company M is the tested party to the transaction, the tax authority (or even
the MNE itself, when seeking compliance) would require that the transfer price 𝑃𝑚 be
reduced to lower the operating margin to its arm’s length level, 𝛽 𝑀 , a move that would
further increase the profit shift.
4. Production Externalities and Vertical Integration
It may be difficult for the readers to understand the importance of such initial
findings. After all, how many such cases—two related companies that are situated side
by side (or at least close enough for the pollution of one to affect the other) and trading
with one another are separated by a border—could there be? In fact, this scenario is
more common than one would think, and it exists when in vertical integrated MNEs. In
this section I begin by defining vertical integration and then provide two examples in
which vertical integration generates the transfer pricing issues discussed above.
A firm is vertically integrated if it owns (at least) two production processes, where
part or all of the output from one production process serves as input in the production of
a product from another production process. 10 In other words, a vertically integrated
enterprise produces part or all of the intermediate goods for the production of its own
final product. Vertical integration is the result of three major factors: market
imperfection, transactional economies and technological economies. Market imperfection
occurs, for instance, when there is imperfect competition between two unrelated firms
involved in trade or when there is information asymmetry. But it can also exist when
externalities are present. Consider the model presented in section 3, but this time
10
See Perry (1989). The textbook definition of vertical integration excludes the case where part of
the intermediate goods function as partial input for the final product. This situation is defined as
“partial vertical integration.” However, this restriction has no relevance in the analysis of this
paper.
13
assume that the production of d is increasing in x. If company M increases its production
level, company D’s profits will increase as would the aggregate profit. Company M,
however, does not increase its level of production because it only maximizes its own
profit. But if the two companies integrate, the production levels of both will be higher,
resulting in a higher total profit for the MNE.
Suppose now that companies M and D are unrelated and reside in different tax
jurisdictions. Company M is a manufacturer of some good, and company D, the
distributor of that good, also provides post-sale services such as installation and
maintenance.11 It is reasonable to assume that a higher quality of post-sale service on
behalf of company D will increase demand for the product manufactured by company M.
However, company D determines the quality of services in terms of maximizing only its
own profit. Although company M’s profit is also determined by the performance (level of
input) of company D, it has no control over company D performance levels. Should these
two companies undergo integration, the owner of the new MNE increases the level of
effort invested by entity D in the quality of its services, which would shift profit from
company D to company M, resulting in the transfer pricing issues discussed in section 3.
Profit shifting from vertical integration can occur when production technologies
between the two companies are not matched, a scenario that generates inefficiencies in
transaction. Consider the case in which company M is a manufacturer of a durable
product and company D is the distributor of that product. The two companies are
unrelated and reside in different countries. When company M ships the product m to
company D, it packages the product in large, cardboard boxes. Company D, however,
prefers plastic packaging because it reduces storage costs, but for company M, plastic
wrap is more expensive than cardboard boxes. So cardboard boxes it is. When the two
companies vertically integrate, the owner of the new MNE realizes that although
11
This example is inspired by Pfaffermayr (1997).
14
packaging m in plastic reduces the profits of company M, it increases the overall profit
of the new MNE. As a result of this business integration, therefore, profit shifts from
company M to company D, but the overall profit of the MNE is higher than the
aggregated profits of the unrelated entities M and D.
Since MNEs consist of more than one entity, the effect of such integration on
transfer prices, and therefore on total profitability (for tax purposes), is crucial. As
mentioned, the tax regulations of MNEs consist of the arm’s length principle, according
to which all entities within a MNE should trade with each other as if they are unrelated.
But as described above, this stipulation is virtually impossible to enact when
externalities are present. The MNE prepares its transfer pricing analysis based on
comparable companies that operate in the same environment and are involved in the
same activities as the tested party but that do not have intercompany transactions. As
these comparable companies will not use the same technology (e.g., they will still use
boxes to package intermediate good m), by definition, they cannot be considered
comparable companies. In the next section I examine the effect of corporate taxes on the
profit shifting caused by externalities.
5. Production Externalities with Taxes
I now extend the model presented in section 3 and assume that taxes are present
and different across jurisdictions. The profit function of the MNE is given in equation 9,
and the first order conditions of the benchmark (when the companies are unrelated) are
presented in equations 4-6. Taxes and operating margins in both jurisdictions are
assumed to be positive and less than 50%. The MNE (still interested in complying with
transfer pricing regulations) can either use 𝑃𝑚∗ as the transfer price (CUP method) or
keep the pre-merger operating margin of at least one entity (CPM).
15
5.1. Finding production level with CUP
When using the CUP method, the MNE should maximize equation 9 with x as the
control variable, fixing the transfer price as 𝑃𝑚∗ . The first order condition is:
𝜕𝑑
𝑃𝑑 ∙ 𝜕𝑚 ∙
𝜕𝑚
𝜕𝑥
+ 𝑃𝑑 ∙ 𝑒̅ = 𝜑𝑀𝐷 ∙ 𝑃𝑥 + (1 − 𝜑𝑀𝐷 ) ∙ 𝑃𝑚∗ ∙
𝜕𝑚
𝜕𝑥
(12)
where 𝜑𝑀𝐷 = (1 − 𝑡 𝑀 )⁄(1 − 𝑡 𝐷 ) . Equation 12 implies that the after-tax (direct and
indirect12) marginal contribution of x to the revenues of the MNE (left side) equals the
tax-exempt marginal cost of x (first term on the right side) plus the net tax loss from the
intercompany transaction (second term on the right side). This loss is actually a profit if
𝑡𝐷 > 𝑡𝑀.
Notice first that when taxes are equal across jurisdictions, equation 12 becomes
equation 10 (the “relation, equal taxes” condition). But when taxes are different, the
production level can either increase or decrease, depending on production functions,
market prices and the externality. Fig. 2 describes the conditions for which production
level decreases when the externality is negative. Panels 2a-2c represent the case of 𝑡 𝑀 >
𝑡 𝐷 , and panels 2d-2f represent the case of 𝑡 𝑀 < 𝑡 𝐷 . In all panels the right-hand side of
̃ (x), and the new production level is
equation 12 is represented by the dashed curve Ψ
represented by 𝑥̃. As can be seen from the different panels, thus production level can
either be lower or higher than 𝑥̂ and 𝑥 ∗ , or somewhere between them.
Using comparative statics, we can characterize the effect of taxes on profit shifting.
Proposition 2 determines how changes in tax rates affect the level of production (via the
amount of x purchased by the MNE). To do this, we first assume that 𝑥̃ is the
equilibrium level of x prior to the change in the tax rate.
12
Referred to the intuitive explanation of equation 10.
16
Proposition 2. When two entities in a profit-maximizing MNE trade an intermediate
product, if tax rates vary across jurisdictions, negative externalities exist, and the MNE
uses the CUP method for transfer pricing documentation, then an increase in 𝑡 𝑀 or a
decrease in 𝑡 𝐷 changes the level of production as follows:
a) The level of x decreases if 𝑥̃ < 𝑥 ∗ .
b) The level of x increases if 𝑥̃ > 𝑥 ∗ .
The presence of positive externalities, a decrease in 𝑡 𝑀 or, equivalently, an increase in
𝑡 𝐷 changes the level of production in the opposite direction.
Fig. 3 graphically describes the tax effect on production level. The four panels of the
figure represent the four different scenarios covered by equation 12. Panels a and b of
Fig. 3 represent two cases in which 𝑡 𝐷 < 𝑡 𝑀 . The dashed curve represents the right side
̃ (x)], and the dotted curve [defined as Υ(x)] describes the
of equation 12 [defined as Ψ
̃ (x) as 𝑡 𝑀 increases or 𝑡 𝑑 decreases. The nature of x’s response to changes in
change in Ψ
tax rates is due to the nature of the function Υ(x). When 𝑡 𝑀 (𝑡 𝐷 ) increases (decreases),
the function Υ(x) increases on the domain 𝑥 < 𝑥 ∗ and decreases on the domain 𝑥 > 𝑥 ∗ .
This distinction is important, because if 𝑥̃ is initially lower than in the “no relation”
condition, the MNE will reduce its production when 𝑡 𝑀 (𝑡 𝐷 ) increases (decreases), as
shown in Fig. 3a; otherwise, it will increase its production (Fig. 3b). Panels c and d of
Fig. 3 graphically represent the situation 𝑡 𝐷 > 𝑡 𝑀 . Although the graphs are slightly
different, their descriptions are the same.
Proposition 2 has two important implications. First, the difference in tax rates does
not necessarily distance production further from the arm’s length level. In fact, it can
increase production back to that level. Second, even if different tax rates contribute to a
profit shift compared to the “no relation” condition, an increase in 𝑡 𝐷 or a decrease in 𝑡 𝑀
can, in fact, diminish the profit shift caused by externalities. This result seems counter
17
intuitive, because it is usually an increase in 𝑡 𝐷 that drives profits to jurisdiction m.
However, it is the negative externality that shifts profit back, and the profit shift caused
by the externality (and not the difference in tax rates) is the one that is balanced by an
increase in 𝑡 𝐷 or a decrease in 𝑡 𝑀 .
In summary, tax rates affect profit shifting, but the direction of the shift is
determined by the initial level of production. So when using a CUP method in the
presence of externalities, changes in tax rates can shift profits either way, depending on
the direction of the change.
5.2. Finding production level with CPM
The MNE’s second alternative is to set the operating margin of one of its entities to
the arm’s length operating margin. In so doing, the MNE maximizes equation 9 with
either equation 7 or 8 as a constraint and both x and 𝑃𝑚 as control variables. If the MNE
chooses company M as the tested party, the constraint is equation 7, which tells us the
relationship between the two choice variables:
𝑃 ∙𝑥
(13)
𝑥
𝑃𝑚 = 𝑚(1−𝛽
𝑀)
The objective function is therefore:
𝑃 ∙𝑥
𝑃 ∙𝑥
𝑥
(1 − 𝑡 𝑀 ) (𝛽 𝑀 ∙ 𝑥 𝑀 )
𝜋𝑀𝑁𝐸 = (1 − 𝑡 𝐷 ) (𝑃𝑑 ∙ 𝑑 − 1−𝛽
𝑀) +
1−𝛽
(14)
The first order condition with respect to x is:
𝑃𝑑 ∙
𝜕𝑑 𝜕𝑚
∙
𝜕𝑚 𝜕𝑥
+ 𝑃𝑑 ∙ 𝑒̅ = 𝑃𝑥
1−𝜑𝑀𝐷 ∙𝛽 𝑀
1−𝛽 𝑀
(15)
Assuming that taxes and the operating margin do not exceed 50%, the right-hand side of
equation 15 is positive. Far less intuitive than equation 12, because the requirement
under the CPM is to keep the operating margin of entity M constant. Equation 15 also
tells us that the production level would be similar to the “relation, equal taxes” condition
18
only if 𝑡 𝑀 = 𝑡 𝐷 . The level of production is therefore determined by the difference between
taxes. Particularly, when 𝑡 𝑀 < 𝑡 𝐷 , the right-hand side of equation 15 is lower than 𝑃𝑥 ,
which means that production is higher. If the externality is negative, then the profit
shift is lower than under the “relation, equal taxes” condition. This can be captured by
looking at fig. 1 and assuming that the 𝑃𝑥 line is now lower. When 𝑡 𝑀 > 𝑡 𝐷 , the opposite
occurs.
Proposition 3 tells us how the MNE determines its level of production when the CPM
is used for transfer pricing documentation and entity M is the tested party. In addition,
Proposition 3 also determines how changes in tax rates affect the profit shifting caused
by externalities.
Proposition 3. When two entities in a profit-maximizing MNE trade an intermediate
product, if tax rates are different across jurisdictions, negative (positive) externalities
are present, and the MNE uses the CPM for transfer pricing documentation with
company M designated the tested party, then:
a) Production is further reduced and profit is further shifted if 𝑡 𝑀 > 𝑡 𝐷 (𝑡 𝑀 < 𝑡 𝐷 ).
b) Production is increased and profit shifting is lowered if 𝑡 𝑀 < 𝑡 𝐷 (𝑡 𝑀 > 𝑡 𝐷 ).
c) An increase in 𝑡 𝑀 or a decrease in 𝑡 𝐷 reduces (increases) production and increases
(decreases) profit shifting.
If entity D is the tested party, then equation 9 is maximized with equation 8 as the
constraint. The first order condition with respect to x in this case is:
𝜕𝑑
𝑃𝑑 ∙ 𝜕𝑚 ∙
𝜕𝑚
𝜕𝑥
𝜑𝑀𝐷
+ 𝑃𝑑 ∙ 𝑒̅ = 𝑃𝑥 𝛽𝐷 +𝜑𝑀𝐷 (1−𝛽𝐷 )
(16)
Interestingly, when entity D is the tested party, the relationship between the difference
in taxes and the profit shift is the opposite of the case in which entity M is the tested
party, as stated in proposition 4:
19
Proposition 4. When two entities in a profit-maximizing MNE trade an intermediate
product, if tax rates are different across jurisdictions, negative (positive) externalities
are present, and the MNE uses the CPM for transfer pricing documentation with
company M designated the tested party, then:
a) Production is further reduced and profit is further shifted if 𝑡 𝑀 < 𝑡 𝐷 (𝑡 𝑀 > 𝑡 𝐷 ).
b) Production is increased and profit shifting is lowered if 𝑡 𝑀 > 𝑡 𝐷 (𝑡 𝑀 < 𝑡 𝐷 ).
c) An increase in 𝑡 𝑀 or a decrease in 𝑡 𝐷 increases (decreases) production and decreases
(increases) profit shifting
For graphic depictions of the determination of x when the MNE uses the CPM we can
use Fig. 1 and shift the 𝑃𝑥 line up or down, depending on the values of the tax rates.
In summary, externalities in production may contribute to a profit shift that, if not
incorporated in proper transfer pricing documentation, will result in improper use of the
arm’s length principle. Ironically, it may be taxes that shift profit back, but even so, one
cannot rely on an arbitrary difference in tax rates between two jurisdictions to solve this
distortion.
6. Conclusion
Transfer pricing documentation based on the arm’s length approach is currently the
most widely used method to enforce transfer pricing regulations around the world. The
sole objective of these regulations is twofold: to prevent companies, in their efforts to
reduce their tax burden, from shifting their profits between countries and to ensure that
every country receives its fair share of tax revenues.
It is therefore crucial that the chosen transfer pricing method be the most accurate
from among the available alternatives. The arm’s length approach has been criticized for
its legal weaknesses and for the flexibility transfer pricing analysts are allowed to
exercise in interpreting their clients’ business. The economic concepts at its foundation,
20
however, are generally accepted as valid by tax authorities, transfer pricing
practitioners and other experts.
This paper directly challenges the validity of the arm’s length approach. Relevant to
contemporary international business relations and widely applicable, the analysis
focuses on a flaw integral to any comparison made between entities whose business
involves intercompany transactions and companies whose business does not. Business
news often contains accounts of mergers or acquisitions. Typically, we expect a company
that was purchased by, or merged with, another, to undergo some structural changes
characterized by major layoffs, management reorganization, or changes to distribution
methods or even to production processes. As a result the company, which is now part of
a larger, profit maximizing organization, will no longer operate as a single, economically
independent entity. Therefore, any comparison of the financial results of this entity in
its new form as part of a bigger organization to those of economically independent
companies should expose the differences that arise in the wake of such structural,
organizational and business changes.
In other words, profitability level comparisons between companies with and without
intercompany transactions are invalid, as there is no basis to compare such essentially
different companies (unless, of course, an economic adjustment is incorporated to
overcome this difference). Some may think that this distortion can only occur when the
CPM is used and that the CUP preserves the validity of the arm’s length approach
because prices are determined in markets and not by companies. Under this scenario, as
long as the price is competitive, then the intercompany transaction faithfully upholds
the principle of arm’s length. But several other issues must be addressed here. First, the
CUP is rarely used in transfer pricing analysis because most intercompany transactions
involve either proprietary products or a product that is not largely traded. Second, even
if the product is sold by other companies, reliable price information is often not
21
available. Third, the CUP method is based on what economists refer to as “the law of
one price,” which occurs under the theoretical state of perfect competition characterized
by large numbers of similar companies and consumers, all of who have all the
information they need to make informed decisions. However, in most (if not all) markets,
“the law of one price” does not exist. Instead, corporations usually have some level of
market power. Where perfect competition has been replaced by monopolistic
competition, different products are sold at different prices. We therefore expect, for
instance, that the engines of two different cars sold for different prices cannot be argued
to be worth or to cost the same.
Ultimately this distortion caused by externalities can have, and probably has,
different effects in different cases. In fact, it is reasonable to assume that the impact
externalities have on transfer pricing analysis depends on the industry in which the
companies to the transaction operate. This effect, however, is very difficult to measure
because related entities do not publish their segmented financial statements. However,
an empirical analysis that can measure this effect will not only shed light on its
magnitude, it will also suggest ways to adjust for it, thereby improving the transfer
pricing analysis and the accuracy and validity of the results. Such a study is therefore
highly recommended as a continuation to this theoretical study.
22
Appendix A
This appendix describes the proof of proposition 1. According to Lemma 1 and assuming
negative externalities, the profit of company M is lower and the profit of company D is
higher after the merger. I define 𝑥1 as the pre-merger quantity of x purchased by
company M and 𝑥2 as the quantity purchased after the merger, so 𝑥1 > 𝑥2 , or
equivalently:
(A1)
𝑥2 = 𝛼 ∙ 𝑥1
where 0 < 𝛼 < 1.
Assuming decreasing returns to scale in production, by definition:
(A2)
m(α ∙ x1 ) > α ∙ m(x1 )
This implies:
(A3)
𝑚(𝑥2 ) > 𝛼 ∙ 𝑚(𝑥1 )
Combining equations A1 and A3:
𝑥1
𝑚(𝑥1 )
𝑥
(A4)
> 𝑚(𝑥2
2)
Therefore:
𝑃𝑥 ∙𝑥1
𝑚 ∙𝑚(𝑥1 )
𝛽1𝑀 = 1 − 𝑃
𝑃𝑥 ∙𝑥2
𝑚 ∙𝑚(𝑥2 )
<1−𝑃
= 𝛽2𝑀
(A5)
= 𝛽2𝐷
(A6)
Similarly:
𝛽1𝐷 = 1 −
𝑃𝑚 ∙𝑚(𝑥1 )
𝑃𝑑 ∙𝑑1
<1−
𝑃𝑚 ∙𝑚(𝑥2 )
𝑃𝑑 ∙𝑑2
where 𝛽1𝐽 and 𝛽2𝐽 represent the operating margin of company j before and after the
merger respectively. The pre-merger profit margin of each entity represents its arm’s
length profit margin. If the chosen transfer pricing method is the CUP, then the profit
margins of the two entities are different than before the merger. If the chosen transfer
23
pricing method is the CPM, then according to equation A5, in order to regain the premerger profit margin of company M, the MNE must decrease 𝑃𝑚 . But according to
equation A6, decreasing 𝑃𝑚 increases 𝛽2𝐷 even more.
In the same way, increasing 𝑃𝑚 in order to decrease 𝛽2𝐷 will increase 𝛽2𝑀 even more. It
remains to conclude that there is no level of 𝑃𝑚 that can regain the same profit margin
to both entities.
The same holds in the case of positive externalities.
24
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26
0.5
0.4 5
Ψ ̅(x)
Ψ(x)
0.4
P(x)
0.3 5
0.3
0.2 5
0.2
0.1 5
0.1
0.0 5
0
1
2
3
4
5
6
7
8
9
10
𝑥̂
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
𝑥
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
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81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
∗
Figure 1: Graphic description of the determination of production level in the cases of “no relation”
̅ (x)] conditions. The graph represents negative externalities.
[Ψ(x)] and “relation, equal taxes” [Ψ
27
Fig 2a: 𝜏 𝑀 > 𝜏 𝐷 and production is reduced compared
to “no relation” and “relation, no taxes” conditions.
Fig 2d: 𝜏 𝑀 < 𝜏 𝐷 and production is reduced compared
to “no relation” and “relation, no taxes” conditions.
0.5
0.5
0.4 5
0.4 5
0.4
0.4
0.3 5
0.3 5
0.3
0.3
0.2 5
0.2 5
Ψ(x)
0.2
0.2
Ψ(x)
̃ (𝑥)
𝛹
0.1 5
0.1 5
0.1
0.1
̂ (x)
Ψ
̂ (x)
Ψ
0.0 5
0.0 5
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
𝑥
𝑥̃ 𝑥̂
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
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82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
1
2
3
∗
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
Fig 2b: 𝜏 𝑀 > 𝜏 𝐷 , production is reduced compared to
“no relation” but increased compared to “relation, no
taxes”.
0.5
0.4 5
0.4 5
0.4
0.4
0.3 5
0.3 5
0.3
0.3
0.2 5
0.2 5
Ψ(x)
0.2
31
32
33
34
35
36
37
38
39
40
41
42
43
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46
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48
49
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81
82
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84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
Fig 2e: 𝜏 𝑀 < 𝜏 𝐷 , production is reduced compared to
“no relation” but increased compared to “relation, no
taxes”.
0.5
0.1 5
30
𝑥∗
𝑥̃ 𝑥̂
̃ (𝑥)
𝛹
Ψ(x)
0.2
0.1 5
̃ (𝑥)
𝛹
0.1
0.1
̂ (x)
Ψ
0.0 5
̂ (x)
Ψ
0.0 5
0
0
1
2
3
4
5
6
7
8
9
10
11
12
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79
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81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
1
2
3
4
5
6
𝑥∗
𝑥̃
𝑥̂
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Fig 2c: 𝜏 𝑀 > 𝜏 𝐷 and production is incerased
compared to “no relation” and “relation, no taxes”
conditions.
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
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51
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83
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86
87
88
89
90
91
92
93
94
95
96
97
98
99
𝑥∗
𝑥̂ 𝑥̃
Fig 2f: 𝜏 𝑀 < 𝜏 𝐷 and production is incerased
compared to “no relation” and “relation, no taxes”
conditions.
0.5
0.5
0.4 5
0.4 5
0.4
0.4
0.3 5
0.3 5
0.3
0.3
0.2 5
0.2 5
0.2
̃ (𝑥)
𝛹
0.2
Ψ(x)
0.1 5
Ψ(x)
0.1 5
̃ (𝑥)
𝛹
0.1
0.1
̂ (x)
Ψ
̂ (x)
Ψ
0.0 5
0.0 5
0
0
1
2
3
4
5
6
7
8
9
10
𝑥̂
11
12
13
14
15
16
17
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83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
1
𝑥 ∗ 𝑥̃
2
3
4
5
6
7
8
9
𝑥̂
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
𝑥∗
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
𝑥̃
Figure 2: Production levels with taxes. When the effect of taxes is included, production level can
either increase or decrease, depending on the prices of inputs and output, the production functions,
and the externality.
28
Figure 3: Graphic description of production level determination for cases under the “relation, with
taxes” condition.
29