Economy & Energy
Ano XII-No 78
June - September
ISSN 1518-2932


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Capital Productivity in the Brazilian Electrical Sector

Description of the software developed for calculating Capital Productivity in Enterprises

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Description of the software Developed for Calculating the Capital Productivity of Enterprises

Lothario Deppe

1 – Introduction

The Economy and Energy Organization – e&e, has developed a software in Excel format that incorporates a calculation logic that permits the evaluation of the Productive Capital Stock (PCS) of an enterprise. The calculation shows how productively the capital is used in order to generate the added value in the analyzed enterprise serving its statutory purposes. The methodology is based on the recently published report of OECD (Ref. 1).

 Capital productivity reflects the combined influences of manpower, intermediary input factors, technical changes, efficiency changes, scale economy and utilization of the installed capacity. The productivity measurements are based on the Net Added Value (NAV) Index that is less influenced by any change in the intermediary factors and manpower relationship at the vertical integration level or by substitution processes in the intermediary inputs and capital.

 The software considers an enterprise whose statutory purpose is the production of goods but not a financial enterprise. Any financial income (or expense) is not considered as part of the enterprise production.

 The software was developed particularly for enterprises of the Brazilian electrical sector but it can easily be adapted to enterprises of other sectors. Due to the peculiarities of the electrical sector, it will certainly be necessary to make some adaptations that are not difficult at all.

 Data are directly obtained without further manipulations from the Annual Reports of the companies, specifically:

- Balance Sheet;

- Demonstration of Results;

- Demonstration of Added Value Destination;

- Different Explanatory Notes, specially those that give details of Immobilized in Service, Intangible in Service, Special Obligations, etc;

- Descriptions that permit to visualize the Immobilization pace carried out by the company since the start of operation.


The Productive Capital Productivity Index is a perfectly defined index and reflects the efficiency of the company to reach its statutory objectives.  In the measurement are included the effective physical production of the company and part of its capital stock that is used in effective productive process and called Productive Capital Stock.


The advantage of this indicator is that it is easy to understand. The disadvantages are a set of factors that are not included and also that sometimes it is confounded with financial yield of the total capital stock or total capital return.


The definition used in the present report is the following:


Capital  Productivity =

Net Value Added to production (Y)

Productive Capital Stock for production (K)


The measurement unit is “per time”. This ratio is sometimes called Y/K Ratio that measures the existing productive Capital Stock productivity usually expressed % per year.


The questions to be discussed are the following:


- Measurement of  Productive Capital Stock (PCS) (K)

- Measurement of Net Value Added (NVA) to production (Y)


The software permits to calculate de mentioned items and the calculation of K/Y and Y/K ratios in a reasonably simple way.




For any type of assets there is a flow of productive services delivered by the capital stock accumulated by past investments. This service flow is called capital service of an asset and it is the appropriate measurement of the capital input factor in order to analyze production and productivity. The capital stock that produces these calculated services is called productive stock of a determined asset.


Practically four (4) basic ingredients from the Total Assets of a company are necessary to measure the Productive Capital Stock using the Balance Sheet of an enterprise:


- Determination of the categories in the Balance Sheet that are part of the Productive Capital Stock;

- A expenditures temporal series of investments considering that a type of asset will actually consist of different assets and that heterogeneity should be minimized in the aggregations;

- The producer price indexes used to deflate the expenditures temporal series;

- A profile of productive capacity loss (involving considerations relative to the above mentioned profiles: age-price, age-efficiency and out-of-service), but obtained from the Balance data.


2.1 –Categories that are part of the Productive Capital Stock (PCS)

The exact concept that must be used for defining the Productive Capital Stock used in productivity analysis should be that of identifying the capital services that a determined asset can deliver as an input factor in a determined production process, as already mentioned. Productive Capital Stock so calculated is related only to the productive operations of an enterprise.


We reproduce below, as an example, categories of CEMIG CONSOLIDADA’s Balance Sheet as published in the 2008 Administration Report.



ITEM (CEMIG nomenclature)


Accum. Depr.























Table 2.1–Summary of categories part of Productive Capital Stock

 2.2 – Deflation of Immobilized and of Depreciation

In order to obtain a temporal series of investments it would be necessary to evaluate the same categories of the Balance Sheets relative to previous years in the company. The objective would be to obtain a temporal series of expenditures at the producer level and for each type of product, a base to deflate them.


Obtaining price indexes at the producer level can be very difficult for the Brazilian case if very long periods are involved. The periods of extremely high inflation that occurred in the 1990s has evidently distorted any statistics referring to this period.


The software uses the simplified methodology of considering average weighted data for Immobilizations e Depreciations. Data should be established from the company’s historical ones. For example, in the case of an electric energy company a preponderant factor is the start of operation of the generation plants that can be considered as the effective Immobilizations.


With these data it is possible to deflate the accumulated historical Immobilized and the accumulated Depreciation. Particularly, it is also possible to calculate the total fraction of investment already depreciated after deflation and compare it with that calculated from CEMIG’s Report data, as shown: 

- Immobilized already depreciated after deflation correction (%) 41,31

- Immobilized already depreciated by the Annual Report (%)      46,58


For evaluating the precision obtained with the simplified methodology of the average weighted dates a calculation was carried out with realistic data estimated for an enterprise (again CEMIG CONSOLIDADA)   in a period of a dozen years and a reasonable deflator and the obtained data were compared. The final results of Immobilizations and deflated Depreciations were always within a reasonable error margin (less than 10%) in spite of high corrections results for the period due to the still high inflation, even after 1995.


The result of this comparison shows that the used methodology permits to obtain reasonable values using data normally obtained from the company’s reports, even with elevated calculated deflations.

 2.3 – Re-evaluation of Depreciation

 The electric sector regulated by ANEEL has very clear rules for calculating depreciation of the several company assets. The depreciation method is linear and the periods are relatively short. It is given below some examples of the used prescribed indexes and the average real results.




Depreciation (%/y)

Life (y)

CEMIG Average       - Consortium of plants



FURNAS Average    - General



ANEEL Prescription - Reservoirs, dams



                                   - Hydraulic turbines



                                   - Concrete struct., buildings



                                   - General equipment



                                   - Vehicles



            Table 2.1 – Usual depreciations in enterprises (example: electric sector)

Depreciation measures the loss in value of a capital good along it ageing process. Therefore, it is associated with the net value of capital stock and it should be distinguished from efficiency decrease which reflects the loss of productive services that can be obtained from a capital good. Therefore, efficiency decrease is associated with capital productive stock whereas depreciation is an accounting estimate relative to the market value loss of a good. For example, a truck in one year would be depreciated by 20% of its initial market value using ANEEL rules but it has not necessarily lost 20% of its capacity of transporting goods from one place to another (and this is of interest in Productive Capital measurement) and it probably is practically the same. So, unless the truck is sold in this short period (which is rarely the case):

- neither its capacity of delivering productive services,

- nor the capital cost that should be assigned to it,

follow the prescribed linear depreciation rule.

Additionally and more flagrant, the use of linear depreciation certainly does not reflect

the effective efficiency decrease of Immobilizations and of capital services it causes, being too low. The services delivered by Immobilizations (and which are the basis of evaluations relative to productivity) certainly do not decrease in the proportion suggested by the depreciation rules used.


On the other hand, it is of interest of the enterprises to have a high Depreciation because it is considered as cost in the Balance Sheets and it reduces the direct taxes on production (Income Tax, PIS/PASEP, COFINS).


So, it is necessary to apply a correction to the informed Depreciation values in order to have a more adequate measurement of the efficiency loss of the Productive Capital Stock.


The software permits to correct Depreciation through the use of more smooth average depreciation methodology for the enterprise, to be chosen. The curve is represented by a 6th degree polynomial as a function of the time fraction between the start of life until the present time. This means that on the average the Productive Capital Stock of the company keeps the capacity of delivering productive services as indicated by this polynomial.


Additionally, the software permits to evaluate (for more or for less) the average remaining life time of Immobilizations through an arbitrary act. This should be done as a function of the physical characteristics of the Immobilization and of the remaining life time.


For a more realistic calculation of this Depreciation it was considered a weighted year for Immobilizations and the reformulated logic regarding Depreciation was applied from this date on.




Basic prices valuation should be distinguished: producer prices and buyer prices. Basic prices aim at measuring the values that are actually retained by the producer. Therefore, it excludes taxes to be paid but includes subsidies to be received as a consequence of production or sale. Since the basic price measures the value that is retained by the producer, it is the most relevant price for his decision-making. Therefore, it is recommended that the basic prices valuation should be the preferred method for valuating the output value (production), specially when there is some type of tax on added value or a similar one.


Another production valuation is at producer’s prices. Contrary to basic prices valuation, this valuation includes taxes and excludes subsidies to products. This changes the valuation of measurement from the value actually retained by the producer (basic price) to a value in which transactions or a business is concluded.


A third evaluation is at buyer prices. It measures the value actually paid by the buyer in order to take possession of a determined good or service in a specific point in time and space. Therefore, buyer prices are the relevant prices for buying decisions, including transport costs and commercialization margins. As a consequence, it is recommended the use of buyer prices to measure the expenses on goods and services to be used by enterprises as intermediary input factors.

 3.1 –Categories that are part of the Net Added Value (NAV) to production

It arises now the following question: does the information obtained in the Financial Demonstrations of the enterprises reflect the above described procedure and how to correct them so that they will reflect in the best possible way the Net Added Value (NAV) to production generated by the enterprises, calculated and valuated as recommended by the OECD Manual?


Once more, for the electric sector companies regulated by ANEEL there are precise rules concerning the accounting of results, in spite of the fact that the nomenclature of the accounts is not totally uniform, sometimes they are not totally informative and they cast some doubts. There is a trend to equalize Revenue and Operational Costs (definition used by all companies) with Revenue and Productive Costs (as defined by OECD). It can be necessary to purge the first ones from “non productive” categories, in spite of the fact that this is not evident in the Annual Reports published by the enterprises.


Practically, the value corresponding to Personnel and Similar Expenses is better obtained directly not from the Financial Demonstrations but through a calculation that is presented by the enterprises and denominated Distribution of Added Value that better consolidates this category.


All enterprises have a combined category denominated “Depreciation and Amortization”. According to the OCDE Manual, the Net Added Value should be gross only for Depreciation. Separation of these two values using data from the companies’ reports requires some manipulation of the Balances but it is automatically carried by the software using data from the Balance.

 3.2 – Corrections of values informed by the accounting

 There are two questions that should be evaluated and should be used with due criterion when the software is used and that will be commented in what follows:

- Incorporation (or not) of financial revenues and expenses in the results and

- Additional correction to be introduced in the Depreciation value for calculating the Net Added Value.

The accounting categories presented by the electric sector enterprises frequently do not include any category that reflects any financial revenue (or expense), for example, interests from money invested in banks or funds. The values would not be relatively high and for this reason they are not explicitly declared. However, in some cases specific categories relative to these items are presented.


In order to obtain an estimate of the non-operational financial earnings, estimates can be made from categories in the Circulating Capital and Long Term Realization. One part of this money should correspond to current accounts that do not pay interest but certainly one part must be invested somewhere or somehow earning interest.


The calculation is made and can be included (or not) in the results. Anyway, in the case of the electric sector enterprises, the influence is very small.


In reality, the depreciation (indirectly) informed by the enterprises is a result of accounting considerations imposed by the regulation and produces values different from those that would be obtained using the depreciation utilized by the software for calculating the accumulated depreciation to correct the Immobilized and that is “slower”.


The annual depreciation informed (that represents the value of the capital services for production) can also be corrected by the software for the purpose of calculating the Net Added Value, if the user chooses to do so. Again, the influence on the results is not large but it is recommended to use a correction in order to maintain coherence with the general methodology used for calculating the Immobilized.


(1)  Measuring Productivity – OECD Manual; Measurement of Aggregate and Industry-Level Productivity Growth; 2001




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Wednesday, 04 January 2012

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