Two Parameters for Seven Companies

Fitting the Enterprise Model into the Real World

The two-parameter Enterprise Model described earlier can represent a real enterprise when realistic values of the two parameters xsd and qs can be specified.   To estimate these model parameters we can deploy the Least Squares Method whereby a numerical model can be ‘fitted’ to real-world commercial data for units sold, income, profit and so on, which are widely measured and reported.  In this way the parameters become the link between model and real world, and their estimated values provide an insight into the latter that is otherwise inaccessible.

  • The standard deviation xsd records the statistical propensity of consumers to value the goods. In this way xsd describes the ease the Value Surface can be raised by investments that are made by the enterprise.  Whilst the Value Surface may be seen as being constantly in motion, it is assumed that that xsd remains constant over the duration of a model simulation, to become a fundamental parameter that describes consumer preferences for a particular commodity.
  • Parameter qs specifies the recruitment of new consumers when existing ones cease to contribute following their departing Sale Event. Such a recruitment is essential for a sustainable operation.

Sale Events occur at points where the hoisted Value Surface passes the level of the set price, and income is then returned to the enterprise equivalent to the price multiplied by the number of Sale Events achieved.  Investment, income and profit are reported in company accounts.  It remains to associate this information with analogous terms in the Enterprise Model.

Company accounts income statements conventionally divide overall investment into Cost of Goods Sold (COGS) and Operating Expenses (OPEX).  COGS include only those costs that are directly associated with the production of the commodities. These can include the cost of materials and direct labour costs used to produce the goods.  With each Sale Event it is the investment in COGS that is lost from the Value Surface with a product sale.  OPEX on the other hand may be considered to comprise the remaining portion of the investment that is retained as a potential within the Value Surface after product sale[1].

OPEX contribute to the raising of the Value Surface to encourage Sale Events.  These Operating Expenses should enhance consumer perception of value but are independent of the actual goods themselves: brand image, customer service, sales-force, technical capability, administrative competence, etc.[2]

This association of the conventional items of company accounts with equivalent features of the viscoelastic model of a commercial enterprise are summarised in the table below.  They provide the associated correlations we will employ in matching the two-parameter Enterprise Model behaviour to the real-world commercial data to estimate the model parameters[3].


Relationship between the financial items of a company’s accounts and their equivalent features in the two-parameter Enterprise Model

Company Account Item Two-Parameter Enterprise Model
Total Investment (COGS + OPEX) Total potential used in raising the model Value Surface.
Cost of Goods Sold (COGS) Potential lost from the product Value Surface, that is dissipated by the Sale Events.
Operating Expenses (OPEX) Residual Value Surface potential stored within the products, services and systems of the organisation.
Total Income (Revenue) Price x Number of Sale Events.


A Comparison of Seven Companies:       For each company account item in the table above, real commercial data has been obtained from quarterly reports (10Q and 10K) from 2008 to 2014 obtained from the US Securities and Exchange Commission EDGAR database[4] for seven companies selected to cover a range of sectors: 3M, Amazon, Apple, Intel, Kodak, Microsoft and PepsiCo.   The best-fit qs and xsd estimates that replicate as closely as possible the real world data from the EDGAR database have been found using the Least Squares Method, where the fit of the model simulation is matched to replicate both Total Income and Operating Expenses as determined by the Total Investment deployed over time.

Here, rather than considering an individual commodity commercial performance, as this data is generally not available in the public domain, the overall performance of a company is considered.  This is equivalent to the commercial trading of a single commodity that is representative of the entire enterprise.  This approach is useful as it enables a comparison of entities that are fundamentally similar, rather than a comparison of their dissimilar products.


Parameter estimates obtained by fitting the enterprise simulation to the financial data of seven companies.   

Company Parameter Values V1

The best-fit estimates of qs and xsd for the seven commercial organisations are presented in the above table.  The enterprise simulation provides an extremely close fit to real commercial data, the minimum error being less than 1% in all cases.  Also, the stability of these qs and xsd parameter estimates when the least squares best fit is repeated with different start points and with different time increments is high and indicative of unique points of minimum error.

click image to enlarge

Apple Simulation vs Actual


Microsoft Simulation vs Actual

Best fit of simulated Total Income and Operating Expenses to the equivalent real commercial data from Apple and Microsoft for 2008-2014.  Also shown is the company investment that was the input into the Model Enterprise over this period.

A simple Enterprise Model with properties controlled by just two parameters qs and xsd appears to be able to reproduce quite complex real world behaviour with considerable accuracy.  Now, we need to understand what these parameter values mean to the businesses they describe?  To answer this question we need to consider and compare the behaviour of organisations for which commercial considerations would not normally apply.


Technical Note:  As the values of parameters qs and xsd and price are estimated from published company data, it has become apparent that specific values of the time increment tr, at which the market simulation is iterated, and the price of the goods are related.  As tr is shortened, the greater number of iterations over a simulation period will generally affect the quantity of goods sold through the simulated market place.  The Least Squares Method then automatically adjusts the price estimate to bring the simulated income to match the real total operating income apparent in the commercial data.  Meanwhile, the values of qs and xsd are generally only marginally affected by the size of the tr increment.  Hence, there is no need to specify actual values for tr and price, although these could become important as they reflect the period over which investment is deployed and returned as income.



[1] If there were no retained potential, then the Value Surface would collapse to zero height.

[2]  The precise definition of the activities that contribute their cost to COGS or Operating Expenses may differ from one business to another depending on whether costs are determined to be direct and variable with the sales of the products.  The relationship of these two cost items with the Value Surface remains consistent however the investment is allocated.

[3] What is not included in the analysis are the Capital Expenses (CAPEX) that typically appear on company balance sheets as property, plant and equipment.   The effects of such capital investment appear in the value created by the operational activities, which is itself represented by the model parameter values xsd and qs.




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