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Back to the allocation of overhead costs in managerial accounting: how to well specify the activities and their cost drivers?
Michel GERVAIS a, Cédric LESAGE b
a: Professor in Managerial Accounting at the University of Rennes 1, IGR-CREM CNRS 6211 b: Professor in Accounting at the University of Paris 1 La Sorbonne, IAE Paris-GREGOR.
Contact: Cédric Lesage IAE de Paris 21, rue Broca 75240 Paris Cedex 05 France
[email protected],
[email protected]
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Back to the allocation of overhead costs in managerial accounting: how to well specify the activities and their cost drivers? Abstract: In literature on the ABC method, it is supposed that the setting of activities enables a better allocation of overhead costs. Through a mathematical formulation, this paper recalls the conditions for a good allocation. Then it reviews both families of models (heuristic and statistical) that have been proposed to determine cost drivers explaining at the best the level of costs. The analyse leads to a reformulation of the allocation problem. Keywords: Activity, cost driver, allocation, cost specification, specification error.
Introduction The usual methodology for implementing an Activity-Based-Costing consists in taking as starting point a badly specified model (the current model) and improving the part considered to be worst by breaking up it into activities in order to find a satisfactory explanation of the behaviours of costs. In order to avoid the recording of too tiresome information, the activities will be then reassembled either in grouped centers with an identical cost driver, or by process. The general methodology can be formalized as follows: 1) To be informed of the current cost accounting model 2) To identify the parts of the model considered as badly specified, 3) To divide that part into more activities, 4) To reassemble these activities into cost centres or process.
This paper deals with the core problematic of the model specification as presented into research literature. This review of art will lead us to reformulate the specification question from the point of view of the improvement of a given current cost accounting
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system. After having assessed the risk of a bad specification (section 1), the two main approaches that have been suggested will be analyzed: heuristic methodologies (section 2) and statistical methods (section 3). Then we will draw the conclusions for a concrete improvement of a given cost accounting.
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Risks related to a bad specification We will first recall the concept of model specification, then we will focus on the risks related to a bad specification.
1.1 The concept of specification of a cost accounting model In management accounting, the procedure of allocation consists first in allocating the amount of the indirect costs between various activities, then in defining a cause of consumption of the resources (cost drivers) which makes it possible to allocate amounts of costs of activity (or cost centers) on the cost objects. Two conditions are necessary to carry out this operation correctly: the existence of independent activities whose cost is entirely explained by a unique cause and a use of the resources in the same proportions (equiproportionnality of resources consumption) for all tasks completed inside the same activity. The use of an activity-driver supposes indeed that there is an explicit relation between the cost of the activity and the volume of the chosen cost driver: the indirect cost is supposed to be completely proportional to the used volume of the cost driver. It is thus necessary to check the following points (Trahand, Morard, Cargnello-Charles 2000): 1) there exists a relation such as:
D jt = π j Pjt + ε t
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with Djt : cost of the activity measured at t, with t = 1…T
π j : the unknown unit cost of the cost driver. Pjt : the volume of the cost driver measured at t εt : the random residual term, with a null average and a constant variance.
2) this relation remains stable over time. The quality of the model is assessed by verifying that the coefficient of correlation equals around 1. By generalizing, the set of overhead costs is allocated on the various activities according to the following equation: J
J
j =1
j =1
∑ D j = ∑ π j Pj Such a model will be statistically well specified if factors of consumption of resources are not forgotten and if the Pj present weak interrelationships, i.e. if the activities are sufficiently independent between them. However, the accounting specification is different. The costs are first allocated, or broken down using an allocation coefficient on the various activities, then the best cost driver is searched. It is not thus a question of determining the variables which explain the best the whole of the indirect costs, but of allocating (on an unquestionable or uncertain basis) the costs on activities considered as sufficiently independent, for then seeking a correlation between their cost and the volume of the selected cost driver. So that the allocation be correct, it is necessary to abide the equiproportionnality of consumption of resources, i.e. to make sure that the activity is homogeneous
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(Gervais 2000, p. 55). In other words, each time the activity is started, the elementary tasks which make it up must all be carried out and always be used in the same proportion. Thus a monetary unit spent in task A always involves an expenditure of x monetary units of the task B, y monetary units of the task C, etc. Indeed, if the proportions between consumption of resources remain stable whatever the works are, the tasks which forms the activity can be treated as a whole and be linked to the same unit allowing the allocation (Bouquin 2003, p. 80). “A section, to be homogeneous - tells us Rimailho (1936, p. 53) – is built in such a way that the various professional segments which make it up, are employed in theory in the same proportion for all the works carried out by the section, and that elements [of costs]... who are linked in each speciality are used themselves in the same proportion on all works “. In this paper, we will focus only in the specification of the function defining the activities and their cost drivers; the problem of the equiproportionnality will be the subject of a later study. 1.2 The risks of a bad specification An unsuited specification can be due to four types of error: • Using a too approximate coefficient of allocation to break down costs on the activity; • Forgetting significant cost drivers; • Having a non proportional relation between the cost of the activity and the volume of the possible cost driver; • Having an interdependence between the activities.
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1.2.1 Using a too approximate coefficient of allocation The use of such coefficients results in an error of measurement on the allocated cost. The impact of such an error on the cost of the products (or the objects of cost) is a function of the weight of the cost in the total cost to be determined. This error is generally taken into account by the practitioners in an intuitive way.
1.2.2 Forgetting significant cost drivers Let suppose that the model is well specified by using J activities. If the volume Pj of the cost driver j is the cause of the overhead cost D j , then the unit cost of the cost drivers is: π j = D j / Pj .
The costs of the activities are allocated on a proportional base to the volume used by the cost driver. Given Vij the volume used by the cost driver j for an object of cost i. With I objects of cost, the total volume total used of cost driver j is: I
Pj = ∑ Vij i =1
and the activities costs allocated to the object i are: J
J
D j × Vij
j =1
j =1
Pj
U i = ∑ π j × Vij = ∑
J
= ∑ D j × Vij
(1)
j =1
with Vij = Vij / Pj : the proportion of the volume of cost driver j used by the object i.
Given a responsibility centre that appears to consist of three activities allocating on five products (Table 1):
- Insert Table 1 -
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The allocation based on equation (1) gives the costs on Table 2:
- Insert Table 2 -
If the model is badly specified, then M activities are not taken into account. The cost of the forgotten activity Dm is included into the cost of the k activities J −M
taken into account according to the formula:
∑λ k =1
mk
× Dmk
With: •
J −M
∑λ k =1
mk
=1 ;
•
λ mk : % of Dm included into Dk ;
•
λ mk × Dmk : the amount of Dm included into Dk . The cost Dm is then allocated on the objects i, not according to the proportion Vim J −M
but according to the proportion
∑λ k =1
mk
Vik , and the difference of allocation on each
object is: ⎛
δ im = U i − U im = Dm × ⎜Vim − ⎝
J −M
∑λ k =1
mk
⎞ × Vik ⎟ ⎠
In the example, if the activity « Management of batches » is not considered, its cost of 450 200 is included by 50,8218 %, i.e. 228 800 into the cost of “Manual activity”, and by 49,1782 %, i.e. 221 400 into the cost of “Automatic activity” (Cf. Table 3).
- Insert Table 3 -
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If several activities are forgotten, then: M J −M
M
∑D m =1
m
= ∑ ∑ λ mk × Dmk m =1 k =1
and the difference of allocation on each object is: M
M
⎛
δ im = U i − ∑ U im = ∑ Dm × ⎜Vim − m =1
m =1
⎝
J −M
∑λ k =1
mk
⎞ × Vik ⎟ ⎠
In the example, if the “Machine” activity and the “Management of batches” activity are not taken into account, their cost of 647 800 and 450 200 are included into the cost of “Manual activity” with the coefficient λ mk = 1 (Cf. Table 4).
- Insert Table 4 -
On the example, the error in absolute value equals 59,22 % on average[(111,89 + 33,62 + 79,33 +7,77 + 63,29) / 5] when only one activity is selected. It falls to 25,64 % when 2 activities are selected, but the error on products 4 and 5 increases (from 7,77 % up to 11,45 % for product 4 and from 63,29 % up to 71,29 % for product 5).
1.2.3 Having a non proportional relation between cost and volume When a part of the overhead cost D j is independent from the volume of the possible cost driver (i.e. a part of the cost D j is fixed), then the cost of the activity j is:
D j = π j Pj + b j It then must be allocated only: U ivar = ∑ (D j − b j )× Vij J
j =1
If the total cost is allocated, then:
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⎛ J ⎞ ⎛ J ⎞ U i = U ivar + U i fixe = ⎜⎜ ∑ (D j − b j )× Vij ⎟⎟ + ⎜⎜ ∑ b j × Vij ⎟⎟ ⎝ j =1 ⎠ ⎝ j =1 ⎠
The fixed part is allocated in proportion to the volume of the cost driver, which is contrary to the observed relation. Let notice that, in a full cost calculation, when there are unused production capacities, the under use costs are assessed the same way.
1.2.4 Interdependence between cost drivers If the activities are interdependent, i.e. if the cost of an activity is not only explained by the volume of its cost drivers but also by the volume of the cost drivers of the other activities, then the use of a linear function becomes controversial (the use of such a function supposes the independence of the activities). The specification can take the form suggested by Longbrake (1962): J
J
∑D j =1
j
= b0 ∏ Pj
πj
j =1
This can also be described by: J
J
j =1
j =1
ln ∑ D j = ln b0 + ∑ π j ln Pj
Noreen and Soderstrom (1994), Banker, Potter and Schroeder (1995), Thenet (1995) use this type of functions to study the behaviors of costs of activities in varied business segments such as hospitals, electronics, manufacture of machine tools, automotive engineering or bank.
By analogy with the method of usual specification and by removing the constant term, the model would become:
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πj
D j = Pj But:
V
ln D j = π j ln Pj , and with Vij = Pj ij : I
πj
( )
D j = ∏ Vij i =1
This function makes it possible to better understand the behaviour of the activity cost (better statistical specification), but it cannot make the allocation, because it would require that the amounts of allocated costs on each object are summable.
- Insert Table 5 -
The product of the costs allocated to each product enables us to well specify the cost of the activity, but it is not possible with such a function to say which amounts of the various costs of activity will be distributed on each product.
This section has mentioned the importance of a well specified model to evaluate a reliable cost. Different methods have been suggested to optimize the nature and number of activities. However, these approaches must face the Datar and Gupta’s (1994) critics.
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The heuristic approaches and the Datar and Gupta’s critics
These analyses focus specifically on the way of carrying out the regroupings (Babad and Balachandran 1993, Homburg 2001). They do not deal with the problem of the possible interdependence between the activities. As indicated previously, if many studies use multiplicative functions to explain the behaviours of the indirect costs, these studies do not consider the charge: they seek the best statistical relation
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between the indirect costs and the cost drivers. The analyses are also little concerned with a cost insensitive with the volume of the cost driver. However Datar and Gupta (1994) show that a heuristic approach does not necessarily lead to a better knowledge of the costs (with more satisfactory segments), because it tries to improve the cost accounting system by being unaware of the impact of the modification on the mechanisms of compensation the errors leading to the total error of charge. They also show that the error of measurement due to the use of coefficient of allocation can grow as disintegration in activities increases. 2.1 Approaches aiming to reduce the number of cost drivers
Babad and Balanchandran (1993) just as Homburg (2001) make the assumption that a segmentation into activities gives a model well specified from an accounting perspective; they seek to reduce the number of cost drivers used in order not to complicate the representation by using heuristics of selection of the indicators to be eliminated. Indeed, if a high number is necessary to measure the use of the resources exactly, a system with fewer cost drivers is less expensive and easier to be understood by management (Merchant and Shields 1993), therefore more useful to make decisions. Babad and Balanchandran replace a cost driver by another already existing but having a worse correlation with the level of the costs in the activity concerned; Homburg carries out substitution by means of a combination of the remaining cost drivers. Whatever the solution suggested, the authors seek to reduce complexity, while maintaining an error rate acceptable in the allocation.
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With Babad and Balachandran (1993), the problem becomes to replace the cost driver m with another already identified. In that case, the cost Dm must be allocated by one of the J–1 remaining cost drivers. If the cost driver k is selected, its cost increases from Dk à Dk + Dm and its unit cost to:
π k' = π k +
Dm Pk
If U imk is the new activity cost allocated to the object i through cost driver k, the specification error on the object i equals to (Babad et Balachandran 1993, p. 566): mk ∆mk = Dm × (Vim − Vik ) i = Ui −Ui
Instead of using one of the other identified cost drivers, Homburg (2001) uses a combination of the remaining J–1 cost drivers. In that combination, each cost driver has a weight determining the proportion of Dm that it allocates. If, in the allocation of Dm, the weight λ mk ≥ 0 is allocated to the cost driver k, the new cost becomes Dk + ( λ mk × Dm) and the new unit cost is:
π k' = π k + λ mk
Dm Pk
The specification error on the new cost of activity U im allocated to the object i is: J
δ im = U i − U im = Dm × (Vim − ∑ λ mk × Vik ) k =1
with λ mm = 0 and
J
∑λ k =1
mk
=1
By replacing a cost driver by another, the selected cost driver is overweighed (one creates a new error). The attention is likely to be concentrated on this cost driver. With the use of a combination of cost drivers, focusing is reduced. The problem is to
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consider how the cost of the removed activity was allocated before on the other activities (see § 1.2). We come back to a traditional error of specification: forgetting an explanatory variable. Homburg then seeks a balance between a sufficiently precise cost and the information costs which it induces (between a specification sufficiently good but not too complex). The algorithm stands as follows: • Given a binary variable xm (= 1 if cost driver m is replaced with a combination of cost
drivers; = 0 if no replacement) for all cost drivers m = 1, …, J. • Let Cj the information cost of the cost driver j and C the limit tolerable total
information cost. • Let J the limit number of cost drivers that the company would like to keep.
The problem can be described by: ⎛ J I ⎞ min⎜ ∑∑ (δ im ) 2 × x m ⎟ ⎝ m =1 i =1 ⎠ under the constraint that: •
J
∑ C × (1 − x ) ≤ C m
m =1
m
J
• J − ∑ xm ≤ J m =1
•
J
∑λ k =1
mk
= x m for each m = 1, …, J
• 0 ≤ λ mk ≤ 1 − x k for each m,k = 1, …, J • x m ∈ [0;1] for each m = 1, …, J
1
2
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Both studies which we have just recalled postulate that the implementation of an Activity-Based-Costing leads to an optimal allocation. However this assertion is not inevitably true, as demonstrated by Datar and Gupta’s study (1994).
2.2 The impact of a better specification on the costs allocated to the cost objects in a heuristic approach
When an Activity-Based- Costing is implemented, the starting point is generally an accounting model badly specified (the segments and the causes of consumption of resources are considered to be not very satisfactory). One starts by modifying the part of the former system considered being worst and the analysis stops when it seems that the new system apprehends reality correctly. Datar and Gupta (1994) show however that this practice does not necessarily improve knowledge of the costs. The recourse to a new system using better cost drivers and a greater number of activities is based on the implicit assumption than these improvements will allow a more reliable calculation. However, their study reveals that it may be not true. The phenomena of compensation of the errors and the fact that the error on the allocation to the cost objects is unknown may lead to an opposite result.
Starting their demonstration with a simple case based on 2 activities, the authors show that if the cost model is initially bad specified, then the improvement o the cost accounting of one activity may lead to increase the overall error. That apriori paradox is due to the compensation effect that the initial partial error may have on the overall error.
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Datar and Gupta generalize that observation by measuring the allocation error on the cost of products by the following formula (k activities are selected instead of j): 1 I E ( K ) = ∑ Ei ( K ) I i =1
2
They suppose that the kth activity is segmented into several under activities, the others remaining unchanged. With E(K’) the error on the cost of products in the new system, it can be described by :
( )
E (K ) − E K ' =
(
1 I 1 I 1 I 2 2 E i (K ) − ∑ E i ( K ' ) 2 = ∑ E i (K ) − E i ( K ' ) 2 ∑ I i =1 I i =1 I i =1
)
After mathematical resolution, the authors show that he amount of the error depends
(
( ))
2 1 I Ei (k ) 2 − Ei k ' ∑ I i =1 first of the error on the cost of products due to the activity k:
But it also depends of the sum of covariances between the error of the cost of product due to the activity k and the errors on the cost of the products due to the other activities:
(
( ))
1 I 2 Ei (K − 1)E i (k ) − 2 Ei (K − 1)Ei k ' ∑ I i =1
A better specification can also have an effect on the errors of measurement due to the use of the coefficient of allocation. The allocation of the costs on a very
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aggregate activity using a coefficient of allocation can be relatively exact; the bases of the allocation can become more dubious when they relate to finer segmentation1. While postulating that a segmentation in activities inevitably makes it possible to find a more satisfactory explanation of the behaviours of costs, the heuristic approach pass beside the true questions; moreover, insofar as the error of allocation is unknown, their way of tackling the problem can sometimes lead to an increased error.
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Statistical approaches
Parallel to the heuristic approaches, statistical methodologies were developed. Their objective is to free themselves from an empirical procedure primarily based on the human judgement and to propose a formalized approach making it possible to select the causal factors by optimizing the cost of information. In other words, it deals with: • identifying the causal factors of the costs: correlation; • selecting the most significant factors: classification; • minimizing the costs of information: optimization.
Three approaches have been proposed: • Analytical hierarchy procedure; • Principal components analysis; • Genetic Algorithm.
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The authors recalls the problem, without really deepening it.
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3.1
The Analytic Hierarchy Process
The hierarchical analysis (or Analytic Hierarchy Process or AHP) is a technique of data processing used in situations of decision making between various cases, based on multiple decision criterion of a competing nature. The general procedure (Saaty 1980) consists in building a preference vector: w ABC = ( wi ,...., wn ) j
where the w j are the assigned preference to the n possible cost drivers. Schniederjans and Garvin (1997) thus applied a AHP to the problem of the cost driver selection decision problem. Given a decision maker who must select a cost driver among three (A, B or C). The process of selection uses four criteria, inspired of the rules suggested by Turney (1992): • correlation with cost; • reduction of the number of the cost drivers; • incentive of the user to the performance; • cost of measure. The decision makers are asked to explicit if they prefer cost driver A to cost driver B according to each criterion. The preferences are expressed on a scale rated from 1 ("equally preferred") to 9 ("extremely preferred"). A procedure of standard calculation ("right eigenvector") makes it possible to obtain the relative weights given by the decision makers to each cost driver (A, B or C). A matrix of the preferences is thus built for each pair (criterion/cost driver). An aggregation
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procedure of the calculated weights enables the users to classify the cost drivers. The application of method AHP thus tends to privilege cost driver A. The hierarchy analysis ensures obtaining a consistent overall judgement with the expressed individual judgements. It can be useful only once the problems of specification are solved and all necessary information for a good decision making has been gathered.
3.2 Principal Components Analysis
The Principal Components Analysis (or PCA) is a possible solution to deal with the problem of the interdependence of the activities. Indeed, a way of dealing with the problem is to consider that these interdependent activities can be statistically made up in independent business portfolios, each portfolio corresponding to a linear combination of activities. The principal components analysis may be used for that purpose. It consists in diagonalizing the matrix of variance-covariances of the function of specification. The diagonalisation is the operation which consists in transforming a square matrix into diagonal, i.e. all the values other than the values of the diagonal are equal to zero, but the sum of the values of the diagonal remains unchanged. The diagonalisation of the matrix of variance-covariances makes it possible to cancel covariances (to find business portfolios independent), while preserving the sum of the variances (known as eigenvalues of the initial matrix variance-covariances) identical.
Ittner, Larcker and Randall (1997) used a PCA to solve the following research question: are the possible cost drivers in a manufacturing company actually driven
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by cost hierarchy listed by Cooper and Kaplan (1991)? According to them, the main causes of costs are: • Unit level: the volume of units produced; • Batch level: the number of batches; • Product-sustaining: activities performed to support a product portfolio; • Facility- sustaining: activities performed to maintain a facility.
Ittner, Larcker and Randall (1997) studied 14 monthly physical indicators being able to be used as cost drivers, over 41 month period from July 1992 to November 1995. These indicators were obtained from a manufacturer of outdoor packs, producing four related product lines in a single facility.
The CPA enables the authors to know if the 14 operational measurements can be reduced in a more restricted number of cost drivers. By retaining only the variables whose coefficients of correlation are higher than 0.5, the authors show that measurements of this company can be explained by three independent factors representative of "units", of the "product", and the "batch", which corresponds to the first three categories of classification of Cooper and Kaplan (1991) (the fourth being here without object since it corresponds to a multisite localization whereas the case relates to a mono-site company). These three factors explain 80% of the original variance, which enables the authors to arrive at the relevance of the classification suggested by Cooper and Kaplan. The 14 cost drivers could thus be gathered in three great families which answers to the initial question research of Ittner and alii. Regarding our own concern, this study highlights that the possible cost drivers are
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more or less interdependent. For example, the total number of produced packing is strongly correlated with the factor "Unit", but is also correlated with the factor "Batch" and the factor "Product". If one wants to well specify the additive function, it is thus necessary to seek to eliminate to the maximum of covariances between the cost drivers. The CPA goes well in this direction. In our optics, one could also continue the authors’ reasoning while trying to find a cost driver which is the most representative of each three axis. In this way, one could reduce the number of cost drivers while fulfilling the condition of independence between the cost drivers.
3.3 Genetic Algorithms
The Genetic Algorithms belong to the connectionist approaches, which constitute a family of methods of selection, classification and optimization based on certain biomimetic processes (Lesage, Cottrell 2003). These methods, nonparametric and nonlinear, tend to obtain better results in problems where the interrelationships between the variables are a priori unknown. GA (genetic algorithm) is a algorithm of research based on the concept of "survival of the best" (Golberg 1989). The general methodology of a GA consists in seeking a solution optimized in a space of possible solutions, guided by a simulation of the mechanisms of reproduction, mutation and selection of the individual-solutions (Adeli and Hung 1995). The first step of GA consists to represent the problem in a compatible way with its methodology (here, to find the cost drivers which explains the best the total amount of the indirect costs), by using the concepts of "chromosomes" made up of "genes":
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• A chromosome is the set of the possible solution = the set of the variables describing the phenomena; • A gene is the value allotted to each variable, very frequently represented by a binary code. For example, a chromosome is made up of the whole set of the candidate-cost drivers (variable) possible, each gene having a value 1 or 0 according to whether the cost driver (variable) is selected or not: Cost driver A Chromosome 1
Cost driver Cost driver C B
0
1
Cost driver D
Cost driver E
0
1
1
The second stage consists in randomly generating by an initial population of chromosomes, representing the first generation of possible solutions. Each one of these chromosomes is then evaluated by a function of "fitness" (i.e. a function assessing the performance of the generated solution). This "fitness" function can be the cost of information, the percentage of explained variance, etc. Cost driver A Chromosome 1 0 Chromosome 2 1 Chromosome 3 0 Chromosome 4 1 (*: % explained variance by CPA factors)
B 1 0 0 1
C 1 1 0 0
D 0 1 0 1
E 1 0 1 0
Fitness* 50 40 20 60
The third step consists in selecting the best chromosomes according to their score of fitness, then to make them reproduce, in order to obtain a second generation more powerful than the first. This generation results from the first one by using the following operators: •
an operator of selection: he indicates which individual-parents will survive in the second generation (for example the 50 % most powerful): Cost driver
A
B
C
D
E
Fitness
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Chromosome 1 Chromosome 4
•
0 1
1 1
1 0
0 1
1 0
50 60
an operator of cross- over: it indicates which parts of the chromosome of the parents are retained to create that of the child (for example, the cross over is made at the 3rd gene: genes 1 to 3 of chromosome 1 and genes 4 and 5 of chromosome 4 are combined to give a new chromosome n°5 of second generation). Cost driver Chromosome 5 Chromosome 6
•
A 0 1
B 1 1
C 1 0
D 1 0
E 0 1
an operator of mutation : it indicates the range of modifications randomly made during the replication of the parents’ chromosomes (for instance a gene randomly changes its value, here gene 3 of chromosome 6) Cost driver Chromosome 5 Chromosome 6
A 0 1
B 1 1
C 1 1
D 1 0
E 0 1
We thus obtain the second generation population and their related fitness scoring: Cost driver Chromosome 1 Chromosome 4 Chromosome 5 Chromosome 6
A 0 1 0 1
B 1 1 1 1
C 1 0 1 1
D 0 1 1 0
E 1 0 0 1
Fitness 50 60 40 70
These steps are repeated until the algorithm converges towards a quasi optimal solution. Levitan and Gupta (1996) proposed the genetic algorithm as an alternative to the objectives functions developed by the heuristic approaches. Using data resulting from cases present in the literature, they conclude that the use of a genetic algorithm not only reduced the costs of information due to the selection of a lower number of cost drivers, but also obtained a better specification scoring, even in the presence of a smaller number of cost drivers. Kim and Han (2003) also suggest the use of the genetic algorithm for the selection of the cost drivers. But they
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supplement this phase of selection by the use of another category of connectionist methods, the neural network, in order to take into account the nonlinearity of the cost specification models.
Conclusion
To correctly specify a specification allowing the allocation of the overhead costs, four conditions are thus to be respected: • to use the least possible coefficients of allocation, • to avoid cross subsidizing by forgetting a significant cost driver, • to check the existence of a proportional relation between the cost of the activity and the volume of its cost driver, • to take care that the cost drivers are sufficiently independent between them.
The heuristic approaches are focused on the cross subsidizing question and the need for reducing the number of cost drivers not to have a too complex system, but the solutions which they propose make return back to the problem of subsidizing. Datar and Gupta show in addition that an empirical approach can contribute to the increase in the total error, because the activities are often interdependent and one does not know how the errors are compensated. They also insist on the fact that nothing is solved if the costs are segmented into finest by coefficient of allocation. The statistical approaches highlight that the principal components analysis and the genetic algorithm make it possible to eliminate the interdependence between the activities and to reduce the number of cost drivers. The hierarchy analysis, finally,
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has utility only at the final stage of the process: at the moment of the final compromise to be found between the various constraints.
These various observations bring us to the following conclusions: • Implementing a managerial accounting demands to understand that a cost come always from a rigorous construction. If it is not thouroughly enough studied, calculus have great risks to be arbitrary and without relevance for management. • If it is important to start from the firm’s objectives and value adding processes, the new system must consider “technico-accountant” point of view. That will enables the management to have meaningful categories for the technician and on which the accountant will be able to put the most possible direct costs. • The question would be then to relate each cost driver to an activity to which it refers and to check if, on these activities with "optimal cost drivers", one can relate all costs without too many approximations. It would finally be necessary to check the robustness of the analysis over time, by studying the stability and homogeneity of the resource consumption structure.
It seems to us that the algorithm of resolution of the whole problem remains to be proposed. The classical empirical approach does not lead to a better knowledge of the costs, and the heavy use of allocation rate (as influenced by numerous ERPs) does not contribute to a satisfactory solution. Indeed, either you “trace” the costs, and there is no need for allocating, or you allocate, which demands in that case a good specification of the cost function, and stable relations. At that level, large improvements remain to be made.
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References
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Table 1 – Data Product i
i i i i i
=1 =2 =3 =4 =5
cost Dj nature driver volume driver
% activity j used by product (Vij ) j = 1 manual j = 2 machine j = 3 batches activity activity activity 0,4918 0,1464 0,1091 0,1967 0,3658 0,2909 0,0246 0,2287 0,0546 0,2623 0,2439 0,3636 0,0246 0,0152 0,1818 427 000 Direct labor hour 30 500
647 800 machine hour 16 400
450 200 batch 275
Produced units
600 000 400 000 150 000 200 000 50 000 Total 1 525 000
29
Table 2 – Product i i =1 i =2 i =3 i =4 i =5 Total
Allocation of overhead costs with 3 activities
Allocated cost (Dj × Vij ) Activity Cost j =1 j =2 j =3 of Product (a) 209 998,60 94 837,92 49 116,82 353 953,34 83 990,90 236 965,24 130 963,18 451 919,32 10 504,20 148 151,86 24 580,92 183 236,98 112 002,10 157 998,42 163 692,72 433 693,24 10 504,20 9 846,56 81 846,36 102 197,12 1 525 000,00
30
Table 3 – Allocation of overhead costs with 2 activities Product i i =1 i =2 i =3 i =4 i =5 Total Product i i =1 i =2 i =3 i =4 i =5
Allocated cost j =1 j =2 322 522,44 127 250,88 128 995,86 317 953,36 16 132,68 198 786,04 172 016,34 211 997,88 16 132,68 13 211,84 655 800,00 869 200,00 Dm 450 200 450 200 450 200 450 200 450 200
Activity cost of prod (b) 449 773,32 446 949,22 214 918,72 384 014,22 29 344,52 1 525 000,00
Deviation Relative error (a) - (b) -95 819,98 -27,07% 4 970,10 1,10% -31 681,74 -17,29% 49 679,02 11,45% 72 852,60 71,29% 0,00
0,508218 Vi1 0,491782 Vi2 Vi3 0,1091 0,24994161 0,07199688 0,2909 0,09996648 0,17989386 0,0546 0,01250216 0,11247054 0,3636 0,13330558 0,11994563 0,1818 0,01250216 0,00747509
Deviation -95 819,9 4 970,1 -31 681,8 49 679,0 72 852,6
31
Table 4 – Allocation of overhead costs with one activity Product i i =1 i =2 i =3 i =4 i =5 Total
Product i i =1 i =2 i =3 i =4 i =5
Allocated cost Activity cost j =1 of product (c) 749 995,00 749 995,00 299 967,50 299 967,50 37 515,00 37 515,00 400 007,50 400 007,50 37 515,00 37 515,00 1 525 000,00 1 525 000,00
D3 450 200 450 200 450 200 450 200 450 200
D2 647 800 647 800 647 800 647 800 647 800
Vi3 0,1091 0,2909 0,0546 0,3636 0,1818
Deviation (a) - (c) -396 041,66 151 951,82 145 721,98 33 685,74 64 682,12 0,00
Vi1 0,4918 0,1967 0,0246 0,2623 0,0246
Vi2 0,1464 0,3658 0,2287 0,2439 0,0152
Relative deviation -111,89% 33,62% 79,53% 7,77% 63,29%
Deviation -396 041,66 151 951,82 145 721,98 33 685,74 64 682,12
32
Illustration of the cost of interdependent activities with a multiplicative function
Table 5 –
j = 1 manual j = 2 machine j = 3 batches activity activity activity 160,46439 4,14050 1,84557 7,62187 34,81688 5,12391 1,28918 9,20311 1,35890 15,00486 10,66597 7,70799 1,28918 1,15895 2,77633 30 500 16 400 275 1,255868 1,378803 2,317603
P j V1j P j V2j P j V3j P j V4j P j V5j Vij ΠP i
πj
(P j V1j ) π j
587,54946
7,09243
4,13796
(P j V2j ) π j
12,80870
133,60573
44,11392
1,37565
21,33421
2,03552
(P j V4j ) π j
29,98204
26,14631
113,65230
1,37565
1,22556
10,66078
427 000
647 800
450 200
(P j V3j ) π j (P j V5j ) π j
Π(P j
Vij
)πj
