Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
Expected Penalty and Transfer Pricing: Taiwan Electronic Industry
Empirical Evidence
So-De Shyu*, Jen-Jsung Huang† and Huo-Lien Tsai‡
Considering the threat of expected penalty to multinational corporations, we derive an
optimal transfer price model for the issue of multinational corporations global profit
maximization. In the determinant factors of the optimal transfer price, we add
corporate variables (characteristics) to the optimal transfer price model, and find that
annual revenue and income tax expense have significant impact on the optimal
incentive transfer price. Our empirical evidence shows that the optimal transfer price
is applicable and practical for Taiwan-based multinational corporations.
JEL Codes: F23, H26 and H32
1. Introduction
Hirshleifer (1957) first used marginal analysis to study transfer price for multination corporation
(MNC) profit maximization, and studied the equilibrium pricing model under idea assumptions
(complete information, no trading cost, no tariffs and no profit income tax). But those assumptions
withdraw from the reality. Later researcher gradually released the conditions of transfer pricing
model to close real environment. Gould (1964) went on with this issue and analyzed the internal
transfer price problem of centralization firms under external market. In addition, Horst (1971)
showed that transfer price was exogenous variables, so transfer price may be as high as possible
or as low as possible. In other words, transfer price was on the boundary value. Kant (1988)
though that transfer price should be an endogenous variables under the consideration of profit
income tax and tariffs, also suggested that transfer price was between the threshold price and
arm’s length transfer price when MNC faced a threat of a penalty. He also mentioned an expected
penalty function, but did not further discuss yet. This method approaches to real world. One of the
main contributions in this article is that penalty function can be described in terms of the
cumulative normal probability distribution, and it will be used to investigate the optimal transfer
price. We use the event probability of tax investigation in host country to judge the future expected
penalty probability, and provide the early plan for a MNC’s transfer price policy. Therefore, a MNC
can select proper assessment method for corporate income tax.
Accordingly, the international transfer pricing environment is becoming more complex as tax
authorities become more aggressive, particularly in the field of penalties. Therefore, we focus on
the transfer price of intermediate product between subunit 1 for production and subunit 2 for
product processing and sales, and select a strategic transfer price to pursuit tax profits, also
consider the expected penalty at the same time. Finally, we apply the theoretical results to conduct
the empirical tests on Taiwanese listed electronic companies.
The plan of this paper is as follows. Section 2 makes a discussion of expected penalty. Section 3
constructs the model of the optimal transfer price, and incentive transfer price. Section 4 discusses
hypotheses regarding transfer pricing. Section 5 discusses the determinant factors of the optimal
transfer price. Section 6 gives concluding remarks.
*
So-De Shyu, Department of Banking and Finance, Takming University of Science and Technology. Taipei, Taiwan. Email:
dshyu@takming.edu.tw
†
Jen-Jsung Huang, Department of Finance, Sun Yat-Sen University, Kaohsiung, Taiwan. Email: jthuang@cm.nsysu.edu.tw
‡
Huo-Lien Tsai, Department of Finance, Sun Yat-Sen University, Kaohsiung, Taiwan. Email: huolien.tsai@gmail.com
Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
2. Expected penalty
The tax authority audits transfer price data and does not investigate if the report transfer price is
located on inside the range of 25% to 75%, but the tax authority will investigate the report transfer
price when it is located on outside the range of 25% to 75%. We can use empirical penalty
accumulation distribution function to judge a MNC’s transfer price is located on which point of
probability function  (wˆ  w) and associated with relative reference data to judge that it need to
investigate or not. Kant (1988) assumed that penalty is driven by a certainly percent ( q ) of exceed
arm’s length price, thus the transfer price penalty is equal to probability multiply expected penalty,
that is [ 2 (wˆ  w)m] . Therefore, we can obtain the following result: expected penalty Ψ is positive
when  > 0 and (wˆ  w)  qw ; and expected penalty Ψ is zero when  = 0 or (wˆ  w)  qw . Assuming
the transfer pricing evaluation by tax authority does not change, but its attitude changes. The tax
authority attitude tends to strictly follow the tax laws. In other words, more supervise management
works and wider investigation is executed. These two factors will enhance tax investigation
strength. Therefore, the probability density function can be expressed as  ( g,(wˆ  w)) , where g is
transfer parameter (Kant, 1988). A MNC moves its transfer price toward the arm's length price, but
the transfer quantity will change in opposite direction. Therefore, the problem of Prisoner's
Dilemma is that the tax authority’s supervise management tends to strictly follow tax laws. This
behavior will also generate capital shift outside and reduce the labor quantity. In contrast, the
behavior of tax administrator will reduce income taxation when countries with more relaxed tax
policies. MNC use different accounting systems for tax and managerial purposes. Moreover, we
discuss the optimal incentive transfer price and the optimal tax transfer price between oversea
subunit 1 and subunit 2. We make single side trading assumption, each oversea subunit has
revenue function ( Ri ( pi , xi ) ), where p i is import (or export) price and x i is net import (or export)
quantity, and satisfies Ri' ( pi , xi )  0 and Ri" ( pi , xi )  0 , at the same time, profit function (  i ) is a
concave function for every subunit. We also assume that a MNC has two oversea subunits. Every
oversea subunit belongs to different country. The tax authority uses transfer pricing model (
Hirshleifer, 1957) to calculate a arm’s length price, and sets up a receivable range 0  w  wˆ  w ,
where ŵ is theory transfer price. We discuss the MNC global profit maximum problem, and do
analysis as follows:
Our mainly object is to consider both incentive transfer price ( s ) and tax transfer price ( t ) to use
tax transfer price to gain tax deduction. Unpaid amounts are X   2 (wˆ  w)m and MNC will be
punished when tax arbitrage is detected. First, Expected penalty ( 2 (wˆ  w)m) is assumed to be a
smooth convex function, and satisfies the following conditions: (0)  lim  '(X)  0 ,  '(X)  0 and
X 0
(X)  0 .
In addition, MNC profit function is as follows: max(1 1 )[ R ( p , x)  wx
ˆ  r1 x]  (1   2 )[ R2 ( p 2 ,  x)  r2 x  wx
ˆ ],
1
1
x,w
where transfer quantity x  0 (or m  0 ) and ad-valorem tax r1 , r2  0 and w  wˆ  w , so rewrite the MNC
ˆ  [(1   2 )r2  (1  1 )r1 ]x . Then, we
profit function as follows: max[(1 1 ) R1 ( p1, x)  (1   2 ) R2 ( p2 ,  x)]  ( 2 1 )wx
x,w
discuss that MNC faced two scenarios under two oversea subunits, external market and nonexternal market. Moreover, discuss steady analysis between subunit 1 and subunit 2. When
r1  r2  0 , global profit function can be written: max(1  1 ) R1 ( p1, x)  (1   2 ) R2 ( p2 ,  x)  ( 2  1 )wx
ˆ , where x  0.
x,w
_
We attempt to obtain w to maximize MNC profit when  2  1 , and obtain w to maximize MNC
profit when  2  1 , and transfer price will not affect MNC profit when  2  1 .
Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
3. Model of the optimal tax transfer price and incentive transfer price
The optimal incentive transfer price was on comparable condition and also did not take into
accounts import tariff. Therefore, we try to derive a more general model including both tax rate and
tariff. Assuming a MNC is forced ad-valorem tax r1 (or r2 ) and imports (exports) goods tariff
amounts mwr
ˆ 1 (or mwr
ˆ 2 ) in internal tangible product transfer. We also assume that the transfer
intermediate product quantity ( m ) of subunit 1 to subunit 2 is under single trading. In addition, the
cost function of subunit 1 is represented by C1 ( p1 , m) . The revenue function of subunit 2 is R2 ( p 2 , m) .
Moreover, the manufacture cost ( C ( p, m) ) is equal to unit cost multiply transfer quantity, where unit
cost is a constant. Furthermore, the tax rate of subunit 2,  2 , is higher than the tax rate of subunit
1,  1 , and the export tariff duties of subunit 1 is r1 and the import tariff duties of subunit 2 is r2 . For
the convenience of deriving the optimal incentive transfer price and the optimal tax transfer price,
we replace theoretical transfer price ŵ with tax transfer price ( t ). The incentive transfer price ( s ) is
real intermediate product transfer price in derived processes. First, we assume that the subunit
manager has the right to decide transfer quantity of intermediate product import.
Then the profit function of subunit 1 can be expressed by 1  (1 1 )[wx
ˆ 1  C1 ( p1 , x1 )  r1 x1 ] ,
where x1  m and the profit function of subunit 2 is:  2  (1  2 )[R 2 ( p2 , x2 )  r2 x2  wx
ˆ 2] ,
where x2  m . Then each affiliate’s objective becomes:
ˆ 1  C1 ( p1 , x1 )  r1x1 ]  c1 m sm 1 ( c1m tm)  (1  1 ) r1m  (1  1 )( c1m r1m)  sm 1tm
 1  (1 1 )[wx
and
ˆ 2 ]  (1   2 ) R2 (m)  m   2tm  (1   2 )r2 m  [ 2 (t  m)m]
 2  (1   2 )[R 2 ( p2 , x2 )  r2 x2  wx
 (1  t2 )[ R2 (m)  r2 m]  (s   2t )m  [ 2 (t  w)m] .
is:
The objective for the MNE as a whole
 T  (1   2 )( R2 (m)  r2 m)  (s   2t )m  [ 2 (t  w)m] (1  1 )(c1 m  r1m)  sm  1tm
 (1   2 )( R2 (m)  r2 m)  [ 2 (t  w)m] (1  1 )(c1m  r1m)  ( 2  1 )tm
We do both of partial derivative of the total profits function  T with respect to the variable m and
partial derivative of the profit function  2 with respect to the variable m , respectively, also let two
partial derivatives are equal. Finally, we gain the optimal incentive transfer price as follows:
(1)
S  1t  (1   ) 2 (t  w)[ 2 (t  w)m]  (1 1 )(c1  r1 ) .
where c is subunit unit cost, and  1 and  2 are income tax rate for subunit 1 and subunit 2,
respectively. We do a comparison between Choe and Hyde (2007) and above equation (1), there
are the same result as Choe and Hyde (2007) when r1  r2  0 , in another word , the difference is
tariff between both. S price is the weight average of arm’s length transfer price and subunit 1 unit
cost and its tariff and plus the expected penalty adjustment item. For expected penalty analysis,
we find that transfer price difference t  w will affect compensation items. The partial derivative of
total profits with respect to the variable t is:  T   2 m[ 2 (t  w)m]  ( 2  1 )m  0 . Let t  T , and get
t
the optimal tax transfer price T:
T  w

1
1 (1  1 )
 2m
2
(2)
where  1 and  2 are income tax rate for subunit 1 and subunit 2, respectively. Finally,
expected penalty depends on price difference, t  w . Due to t is selected by MNC and transfer
quantity ( m ) is decided by subunit 2. Therefore, if there is no tax penalty in high tax country, then
high-tax subunit manager should increase transfer quantity to reach the optimal level.
Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
4. Hypotheses Regarding Transfer Pricing
The OECD statistical data from 2003 to 2010 indicated that 40% Taiwanese electronic
commodities exported to west EURO and United States. Many Taiwanese electronic companies
receipted the order of international company. When a Taiwan-based MNC receives U.S.
customer’s order, the MNC exports raw material to Mainland China subunit, then buys complete
products and again sells to U.S. customers, so-called “Mainland China export, Taiwan negotiation”.
The research data come from the Taiwan Economic Journal (TEJ) database and the website of
the Taiwan Stock Exchange (TWSE). It includes 335 TWSE-listed and OTC-listed electronic
companies in 2003. Due to intermediate product transfer, we need listed firms to have both
oversea Mainland China subunit and U.S. subunit in sample period. Our sample selection criteria
require listed firms to have complete financial data and intermediate products for local reprocessing data from TEJ during the sampling period. Therefore, we exclude any other listed firms
by non-intermediate products for local re-processing such as telecommunication equipment
companies and semiconductor companies. Non-manufacturers (i.e. information service firms,
channel firms, IC design firms) are also excluded. Overall, this study is based on firms publicly
listed in the TWSE, but the sample observations exclude remaining restrictions on intermediate
products for local re-processing. This selection process results for 37 firms in 2003 - 2010.
Table 1 provides descriptive statistics for intermediate products transfer price and unit price.
Overall, four variables on both average value and standard deviation have the highest value in
2003, and decreasing in period 2004 to 2008, but has a little raise on both average value and
standard deviation in 2010. The trend are consistent as expected because multinationals transfer
price document report since May 2005 and financial crisis was happen in July 2008.
Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
TABLE I: SUMMARY STATISTICS
This table presents the summary statistics for the main variables used in the empirical analysis. The sample
period was from 2003 to 2010. In panel A, normal trading price (unit price, external market trading price) is
equal to annual sales amounts divide by annual sale quantity. Intermediate product transfer price ŵ is equal to
the sum of intermediate product unit various cost and other products unit marginal contribution, as negotiated
price. In panel B, S price, optimal incentive transfer price, is the weight average of marginal cost and the optimal
tax transfer price, plus regulation item coming from the compensation of expected penalty. T price, optimal tax
transfer price, is consists of arm’s length transfer price and the compensation of tax difference between the two
subunits. STD stands for standard deviation.
Panel A
unit price
theory transfer price
Year
average
minimum
maximum
STD
average
minimum
maximum
STD
2003
5.27
50986.20
5.78
54253.62
11550.86
10.31
38510.06
11112.25
9337.91
6698.66
2004
6301.64
5732.84
6042.49
10.54
41060.89
9669.86
2005
4959.92
31981.16
7900.56
5196.47
10.81
33589.45
8149.97
2006
21659.04
6296.47
4482.94
12.51
21659.04
6606.78
2007
4201.91
4395.65
9.86
10.59
11.25
13.48
21717.79
6762.06
4250.44
11.18
6615.07
6139.26
4575.06
2008
21631.96
20251.93
4456.54
11.09
20251.93
6258.44
2009
4959.59
10.48
19452.86
6405.72
5175.06
15.61
19452.86
6588.39
2010
5146.97
10.35
31143.49
7202.66
5384.61
12.16
31143.49
7428.99
Panel B
S price
T price
Year
average
minimum
maximum
STD
average
minimum
maximum
STD
2003
5.15
39516.12
10.31
38512.35
11113.10
9338.65
2005
4295.88
7.58
7.94
6303.08
5734.04
50994.62
31337.07
9199.91
8352.71
5.27
2004
5331.60
5099.75
23819.98
6599.96
4960.03
31981.16
7900.51
2006
3798.35
8.04
20881.33
5706.63
21659.04
6296.37
2007
4226.99
29346.96
6813.04
11.24
21631.96
2008
3791.70
8.17
8.45
4202.33
4395.65
9.86
10.59
19306.24
5512.89
4252.59
20251.93
2009
4344.11
7.47
18067.89
5784.16
4960.01
11.18
10.47
6615.07
6138.74
19452.86
6405.60
2010
4443.60
7.91
23849.60
6257.21
5148.50
10.35
31143.35
7201.90
We want to know what happen in sample period and do empirical analysis. First, we discuss the
expected penalty function, and assume that the affiliates are fully owned. For the convenience of
transfer quantity calculation, this study assumes that OEM quantity for each OEM order is known
because the MNC has an excellent manufacture technology and does not exit trade negotiations
volume. The treatment of expected penalty function, [ 2 (t  w)m] , will be explained below. We
assume that each nation’s income tax rate and transfer quantity are given, so penalty function can
be rewritten as  2 m[(t  w)]   2m[( x)] , where random variable is x  t  w . Its standardization form is
Z  ( x  uX ) /  X . Hence, accumulation distribution function form can be expressed as  2 m[ Z ] , and [ Z ]
is density function. Therefore, empirical accumulation distribution function ( x) and its probability
function ( x) can be yielded by means of history data. In addition, due to statistic software
development, we can calculate empirical probability function (t  w) and its inverse function,
1 (t  w) , where normal trading price ( w ) is given although external market trading price is
different in every year. We do Kolmogorov-Smirnov test and Shapiro-Wilk normality test, and all
statistic values are high significance in 2003 - 2010 in Table 2. In addition, the diagram of ŵ  w
Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
sample probability density function is shown in appendix A. Therefore, the results show that theory
spread tdp = ŵ  w is a normal distribution.
TABLE 2: NORMALITY TEST OF THEORY SPREAD VARIABLE
Intermediate product transfer price ŵ is equal to the sum of intermediate product unit
various cost and other products unit marginal contribution, as negotiated price. Normal
trading price (external market trading price) is equal to annual sales amounts divided
by sales quantity. Ho: The distribution of data is normal. Note: d.f. is degree of
freedom, sig. is level of significance. Levels of significance are indicated by *, **, and
*** for 5%, 1%, and 0.1% respectively.
Kolmogorov-Smirnov test
Shapiro-Wilk normality test
variable
Test value
d.f.
sig.
Test value
d.f.
sig.
tdp2003
0.393
37
0.000***
0.454
37
0.000***
tdp2004
0.432
37
0.000***
0.405
37
0.000***
tdp2005
0.383
37
0.000***
0.340
37
0.000***
tdp2006
0.464
37
0.000***
0.309
37
0.000***
tdp2007
0.426
37
0.000***
0.226
37
0.000***
tdp2008
0.423
37
0.000***
0.310
37
0.000***
tdp2009
0.380
37
0.000***
0.299
37
0.000***
tdp2010
0.423
37
0.000***
0.228
37
0.000***
Based on above discussion of intermediate product transfer price between subunit 1and subunit 2,
we replace theory transfer price ŵ with tax transfer price ( T ), and incentive transfer price ( S ) is
real intermediate product transfer price. The tax transfer price, T  w  [1/ ( 2  m* )]  1[1  (1 /  2 )] , will be
larger than unit price. Because the probability density function can be expressed as  [ g ,(wˆ  w)] ,
where g is transfer parameter (Kant, 1988). So we set theory spread that is equal to theory
negotiated price minus unit price, that is ŵ  w . Intermediate product transfer price ŵ is equal to
the sum of intermediate product unit various cost and other products unit marginal contribution, as
negotiated price. Table 3 indicates that the average values of theoretical spread gradually
decrease from 2003 to 2007, but have a little promotion in 2010. In addition, Table 3 also reports
the spread (dp) description statistics. Here, spread was equal to optimal incentive transfer price
minus unit price. The result shows that there was sharp reduction from 2003 to 2004 in the
average value of spread. Taiwan-based MNC have started to report annual transfer price
document since May 2005. There was significant absolute average value reduction from 2004 to
2007, but have a little promotion in 2010. Recently, each country pays more attention to transfer
pricing taxation. Hence, the transfer pricing policy of intermediate product for MNC tends to unity.
Furthermore, information and communications technology products face keen competition in
international market and sale prices continue to fall in recent years. Therefore, the profit of original
equipment manufacturer has been relative reduction.
Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
TABLE 3: DESCRIPTION STATISTICS OF THEORY SPREAD AND SPREAD
S  1t  (1   ) 2 (t  w)[ 2 (t  w)m]  (1  1 )(c1  r1 ) is incentive transfer price, where
w is
normal trading price, m is OEM intermediate product transfer quantity,  is penalty
probability, c is intermediate product unit cost,  is expected penalty, ŵ is
intermediate product transfer price, t is optimal tax transfer price,  2 is U.S. subunit 2
operation tax rate,  1 is Mainland China subunit 1 operation tax rate. Spread is s  w .
Theory spread is ŵ  w .
theory spread (tdp)
spread (dp)
variable
average
minimum
maximum
average
minimum
maximum
2003
397.02
-238.28
4577.30
-970.04
-11470.08
1786.17
2004
322.51
-57.47
4412.39
-633.10
-7172.99
297.97
2005
230.39
-436.28
5071.02
-664.04
-8989.07
1557.80
2006
261.42
-374.92
5627.03
-403.56
-3868.17
3109.45
2007
180.10
-354.08
5555.85
-168.66
-4506.27
7714.99
2008
196.13
-388.78
4735.72
-458.74
-3010.56
963.85
2009
207.95
-405.69
5366.05
-615.48
-3944.92
849.37
2010
235.42
-410.35
7266.89
-703.37
-7293.88
345.99
We discuss the comparison relation between transfer price and unit price. Due to information and
communications technology products face keen competition, intermediate product prices continue
to fall. The theory spread ŵ  w sometimes positive or negative, hence, the value of X   2 (wˆ  w)m
sometimes positive or negative. In this section, we conduct hypothesis test to check the above
relationship in S price and T price.
1). The optimal incentive transfer price
Because the practical difference is small between theory transfer price and unit price, we assume
that δ function value is 0, so S  1t   2 (t  w)[ 2 (t  w)m]  (1 1 )(c1  r1 ) . Due to  2  1 , MNC will raise
transfer price and transfer intermediate product from subunit 1 with low tax to subunit 2 with high
tax. Therefore, the following assumption can be established: a MNC raises transfer price and
transfer intermediate product from low tax subunit to high tax subunit, high-tax subunit manager
should increase expected penalty compensation S 2 . Therefore, S price should be lower than unit
price. The first hypothesis can be expressed as follows:
Hypothesis 1:
1
： S  price  unit  price
1
： S  price 
HO
H1
unit  price
This test result in Table 4 can indicate that S price was significantly lower than unit price in 2008
– 2010. In addition, sale quantities of consumer electronic product in international transaction had
significant reduction during the period of financial crisis, so it was not significant in 2007.
Multinational companies can minimize the global tax liability by shifting profits from high tax
locations to low tax locations, leading to substantial revenue losses in high tax countries. Hence,
we use the ratio of average of operation revenue to total assets in percent to execute the mean
comparison in Table 4. The result shows that the ratios had significant reduction in 2009 and 2010.
This may explain Taiwan-based MNC lowered incentive transfer price to transfer funds in 2009 2010.
2). The optimal tax transfer price
Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
Because empirical probability density function is a normal distribution, we divide it into two groups
based on the highest point of sample normal distribution probability. One is on the left side and
another is on the right side, and get inverse function diagram of left side sample probability density
function [1  (1 /  2 )] and obtain sample probability density function of right side [1  (1 /  2 )] , then
interpolation method is adopted to calculate inverse function value 1[1  (1 /  2 )] , respectively. We
first discuss the variable 1  (1 /  2 ) , and consider the following conditions. Because statutory tax rate
 2 is larger than statutory tax rate  1 at normal condition, the value of 1  (1 /  2 ) is positive in theory.
There were two kinds of companies still to have negative subunit profit under the environment of
 2 . First, if  1 = 0 % and  2 = 0 % , then 1  (1 /  2 ) will do not to calculate, so we assumed that the
value of 1  (1 /  2 ) is equal to 1. Second, the value of 1  (1 /  2 ) will be a very large negative if 1  0% and
 2  0% , therefore, we assume that the value of 1  (1 /  2 ) is equal to 0. On the one hand, if the value
of  2  0% which maybe exit in practice, then the value of 1  (1 /  2 ) will become indefinite negative.
Therefore, we also set DUMMY=0 when  2  0% and DUMMY=1 when  2  0% . On the other hand,
we also set dummy variable D2 = 1 when 1  0% and set D2  0 when 1  0% . Furthermore, in order
to check intersection item, we add another dummy variable which is equal to D2  MUMMY . Finally,
we obtain the model: T  0 w  1T2  2 DUMMY  3 D2  4 D2 DUMMY   . We consider the effect of above
dummy variables, and run a simple regression. The regression results show that only T2 was
significant, while other dummy variables were not significant. In other words, we do not need to
care the effect of those dummy variables.
Due to  2  1 , MNC raise transfer price and transfer intermediate product from low tax subunit 1 to
high tax subunit 2 in theory, hence profit will be reserved on subunit 1. Therefore, we observe the
following hypothesis: MNC raise transfer price and transfer intermediate product from low tax
subunit to high tax subunit. It should increase the compensation of tax difference ( 2  1 ) for
subunit 2. Therefore, T price should approach to unit price or be larger than unit price.
Hypothesis 2:
HO
2
： T  price  unit  price
H1
2
： T  price  unit  price
The test result reported in Table 4. It shows that T price was not significantly lower than unit
price in 2003 – 2010, besides 2006 and 2009, so we do not reject that T price was larger than unit
price in 2003 – 2010. Therefore, Taiwanese’s MNC had little operation revenue in U.S. subunit in
2003-2010 and could reduce income taxation.
3). Assumption of investigation strength
The third purpose of this study is to discover the difference between tax avoidance of tax payer
and payment for overdue tax. It also prevents firms from continuing to evade tax in the future
(Chen, 2001). Furthermore, the investigation strength  (t  w) of tax authority was different in every
year. Here we assume three cases: 1, 0.5, and 0 probability value. Furthermore, we assume that
MNC have two books, one uses to guide incentives and the other is for tax purpose. The test
hypothesis can be reported as follows: MNC maybe want to evade tax because of two accounting
systems. Therefore, S price should not be equal to T price in practice.
Hypothesis 3: H 03 ：S price = T price
3
H 1 : S price ≠ T price
Table 4 reports the results and expresses that the spread gradually reduce the difference between
T price and S price during the period of 2003 to 2006. While there was more significant difference
between S price and T price in from 2008 to 2010. This implies that S price approached to T price
Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
during the period of 2003 to 2006 because tax authority strictly audited transfer price in the
periods.
TABLE 4: HYPOTHESIS TEST AND THE RATIO OF OPERATION REVENUE TO TOTAL ASSETS
S  1t   2 (1   )(t  w)[ 2 (t  w)m]  (1 1 )(c1  r1 ) is optimal incentive transfer price, and T  w  [1/ ( 2  m)]  ()1[1  (1 /  2 )] is
optimal tax transfer price, where w is normal trading price, m is OEM intermediate product transfer quantity,
 is expected penalty, c1 is intermediate product unit cost, r1 is ad-valorem tax rate, ŵ is intermediate
product transfer price,  2 is U.S subunit 2 operation tax rate,  1 is Mainland China subunit 1 operation tax rate.
We treat penalty function value for hypothesis test 3 in three cases: δ = 0, δ = 0.5 and δ = 1. It statistic values
have the same test results for δ=0, 0.5 and 1, respectively. We use paired -samples t test, and sig. value is
under 2-tailed condition. panel B also shows the descriptive statistics of the ratio of U.S. subunit’s operation
revenue to total assets in percent.
Panel A
Hypothesis 1
Hypothesis 2
Sig.
Mean
Sig.
Mean
Year t value
Correlation
t value
Correlation
(2-tailed)
Difference
(2-tailed)
Difference
2003 -2.501
0.017
0.991
-970.038
1.330
0.192
1
1.440
2004
-2.863
0.007
0.995
-633.098
1.066
0.294
1
1.195
2005
-2.226
0.032
0.985
-664.045
1.449
0.156
1
0.106
2006
-2.231
0.032
0.988
-403.557
1.851
0.072
1
0.414
2007
-0.630
0.532
0.971
-168.660
-0.077
0.939
1
-0.004
2008
-3.233
0.003
0.995
-458.741
1.066
0.293
1
2.149
2009
-3.968
0.000
0.993
-615.479
1.837
0.075
1
0.426
2010
-3.293
0.002
0.991
-703.368
1.041
0.305
1
1.530
Panel B
Hypothesis 3
Year
t value
2003
2.504
Sig.
(2-tailed)
0.017
2004
2.868
2005
Ratio of operation revenue to total assets
Mean
Minimum
0.991
Mean
Difference
971.478
0.6036
-93.37
80.59
25.6848
0.007
0.995
634.293
2.3458
-29.86
40.34
12.7936
2.226
0.032
0.985
664.151
1.8469
-36.44
30.47
12.8322
2006
2.234
0.032
0.988
403.970
0.7961
-35.56
19.62
12.2711
2007
0.630
0.532
0.971
168.656
2.6839
-44.19
59.10
17.7465
2008
3.251
0.002
0.995
460.980
1.7811
-52.36
46.53
14.9174
2009
3.971
0.000
0.993
615.905
-1.5608
-61.03
17.15
13.1354
2010
3.300
0.002
0.991
704.898
-1.8317
-102.60
17.55
21.5601
Correlation
Maximum Std. Deviation
What is the effect of one unit change in unit price on both the optimal incentive transfer price and
the optimal tax transfer price? First, the partial derivative of the T price with respect to unit price is
one, this implies that per unit change in unit price and per unit T price change move in the same
direction. Second, S price can be showed in another form: S  1t  (1   ) 2 (t  w)m[ 2 (t  w)m]  (1 1 )(c1  r1 ) .
Because we assume that [ 2 (t  w)m] is a linear expected penalty, and t  w is a random variable.
So, expected penalty function, [ 2 (t  w)m] , can be rewrite as k 2m(t  w) . Then we take the partial
derivatives of S price with respect to unit price and get S / w  2(1   ) 22 (t  w)k , where (1   ) ,  2 , and k
are positive. Therefore, S / w  2(1   ) 22 (t  w)k is a negative constants when t  w , that is, per unit
change in unit price and per unit S price change move in the opposite direction when t  w .
Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
Furthermore, S / w  2(1   ) 22 (t  w)k is a positive constants when t  w , that is, per unit price change
and per unit S price change move in the same direction when t  w . We reach the conclusion that
both the optimal tax transfer price change and unit price change move in the same direction when
optimal tax transfer price is lower than unit price, and both the optimal incentive transfer price
change and unit price change move in the opposite direction when optimal tax transfer price is
larger than unit price. We also can use U.S. subunit operation finance data in annual report to
support this phenomenon. Most U.S. subunits have little or negative operation revenues. This
result may be important for MNC to transfer funds from high tax country to low tax country.
When will happen that S is equal to T . Here we give a explanation, this condition for the marginal
cost pricing rule when compliance with the arm’s length pricing is the MNE’s choice. It is as


1
1   
follows: First, do not consider r1 and  , and replace t  w 
1 (1  1 ) and ( ( 2 1 ))  1  1 in
2
2
m 2
2
equation (2) with the expected penalty adjustment and  1t item of S price in equation (1), let S is


1
1
equal to T , that is
(1  1 )c1  1w  1 (1  1 )  w 
1 (1  1 ) . Finally, above equation is
m
2
 2m
2
1  2

1
1   2 ,
.
We
have
following
result:
If
then
c1 
(
)1 (1  1 )  w
(1  1 )  2 m
2

1 1  2
w  c1 
(
)1 (1  1 )  c1 . If 1   2 and w  c1 , then S  (1 1 )c1  c11  c1  w . Another, t will equal
(1  1 )  2 m
2
to
w
as 1   2 . Therefore, we get T  S when w  c1 and 1   2 .
5. Determinant factors of the optimal transfer price
A large body of transfer pricing theory literature has emerged, We integrate previous research
about the determinant factors of the optimal transfer price, this study summarizes the explanatory
variables to the two dependend variables, the optimal tax transfer price and the optimal incentive
transfer price, as follows: net revenue NRit , income tax expense ITEit , earning per share EPS it . The
following two least square models will be analyzed. Model One:
(3)
Tit  0  1 NRit  4 ITEit  5 EPSit   it
and
(4)
Sit  10  11 NRit  14 ITEit  15 EPSit  it
We first want to understand whether there exit collinearity between explanatory variable and other
explanatory variables, a commonly given rule of thumb is that VIFs of 10 or higher (or equivalently,
tolerances of .10 or less) may be reason for concern. Here, we judge that collinearity is a threat
when VIFs of 10 or higher and find high correlation between NR variable and ITE variable in 2006 2007, and 2010 from table 5. To solve this collinearity problem, we use information from prior
research. For example, suppose previous studies have shown that  ITE  115*  NR . Then, create a
new variable, X 3  115* X ITE  X NR . Then, regress T price on X 3 instead of on X ITE and X NR . bX is
3
then your estimate of  NR and 115*b X is your estimate of  ITE . We get the coefficient of
3
regression change are little after OLS regression, and consider other measures of the determinant
factor of firm characteristics to further isolate the effects of collinearity in our analysis.
We first find that net revenue has high significant in 2003 – 2010, besides 2009 in S price.
Furthermore, income tax expense has significant in 2005 to 2010, besides 2007 and 2009. all
explanatory variables were not significant in 2007, besides net revenue in T price.
Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
TABLE 5: REGRESSION RESULTS
Model 1 is list in Panel A and Panel B. Levels of significance are indicated by *, **, and *** for 10%, 5%, and
1%, respectively. Parentheses represent standard error. Brackets represent VIF.
Panel A: T price
2003
2004
2005
2006
2007
2008
2009
2010
0.000***
0.000***
0.000***
0.000***
0.000**
0.000***
0.000*
0.000**
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
[1.197]
[1.456]
[4.473]
[12.652]
[13.337]
[6.133]
[4.543]
[22.285]
-0.002
-0.011
-0.013***
-0.009*
-0.003
-0.004*
0.001
-0.009*
(0.010)
(0.010)
(0.004)
(0.005)
(0.004)
(0.002)
(0.003)
(0.005)
[1.828]
[1.933]
[4.561]
[14.050]
[14.646]
[6.192]
[4.872]
[23.543]
-578.403
704.064
927.226**
494.421
577.537
343.109
314.348
545.095
NR
ITE
EPS
(1000.228) (658.508) (402.055) (371.199) (432.213)
Adjusted- R
(295.595)
(343.471) (491.456)
[1.640]
[1.410]
[1.068]
[1.512]
[1.385]
[1.228]
[1.305]
[1.310]
0.173
0.353
0.504
0.570
0.448
0.517
0.407
0.288
2003
2004
2005
2006
2007
2008
2009
2010
0.000**
0.000***
0.000***
0.000***
0.000
0.000***
0.000**
0.000***
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
[1.197]
[1.456]
[4.473]
[12.652]
[13.337]
[6.133]
[4.543]
[22.285]
-0.003
-0.010
-0.013***
-0.010**
-0.001
-0.004**
0.001
-0.009**
(0.008)
(0.008)
(0.003)
(0.005)
(0.005)
(0.002)
(0.002)
(0.004)
[1.828]
[1.933]
[4.561]
[14.050]
[14.646]
[6.192]
[4.872]
[23.543]
-473.873
519.877
679.142**
439.638
448.425
274.579
241.383
540.691
2
Panel B: S price
NR
ITE
EPS
(833.713) (559.197) (328.727) (352.900) (488.135)
Adjusted- R
2
(255.198)
(289.261) (402.140)
[1.640]
[1.410]
[1.068]
[1.512]
[1.385]
[1.228]
[1.305]
[1.310]
0.162
0.416
0.525
0.527
0.336
0.553
0.484
0.369
6. Conclusion
In this empirical study, the results show that empirical expected penalty function is a normal
probability density function. We take into accounts expected penalty, and derive the optimal
transfer price for MNC under the condition of global profit maximization. This research tests two
hypotheses by looking at 37 Taiwan listed electronic companies. The result reports that the optimal
tax transfer price was lower than unit price in 2006 and 2009. In addition, the optimal incentive
transfer price was larger than unit price except 2007. These results are consistent with that MNC
raised incentive transfer price, and lowered optimal tax transfer price to transfer funds on two
accounting systems. Regarding firm characteristics, this study adds corporate variables in optimal
transfer price models, and reaches the conclusion that the revenue and income tax expense of
firm characteristics were significant in the model of optimal incentive transfer price. In short, the
main contributions of this research are to derive the models of optimal incentive transfer price and
optimal tax transfer price and find that MNC transfer funds in 2009 - 2010 by means of raising
incentive transfer price and lowering optimal tax transfer price to transfer funds. Furthermore,
financial crisis lead to international trade recession in 2007- 2008, MNC lowered price to sale
consumer electronic products, it might be the reason that this study failed to find transfer funds in
2007-2008.
Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
This analysis emphasizes expected penalty, tariffs, and tax differentials, and ignores factors of
local shareholding and restrictions on profit repatriation in the host country. We find that these
transfer price models are feasible for Taiwan-based MNC electronic industry. The transfer pricing
decisions in multinational corporations may vary depending on the country, region, or industry.
This study gives a research path to discuss manager’s pricing behaviors for MNC global profit
maximization problem. Our results suggest that a company engaging in transfer pricing decisions
may deeply be affected by expected penalty of the administrators.
References
Chen, M. Y. 2007, Cost accounting: management decision and performance evaluation, Taiwan
Westbook publisher, Book two, pp.531~532, ISBN: 986-761-654-5, Taiwan.
Choe, C. and Hyde, C.E. 2007, Multinational transfer pricing, tax arbitrage and the arm’s
length principle, The Economic Record, Vol.83, December, pp.398–404.
Diewert, W. E., Alterman, W. F. and Eden, L. 2005, Transfer prices and import and export
price indexes: theory and practice, CRIW Conference on price index Concepts and
SHRC international Conference on index number theory and the measurement of
prices and productivity, Vancouver, BC, July 2004.
Huang, C. J., Kuo, C. J., Shyu, S. D. and Yu, J. H. 2010, Solution for disputes over
governments’ detection of multinational enterprises transfer pricing - a quantile
regression model approach, International Research Journal of Finance and
Economics, Vol. 38, pp.122-146.
Kant, C. 1988, Endogenous transfer pricing and the effects of uncertain regulation,
Journal of International Economics, Vol. 24, pp.147-157.
Appendix
The summary of (wˆ  w) sample probability density function
Fig. 1. 2003~2006 sample probability density function.
Proceedings of 5th Asia-Pacific Business Research Conference
17 - 18 February, 2014, Hotel Istana, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-44-3
Fig. 2. 2007~2010 sample probability density function.