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Caderno de Estudos

Print version ISSN 1413-9251

Cad. estud.  no.24 São Paulo July/Dec. 2000 



Finishing level and equivalent production units: an empirical and conceptual approach(*)



Reinaldo GuerreiroI; Edgard Bruno Cornachione JrII; Armando CatelliIII

IProfessor Titular e Chefe do Departamento de Contabilidade e Atuária da FEA/USP, Pesquisador da FIPECAFI/FEA/USP
IIProfessor Doutor do Departamento de Contabilidade e Atuária da FEA/USP, Pesquisador da FIPECAFI/FEA/USP
IIIProfessor Doutor do Departamento de Contabilidade e Atuária da FEA/USP, Pesquisador da FIPECAFI/FEA/USP




This paper focuses on how to determine the finishing level used in calculating the equivalent production units in the continuous process costing system. The hypothesis was established that cost accounting theory does not offer an objective solution for the calculation of the finishing level and, consequently, enterprises do not adopt the fundamental theoretical concepts about the inventory evaluation of goods in process and finished goods in continuous production industries. A collection of classic cost accounting works was revised1 , which revealed that there does not exist any objective indication about how to measure the finishing level. In this paper, a method for finishing level measurement is presented and an exploratory study is developed, which aims at obtaining practical knowledge about the reality of the enterprises in relation to the subject discussed in this paper. The bibliographical and empirical researches indicate the validity of the hypothesis established.

Key Words: Equivalent production units, finishing level, continuous production, activity-based production, cost accumulation and inventory valuation.




Almost all papers and books about cost accounting discuss the "process costing" issue. In our opinion, "process costing accumulation system" is a more appropriate definition and denomination. When this subject is studied, authors generally agree on the definition of the basic procedures that involve the quantification of finished production units, the conversion of goods-in-process units into finished units equivalents by means of a finishing percentage, the computation of unit cost and the evaluation of production and goods-in-process inventories. In the heart of these procedures generally accepted by cost accounting authors, the necessity of using the finishing level concept is noted, without which it is impossible to calculate the equivalent production units.

This research was realized based on a selected collection of classic works by renowned cost accounting authors, which revealed that the authors analyzed do not indicate a method for calculating the finishing level. From a conceptual point of view, this aspect represents an exciting gap in cost accounting that causes the companies operating by the continuous process not to use the theoretical procedures of the cost accounting authors in practice. This hypothesis forms the foundation of this paper, namely, that by the non-existence of an objective method for computing the finishing level, companies do not use the basic concepts pointed out by theory.This paper contains a bibliographic revision of the specific issue discussed, proposes a finishing level computation method and develops an exploratory study, aimed at proving the fundamental hypotheses and analyzing what enterprises are doing in practical terms, considering the non-existence of a theoretical solution to the problem presented.



1. Single product manufacturing plant

Consider as given the manufacturing plant of a single homogeneous product (process) where the typical process costing accumulation system is characterized on the level of the cost system. Process cost accumulation cases can be observed in practice, in a typical production environment of cost accumulation by job order, that is, where different products are manufactured simultaneously at the same manufacturing plant. This procedure is realized through use of standard cost and aims at reducing the information system processing expenses, mainly in companies where products are standardized and frequently manufactured in short intervals.This study does not consider this kind of situation.

2. Finishing level

The transformation of units in process into finished unit equivalents is realized through the finishing level concept. In the case of raw materials cost, which is totally introduced in the beginning of the production process, the finishing level is 100%. Every time the raw materials and other resources are joined throughout the production process, the finishing level should be estimated. A very important aspect to be observed is that the finished level must have an economical meaning and not only a physical one.

The finishing level must represent how much a unit in process has received of the cost load that would be needed to start and finish it completely.

3. Equivalent production units

How much of a totally finished good is represented by a unit in process? The answer to this question is given through the finishing level percentage of the unit in process. By using the finishing level percentage, it is possible to make a comparison between the units in process and these same units, considering them as being totally finished. Consequently, in a determined moment the amount of equivalent production units corresponds to the amount of units in process converted into finished units through the use of a defined finishing level.

4.The standard cost is the correct cost

Every decision process involving the product cost must use the standard cost. The actual cost, whose information is extremely important, is simply the cost that happened. HORNGREN (1972, p. 187) defends the use of the standard cost as the basis for performance evaluation and contests the use of historical data for this purpose:

"Merely to compare this month's costs with last month's or with those of the corresponding month of last year is likely to cloud the inefficiencies that may already be reflected in prior costs. Moreover, changes in technology, equipment, and methods limit the validity of comparisons with the past".

In our opinion, the standard cost is the target cost, that is, it is the cost that should happen, it is the right cost, the one that better reflects the economic value of the resources consumption to manufacture one product unit, it is the fair cost, namely, the one that must be used as the basis for performance evaluation.




n = period of time

ct = total production cost of period

qf = finished product quantity of period

qp = end-of-period quantity of goods in process

qe = end-of-period quantity of goods in process expressed as finished unit equivalents

cp = product unit cost in period

ga = finishing level

Considering the following data as occurring in a company that adopts the continuous production system for a single product in a specific period:



The basic question is: how much is the product unit cost? In this case the unit cost (cp) can easily be calculated dividing ct by qf. Consequently:



Allowing for a second subsequent period, in which:



In this case, the computation of cp is not so obvious. Would the total costs (ct) be divided by all units in process (qf + qp)? Or only by the finished units (qf)? Both alternatives would be wrong. In the first case, that is, dividing ct by (qf + qp), both the finished units and the different units in process would have the same unit cost. In the second case, that is, dividing ct only by the finished units (qf) the entire cost would only be allocated to the finished units, leaving the units in process (qp) at zero cost.

The cost accounting authors and researchers have solved this question on the basis of the following fundamental idea: the transformation of the units in process at the end of the period (qp) into finished unit equivalents (qe), by using the finishing level (ga). In this way, it is possible to sum the finished units (qf) and the units in process units now expressed as finished unit equivalents (qe) and consequently, to arrive at a correct amount for calculating the unit cost.

Based on the data presented, we have:



The fundamental question is: How should the finishing level be calculated?



Calculating the finishing level is of primary importance since it is impossible to calculate the equivalent production units without the finishing level percentage of the units in process and therefore, since the computation ofthe unit cost becomes impracticable as the basis for the product inventories evaluation and the determination of profit. Consequently, whichever theoretical discussion of this subject that is presented in cost accounting literature becomes useless since companies cannot adopt a methodology in practice which does not make available any objective operational procedures.



The hypothesis that forms the foundation of this paper is that cost accounting theory does not offer an objective solution to the computation of the finishing level, which must be used for determining the equivalent production units in the companies that use continuous process systems for the production of homogeneous products. In this way, the enterprises do not adopt the fundamental concepts defined by theory in relation to the evaluation of units in process and finished products inventories in continuous production industries.



This paper was developed on the basis of two types of methodological support: on the one hand, the technical literature was revised, focusing on classic cost accounting bibliography; on the other hand, an exploratory research was realized with a selected group of 50 enterprises installed in Brazil with annual revenues above US$ 100 million (fiscal year of 1999).To develop this research, the database of FIPECAFI'- Foundation for Accounting and Financial Research was used. Consequently, due to the nature of the research developed, there is no intention of generalizing the results obtained.



Through the literature research, we realized that the question related to the finishing level computation remains unanswered. Cost accounting authors have not dealt with this specific question in a convincing way, that is, most of them propose the use of the finishing level but do not indicate an objective methodology to calculate it.

Li (1966, p.107) claims that the finishing level for the labor and manufacturing overhead (indirect costs) must always be 50%, unless there are indications to the contrary:

"...for units that remain in the process, unless there are indications to the contrary, it may be assumed that only 50% of labor and manufacturing overhead has been added".

This author justifies his proposition in the following way:

"...this assumption is based upon the following line of reasoning. For an enterprise using continuous processing techniques, the amount of labor and manufacturing overhead added to materials increases at a fixed increment. At any given moment, the amount of labor and manufacturing overhead added ranges from 1% (for the item just introduced into the process) to 99% (for the item just short of transfer to the subsequent process).Together with all other items in the process, they form an arithmetic series (1%, 2%, 3%,...., 97%, 98%, 99%) for an arithmetic series (1%, 2%, 3%,...., 97%, 98%, 99%) for an average completion rate of 50%. This is known as the 50% - completion assumption".

We believe that the author's justification represents much more of a value judgment than of a scientific proof and we agree with HORNGREN's (1972, p.610) opinion:

"The assumption that all conversion costs are incurred uniformly in proportion to the degree of product completion is difficult to justify on theoretical grounds".

BLACK & EDWARDS (1979, p.537) focuses on the equivalent production unit (EPU) saying that:

"...if either of these assumptions is changed, different EPU computations will be required..."

These authors do not provide any indication of how to obtain the finishing level for the EPU calculation.

MOORE & JAEDICKE (1976, p. 292) affirm that:

"in process cost accounting, the problem of determining unit costs is resolved by using equivalents units".

After determining carefully what the equivalent production units are, authors present examples in which the finishing level concept is used to calculate the equivalent production units without any indication of the procedures followed for obtaining it.

LEONE (1980, pp.195) mentions that:

" the beginning of the month, in a determined production center, there were 12 pool balls, 50% finished, that is, only the halves were finished".

Throughout his explanations, the author does not approach the finishing level computation issue.

BACKER & JACOBSEN (1978, p.288), concerning the computation of the equivalent production units, say that:

" such situations the finishing level of end-ofperiod units in process must be estimated by qualified technical staff. In a big and complex production operation, this is a difficult task and sometimes, the estimator's judgment will result in errors in the unit cost values".

In our opinion, the authors transfer the problem to the qualified technical personnel, but who is the qualified technical personnel? Probably the authors refer to the engineering, process control or production control technicians. We observed that the technical personnel will probably be better qualified to calculate the physical finishing level, but not the finishing level in terms of costs. The finishing level that must be used to calculate the equivalent production units is the cost finishing level. In this sense we completely agree with HORNGREN (1972, p.597) when he says:

"...note that unit cost is not calculated on the basis of physical units. It is calculated on the basis of equivalent unit performance - that is, on the basis of charges or doses of cost needed to finish a given unit".

DEARDEN (1976, p.27) emphasizes the basic difficulty in process cost accumulation mentioning:

"...the major problem consists in determining the goods in process inventory in equivalent units terms. (Two units, half finished, are equal one finished unit)".

Like DEARDEN, CORCORAN (1977) does not present any indication of how to calculate the finishing level computation either. The same is valid for MATZ, CURRY & FRANK (1978), MORSE (1981) and DOPUCH (1974).

MARTINS (1998, p.171), like all other authors referred to above, does not present, in an objective way, a finishing level computation method. In the specific chapter of his book dedicated to this specific subject, he shows, however, important contributions to the conception of the proposed method. Among other relevant aspects, this author observes that the equivalent unit must be characterized in costs terms and that:

" equivalent production unit must be used for each type of cost".

Although HORNGREN (1972, p. 609) did not present a finishing level computation method, in our perception, he conceptually started to build a solution proposal:

"Estimating the degree of completion is usually easier for materials than for conversion costs. The conversion costs sequence usually consists of a number of standard operations or a standard number of hours, days, weeks, or months for mixing, heating, cooling, aging, curing, and so forth.Thus, the degree of completion for conversion costs depends on what proportion of the total effort needed to complete one unit or one batch has been devoted to units still in process".

MORSE (1981, p. 559), even though he does not present a solution for the finishing level computation problem either, conceptually indicates the solution when he affirms that:

"Standard cost systems are most frequently used when identical units are produced on a continuous basis. The use of standard costs eliminates the need to compute the cost per equivalent unit.The equivalent unit cost is the standard cost. Additionally, the costs transferred out are equal to the number of units completed times the standard cost per equivalent unit".



In the light of the assumptions established and the arguments presented above, we now want to reflect on and analyze the problem in order to propose a logical way of calculating the finishing level. The proposed method is sustained by the standard cost concept.




Consider as a fundamental assumption that the finishing level must reflect the finishing in costs terms. That is, when it is affirmed that a product is a% finished, this means that the product received a% of all costs that would be required to start and finish it. On the level of each specific production stage, the ga equals the cp/cf. If cost accounting were processed in each specific stage, that is, computing the realized manufacturing costs of the period, calculating unit costs, initial inventories valuation, production costs computation of the production cost transferred to the next stage, final inventories valuation etc., the finishing level problem would be solved.

Keeping in mind that the companies' cost accounting, with rare exceptions, is analytically processed step-by-step, because it would require information and analytical controls that are not always available, the finishing level should be computed at the level of the manufacturing plant or entire enterprise. Concerning this aspect, MARTINS (1998, p. 175) observes that:

" problem that normally occurs in continuous production industries and that usually complicates and sometimes even blocks the unit calculations in the intermediary stages is the non-existence of conditions to know the physical volumes transferred from one department to the other. Without knowledge of these quantities it is not possible to work with unit costs. These can only be known when measuring (weighting) at the end of the production line".

Returning to the fundamental assumption that the finishing level is given in costs terms, we que os produtos em processo, considerando as observe that the goods in process, considering the different quantities in different stages of the manufacturing plant, will be a% finished when they receive a% of all cost required to start and finish them. This means that we must consider the sum of the cp/cf ratios weighted by the respective quantities (qp) that exist in the different stages.

So, realizing the required weighting, we have:



Keeping in mind that cf is always the same for all units:



In order to illustrate the proposed model, a numeric finishing level computation example is presented below. Consider a continuous process manufacturing plant of a unique product with five ep's. At the end of a given period the physical inventory of the goods in process quantity (qp) was made in the specific stage (ep):



Below, the standard unit cost statement of the product is presented, accumulated to the specific stage (cp):



Applying the proposed formula:

Σ(qp . cp)

The amount of $ 1,045,000 represents the cost of all units in process, considering the stage that they have reached, computed as follows:




Represents how much would be the total cost if all units in process were finished:




Finishing level, in cost terms, of the units in process at the end of the period:




An exploratory study was realized to get a general knowledge of the practical procedures used by enterprises in relation to the costing of goods in process in the production segments that work by continuous processes for the manufacturing of homogeneous products.

The study developed is strictly exploratory and, as such, does not pretend to generalize the results to all of the enterprises. A total of 175 questionnaires were sent to pre-selected enterprises (with revenues above US$ 100 million).The analysis of their sphere of action indicated the use of the process costing system.

These enterprises were selected through the database of FIPECAFI. The questionnaire was sent along with a letter signed by the Head of the Accounting and Actuarial Sciences Department of the School of Economics, Business and Accounting (University of Sao Paulo - USP). The results of the 50 companies that responded are analyzed below.

1. Does any segment of the anufacturing plant work as a continuous process, that is, continuous manufacturing of a homogeneous product?

1.1. yes (go to question 2)

1.2 no (the research is finished)



From the total of returned questionnaires, 43 enterprises work by the continuous process and 7 enterprises by the production order system. The following reflections are made on the basis of the information given only by the enterprises that work by the continuous manufacturing process system.

2. What is the main activity of this segment?

2.1. paper and cellulose

2.2. sugar and alcohol

2.3. vegetable oil extraction and refining

2.4. heavy industries

2.5. metals mining

2.6. food production

2.7. petrochemical and chemical

2.8. Other



No company from the area of vegetable oil extraction and refining responded. Most answers are related to food or chemical and petrochemical enterprises.

3. In the segment of the manufacturing plant operating by the continuous process system, does the enterprise use the finishing level and equivalent production unit concepts to realize the costing of goods in process?

3.1. yes (go to question 4)

3.2. no - but these concepts are well known to the enterprise (go to question 6)

3.3. no - these concepts are not known to the enterprise (go to question 6)



Eleven enterprises affirmed that they use the concepts of finishing level and equivalent production units.Twenty three enterprises answered that they do not use these concepts even though they are well known and nine enterprises answered that these concepts are not known internally. Among the 43 enterprises analyzed, 74% do not compute the finishing level and equivalent production units.These observed data are very significant in the context of proving the hypothesis established.

4. Which department of the enterprise computes the finishing level?

4.1. production / manufacturing

4.2. engineering

4.3. production planning and control/process control

4.4. accounting/costs

4.5. other



Evidently the answers to this question were only given by the eleven enterprises that admitted the use of the finishing level and equivalent production unit concepts. The accounting/cost department appears in the first place as the responsible for the finishing level computation.

5. How does the enterprise compute the finishing level? (give us a broad outline)

Only one enterprise answered objectively that it uses a percentage of 80%, not specifying however how this percentage was obtained. Generally, the answers demonstrate that, in many companies, there exists a "misunderstanding" about the finishing level and equivalent production unit concepts. Some explanations given by the enterprises about the finishing level computation are reproduced below.

"It was globally defined that every good in process has an 80% finishing level".

"The cost is computed per product in each process phase. There is a cost matrix that details the specific consumption of each

product cost component for each process

phase. The matrix considers the process benefits and the productivity in each phase or equipment. Every cost computation is made phase by phase for each produced ton. The equivalent production unit is the ton of each product, or for each product code that is specified by type of steel (chemical composition, profile, finishing level, quality level and special flows)".

"Legal quality standards required by the market and measured by laboratories installed inside the manufacturing plants".

"A research was realized by the production department in order to identify the volume of existing equivalent production units in process.This volume results from calculations that were based on the residues, pastes and unfinished cellulose present along the lines, from the entry of wood until the packaging. Consequently, from knowledge of the wood's average efficiency, the entrance cubic volume and finished production of the period were verified.The difference between the cellulose production that the wood will generate and what was effectively produced represents the unfinished volume, on which the finishing percentages of equivalent production units were applied".

"We use production order control on which technical specifications and the operations for the production appear. Through the daily appointment of the manufacturing sectors (lithography, printing and assembly) we register in each production order the operations and the finished production, generating at the end of each accounting period a report which contains the situation and the finishing level of the goods in process".

"It is based on the production standard routines, applied to the specific production phase in which the parts are, weighted by the real consumption and the really spent production hours.This constitutes the basis for the inventory evaluation".

"It is calculated for each type of product

made by the enterprise. For instance, crystal sugar, refined sugar, liquid sugar, hydrated alcohol etc.".

"Considering the product or its final feature".

"We define specific codes that indicate that a given product is in process and, therefore, we can attribute the raw material costs, variable expenses, fixed expenses, depreciation and in some cases the packing material".

"All production is controlled by lots, entries of goods in process and the corresponding finished product".

"Using the physical-chemical quantification and the final use of the product by the client".

Analyzing the answers we can infer that the enterprises, except one, have different perceptions of the finishing level concept. These perceptions of this concept do not coincide with the theoretical definitions established within cost accounting.Thus, it is demonstrated that enterprises do not show the use the finishing level concept as defined within the theory.

6. What procedure does the enterprise use to evaluate the goods in process inventory on a monthly basis?

6.1. uses estimated cost

6.2. uses standard cost

6.3. maintains the same fixed monthly value

6.4. considers the inventory as having "zero" value

6.5. uses the estimated/standard cost as inventory and production evaluation basis. Computes the differences between the actual cost and the estimated/standard cost.The value of the difference computed is applied to production and to inventory in proportion to the estimated/standard values.

6.6. uses another procedure: (give us a broad idea of the procedure)



This question was analyzed for the group of 32 companies that do not adopt the finishing level and the equivalent production unit concepts. None of them use the estimated cost as a basis for the goods in process inventory evaluation; 2 of them answered that they are using the standard cost; none of them gave any information about the maintenance of a fixed value for the goods in process inventory; 7 enterprises consider the final inventory as having a "zero" value because of the characteristics of the productive process, and 9 enterprises, which answered that they are using the standard cost, calculate cost variations and proportionally distribute the variations to production and to the goods in process inventory. The other 14 enterprises did not specify in an objective way which procedures they use. Some of them mentioned the following expressions:

"actual monthly average cost", "we use the average cost to evaluate the inventory", "production orders are opened", "the costing is the actual monthly cost", "joint costs theory and full costing", "the goods in process inventory is very small but we are using the average cost", "average unit cost computation", "monthly average cost", "actual cost per production phase", "use of one costing for each production phase with real appointments of quantities produced in each one of these phases".

In these quotes, we can observe that emphasis is being given to the calculation of the average actual cost. It must be noted, however, that it is exactly for the computation of the average cost that cost accounting uses the finishing level and equivalent production unit concepts. It can be inferred that, in practice, the companies simplify in order to obtain the average cost, treating units in process as being equal to transferred or finished goods in cost terms. Nine companies reveal the use of the scientifically perfect procedure, as will be demonstrated below, that is, the procedure distinguished in item 6.5 of question 6.



Below we present an example of process costing using the finishing level and equivalent production units calculated in accordance with the theoretical solution proposed.The results are compared with the standard costing method, including the distribution of the cost variations to production and to the final inventory, which is configured as the best practical solution used by the companies.

The following data are given:



Applying the conventional cost accounting procedures and using the finishing level for production costing, we would have the following procedures:

1. Computation of the equivalent production units:



2. Computation of the production unit cost of the period:



3. Computation of the total cost of the production delivered to the finished product inventory:



4. Computation of the total cost of the goods in process inventory at the end of the period:



Without using the finishing level and allowing the companies to use standard costing, with the same data of the example, we would have the following situation:

1. Computation of the standard cost of the production transferred to the product inventory:



2. Computation of the standard cost of the final goods in process inventory:



Following these procedures, we have the standard cost of the finished production and the standard cost of the goods in process inventory. We admit that for fiscal, legal and financial objectives, it is necessary to determine the corresponding effective costs.The most appropriate practical alternative, which can be observed in some situations, as was proved by the exploratory study, consists in using the standard values determined as a basis, determining the total cost variation (difference between standard cost and actual cost) and add to the standard cost of the finished production and the standard cost of the goods in process inventory a specific part of the total cost variation, in proportion to the standard values, obtaining, consequently, the accounting values. The analytical procedures involve:

1. Determination of the cost variation:



2. Determination of the accounting value of the finished production:



3. Determination of the accounting value of the final goods in process inventory:



Realizing an analysis of the numbers presented, we conclude that the accounting values of the finished production and the goods in process inventory, determined by means the two methodologies, are identical. This means that, in practice, the companies that use the standard cost and add a part for the variation in proportion to the standard values for determining the financial accounting values, without knowing, obtain the same result that would be obtained by the finishing level and equivalent production units, as in the model proposed.



Through the bibliographic revision we noted that, what the theoretical procedures used for continuous process costing is considered, there is not any indication of an objective method for determining the finishing level of the units in process and for calculating the equivalent production units. The empirical research developed demonstrated that, in practice, the companies do not adopt the general procedures proposed by the theory. Thus, the bibliographic and empiric research prove the hypothesis established.The field of cost accounting contains a genial idea, namely, the finishing level concept, but until now has not provided any objective calculation method. The solution developed in this work for determining the finishing level, with the additional advantage of its simplicity, solves the problem characterized and makes it possible to use the process costing method established in cost accounting theory. On the other hand, the considerations realized throughout this paper prove that one of the procedures used by the companies that work by the continuous process system, namely, the use of the standard cost and the determination of the accounting value of the finished products and the goods in process inventory, incorporating (in proportion to the standard values) the cost variations determined, is perfectly valid, making up for the lack of an objective conceptual indication in an adequate way, since its results are identical to the results obtained with the method proposed for calculating the finishing level.



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(*) Trabalho apresentado no 12th Asian-Pacific Conference On International Accounting Issues, Pequim, China - outubro de 2000.

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