# Breakeven Analysis: Deciding Whether to Take the Plunge

Michael Sack Elmaleh, C.P.A., C.V.A.

Breakeven analysis is a cost accounting technique that helps potential business owners decide whether it is prudent to go into a particular line of business. The idea is to give the prospective business owner some reasonable idea of how much sales activity will be needed to breakeven.

Example. Ma Jong is currently the VP of operations at the Hong Kong Bong company. Having been passed over for a promotion she thinks she richly deserved, she is considering setting up her own wholesale bong distributorship. She needs to know how many bongs she would have to sell in order to breakeven.

The breakeven approach tackles this problem by distinguishing between fixed and variable costs. Variable costs are costs that vary with the volume of units sold. Direct unit manufacturing costs and sales commissions are examples of variable costs. Fixed costs, as the name implies, are costs that do not vary with sales volume. Insurance, office rent, and clerical salary are typical examples of fixed costs.

Example. Ma Jong estimates that she can purchase quality bongs from manufacturers for \$4 per unit. She expects the average sales price to be \$20 per unit and that she will pay a 10% commission for each unit sold, or \$2 per units. So her total variable unit costs are expected to be \$6 per unit. She estimates her fixed costs in rent, insurance, and other overhead to be \$28,000 per year.

To compute the breakeven point, the amount of sales volume needed to breakeven, the following formula is used:

### Breakeven Point in Dollars = (SP-VC)*X – FC

X= Units needed to breakeven

SP= Unit selling price

VC = Unit variable costs

FC= Total annual fixed costs

Often the difference between the unit sales price and unit sales costs (SP-VC) is called the contribution margin (CM). Now the breakeven point in dollars is literally the point where total revenue less total expenses equals 0. So we can restate the above equation as follows:

### \$0 = (SP-VC)*X – FC

Replacing (SP-VC) with CM yields:

### \$0 = (CM)*X – FC

Rearranging the terms in the above formula gives a new formula for the breakeven point in units:

In words this says that the units that must be sold to breakeven equals the total fixed costs divided by the contribution margin.

Example. Since Ma Jong’s unit sale price is \$20 and her unit costs is \$6, her contribution margin, CM, equals \$14. Dividing this into her expected fixed costs of \$28,000 yields a breakeven volume of 2,000 units. You can check this formula by constructing an income statement.

So what does this tell Ma Jong? It tells her that she has to be able to sell 2,000 bongs to just breakeven. But Ma Jong, like most other business owners, needs to do better than just breakeven. She needs to pay herself for her time and effort and get a reasonable profit on her investments. So the above formulas need to be modified to accommodate a required salary and/or profit for the owner. Now this required return for the owner is really just another fixed cost. So the revised formula is:

Example. Let’s say that Ma Jong’s current salary is \$84,000 and she feels that she needs at least this much to justify going into business for herself. So taking (28,000+84,000)/14 yields 8,000 units. This means that if her projected unit revenue, unit costs and fixed costs are accurate, selling 8,000 bongs will yield her a profit or salary of \$84,000. Now Ma Jong has to decide whether she thinks that selling 8,000 bongs is really feasible or is just a pipe dream.

## Warning! Warning! Warning!

Precise numbers and formulas can lull us into thinking that we have greater knowledge than we actually have. In applying breakeven analysis or other cost accounting techniques simplifying assumptions and guesstimates almost always have to be made. Reality will almost always be messier than our formula answers would lead us to believe.

For example in most wholesale or retail businesses more than one type of product is sold. Each different product is likely to have different unit revenue and unit variable cost characteristics. The above breakeven model assumes only one product. To apply the model to a multi product firm requires taking average unit prices and average unit costs. Or perhaps averages weighted by the popularity of products sold. These simplifying assumptions can and will create distortions.

Another important factor in applying breakeven analysis is the fact that the distinction between fixed and variable costs is not always easy to make. Much depends upon the time frame involved. It is often said that in the very short run all costs are fixed and in the long run all costs are variable. How you slice costs between fixed and variable will have a great effect on the results obtained.

In most cases the results of the breakeven analysis should be considered a rough approximation of the kinds of volume needed to achieve desired results.

For tips on using Excel to compute breakeven points click here.

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