An application of input-output modelling to transfer pricing

An application of

input-output

modelling to transfer

pricing

Author: Bert Tinge

1. Introduction

The problem of transfer pricing, pricing goods and services used within a multi-divisional organization, is a highly complex challenge. While theoretical models indicate considerable difficulties, in reality the problem is even harder. The objectives of a firm as a whole and those of the different divisions are often incompatible. Therefore, the problem of a firm is to determine a pricing rule that solves the problem most optimally, taking into account the objectives of the divisions and those of the firm. Since, for example, asymmetry of

information is almost always present, the development of such a rule remains cumbersome. Various methods have been developed to solve the transfer pricing, none of them being fully satisfactory. A number of these approaches will be discussed in a later stage.

The application of input-output models is widely spread in macroeconomics nowadays. While the use of enterprise-level models received some attention from as early as the ‘60’s, this initial use was not perpetual. Strangely enough, the interest for input-output models at enterprise level almost completely disappeared in the ‘80’s. However, while the reasons for this state of oblivion are unclear, there has been a rediscovered interest since a number of years. Input-output models have noticeably been applied at firm level in recent studies. As these studies contemplated the quantity variant of input-output models at firm-level, it might prove worthwhile to apply the price variant of input-output modelling to a multidivisional company. The results obtained by this modelling might reveal valuable insights with respect to the problem of transfer pricing.

2. Transfer Pricing

2.1 Overview

The co-ordination of internal transactions in a multidivisional firm is a complex procedure. The (inter)dependence that exists between multiple profit centres within a single company necessitates a transfer price if these profit centres can buy and sell to each other. These transfer prices pose management for a dilemma, since increasing decentralisation may increase inter-profit centre relationships. Research by Vancil (1978) revealed that ,overall, internal transfers do not negatively affect company performance, indicating that corporate management have found effective and efficient ways to cope with the problem of transfer pricing. However, theoretical predictions of transfer prices are diverging from the solutions found in practice. This dichotomy can be explained by the variety of perspectives, such as organisational, economic and behavioural aspects, that are related to the transfer pricing problem. Grabski (1985) made an extensive review of the transfer pricing problem (1985) by analyzing 81 papers from 1974 to 1983.

An overview of a tackling of the transfer pricing problem in the past is shown in table 1 (Eccles 1985): Economic Theory Mathematical programming Accounting Theory Management theory Principal Criterion Profit maximisation Profit maximisation Profit maximisation Individual fairness

Assumptions Highly restrictive Restrictive Somewhat restrictive

Not restrictive

Completeness Ignores many variables

Ignores many variables

Ignores some key variables

Ignores some key variables

Empirical support

Almost none Almost none Some Some

Usefulness to management

None None Limited Limited

Table 1: Comparison of Transfer Pricing Theories.

The first formal treatment of the transfer pricing problem based on economic theory was made by Hirschleifer (1956). His marginal cost solution, based on the maximisation of profit, comprised the two strong conditions of technological independence and demand dependence. The most general result of Hirschleifer’s model can be summarised by means of transfer prices that should be set at marginal costs. His work (and of those who built upon it) was criticised because it ignores company strategy in its analysis. Furthermore, the theory fails to address the implications of policy considerations with respect to management related issues as performance measurement, evaluation and reward.

In principle the mathematical programming models use iterative responses of divisions. Each iteration advances whatever utility (or utilities) the approach is designed to maximise.

Important contributions have been made by Dantzig & Wolfe (1960), Baumol & Fabian (1964), Hass (1968), Verlage (1975) and Bailey & Boe (1976). Some major shortcomings are concerned with mathematical programming. Firstly, a large amount of information must be analysed by company headquarters, which may be time consuming and complex, making it not suitable for practical employment. Secondly, the iterative nature of the models requires central determination of divisional inputs and outputs. This interferes with the notion of decentralisation. Kaplan (1982) also noted that linear approaches can yield multiple optimal solutions, while only one of them is globally optimal.

Accounting theorists use internal cost data, especially when there is no external intermediate market, to set transfer prices on the basis of profit maximisation. One of its assumptions is that transfer prices affect resource allocation decisions, e.g. make or buy decisions, total production of the divisions and capital budgets decisions. The discussion in the accounting theory primarily focuses on whether market prices should be used or prices should be set at an arbitrary standard. Many accounting theorists argue that no single pricing method is able to satisfy all the needs of a divisionalised company (Solomons, 1965; Farmer & Herbert, 1982). Cassel & McCormack (1987) studied the problem of a company selling an entire project. They suggest a solution of dual-pricing in the case the price that the buying division pays is not equal to the price that the selling division obtains. Antle (1988) argued that there is need for a new approach to the transfer pricing problem, since, as he argues, the real world does not fit with the theoretical models. Cats-Baril, Gatti & Grinnell (1988) approached the transfer pricing problem from the viewpoint of a dynamic situation in which the optimal solution evolves over time. Their primary suggestion is to alter the transfer pricing scheme in time, consistent with the stage in which the life cycle of the final product is.

Management theory consists of a set of approaches in which a broader perspective on the problem of management is common. In general, the profit maximising condition is replaced by a ‘profit satisfier’, and rewards are not tied so strictly to divisional performance as in the previous approaches. These objectives can be both non-financial as financial. The primary focus is individual fairness and administrative process. Transfer prices can be viewed as the result of a bargaining process, in which behavioural aspect become of interest,

underestimating the importance of economic decisions and corporate performance.

Ronen & McKinney (1970) suggested that division managers (and not central management) determine their production levels, while central management chooses the compensation levels This should induce the divisional managers to truthfully reveal their private information. Groves (1976) and Groves & Loeb (1976, 1979) introduced the stronger notion of central management dictating both the compensation level for management, as well as the production quantity of every single division. The solution found by Groves and Loeb achieves optimal outcome not only via a Nash equilibrium, but also via dominant strategies. Green & Laffont (1977) showed that there is in general no balanced mechanism that can generate efficient outcomes which is also incentive compatible by means of a dominant strategy.

2.2 Eccles’ Model

Eccles developed a ‘theory for practice’ in which reasoning and empirical evidence from thirteen American companies was used to describe which transfer prices should be used in practice. This model is considered to be a standard approach nowadays in the transfer pricing problem. Although not being fully satisfactory, it is widely used. The model consists of two dimensions: 1. the degree of vertical integration, and 2. the degree of diversification. The former indicates the degree of interdependence between divisions, whereas the latter reflects the extent of product market segmentation. The notion of fairness is a central aspect in Eccles’ model. Eccles’ model is summarised in table 2 (Emmanuel & Mefadi 1994).

Diversification Vertical

integration Low High

High Co-operative: Mandated full costs Collaborative: Mandated market based Low Collective: No transfer pricing Competitive: Exchange autonomy market price

Table 2: Eccles’ model of transfer pricing.

The model suffers from at least two weaknesses. Eccles underestimated the influence of economic and accounting theory, thereby reducing the multi-disciplinary richness of his theory (Hilton 1980). Furthermore, he doesn’t provide clear guidelines how a firm should position itself within the framework (McAulay & Tomkins 1992). Eccles’ model was extended by Van der Meer - Kooistra (1994), amongst others, by taking information asymmetries, uncertainty and investment-speciality into account.

3. Input-Output models

3.1 Introduction

An input-output model (named after the framework by Wassily Leontief, 1936) is a set of linear equations, in which each equation describes the distribution of a division’s production throughout a company or, equivalently, the distribution of an industry’s production in the economy. Therefore, input-output models are sometimes referred to as inter-industry analysis. Input-output models have a relatively old predecessor; Quesnay listed input-output data in his Tableau Economique as early as the 18th century. In recent eras, the availability of personal computers has greatly aided the development of the input-output models in economics. Input-output models are widely used nowadays in a variety of topics such as “interregional flow of products and accounting for energy consumption, environmental pollution, and employment associated with industrial production” (Miller & Blair, 1985). The basic fundamentals of input-output analysis will be discussed below.

A fundamental assumption in input-output models is that interdivisional flows depend exclusively on the total output of a specific division. In this discussion the emphasis will be on the use of input-output models within a firm, i.e. interdivisional dependence. If it is

furthermore assumed that there are only two primary inputs (capital and labour), the following input-output table can be obtained:

X11 X12 … X1n F1 X1 X21 X22 … X2n F2 X2 : : : : : Xn1 Xn2 … Xnn Fn Xn L1 L2 … Ln 0 L K1 K2 … Kn 0 K X1 X2 … Xn F

Table 3. The input-output model.

In this table, Xij indicates the monetary value of division i ’s supplies to division j, Fi the value of total final demand for product i, Xi the total output of division i, Lj the value of labour used in division j and Kj the value of capital used in division j. From this table the quantity model and price model can be derived (see also Dietzenbacher, 1996).

3.2 The quantity model

In the quantity model capitals will be used to indicate values measured in monetary units, whereas the indications of real quantities, measured in any arbitrary physical units (i.e. litres, pounds, meters, etc.), will be in lowercase letters.

It is now possible to write

where pi indicates the price of product i.

To simplify the model and to avoid discrepancies, it is assumed that each division produces exactly one product and that every distinct product is produced by one division only. If it is furthermore assumed that the prices for labour and capital are equal for each division and are, more precisely, w and r respectively, one can interpret table 2 as the following system of equations: p1x1 = p1x11 + p1x12 + … + p1x1n + p1f1 p2x2 = p2x21 + p2x22 + … + p2x2n + p2f2 : : : : : pnxn = pnxn1 + pnxn2 + … + pnxnn + pnfn wl = wl1 + wl2 + … + wln rk = rk1 + rk2 + … + rkn (4)

which, assuming all prices (pi, w and r) are positive, can be re-written as:

x1 = x11 + x12 + … + x1n + f1 x2 = x21 + x22 + … + x2n + f2 : : : : : xn = xn1 + xn2 + … + xnn + fn l = l1 + l2 + … + ln k = k1 + k2 + … + kn (5)

Now, the total production of all divisions is expressed in a system of n equations with n variables.

To write these equations in matrix form, the so-called technical coefficient and the coefficient

of primary inputs are introduced respectively.

j ij ij x x a  (6) j j 1j x l b  and j j 2j x k b  (7)

The coefficient aij indicates the quantity of product i that is necessary in division j to produce one unit of product j. Analogous, the coefficient b1j(b2j) indicates the quantity of labour (capital) that is needed for the production of one unit of product j.

With equations (6) and (7) one is able to write the system of equations in (5) as

Equation (8) can be written in matrix equations:                                                   n 2 1 n 1 nn n2 n1 a2 22 21 1n 12 11 n 1 f : f f x : x x a ... a a : ... : : a ... a a a ... a a x : x x (9) and                          n 2 1 1n 22 21 1n 12 11 x : x x b ... b b b ... b b k l (10)

This can be succinctly expressed as:

f Ax

x   (11)

Bx

u (12)

where A is the n x n matrix of input-output coefficients aij , B the 2 x n matrix of primary inputs coefficients, x the 1 x n output vector, f the 1 x n final demand vector and u the 2 x 1 primary inputs vector. Equations (11) and (12) together display the quantity model. The coefficients a and b are assumed to remain constant, indicating that economies of scale are omitted.

In reality, it may be very difficult to assign a price to a product, produced by a certain division. This hampers the calculation of matrices A and B. Therefore, the following assumption is made:p₁  p₂  p_n wr1.

This assumption may seem somewhat odd at first, but essentially the assumption is just a change of units. The total production of a divisions is ‘split up’ in units with a value of 1. The total monetary value of the production is not altered, though. As a consequence of this change to new units,X not only reflects the value of the production but also the total quantity i

produced (measured in the new one-value units). Essentially, the distinction between lower-case and upper-lower-case letters disappears, since X_i  p_ix_i  x_i

for p_i 1. Likewise, L_j wl_j l_j for w1, and K_j rk_j k_j for r1

This considerably facilitates the calculation of A and B, since it is now possible to write equations (11) and (12) as:

F AX

X   (13)

BX

U (14)

section 4, a similar exercise will be displayed with the price model, which is explained in the next section.

3.3 The price model

In the previous section, the number Xij in table 3 described the monetary value of the flow of products from division i to j. It was possible to interpret the number Xij as the numbers of physical units of sector i that is sold/supplied to sector j, by means of a convenient choice of units. That is, the value of one physical unit of sector i equals one monetary unit (say, one dollar or euro). As a consequence, all current prices (i.e. all pi, price of labour w and price of capital r) now become one. The price model however, deals with the determination of equilibrium prices, i.e. the prices under which costs equal revenue for every single division. Equilibrium prices in the price model are determined by equalling revenues and costs for each division and expressing them in terms of pi, w and r:

j j ij n 1 i i j jX p X wl rk p 



_   (15) or:

where the terms on the right hand side indicate the costs of intermediate supply and the costs of labour and capital, respectively. The left hand side gives the revenues.

This set of equations can be written in matrix-form:





1 A -I B v B v A p p       (16) where v



w, r



.

If the values for the prices of labour and capital (w and r ) are exogenously given, it is then possible to calculate the equilibrium prices pi. It can be proven that if both w and r are

positive, all equilibrium prices piare positive as well. Furthermore, if the prices of capital and labour (w and r) are assumed to be one and if for every sector j ∑akj + ∑bkj = 1, pi equals one for all i.

The price model can now be used to investigate what the consequences are of a percentage change in one of the exogenously given prices. For example, one might consider an increase in the price of capital of 10%, (i.e.wnew 1.1w). With the price model it is now

straightforward to calculate the impact of this change on all equilibrium prices by means of matrix multiplication. This is the basic of the input output models discussed below. Chapter 4 considers a few of these exercises in the case of GlaxoSmithKline, an international

pharmaceutical company, albeit that the number of primary input factors is expanded up to eleven. This expansion does not influence the complexity of the problem, however, because of the ease of the matrix notation.

3.4 Literature review

Although input-output analysis was developed to analyse macro-economic events, a number of papers have appeared before the ‘80’s that have applied input-output analysis to micro-economic problems. However, this interest for input-output models at enterprise level almost completely disappeared in the ‘80’s. Since a number of years there is renewed attention for these models.

While Richards (1960) was one of the pioneers to make a translation of a business accounting system into an input-output model, indicating the use of such a model for financial planning and control, especially for accounting purposes with respect to the whole enterprise. Farag (1968) developed an input-output model for the divisionalised firm that can be used for

planning the activities of divisionalised enterprises. Bentz (1973) later proved that one version of the so-called matrix cost-allocation-model is equivalent to the input-output model, when applied to the interdepartmental cost allocation problem. Gambling % Nour (1970) noted that confusion may arise from the use of input-output analysis, with its macro-economic roots, to individual enterprises. This is caused by the fact that enterprises use standard cost that “…are build upwards from the lowest basic operations, while economic parameters are broken downwards from aggregated material. Standard-cost data do purport to illustrate the operation of the system, while economic parameters are just weightings which happen to explain the right-hand side of the equations in terms of the selected materials.” Butterworth (1971) (and later Sigloch ,1971) developed a multi-stage input output model, in order to clarify the different manifestations of the existing models. He notices that some input output models are measured as flows of money whereas other models use physical quantities of goods that flow between divisions. Furthermore, he distinguishes between models in which a certain input has to be determined from a given output and occasional models where the opposite holds.

4. Results

In Marangoni & Fezzi (2002), a number of applications of input-output analysis to management control and strategic planning is presented by means of the aforementioned quantity model. The “input-output table encapsulates in a single logical system the complete structure of the company’s [GlaxoSmithKline] profits and losses and allows us immediately to solve a series of problems which could not be tackled by the traditional internal reporting activity.” In this section, the price model is applied to the input-output data from figure 1 in Marangoni & Fezzi (see appendix).

As will be demonstrated, the price model will yield useful data on simulations of constraint possibilities with respect to changes in the (transfer) prices. Marangoni & Fezzi use a larger number of primary inputs (eleven, to be precise), instead of the cost of capital and cost of labour as discussed earlier. Because of the matrix notations, this will not hamper our calculations.

4.1 Increase in (group of) prices

If a certain increase is assumed for the price of some primary input, e.g., v (indicating the i _i

th element of v ), equation (16) will be concordantly adjusted. The price model reveals that

due to this cost increase, all equilibrium prices are influenced. This results in a new price vector, by means of which a new input-output table can be calculated, showing the effects throughout all divisions. Assume that for example the primary input factor ‘costs of sales’ increases. This could be the case in the likely event if for example cost of production or costs of raw materials increases, an event that is not unlikely in the pharmaceutical industry. It is interesting to analyze the impact of an increase on the equilibrium prices. If ‘cost of sales’ increases with 10%, i.e. v₂ 1.1 , the new price vector can be calculated:



1.0006, 1.0320, 1.0017, 1.0017





p

The increase in ‘cost of sales’ has the biggest impact on division 2, leading to an increase of more than 3%. This is obvious, since division 2 is the only division that uses the primary input factor ‘cost of sales’. However, it is more interesting to look at the changes of the equilibrium prices in other divisions. The equilibrium prices of divisions 3 and 4 both show an increase of approximately 0.2%, whereas the equilibrium price of division 1 increases with 0.06%. These changes might not seem paramount, but they clearly indicate the

interdependence of the divisions, since the primary input factor ‘cost of sales’ is only used by division 2.

In the aforementioned example only one division was directly struck by the change in primary inputs. It is interesting to see what happens in the case of a 10% percent increase of the factor ‘other direct costs’, since all divisions are directly dependent of this factor. This primary input factor encompasses a wide variety of possible costs and though it is unlikely in reality that all divisions will experience an exactly uniform increase in costs, general increases are very well possible. In order to make this example more comprehensible it is therefore assumed that all division face the same 10% increase in ‘other direct costs’. Solving the model yields:



1.0151, 1.0046, 1.0132, 1.0366





This result indicates that not all divisions are affected in the same amount. Division 4 suffers the most from the increase with a raise in the equilibrium price of more than 3.6%, while division 2 faces an equilibrium price increase of less than .5%. In view of the total production of each division and the absolute increase of the input factor for each division, the results can readily be interpreted. The total production of division 4 is very small as opposed to that of division 2. Since the 10% amounts to an absolute increase of comparable size for these divisions (as a matter of fact also for division 1), the differences in size of changes of the equilibrium prices can be estimated by the relative size of the total production of each division.

To obtain the updated input-output table for each of these increases, the input-output table should be multiplied with the diagonalized price vector. This is left as an exercise to the reader since the aim in this section is to show the consequences of the divisional

interdependence on the equilibrium price by means of the price model.

4.2 Increase in specific prices

It is also possible that prices of specific primary input factors are altered within the input-output system for only one or a few divisions. Suppose, for example, that the wages are increased with 10% in division 1 only. This scenario is conceivable if it is assumed that division 1 uses, for example, high-skilled labour, whereas the other divisions use low-skilled labour. If the supply of high-skilled labour decreases, wages will have to go up to return to an equilibrium situation. This increase in wages in division 1 will influence the equilibrium prices in all other divisions in the case of the GlaxoSmithKline data. In order to make calculations in this case our input-output table of primary inputs, matrix W (see Appendix), has to be rewritten in a way that allows for this specific change. This is done by constructing diagonal matrices from the row vectors of all of the specific primary input factors and concatenating them vertically. In this case this yields a 44x4 matrix, _W*_.

Since _B _W_xˆ-1_{(where x is the vector of total output), the new equilibrium price vector}

can now be easily calculated. The new vector v will be a 44x1 row vector with ones, except for the 25th element, the primary input factor corresponding to wages in division 1 that is increased with 10% to 1.1 . The problem is now trivially solved:



1.0359, 1.0024, 1.0001, 1.0001





    _{v C}

p .

The increase of wages of (high-skilled) labour in division 1 results in a 3.6% increase of the equilibrium price. Furthermore, the other divisions suffer indirectly from the rise. The effect is most noticeable in division 2 where the equilibrium price rises with approximately .25 %, as opposed to a minor increase of .01% in divisions 3 and 4. Division 2‘s relative large increase can be explained when looking at the input-output table since division 1 only supplies to division 2, making division 2 particularly (relatively) vulnerable when compared to division 3 and 4.

4.3 Restrictions

allowed to increase. The price model allows for the simulations of these cases, in which a primary input is kept constant while calculating the equilibrium prices.

In order to incorporate these restrictions within the model, some mathematical adaptations have to be made in such a way that certain primary inputs are exogenously given, i.e. are kept fixed. Recall equation (16) : p pAvB , and that the matrices B and A can be written as_{A Zxˆ}-1_{and BWxˆ}-1

, where W and Z are the initial input output matrices (see Appendix), and in which a ‘hat’ indicates a diagonal matrix.

It is now possible to write

 

1 A -I W v x B v A x p x pˆ  ˆ~  ˆ   ~  (17) where A~  x_ˆ-1Ax_ˆ.

We partition the divisions in two sets. In the first set, primary inputs are specified

exogenously, whereas equilibrium prices are determined endogenously. In the second set, equilibrium prices are exogenously given, which leaves primary inputs to be determined endogenously. If we furthermore assume v



1,1,...,1



and vWw, equation (17) can be written as:





1 22 21 12 11 2 1 2 2 1 1 A -I A -A -A -I w , w x p , x p                 _ˆ _{ˆ ~}~ ~_{~ , (18)}

where an overbar indicates an exogenously given variable, e.g. a constrained production factor.

It is interesting to view the changes in prices and primary inputs by means of a relative change of the initial quantity. Writing equation (18) in delta-notation, we then get:

              2 22 2 2 12 1 1 2 2 1 21 2 2 11 1 1 1 1 Δw A x p Δ A x Δp x p Δ w Δ A x p Δ A x Δp x Δp ~ ˆ ~ ˆ ˆ ~ ˆ ~ ˆ ˆ (19)

Expressing the endogenous variables in terms of the exogenous variables yields:

                             22 21 2 2 1 12 11 2 1 1 _{A I -A} 0 I x p Δ , w Δ I 0 A A -I Δw , x Δp ˆ ~ ~ ~ ~ ˆ (20)

this can be rewritten as:











 







_                             12 1 11 21 22 1 11 21 12 1 11 1 11 2 2 1 2 1 1 A A -I A A -I A -I A A A -I A -I x p Δ , w Δ Δw , x Δp _{~ ~ ~ ~ ~ ~} ~ ~ ~ ˆ ˆ (21)







_



_{ }

_



_



_

                       12 1 11 21 22 1 11 21 12 1 11 1 11 2 1 1 A A -I A A -I A -I A A A -I A -I Δw , x Δp _{~ ~ ~ ~ ~ ~} ~ ~ ~ 0 , 0 , 2281.6 , 2782.3 ˆ (22)

Solving equation (22) yields Δw₂ 



21.5, 10.1



and Δp₁ 



0.0102, 0.0025



, which is similar to a new equilibrium price: p₁ 



1.0102, 1.0025



. So, the equilibrium price in division 1 increases with approximately 1% , whereas the equilibrium price of division 2 increases with only a fourth of the 1% increase of division 1, i.e. approximately 0.25%. Trivially speaking, this makes sense since the total production of division 2 is about four times higher than the total production of division 1 and, in this case, the change in the primary production factor ‘other direct cost’ is approximately equal for division 1 and 2 in absolute amounts. Furthermore, the primary input factor ‘other direct costs’ decreases for division 3 and 4 with 21.5 and 10.1 respectively, which is caused by the increase in divisions 1 and 2 and the restrictions we made. This decrease in inputs for divisions can be viewed as a decrease in profits for divisions 3 and 4 (see also section 4.4 for an elaboration on this

intuitive argument). Note that these changes in the primary input factor are rather small when compared with the 10% rise in the other two divisions.

4.4 Simulation of changes in primary input factors in two constrained ways

In this simulation we will examine the consequences of an increase of 10% in the primary input factor “wages and other” in division 4 in two ways.

In the first exercise we will set the change of the primary input factor ´wages and other´ in division 1 and 3 to zero, simultaneously with the aforementioned constraint. Furthermore, the equilibrium price in division 2 is also exogenously specified to be zero. This leaves the other variables to be determined endogenously. In the second exercise the only difference will be that the equilibrium price of division 1 now will be the exogenously determined variable, rendering the change of primary input in division an endogenous variable. The two distinct exercises are relevant because they will demonstrate the effect on the primary input factors and equilibrium price respectively of a specific division (in this case division 2), due to (lack of) constraints in another division.

We again make a distinction between the variables. The first set of variables consist of the equilibrium price of divisions 1, 3 and 4, together with the primary input of division 2, and are specified endogenously. In the second partition we place the exogenously determined variables, i.e. the primary input for divisions 1, 3 and 4, as well as the equilibrium price of division 2.

Note that this equation appears to be similar to equation (21), except for the quantity of the change of the primary input factor (now 3704.9). However, p now contains three elements ₁

(i.e., the equilibrium prices of divisions 1, 4 and 3 (i.e. in this order, due to the switching of the rows and columns)), whereasw contains only one element (the change of primary input ₂

factor in division 2). Note furthermore that the augmented matrix at the right-hand side of the equation is adjusted for this different choice of exogenous and endogenous variables, in concordance with the earlier mentioned switching of the second and fourth columns and ditto rows in the matrix Z . Solving equation (24) yields the changes in equilibrium prices of divisions 1, 4 and 3 and the change in the primary input in division 2 respectively, by solving for p and ₁ w (Recall that ₂ p contains three elements and ₁ w is effectively a scalar):₂







2251.3



0.0059 0.0478, 0.0060,    2 1 Δw Δp

Equilibrium prices in divisions 1 and 3 are increased by a small amount of less than 1%, whereas the equilibrium price in division 4 is increased by almost 5%. Furthermore, primary input in division 2 has to be reduced by 2251.3. This decrease in primary input factors can be reflected in any of the primary input factors. However, it is most logically that this change under normal circumstances will be reflected as a change in profits, i.e. a decrease in the primary input factor ‘profit’. Following this reasoning, total profit of division 2 will decrease with 2251.3, which is approximately 0.1%.

It is also possible to solve this simulation in the case the equilibrium price of division 1 is an exogenously given variable, instead of an endogenous variable (leaving primary input in division 1 to be determined endogenously). This second exercise will be a somewhat different calculation, since Δp now will give the change in equilibrium prices of divisions 3 and 4 ₁

(instead 1, 3 and 4), whereas Δw gives the change of primary input in division 1 and 2₂

(instead of only two).

Note that in order to use this notation it is necessary to switch the first and second column with the third and fourth column and interchange the first and second row with the third and fourth row from the initial situation, becauseΔp and ₁ Δw refer to the endogenous variables. ₂

The augmented matrix elements at the right-hand side of equation (24) also have to be re-calculated. The reader may find this procedure peculiar at first, when remembering that Δp₁

revealed the equilibrium prices in division 1 and 2 in calculations earlier in this chapter. However, this contrast is solely due to the switching of the rows and columns for means of convenience.

Solving the new equation yields:







1629.0, 1740.6



0.0478 0.0059,     2 1 Δw Δp

(which was referred to as a decrease in profit) in division 2 is somewhat less than in the first exercise: only 1740.6 instead of 2251.3. This can be explained when the structure of the input-output matrix is studied. As mentioned before, division 1 is solely supplying to division 2. When the equilibrium price of division 1 is not allowed to change, as in the second part of this exercise, the primary input factor of division 2 won’t suffer as much as in the first case, when the equilibrium price of division 1 is allowed to change, as a exogenous variable.

5. Concluding remarks

Input-output modelling at enterprise level has been mostly forgotten in the ‘80’s. However, this thesis shows that the price model of input-output theory at corporate level is a very powerful tool to calculate the effects of changes in primary input factors (like wages, costs, etc.) and simulate capacity constraints. While the quantity model has been used recently, this application of input-output modelling to transfer pricing is a new initiative. Although

nowadays most enterprises show a high degree of divisional interdependence, the price model proves to be highly suitable for the calculation of equilibrium prices between divisions. Other methods for solving the transfer pricing problem were discussed, none of them being able to satisfyingly solve the problem.

The results of the model applied to the case of GlaxoSmithKline input-output data, show that the price model of input-output modelling is a relatively simple and elegant tool to explore constraints. Equilibrium prices can be calculated and constraints of primary input factors can be incorporated easily. Since the problem of transfer pricing is a subject that still receives wide attention in academics, this model seems a new and promising approach that will aid to tackle the transfer pricing issue and thereby assist to financial planning on enterprise level. A point of criticism on input-output modelling is that it tends to make a number of over-simplifying assumptions, like the use of constant technical coefficients. However, while this argument may be true, the application of the price model to transfer pricing yields fruitful results and therefore proves to be promising for the future. Further research could focus on the incorporation of more complex constraints, while taking into account a wider range of

6. Acknowledgement

7. Bibliography

Albino, V., E. Dietzenbacher and S. Kühtz (2003), Analyzing materials and energy flows in

an industrial district using an enterprise input-output model, Economic Systems Research,

vol. 15, pp. 457 - 80.

Albino, V., C. Izzo, and S. Kühtz (2002), Input-Output Models for the Analysis of a

Local/Global Supply Chain, International Journal of Production Economics, vol. 78, pp.

119-31.

Antle, R. (1988), Intellectual Boundaries in Accounting Research, Accounting Horizons, vol. June, pp. 103-9.

Bailey, A.D. and W.J. Boe (1976), Goal and Resource Transfers in the Multigoal

Organization, Accounting review, vol. 51, pp. 559-73.

Baumol, W. and T. Fabian (1964), Decomposition, Pricing for Decentralization, and External

Economies, Management Science, vol. 11, pp. 1-32.

Bentz, W.F. (1973), Input-Output Analysis for Cost Accounting, Planning, and Control: A

Proof, Accounting Review, vol. 48, pp. 377-80.

Butterworth, J.E. (1971), A Generalized Multi-Stage Input-Output Model and Some Derived

Equivalent Systems, Accounting Review, vol. 46, nr. 4, pp. 700-16.

Cassel, H.S. and V.F. McCormack (1987), The Transfer Pricing Dilemma and a Dual Pricing

Solution, Journal of Accountancy, vol. 64, pp. 166-175.

Cats-Baril, W., J.F. Gatti and J. Grinnell (1988), Transfer Pricing in Dynamic Market, Management Accounting, vol. 66, February, pp. 30-33.

Chalos, P. and S. Haka (1990), Transfer Pricing Under Bilateral Bargaining, The Accounting Review, vol. 65, pp. 624-641.

Dantzig, G.B. and P. Wolfe (1960), Decomposition Principle for linear programs, Operations Research, vol. 8, pp. 101-11.

Dietzenbacher, H.W.A. (1996), Collegedictaat Modelleren, University of Groningen.

Donnenfeld, S. and T.J. Prusa (1992), Corporate Governance in Multinational Enterprises, Working Paper, 3-92, Faculty of Management, Tel-Aviv University.

Eccles, R.G. (1985), Transfer Pricing, a theory for practice, Lexington, Massachusetts. Emmanuel, C. and M. Mefadi (1994), Transfer Pricing, Academic Press, London.

Farmer, D. H. and P.J.A. Herbert (1982), The dilemma’s of transfer pricing, Journal of General Management, vol. 7, pp. 47-56.

Gambling, T.E. and A. Nour (1970), A Note on Input Output Analysis: Its uses in

Macro-Economics and Micro-Macro-Economics, Accounting Review, vol. 45, nr. 1, pp. 98-102.

Gavious, A. and Y. Tauman (1995), Transfer Pricing in Matrix Organizations, Managerial

Economics and Operations Research, vol. 19, pp. 134-42.

Green, J. and J. Laffont (1977), Characterization of Satisfactory Mechanisms, Econometrica, vol. 45, pp. 427-38.

Grabski, S.V. (1985), Transfer Pricing in Complex Organizations, A Review and Integration

of Recent Empirical and Analytical Research, Journal of Accounting Literature, vol. 4, pp.

33-75.

Groves, T. (1976), Incentive Compatible Control of Decentralized Organizations, Discussion Papers 166, Northwestern University, Center for Mathematical Studies in Economics and Management Science, USA.

Groves, T. and M. Loeb (1976), Reflection on 'Social Costs and Benefits and The Transfer

Pricing Problem, Journal of Public Economics, vol. 5, pp. 353-359.

Groves, T. and M. Loeb (1979), Incentives in a Divisonalized Firm, Management Sciences, vol 25, pp. 221-30.

Hass, J.E. (1968), Transfer Pricing in a decentralized firm, Management Science, vol. 14, B-310 – B-331.

Hilton, I. (1980), Transfer Pricing, The Australian Accountant, vol. 50, June, pp. 336-8. Hirschleifer, J. (1956), On the Economics of Transfer Pricing, Journal of Business, vol. 29, pp. 172-84.

Kaplan, R.S. (1982), Advanced Management Accounting, Prenctice-Hall, Englewood Cliffs. Leontief, W.W. (1936), Input-Output Economics, Oxford University Press, New York. Lin, X. and K.R. Polenske (1998), Input-Output Modelling of Production Processes for

Business Management, Structural Change and Economic Dynamics, vol. 9, pp. 205-226.

Marangoni, G. and G. Fezzi (2002), I-O for Management Control: The Case of

GlaxoSmithKline, Economic Systems Research, vol. 14, pp. 245-256.

McAulay, L. and C.R. Tomkins (1992), A review of the contemporary transfer pricing

Meer - Kooistra, J. van der (1994), De besturing van interne transacties; een verrijking van

de theorie van Eccles, Maandblad voor Accountancy en Bedrijfseconomie, vol. 68, nr. 7/8,

pp. 402-14.

Miller, R.E. and P.D. Blair (1985), Input Output Analysis, Foundations and Extensions, Prentice-Hall, Englewood Cliffs.

Prusa, T.J. (1990), An Incentive Compatible Approach to the Transfer Pricing Problem, Journal of International Economics, vol. 28, pp. 155-72.

Richards, A.B. (1960), Input-Output Accounting for Business, Accounting Review, vol. 43, nr. 2, pp. 429-37.

Ronen, J. and G. McKinney III (1970), Transfer Pricing for Divisional Autonomy, Journal of Accounting Research, vol. 8, pp. 99-112.

Sigloch, B. (1971), Input-Output Analysis and the Cost Model: A comment, Accounting Review, vol. 46, nr. 2, pp. 374-5.

Solomons, L. (1965), Divisional Performance Measurement and Contro, Financial Executives Research Foundation Inc., New York - later published by Richard D. Irwin. Stoughton, N.M. and E. Talmor (1989), Transfer Pricing in a Multinational Enterprise

Under Asymmetric Information, Working Paper 88-9, Graduate School of Management,

UCLA, California.

Vancil, R.F. (1978), Decentralization: Managerial Ambiguity by design, Dow Jones- Irwin, Homewood.

Verlage, H.C. (1976), Transfer Pricing for Multinational Enterprises: Some remarks on its

Appendix

Profit & Loss Account – Input-Output Table GLAXOSMITHKLINE 1998 (ITL billion)

S&D M&S R&D ADMIN TOTAL SOLD SERVICES GROUP TRANSFERS LICENCEES DIRECT SALES TOTAL FINAL

DEMAND PRODUCTION TOTAL

S&D 85.715 85.715 187.694 187.694 273.409

M&S 2.638 8.693 4.072 15.403 366.469 892.757 1259.226 1274.629

R&D 10.451 114.700 1.386 126.537 56.571 56.571 183.108

ADMIN 32.807 22.205 22.727 77.738 77.738

TOTAL BOUGHT SERVICES 45.896 222.619 31.420 5.458 305.392 423.040 187.694 892.757 1503.491 1808.883

GROUP CHARGES 327.690 68.328 396.018

COST OF SALES 405.578 405.578

PROMOTION _{53.308 53.308}

OTHER DIRECT COSTS 27.823 22.816 15.353 28.109 94.101

SUNDRY 21.896 2.654 24.550

EXTRAORDINARY ITEMS 2.941 -927 9.134 5.351 16.499

TOTAL EXTERNAL COSTS 105.968 755.157 92.815 36.114 990.054

WAGES AND OTHER 98.082 43.733 41.661 37.049 220.525

DEPRECIATIONS AND AMORT. 143 17.331 17.212 4.591 39.277

INTEREST PAID -5.474 -5.474

TAXATION 10.835 109.559 120.394

PROFIT _{12.484 126.231 138.715}

VALUE ADDED 121.545 296.853 58.873 36.166 513.437

TOTAL PRODUCTION 273.409 1274.629 183.108 77.738 1808.883