AC_DC and Breakeven Analysis

A single procedure suffices, just one and the same algorithm, both to elaborate various AC_DC calculations (AC: Absorption Costing or full costing. DC: Direct Costing or marginal costing or differential costing) and to perform breakeven analysis to the fullest extent. Breakeven analysis, under the assumption ‘production volume is equal to sales volume’, results in one or a few breakeven points. These points however belong to a breakeven line. A general maxim exists of which classical breakeven analysis is merely one of the applications.

Total turnover of a certain good in a period is the amount of sales (sales volume) multiplied by the (proportional) selling price per unit. The eventually existing difference between sales volume and production volume is the mutation of the supply, i.e. a number of units (positive or negative) that can be multiplied either by the standard unit-cost of the finished goods in supply (in case of AC calculation) or by just the differential costs of such a unit (in case of DC calculation).

Not only the mutation(s) of the finished goods must be calculated, but also the mutations of the various stocks of work in progress. In case of AC, fixed costs are part of the valuation (costs) of both work in progress and finished goods. In DC calculations, fixed costs are not included in product costs. The gross performance is total turnover added to the mentioned multiplication product being the mutation supply measured in money units. This performance less total costs, variable as well as fixed costs, results in the AC and respective DC profit figure at the bottom line. The calculation in fact represents a formula. One single formula that is applicable, either for calculations AC and DC or for everything imaginable with regard to breakeven analysis and profit isographs.

Cost calculation sets tongues wagging. Every bit in business is involved with money. Costs are guidelines to act in a reasonable way. However, one often does not have to calculate all costs in order to arrive at sensible conclusions. Generally AC is to be preferred in case of main problem definitions in the long run. Questions like ‘which place of business?’ and ‘which means or which method of production?’, oblige one to calculate all involved costs. In the relatively short run however, DC can solve many problems. DC costs less time, effort and money compared to AC (being efficient), whilst the same optimum solution still is attainable, so DC can be effective as well.

Within DC, one only has to calculate the so-called ‘opportunity costs’ i.e. the differential costs, the marginal costs, often in short the variable costs. If DC happens to be effective too (both roads lead to Rome; DC is more efficient beforehand), one naturally chooses DC. Literature as well as practice are swarming with disputes between advocates and opponents of AC and DC. Divergent ‘solutions’ are given even in the case of a classic example.

A simple sum ends up in different results, AC versus DC. It looks like magic. It would not be wise to become an advocate of neither AC nor DC. Make sound choices, one time AC, another time DC. If possible DC should be chosen in order to solve a problem, but remember there are particular problem definitions for which AC is a must. For instance, there is no free choice to practice either the AC or the DC method to calculate the net period profit of a business.

It has to be AC regarding the figure at the bottom line of a company as a whole. And it is wise to practice DC in reporting to headquarters the results from different business units within a company. Generally speaking, an arbitrary choice AC or DC is out of the question. Balance sheets and the ultimate profit and loss accounts should encompass literally everything.

Breakeven, classic case, sales volume is equal to production volume i.e. the volume is X [number]. Selling price/unit (normal) is s (proportional), f.i. 27 money units. Normal production and sales volume is N (each period). Fixed costs (normal) are C (each period), f.i. 600,000 money units. Differential costs/unit (normal) are d (proportional), f.i. 12 money units.

Breakeven: total proceeds = total costs

27 · X = 600,000 + 12 · X     →     15 · X = 600,000

It follows: X breakeven = 40,000 units (central theme in production)

40,000 units · 27/unit = 1,080,000 breakeven turnover (key item in sales)

Breakeven, in general, Sales volume is V and Production volume is P

SUC (Standard unit-cost) is:    C/N + d

Total proceeds = Total sales + Mutation supply (in money units)

Total proceeds = V • s + (P -/- V) • SUC  in case of AC calculation

So, it holds:

{V • s + (P -/- V) • SUC -/- Total costs} • (1 -/- quota) = Net profit

{V • s + (P -/- V) • SUC -/- P • d -/- C} • (1 -/- quota) = Net profit

Quota belongs to the exchequer; consequently the remaining part is net profit.

This formula is simply to keep in mind, not in parameters but in words.

Sales + Mutation supply [money] i.e. Total proceeds -/- Variable costs -/- Fixed costs = Result

Mutation supply [money]: (P -/- V) • SUC in case of AC calculation or (P -/- V) • d in case of DC calculation

AC is trying to accrue the fixed costs in the best possible way (the credo is who or what makes filthy has to pay) whilst DC dismisses the matter lightly. DC simply calculates a pro rata division for the fixed costs all through the different parts of a particular time period. In case of DC calculation, the result is independent of the number P. No matter what the level of production is, more or less sales only will determine the DC figure at the bottom line.

Re free downloadable paper ‘Calculations AC_DC and Breakeven Analysis‘.

Business Economics VI Groundbreaking, learning content Chapter 7, Calculating with all costs (integral costs) versus calculation with only those costs that change if this or that is chosen. Which costs will be different and which costs will not be affected by what you choose or do not choose in a particular situation? And learning content Chapter 8, Determining minimum sales price; Breakeven Analysis. After Chapter 8 you can clearly indicate the point(s) above which profit is made and where loss is suffered.

AC_DC is just one of the 8 Main Items in my book, not to be neglected, suitable for self-study, hardly needing a teacher.

My book THEORY, No. 1 from a triptych, is indeed groundbreaking with even more than these 8 Main Items, available at Amazon.

I am independent researcher Business Economics and inventor of The Profit Formula®: The Way to Easy Profit Measurement. I have more than 20 years of experience as a lecturer in Business Economics, and I have always been critical of what was in many textbooks. My book goes beyond the borders of set science, and rewrites large tracts of Business Economics as it is currently badly taught worldwide.

Business Economics is a training course of making sums.

No. 2 from the triptych Exercises, Problems, Questions is for everyone the ultimate test:

No. 3 from the triptych Elaborations, Answers gives everyone the ultimate solution:

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