Profit model

Profit model

The Profit model is the linear, deterministic algebraic model used implicitly by most cost accountants. Starting with, profit equals sales minus costs, it provides a structure for modeling cost elements such as materials, losses, multi-products, learning, depreciation etc. It provides a mutable conceptual base for spreadsheet modelers.

Background

The justification for modelling profit is given by Mattessich in 1961.

'To some operations analysts the mere translation of accounting models into mathematical :terminology, without a calculus for determining an optimum, might appear to be a rather :pedestrian task. We are convinced, however, that as long as accounting methods are acceptable :to the industry the mere change to a mathematical formulation will be advantageous for :several reasons: (1) it can be considered a prerequisite for applying electronic data :processing to certain accounting problems, (2) it articulates the structure of the accounting :models and illuminates accounting methods from a new point of view, revealing many facets so :far neglected or unobserved, (3) it enables a general and hence more scientific presentation :of many accounting methods, (4) it facilitates the exploration of new areas, thereby :accelerating the advancement of accounting, (5) it leads to more sophisticated methods and :might help to lay the foundations for close cooperation of accounting with other areas of :management science.'

Most of the definitions in cost accounting are in an unclear narrative form, not readily associated with other definitions of accounting calculations. For example, preparing a comparison of fixed cost variances in stock under different stock valuation methods can be confusing. Another example is is modelling labour variances with learning curve corrections and stock level changes. With the absence of a basic profit model in an algebraic form, confident development of such models is difficult.

The development of spreadsheets has lead to a decentralisation of financial modelling. This has often resulted in model builders lacking training in model construction. Before any professional model is built it is usually considered wise to start by developing a mathematical model for analysis. The profit model provides a general framework plus some specific examples of how such an a priori profit model might be constructed.

The presentation of a profit model in an algebraic form is not new. Mattessich's model (1), while large, does not include many costing techniques such as learning curves and different stock valuation methods. Also, it was not presented in a form that most accountants were willing or able to read. This paper presents a more extended model analysing profit but it does not, unlike Mattessich, extend to the balance sheet model. Its form, of starting with the basic definition of profit and becoming more elaborate, may make it more accessible to accountants.

Most cost accounting textbooks explain basic Cost Volume Profit modeling in an algebraic form, but then revert to an 'illustrative' approach. This 'illustrative' approach uses examples or narrative to explain management accounting procedures. This format, though useful when communicating with humans, can be difficult to translate into an algebraic form, suitable for computer model building. Mepham extended the algebraic, or deductive, approach to cost accounting to cover many more techniques. He develops his model to integrate with the optimizing models in operations research. The profit model comes out of Mephams work, extending it but only in a descriptive, linear form.

Model basics

Using:

• Sales revenue = p * q = price x quantity sold
• Opening stock = go * wo = opening stock quantity * unit cost
• Cost of stock = g1 * w1 — closing stock quantity * unit cost
• Cost of production = w * x = unit production cost * quantity made
• Cost of sales = w * q = unit cost * quantity sold
• Administration, selling, engineers, personnel etc = Fn = Fixed post manufacturing overheads
• Profit = π

Thus the profit can be calculated from:

π = pq — [Fn + wq]............ (equation 1)

Notice that v (average unit production cost) includes the fixed and variable costs.

The square brackets contain the cost of goods sold, that is 'q' is present.

If the stock adjustment and cost of goods made (x) is to be used, then the model will look like

π = pq-[Fn + w x + gowo – g1w1].......... (equation 2)

Whilst this basic model could be simplified it will be left in the traditional form profit equals sales less costs.

Presenting the profit calculation in this form immediately demands that some of the costs be more carefully defined.

More to be added here...

Also see

• Cost accounting
• Income statement
• Management accounting