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					INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING
International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
6979(Print), ISSN 0976 – 6987(Online) Volume 3, Issue 1, January - June (2012), © IAEME
               RESEARCH AND DEVELOPMENT (IJIERD)
ISSN 0976 – 6979 (Print)
ISSN 0976 – 6987 (Online)
Volume 3, Issue 1, January- June (2012), pp. 30-42
                                                                         IJIERD
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      COMPATIBILITY BETWEEN THE MIXBC -MIX BASED COSTING -
              METHOD – AND COSTING PHILOSOPHIES


                             LEANDRO TORRES DI GREGORIO

 M.D., Graduate Program - Civil Engineering –Fluminense Federal University, Ph. D. Student,
  leandrogregorio@ig.com.br.Address: Rua Primeiro de Janeiro, 43, Vila Madalena, Belford
                             Roxo, RJ, Brazil, CEP 26130-320

                          CARLOS ALBERTO PEREIRA SOARES
    Ph.D., Graduate Program - Civil Engineering –Fluminense Federal University, Associate
                                          Professor

                               ORLANDO CELSO LONGO
    Ph.D., Graduate Program - Civil Engineering –Fluminense Federal University, Associate
                                          Professor

                            WAINER DA SILVEIRA E SILVA
    Ph.D., Graduate Program - Civil Engineering –Fluminense Federal University, Professor

ABSTRACT

After a bibliographic research on costing methods / philosophies, and an analytical deduction of
MIXBC- Mix Based Costing method, we sought to verify the compatibility of this methodwith
the "Traditional Cost Accounting”, "Variable" and "Full" costing philosophies.This was
conducted through an analytical approach in which the results of MIXBC were applied to the
income statements of each costing philosophy. Compatibility with all situations was
demonstrated. The analyses of different production scenarios show that the MIXBC is a method
that allows the distribution of costs and indirect costs to products without the subjectivity and
uncertainty typical of traditional apportionment.

Keywords
Cost management. Cost accounting. MIXBC - Mix Based Costing. Apportionment-Free Costing.




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International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
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1 INTRODUCTION
        The aim of this paper is to demonstrate the compatibility of the Mix Based Costing
(MIXCB) method with the “Traditional Cost Accounting ”, “Variable”, and “Full” costing
philosophies.
        The major drawback of all costing methods is that they include subjective and arbitrary
elements in the determination of production costs when dealing with the apportionment of
indirect costs. These uncertainties may become more significant according to the costing
philosophy adopted. Not only that, but also the only philosophy legally accepted in Brazil is
Traditional Cost Accounting, which is not always the most adequate for managerial decision
making. Hence the need for a method that may be coherently applied to all costing philosophies
presented.
        It is our aim to demonstrate that the Mix Based Costing (MIXBC) method is compatible
with all the costing philosophies mentioned above, thus making it possible to significantly reduce
arbitrary and subjective elements caused by the apportionment of indirect costs not only in
financial accounting, but also in managerial accounting.
        The methodology adopted was bibliographical research, followed by an analytical
approach in which the results of the MIXBC were applied to the income statementtypicalof each
costing philosophy.
        The advantages resulting from this work include the improved quality of accounting
information in general, not only for financial but also managerial purposes, thus contributing to
more consistent decision making.

2 COST ACCOUNTING AND PRODUCTION STRATEGIES

        MARTINS (2010) explains that costing means cost appropriation. To this it can be added
that a costing system can be regarded as the whole structure necessary to accomplish the task,
including the philosophy and the costing method. In this sense, the costing system can be
considered as defining and applying a costing philosophy / method to a particular organizational
reality. This encompassesthe structuring of the measurementsnecessary to the production
process, the definition of responsibilities, data collection, data treatment, recording of data
generated, the decision of whether or not to use computer systems, etc.
        In this context, Cost Accountingplays an important role, and whenused witha costing
system that is both efficient and coherent with the characteristics of the organizationit provides
an understanding of product profitability, and of possible ways to reduce costs.BEUREN et al
(2003) state that cost information may be useful in cost structure reduction, expansion of
production capacity, launching of new products or calculation of sales price.
        The basic outline for Cost Accounting is made up of the following steps, adapted from
MARTINS (2010). The greatest variation among the methods is found in step 3 (or in its
absence).
        STEP 1: Separation of costs and expenses;
        STEP 2: Appropriation of direct costs;
        STEP 3: Appropriation (apportionment) of indirect costs;
        STEP 4: Record keeping of costs.
3 DISTINCTION BETWEEN PHILOSOPHIES AND COSTING METHODS

       A distinction between philosophies and costing methods is proposed. This distinction is
simple: the costing philosophies (or principles) are made up of ways of recording data in order to
reach a certain result, whereas costing methods are made up of ways of generating and applying
data according to a certain philosophy. For example, costing philosophy is responsible for


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International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
6979(Print), ISSN 0976 – 6987(Online) Volume 3, Issue 1, January - June (2012), © IAEME

determining whether indirect costs should be directly incorporated to the products (thus
pertaining indirectly to stock and being registered when the income is obtained) or whether they
should be treated as expenses (thus pertaining directly to the results, with no relation whatsoever
to stock), or whether expenses and indirect costs should be totally aggregated to products,
therefore not being treated globally. It is clear that the accounting treatment of the information is
different in each case. On the other hand, costing methods are responsible for decisions on how
to obtain indirect costs, such as, for example, those related to ways of performing cost tracking
or apportionment. Costing methods, then, need to be set in a costing philosophy in order to reach
a certain result.
        Examples of cost philosophies include Traditional Cost Accounting, direct or variable
costing, and full costing. As regards costing methods, examples include standard cost,
departmentalization costing, production effort unit method, RKW, process and job-order costing,
target method, and Activity-Based Costing (ABC).

4 COSTING PHILOSOPHIES

“Traditional Cost Accounting” philosophy

         This philosophy consists in the appropriation of all production costs to the
productsproduced, and only those of production (MARTINS, 2010). Traditional Cost
Accounting philosophy is not concerned about the distinction between fixed and variable costs.
Its basic premise is the separation ofcosts from expenses. Costs are appropriated to products so
that when these are sold, costs are comparedwith the sales generated, and expenses are recorded
directly in the resultof the period (BEUREN et al, 2003). HORNGREN et al (2004) state that
[…]Traditional Cost Accounting is the stock costing method, in which all manufacturing costs,
variable and fixed, are considered countable costs. That is, stock absorbs all manufacturing costs.
It is the only method accepted for tax purposes in Brazil.
         AZEVEDO et al (2006) point out that Traditional Cost Accounting is useful in the
evaluation of business stock and in aiding price decision taking for products and services,
provided the part apportioned be small. For managerial decision taking, however,
complementary information is necessary. SILVA (1998) mentions that Traditional Cost
Accounting cannot be used indiscriminately, without taking into consideration problemsthat may
be entailed, particularly its incentive to overproduction.
         The basic outline for DRE (Income Statement) for managerial or tax purposes is:

Sales
(-) Cost of Products Sold (direct and indirect distributed)
(=) Gross Profit
(-) Expenses
(=) Result before Income Tax

            Table 1 Typical DRE for “Traditional Cost Accounting” Philosophy
                               Source: MARTINS (2010)

“Variable” or “Direct” costing philosophy

        ANDRADE et al (2004) suggest that the variable costing system tries to reduce the
distortion present in the apportionment required by the Traditional Cost Accounting system: “[...]
In the Traditional Cost Accounting system, fixed costs are apportioned to products and/or

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International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
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services, whereas in variable costing these costs are treated as expenses and as such are recorded
directly in the result.
         MARTINS (2010) stresses that, although all variable costs are by nature always direct, it
does not always compensate to track and measure them individually according to product; this is
the reason why some are treated as indirect. MARTINS(2010) also presents the concept of Unit
Contribution Margin, “[...] which is the difference between sales price and Variable Cost for
each product; it is the value that each unit effectively brings to the business, the difference
between its sales and the cost it actually represented and what is unmistakably imputable to it
[...]”, and which “[...] multiplied by the amount sold and added to the remaining (products),
makes up the a Total Contribution Margin”.
         A little further MARTINS (2010) points out that “[...] the concept of Contribution Margin
is somewhatwider than the concept previously mentioned, since it is the difference between the
Sales Revenue and the sum of Costs and Variable Expenses [...]” (among which the main are
sales expenses, such as commissions), and not only between revenue and variable costs.
MARTINS (2010) also reminds us that the revenue to be considered must be netrevenue, that is,
after the deduction of taxes leviedon it, and that despite the fact that Variable Expenses are used
to calculate the Contribution Margin; they are not aggregated to the product for stock purposes.
The best solution is to treat them as a reduction in the sales price, which does not alter in the
least the calculation of the Margin, but it makes it easier to solve the problem of what to quantify
as product cost.
         Variable Cost goes against accounting principles, particularly that of Sales Earning,
which determines accounting recognition of the result (profit or loss), only when sales are
actually earned (in Variable costing, fixed costs of the products are recorded in that period and
not when they are sold). This philosophy, then, can only be used for managerial purposes.
         The basic outline for DRE (Income Statement) for managerial purposes is:


Sales
(-) Taxes levied on Sales Revenue and Variable Expenses
(=) Net Sales
(-) Cost of Products Sold (variable direct and variable indirect costs)
 (=) Contribution Margin
(-) Fixed Expenses and Fixed Costs
(=) Result

            Table 2 Typical DRE for “Variable” or “Direct” Costing Philosophy
                               Source: MARTINS (2010)

        In case there are fixed costs that may be identified with a product or a group of products,
these are called Identified Fixed Costs, and the remaining, Non-Identified Fixed Costs. When
these concepts are inserted in the DRE, the Contribution Margin may be presented in a sequence,
as follows:




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International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
6979(Print), ISSN 0976 – 6987(Online) Volume 3, Issue 1, January - June (2012), © IAEME


Sales
(-) Taxes levied on Sales Revenue and Variable Expenses
(=) Net Sales Revenue
(-) Cost of Products Sold (variable direct and variable indirect costs)
(=) 1st Contribution Margin
(-) Identified Fixed Costs
(=) 2nd Contribution Margin
(-) Non-Identified Fixed Costs
(=) Result

  Table 3 Typical DRE for “Variable” Costing using Contribution Margin in a sequence
                              Source: MARTINS (2010)

“Full” Costing philosophy

       Santos (apud BEUREN et al, 2003) describes full costing philosophy as “characterized
by the appropriation of all costs and expenses to manufactured products. These costs and
expenses are direct and indirect costs, fixed and variable costs, as well as those related to
commercialization, distribution, general administration, etc. Because this philosophy goes
against accounting principles, it can only be used for managerial purposes”.
       The basic outline for DRE (Income Statement) for managerial purposes is:


Sales
(-) Cost of Products Sold (direct, indirect and expenses)
(=) Result (numerically equal to gross profit)

                     Table 4 Typical DRE for “Full” Costing Philosophy
                                      Source: authors

5 MIX BASED COSTING METHOD

What it is

        MIX Based Costing is a costing method that allows the reduction of uncertainties caused
by arbitrary apportionment of indirect costs and expenses in product cost.
        The MIX-Based Costing method was built on the analyses of the product mix (rather than
on that of products individually), and also on the hypothesis that the absence of a certain product
in the mix provides clues as to the degree of utilization of shared costs (costs shared by one or
more products, usually indirect) by that particular absent product.
        MIXBC allows costs and indirect shared expenses -- which cannot be actually separated
for each product -- to be treated in a mathematical and coherent way. This contrasts with the
other methods, which usually apportion or track expenses. In this sense, it is an apportionment-
free costing system, since the uncertainties are calculated by a process of cost inference, based
on the exclusive production (only the product analyzed is produced) and excludent production
(only the product analyzed is not produced) scenarios.




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The distribution of fixed indirect costs

      Let us examine the hypothetical case of a business that produces three products
(exemplified as Alpha, Beta, Gamma), which have total fixed costs (CF) and fixed expenses
(DF).




    Figure 1 Graphic representation of the universe of fixed costs for a business which
                      produces products Alpha, Beta, and Gamma
                                    Source: authors

       Thus, the total fixed cost (CF) of the Product Mix (Alpha, Beta, and Gamma) can be
written as:

                                                                                 (Eq. v)

       Considering the situation in which product Alpha is discontinued by the business and its
production is not substituted by any other product, the new distribution of fixed costs would be:




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International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
                                               3,                           ),
6979(Print), ISSN 0976 – 6987(Online) Volume 3 Issue 1, January - June (2012), © IAEME




    Figure 2 Graphic representation of the universe of fixed costs for a business which
                         produces products Beta, and Gamma
                                    Source: authors

           e
        The total fixed cost for the new p          ix
                                           product mix (only Beta and Gamma, without the
participation of Alpha) can be written as:

                       -                                                (Eq. vi)

        Substituting Eq. vi in Eq. v, we find:

                                                 -          (Eq. vii)

        This can also be considered as the Minimum Fixed Cost that can be ascribed to product
Alpha               ):

                                                      (Eq. ix)

       On the other hand, if there were only product Alpha (without the other mix products), the
fixed costs related to it would be maximum and would be calculated by:

                                                                        (Eq. x)

        Substituting Eq. ix in Eq. x, we find:

                                       -                                    (Eq. xi)




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International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
6979(Print), ISSN 0976 – 6987(Online) Volume 3, Issue 1, January - June (2012), © IAEME

        In which the term                                  could be considered as the range of
variation of fixed costs for product Alpha and it represents the extent of use of the mix structure
by product Alpha, or the extent to which product Alpha depends on the mix structure.
        The fixed cost of the structure shared by the product mix can be defined by:

                                O                                                                           (Eq. xviii)

          Applying the same reasoning and substituting in Eq. v, we find:

                                                                                                              O            (Eq. xix)

       That is, the fixed cost of the structure shared by the mix can be determined by subtracting
from the present situation the minimum fixed costs for each product (determined by the scenarios
of absence of each one, sequentially).

      O             -       -            -           )-             -                -            )-           -      -         )      (Eq. xx)

          Thus,

                   O            -                          -                             -             -2                 (Eq. xx-a)

          Generalizing for a mix of “N” products, we find:

                        O           -1                -2       …                     -       -    -1)                     (Eq. xxi)

       As previously seen, the ranges of fixed costs for each product ( i ) show the utilization
of the mix for each product, respectively. Thus, to define the degree of use of the Mix for
product I, based on costs (UC%), we find:

                                        U %i                   i
                                                                   x100                          (Eq. xxii)
                                                           O


       Thus, in order to define the participation of each product in the Fixed Cost of the Mix
(the amount each of them absorbs from the mix, when compared with the remaining products), it
is necessary to normalize the UC% parameter, obtaining what was called FACTORS OF COST
PARTICIPATION (FPCs), that is:

                                                     U %i                    i
                                             i                                                    (Eq. xxvi)
                                                     1 U %j         1            j


      Thus, the total fixed cost for a particular product in terms of its shared structure in the
mix can be written as:

                                    i            i                 i*            O                     (Eq. xxx)




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International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
6979(Print), ISSN 0976 – 6987(Online) Volume 3, Issue 1, January - June (2012), © IAEME

Checking coherence

       The situations in which the model loses its coherence may be due to misevaluation by the
cost analyst, or due to a degree of coherence that is not easily perceived by the analyst, thus
inducing to error.
    • Individual conditions
           o In the exclusive production scenario for product “i”, resources should notexceed
               amounts available in the mix;
           o In the excludent production scenarios for product “i”, resources should not exceed
               the amount available in the mix;
           o In the exclusive and excludent scenarios for product “i”, resources should not be
               lesser than the amount available in the mix;
           o For a certain product, the maximum resources shouldbe greater than the minimum
               resources defined from the mix;
    • Collective condition: Resources shared in the production mix should not be negative.

THE MIXBC METHOD TO COSTING PHILOSOPHIES
MIXBC applied to Traditional Cost Accounting philosophy
        MIXBC also allows the Traditional Cost Accounting philosophy – the only one to be
legally accepted in Brazil -- to be used more consistently. Thus, we believe we have found a way
of improving managerial decisions within the philosophy acknowledged by the legislation,
aligning purposes and optimizing resources.
        Returning to the DRE model typical of the ‘Traditional Cost Accounting philosophy:


     DRE /                ALPHA               BETA             GAMMA                TOTAL
  PRODUCTS
   Net Sales
    Revenue          Q        *          Q        *       Q        *                    Qi *            i

     (-)Cost of
  Products Sold
 (variable direct
                     −Q           *      -Q       *       -Q       *            -        Qi *           i
costs and variable
   indirect costs
         part)
     (-) Cost of
  Products Sold           -                   -                -                    -           i
 (fixed cost part)
  = Gross Profit
                                                                                                    i

(-) FixedExpenses                                                                    (-
                                                                               )Fixedexpenses
    (=) Profit
beforeIncomeTax                                                                     (=) LAIR

   Table 5 Typical DRE model for Traditional Cost AccountingPhilosophy, applying the
                                   MIXBC method
                                   Source: authors

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International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
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        Note that the “Gross Profit” parameter characteristic of each product makes it possible to
determine more safely the product that shows best result, which is extremely useful for
managerial decisions. It is important to point out that the gross profit of a certain product is
determined by the unit contribution margin ( i - i ), by the amount produced (Qi ) by the fixed
costs exclusive of the product     i    ) and by the participation factor of the product in the mix
structure ( i * O ). It is therefore a characteristic the product shares with others in the mix
(by means of the parameter        O ) rather than a characteristic of the product itself. This is
reasonable in a shared structure.

MIXBC applied to the “Variable” costing philosophy

       The DRE typical of the “Variable Costing” philosophy would be:


     DRE /                 ALPHA                BETA             GAMMA                  TOTAL
   PRODUCTS
Net Sales Revenue     Q        *           Q        *       Q        *                      Qi *        i
(-) Cost of Products
    Sold (variable
   direct costs and  -Q        *           -Q        *      -Q       *              -        Qi *       i
  variable indirect
        costs)
        (=) 1st
ContributionMargin             1                        1            1                              1i

  (-) FixedCosts           -                    -                -                      -           i
      (=) 2nd
                               2                        2            2                              2i
ContributionMargin
                                                                                         (-
(-) FixedExpenses
                                                                                  )FixedExpenses
     (=) Result                                                                      (=) Result

   Table 6 Typical DRE model for “Variable Costing” Philosophy, applying the MIXBC
                                       method
                                   Source: authors

MIXBC applied to the “Full” costing philosophy

Apportionment of fixed expenses
         Fixed expenses can also be analyzed in the light of MIXCB, that is, by applying the same
sequence of reasoning used to solve the problem of fixed costs.
         In managerial terms, applying MIXBC to fixed expenses is extremely reasonable, since in
a business, every expenditure (cost or expense) exists (or should exist) to somehow make
possible the production and commercialization of one or more products. From this point of view,
it is reasonable to associate expenses to products, which is possible with the MIXCB method.



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International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
6979(Print), ISSN 0976 – 6987(Online) Volume 3, Issue 1, January - June (2012), © IAEME

       Applying the MIXCB to fixed expenses (DFs), the following equations for product “i” of
a Mix of “N” products areto be found:

                                   D       i            D             -D    MIX-"i"               (Eq. xxxiv)

                                                    D   i              D    i              (Eq. xxxv)

                                           D    i       D   i          -D       i                (Eq. xxxvi)

            D     O       D           -1       D            -2    … D                  -   -    -1)D               (Eq. xxxvii)

       Likewise, the degree of use of the structure (U%) and the participation factor (FP) must
be calculated using the parameter “Fixed Expenses”, expressed as:

                                                                 D i
                                       UD%i                 D
                                                                       x100                    (Eq. xxxviii)
                                                                 O


                                                        UD%i                    D i
                                               Di                                                (Eq. xxxix)
                                                        1   UD%j            1    D j


                           D i D i          Di *D O          (Eq. xl)
       It must be pointed out that the MIXBC could have been applied to the fixed costs + fixed
expenses set (and in that case participation factors corresponding to the whole set would be
obtained, FPCDs) or it could have been applied separately to the fixed costs (with cost-specific
FPs, FPCs) and then to the fixed expenses (with expense-specific FPs, FPDs).
       Thus, the DRE typical of the “Full Costing” philosophy would be:

     DRE /                    ALPHA                                     BETA                           GAMMA                    TOTAL
 PRODUCTS
    Net Sales
                      Q            *                              Q         *                     Q            *                    Qi *        i
    Revenue
   (-) Cost of
 Product Sold
(variable direct
                      -Q              *                          -Q             *                 -Q           *            -        Qi *       i
    costs and
variable indirect
      costs)
 (-) FixedCosts               -                                        -                               -                        -           i
      (-)
                              -D                                       -D                              -D                       -     D     i
 FixedExpenses
   (=) Result                     R                                         R                              R                               Ri

 Table 7 Typical DRE model for “Full Costing” Philosophy, applying the MIXBC method
                                   Source: authors




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International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
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6 CONCLUSIONS

        The MIX based costing is a method that allows product cost to be obtained from a
sequence of analyses performed on the production mix. Its application is particularly useful for
the treatment of indirect costs, in the hypothesis that the absence of a particular product in the
MIX provides clues as to the degree of utilization of shared costs (costs that are common to one
or more products, and that are usually indirect) for the absent product.
        The major advantage of the method may lie in allowing costs and indirect shared
expenses -- which cannot be actually separated for each product -- to be treated in a
mathematical and coherent way. This contrasts with the other methods, which usually apportion
or track expenses. In this sense, it is an apportionment-free costing system, since the
uncertainties are calculated by a process of cost inference, based on the exclusive production
(only the product analyzed is produced) and excludent production (only the product analyzed is
not produced) scenarios.
        It should be pointed out that MIXBC is a method strongly dependent on the experience
and on the systemic vision of cost analysts, who should have an in-depth knowledge of the
reality of the business operations. The good foresight of these professionals shall be responsible
for building coherent scenarios of resource consumption, and the application of the method shall
lead to the safe completion of the cost distribution task and to results free of arbitrary
apportionments. It is recommended that the scenario analyses be performed by a
multidisciplinary team, comprising professionals from human resources, production and
administrative managerial level.
        It was noticed that MIXBCis perfectly compatible with the Traditional Cost Accounting
philosophy. The method may be applied together with this philosophy in order to obtain the
typical income statements,in which the “gross profit” parameter is the most adequate to evaluate
the results of each product.
        It was also observed that MIXBC is perfectly compatible with the “Variable” costing
philosophy and it may be applied together with this philosophy in order to obtain the typical
income statements, in which the “contribution margin” parameter is the most adequate to
evaluate the results of each product.
        It is important to notice that MIXBCcan also be applied to expenses, being perfectly
compatible with the “Full” costing philosophy and it may be applied together with this
philosophy so as toobtain the typical income statements, in which the results for each product
can be directly obtained. The “Full” costing philosophy is believed to be the most informative in
terms of managerial decisions.
        In general terms, it was observed that MIXBC is compatible with the three costing
philosophies mentioned above. It is therefore a valuable tool in the distribution of costs to the
products. This method reduces the arbitrariness caused by apportionment, contributing to
improve informationnot only in financial accounting but also in managerial accounting, allowing
the elaboration of more consistent and more profitable production strategies.




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International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
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REFERENCES

   1. ANDRADE, Nilton de Aquino, BATISTA, Daniel Gerhard, SOUSA, Cleber Batista de,
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   2. AZEVEDO, Ana P. F., GOUVÊA, Josiane B., OLIVEIRA, Ualison R., “Custeio por
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   4. HORNGREN, Charles T., FOSTER, George, DATAR, Srikant M., “Contabilidade de
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   5. MARTINS, Eliseu, “Contabilidade de Custos”,São Paulo, SP: Ed. Atlas, 2010.

   6. SILVA, César A. T., “Utilização do Custeio por Absorção para Fins Gerenciais”, Revista
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      article/view/98/pdf_6>. Accessed on May 20 2011.




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