Breakeven Analysis

Part 1 - Current Opinion

David J. Newlands IESEG School of Management, Catholic University of Lille

The conventional breakeven calculation approaches, in their present form have been around since the 1930s. Enterprises need to identify the optimum sales price to determine the highest profit, and ensure they have sufficient capacity to achieve the volume required. Hence, most entrepreneurs approach the problem by undertaking a series of breakeven calculations. This approach suggests an optimum production volume to maximise profit. The fundamental underlying perception is that manufacturing enterprises produce goods as independent entities. This article examines conventional breakeven calculations that assume the supplier is the sole source. Part 2 then uses the same calculations in a dual supplier scenario that takes account of two modern manufacturing paradigms: concurrent engineering and customer supplier relationships.

CONVENTIONAL PROFITABILITY CALCULATIONS

Breakeven analysis is based on the assumptions that (1) there are both fixed costs and variable costs and (2) either only one product is manufactured or it is possible to assign a chunk of fixed costs to each product being manufactured. The fixed costs are represented graphically by a straight line (fixed costs are independent of volume). Variable costs are represented by a straight line starting at the origin (the more that are made, the higher the cost). Total costs therefore are represented as shown. Total revenue is directly proportional to sales volume for a given price. The higher the price, the steeper the straight line becomes. There are an infinite amount of

Figure 1
Breakeven volume basic construction

Revenue Profit

ue en ev R

it Prof

Contribution
st l Co Tota

Fixed Cost

ss Lo
Variable Cost

Price

Break-even Volume/yr

Volume/year Operating Volume/yr

possibilities for this family of total revenue lines (as there are an infinite number of possibilities for the price). The total cost graph is realistic in the sense that the more sold the more the total cost. However, the total revenue graph for a given price is theoretically true (the more that are sold, the greater the revenue), as shown in Figure 2. However, the actual amount of total revenue is dependent on the quantity that can be sold, so there is a practical limit to how far up the revenue line it is possible to go. This can be illustrated by considering the cost of a commodity like beer. If beer was 20 per litre the total revenue graph would be very steep, however not many litres would be sold, so the practical limit would be determined by a very small sales volume and therefore a very small amount of total revenue. If beer was 0.10 per litre there likely would be huge sales, however there would still be a practical limit to the amount of beer to be consumed. The point at which the total revenue line for a given price crosses the total cost line is the point of zero profit, because here the total revenue equals total cost. This is known as the breakeven point. Above the total cost line there is a profit, below it there is a loss. Clearly if the price is less than the variable cost the total revenue will never reach the total cost line, so there will be no breakeven point and there will always be a loss situation. It is possible therefore to work out graphically q The breakeven volume for a given price q The breakeven revenue and therefore the breakeven price for a given volume.

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It is also possible to add an amount of profit onto the graph and calculate sales volume to give this profit for a given price and the prices to give this profit for a given volume. Conventional profitability calculations typically are based on a relationship between price and sales volume shown in Figure 3. The trend suggests that a lower sales price generates more interest from potential customers, which translates to increased sales volume. A relatively linear (or curvy-linear) trend starting from zero typifies this type of analysis, especially for academic examples. Such data may be formulated from a number of sources, typically including competitor analysis, market survey data, respected analysts opinion and intuition.

Figure 2
Breakeven volumes increased by decreasing price
Break-even Volumes
Total Revenue for a given price (decreasing) Euros

Total costs (fixed + variable

Fixed Costs

Volume

Figure 3
An example of a price to sales curve
Euros 1,60 1,40 1,20

Price Sales Curve

units and make a given percentage return on sales? and "What volume needs to be sold at this price to breakeven?" Taking the mathematical approach, known parameters are variable and fixed costs. The unknowns are profit, volume and price.
Price Sales Curve

Sales Price

1,00 0,80 0,60 0,40 0,20 0,00 0 10 000 20 000 30 000 40 000 50 000

Variable cost = vc Fixed cost = fc Price = P Volume = x Price = y We know that Profit = Total revenue total cost. P = x.y - [x.vc + fc]

Sales Volume

For completeness, here is a table showing the calculations used to generate the trend graphs shown in this article. The table shows a spreadsheet used to calculate data plotted graphically in Figures 2, 3 and 5. Revenue is calculated from the anticipated sales volume, multiplied by the sales price. Total variable costs are the number of units sold, multiplied by the variable cost per unit. Fixed costs remain constant. Profit, or loss, is calculated by subtracting total variable cost and the fixed costs from total revenue. Total costs are fixed costs plus total variable costs. Lines of enquiry include "What price do we need to charge to sell N

Table Breakeven calculations of various volumes to prices

Euros 10 000.00 0.25 1.25 1.00 0.75 Revenue Total Var. Cost Fixed Cost x.y x, 0,25 10 000,00 0 12 600 21 400 26 400 27 600 25 000 0 2 500 5 000 7 500 10 000 12 500 10 000 10 000 10 000 10 000 10 000 10 000 Profit Rev.-Vc-FC 10 000 100 6 400 8 900 7 600 2 500 Total Costs (Vc.x)+Fc 10 000 12 500 15 000 17 500 20 000 22 500

Total Fixed costs Variable cost/unit Sales price 1 Sales price 2 Sales price 3 Anticipated sales x 0 10 000 20 000 30 000 40 000 50 000

Price y 1,40 1,26 1,07 0,88 0,69 0,50

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This equation has three unknowns and therefore is unsolvable. It is however possible to fix profit. Figure 1 suggests profit will be zero at the breakeven point, hence: let P = 0. The equation thus becomes 0 = x.y - [x.vc + fc] Two unknowns still remain. However, it is now more meaningful to fix either the price (y) or volume (x) and with the chosen value thus work out the other unknown. Market pricing, design or target cost and strategic judgement can be applied. These require market research to be undertaken and volume expectations to be set. Management must use a sanity check to determine the reasonableness of the answer. Sanity checking is used in the West. However, Japanese companies focus on target costing. Typically they will know what the volume capacity of their factory is. They set the sales price at or below market average. They fix the profit they wish to earn at a specific amount or rate for the volume they intend to produce to cover the fixed cost element. They then focus on reducing the variable cost to achieve the objective of breaking even. Variable costs are reduced using quality techniques to eliminate re-work, scrap etc. Value analysis is used to identify tasks that add no value, and stop spending money on these. Product designs are analysed to reduce the amount of work necessary (and hence cost) to produce them. The Japanese also eliminate supervision, since this is associated with quality control. Workers inspect their own output and maintain the capability of the processes. Japanese firms also were able to make use of material providers within their keiretsu [1]. "What volume do we need to breakeven at a price of 0.50? . 1.00? . 1.40?" These quantities can be calculated using the equation above. The solutions to these can then be used to aid operations, marketing and strategic decision making. Is the company going to be a follower, a design leader, a co-developer, a unique source of supply, or a company that sells machine time? Equally valid is to ask the question

in the opposite direction. For instance, if factory capacity is limited to a certain number of units, "What price do we need to charge to breakeven at this volume?" Judgement can then be applied "It seems realistic", "Selling that volume at that price is not likely" or "Orders will come in so fast we wont keep up with demand. Reactions depend on the price - if it is about right, too high or too low. The profit can be put to any figure, not necessarily zero. It could be put to 10,000. 10,000 = x.y - [x.vc + fc] or 10% return on sales. In this case the profit would be 10% of total revenue or 0.1x.y 0.1x.y = x.y - [x.vc + fc] Similar questions can now be asked regarding the profit point about prices and volumes. Figure 4 depicts two trend lines: a revenue line (volume multiplied by sales price) and a total cost line (fixed costs and variable costs). This example shows a breakeven point at 10,000 units, providing 12,500 revenue. A second breakeven point can be extrapolated toward the high end of the graph at 55,000 units. Between these two volumes, assuming the price to volume ratio shown in Figure 3 is adhered to, the company would have a variable amount of profit. The company may decide to choose a certain volume to maximise profit, or to maximise volume in order to take market share. A third option is

to break the market into segments and fulfil niche requirements. Figure 5 shows the financial profit or loss for various volumes. From this, one could determine that producing 30,000 units would be the most profitable solution. This answer might well be chosen if the business is simply trying to use up spare manufacturing capacity. It certainly is not the approach exemplified by Japanese companies. They tend to choose the volume they wish to produce, determine the amount of profit they intend to make, and then engineer the total costs, in what has been termed target costing, in order that they produce the required profit. Core to this argument is that companies have within their options, the choice of creating engineering solutions to reduce total costs. As volume rises, the choice of what type of technology is employed in the manufacturing system becomes more critical. Suppliers can also be commissioned to develop new technologies or variants that integrate functionality, previously provided by separate components. Such commissions can be in the form of non-recurring expenditures. These tend to be fixed sum development contract payments granted to suppliers. It is relatively straightforward to use calculus to fit a quadratic equation to generate the optimum identified by profit and to identify both the maximum and minimum volumes, and maximum and

Figure 4
An academic example of a cost to profit trend
Euros 30 000 25 000

cost/profit graph
Revenue Total Cost

Cost/Profit

20 000 15 000 10 000 5 000 0 0 10 000 20 000 30 000 40 000 50 000

Sales Volume

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Figure 5
Euros 10 000 5 000 Profit/Loss 0 0 5 000 10 000 15 000 10 000 20 000 30 000 40 000 50 000 Profit/Loss on Various Volumes Sales Volume

Profit/loss on various volumes

Irwin, Homewood, Il., (1993). Dyer, J. How Chrysler created an American Keiretsu, Harvard Business Review, July-August, 1996, pp42-54. Miyashita, K. and Russell, D., Keiretsu: Inside the Hidden Japanese Conglomerates, McGraw-Hill, London, (1996) .
There is no concise translation for the Japanese term keiretsu. The word does not change from the singular to plural. Synonyms in English include corporation, group, alliance, association, cartel, portfolio and cluster. Six principal keiretsu predominate in Japanese industry. They are: Mitsubishi, Mitsui, Fuyo, Sanwa, Sumitomo, DKB. The 6 keiretsu in Japan each have a central banks to assist co-ordinating research, production and development.

minimum unit sales prices. The total cost gradient is calculated using y=mx+c while the curvy line is defined by y = (- bb-4ac)/2a The approach requires some differentiation calculus and assumes symmetrical parabola to achieve a satisfactory solution. Further details about this method are found in Drury [2].

CONCLUSIONS
The profit/loss line shows a steady trend similar to the theoretical model shown in Figures 3 and 4. Companies could use smoothing coefficients to make a best fit. Conventional profitability calculations have a number of tacit assumptions. Significant amongst these are: 1. the falsity that the market is unlimited 2. the relationships are linear, or at least curvy-linear and 3. that one set of relationships exist to govern each volume and price. To achieve high profits though manufacture, suppliers need to develop discrete technical capabilities that reduce the fixed administrative costs and convert materials better, faster and cheaper than they currently can imagine. Increasing the speed reduces the time required, hence allowing greater volume to be produced on the same number of tools, or allows fewer tools to be used and liberates capacity for other products. Automating processes

(numerical control for example) provides quick response and flexibility. Process controls (Andon) eliminate the need for humans to monitor processes, hence the variable costs per unit reduce to the material purchase price, power consumption, tool maintenance and wear. Sub-contracting companies should actively become involved in target costing activities in order to understand where value is achieveable and define their operations strategies accordingly. Part 2 resets the discussion about the breakeven volumes. The arguments in Part 1 use a sole sourcing scenario. Part 2 briefly reviews dual, multi, sole and single sourcing strategies used by procurement functions to ensure their businesses obtain appropriate quality, low purchase price and reliable deliveries [3]. The article examines conventional breakeven calculations by assuming a dual supplier scenario that takes account of two modern manufacturing paradigms: concurrent engineering [4] and customer supplier relationships. A non-attributed financial case study demonstrates significant differences in profitability profiles from the conventional theoretical smooth profit profile that results from competitive bidding and dual sourcing.

[2] Drury, C. Management and Cost Accounting, 4th Ed., Thomson Business Press, London, (1996) . [3] Baily, P., Farmer, D., Jessop D., and Jones, D. Purchasing Principles & Management (7th Ed), Pitman Publishing London (1994). [4] Newlands, D. Supply Chain Re-engineering: A Case Study, Control, February 2003, pp 18-20.

About the author

David J Newlands has worked in various industrial positions, from his apprenticeship through to sales, system calibration, test engineering, lecturing and research into supply chain issues. He gained a B.Eng. in Manufacturing Systems Engineering and his PhD in supply chain methodologies that focused on supplier development. David is Senior Assistant Professor of Operations and Industrial Management at the Institut dEconomie Scientifique et Gestion. IESEG School of Management is part of the Catholic University of Lille, North France.

REFERENCES
[1] Burt, D. and Doyle, M. The American Keiretsu: A Strategic Weapon for Global Competitiveness, Business One

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