New light on an old chestnut: Break-even analysis from a pedagogical perspective

THE ORIGINS OF BREAK-EVEN

Back in the 1940s, accounting specialists at Harvard University developed a new way of looking at business performance. Their method depended on the propositions that

* total cost can be subdivided into fixed costs ad variable costs

* some costs are independent

* some costs vary in more or less direct proportion to changes in output

* the difference between unit revenue and unit variable cost can be labelled contribution, which is the amount of gross revenue that is attributable to paying fixed costs and, ultimately, providing profit.

These propositions led to a simple but powerful calculation. Since variable cost is accommodated in the contribution calculation, it follows that only fixed costs remain to be covered. Thus, total fixed cost ((FC) divided by unit contribution (which we can designate by small c) yields a quantity statistic for the point at which all costs are covered: the break-even point. IMAGE FORMULA 6IMAGE FORMULA 7

So far, so good. Maybe a ragged but heartfelt cheer rose from Harvard MBA students. No longer were they locked into the tyranny of constructing a profit/loss account and doing those pesky analytical sums in order to judge business performance. It sufficed to calculate break-even. Disillusionment would set in later as their course materials plumbed the depths of the contribution margin, semivariable costs, relevant ranges of costs and even determining the relevant ranges of fixed cost burdens.

While they were on course for their MBAs, it may perhaps have escaped their notice that the identification of costs is a more difficult proposition in real life than it is in the neverland of business textbooks. As we say in the trade, however, we simply provide them with the tools; it's up to them to determine their applicability. In addition, and more legitimately, we surely should transmit clear, straightforward messages to any group of learners on their first acquaintance with a body of knowledge, retaining some complications for subsequent enquiry.

SOME TERMINOLOGICAL ISSUES

The nomenclature break-even itself perhaps deserves some scrutiny. It properly focuses on the essential feature of this forecasting tool: the point at which neither profit nor loss is made. Up to that point, contributions are towards covering total fixed costs. Beyond that point, the contributions are towards profit.

Given, though, that the profit motive drives much business activity, the alternative name of Cost-Volume-Profit (CVP) analysis merits more consideration. It shifts attention towards the statistic that really matters in break-even and which matters also for profitability: the quantity or volume statistic. To argue that CVP nomenclature helps learners is to do more than simply apply another name to a rose and assume that its odour doesn't change. It really must matter that learners of break-- even (as opposed to practising accountants or business analysts) should use terms that focus on essentials. Much teaching consists of defining terms. Much learning depends on the learners' generating lists which the teacher then shows them how to categorise into concepts and principles.

And another thing: in dealing with break-even, some textbooks underplay the importance of selling the output. Some authors seem almost to subscribe to the old Eastern European commonplace of imputing profits on the accumulation of stocks. Not even Eastern Europeans now believe that production is of its very nature profitable. In short, the omission of the phrase sold output from the treatment of break-even in many textbooks carries with it the complacent assumption that Say's law (supply generates its own demand) operates to the advantage of business enterprises in the short term. It doesn't.

Another difficulty in textbook treatments of break-even can occur when we consider the use of margin of safety. When sold output exceeds break-even output, profit is

Margin of safety x unit contribution

Here again the needs of learners of accounting theory may well differ from the needs of practitioners. The original work on break-even was for university teaching and was directed towards those who aspired to be leaders of industry. For twenty or thirty years we have taught those same processes to 14-year-olds. Having regard to the needs of such immature learners, it may be advantageous to introduce the term 'margin of danger' into the analysis to describe the situation where achieved quantity of sales falls below break-even level. In such situations, the resultant loss is

Margin of danger x unit contribution.

Admittedly, the term margin of danger isn't in the books, but ... so what? The phrase means something and merits consideration on pedagogical grounds, ie in relation to good communication with classes.

BUT THAT'S NOT THE WHOLE STORY ...

So far this article amounts for the greater part to a critique of some conventional textbook terminology. It could be argued that it takes more than that to merit attention. So, let's also take one small step towards changing the pedagogy associated with break-even.

In communicating to pupils the key processes in accounting and business analysis, there is a well-- trodden path towards success. Following that path involves demonstration and emulation. The teacher deconstructs a body of knowledge and feeds it to classes in assimilable bits. Teacher then shows classes how to reassemble the bits into a meaningful whole. Pupils practise until they are familiar with the bits and are also competent in assembling the cognitive structure that holds them together. This works well, but tends to make lessons on analysing business information stereotypical.

Importing contextual information into the classroom, ir the form of computer programs, video and journal evidence are all very laudable ploys, but what might we gainfully do to change those classroom transactions over which the teacher has direct control? By controllable transactions, I mean the materials that a teacher may choose to construct or adapt, as opposed to those that have been made under the control of a programmer, a producer or another writer.

THROUGH THE JUNGLE OF ACCOUNTING LOGIC

There is a classic cheap and readily available resource for introducing break-even. It is Rex Anderson's An Accounting Accounting, or Through the Jungle of Accounting Logic with Gun and Camera. The author was Vice-- President of the Life Insurance Company of North America. He wrote An Accounting Accounting for staff training purposes, with the prime aim of enabling colleagues without an accounting background to get through the forest of verbiage that seems sometimes to spring up around accountants' explanations of the simplest business phenomena.

We don't need a quotation from Anderson's work to catch the flavour - it's in the title. An Accounting Accounting is a lighthearted dialogue. Unfortunately for those who suffer from the delusion that accountants often have worthwhile things to say, the Accounting Efficiency Expert, one of the protagonists in the piece, is also a wally.

Some years ago I took the ideas contained within Accounting Accounting and re-worked them with the aims of retaining all that is good in Anderson's stuff and also of removing the stain that he had left on the escutcheon of the accountancy profession. In my re-write (see panel, Working through a Wet Weekend) the accountant is the smarty.

APPLYING LEARNING THEORY TO TEACHING BREAK-EVEN

Working through is founded on three bodies of learning theory. First, there is the notion of active learning. Working through is a dialogue that can be read/acted by members of the class. This introduces a novel activity to the process of learning about analysing business performance. Active learning is, however, more than just acting out a situation, and it is much more than the passive reception of bits of knowledge.

Authorities such as Bonwell & Eison (1991) have defined active learning as a context in which students 'read, write, discuss, or (are) engaged in solving problems. Most important ... students must engage in such higher-order thinking tasks as analysis, synthesis and evaluation'. On a hierarchy of learning behaviour, Working through certainly takes learners as high as analysis. By her skilful questioning, our heroine, Ann Accountant, leads Fred

* to a realisation of the contribution concept

* on to the break-even principle

* and on again to the margin of safety and its relationship to profit.

Learners can apply Fred's reasoning to a series of problems that make use of data for fixed costs, unit variable cost and unit revenue.

Mention of concepts and principles brings to mind the work of Gagne, whose analysis of intellectual performance put concept learning, principle learning and problem-solving at the summit of his hierarchy of learning behaviour. As an educational theorist, Gagne was sufficiently bold to add a method of instructional design onto his theory so as to carry it into practice. That method was Task Analysis, according to which we can devise instructional materials in one of two ways:

either on a bottom-up basis: Where do the learners start? What should they be able to do next?

or on the basis of top-down analysis: What is the principle that I want to teach?

Which concepts relate directly to that principle?

In Working through the principle is summed up in the break-even equation. The relevant concepts are those of unit cost, unit revenue and unit contribution.

The final learning theory that shed some light on the design of Working through is Ausubel's work on meaning. He developed the neologism 'subsumption' as a shorthand for all the cognitions, takes-for-granted and ways of working that learners bring to new tasks. Insisting that 'the most important single factor influencing learning is what the learner already knows' Ausubel put the active learner at the heart of his theory, and addressed himself not to laboratory tests of behaviour but to the reality of classroom transactions.

Working through aims to corral some subsumptions and channel them towards worthwhile knowledge. The subsumptions can be easily described: simple arithmetic and common sense. Using only these tools, learners can make sense of the dialogue.

The carry-over into drill and practice, essential if learners are to get sufficient,time on task to make the key concept and principle their own, is much smoother than in a situation where break-even is introduced simply as a sequence of rules and propositions that have to be learnt and applied. Recalling the dialogue (and isn't recall a substantial part of learning?) may also assist recall of the embedded cognitions.

So, there it is: a small step in what could be, for teachers and their classes, a long but worthwhile journey.