# Break-Even Analysis

In an earlier lesson, we suggested that one of the advantages of our coffee shop idea was that the venture could break even at what seems to be an easily achievable volume. This was a rather cursory reference to an important tool called break-even analysis. A break-even analysis examines the interaction among fixed costs, variable costs, prices, and unit volume to determine that combination of elements in which revenues and total costs are equal.

Fixed costs are those expenses necessary to keep the business open, and are not impacted by sales volume. They will include such things as rent, basic telephone expenses and utilities, wages for core employees, loan or lease payments, and other necessary expenditures. An entrepreneur should also include a living wage for himself/herself as a fixed cost.

Variable costs include those expenses that change as a result of sales volume. This can be a relatively simple relationship, as in cost of goods sold, where for example the variable cost of baked goods sold at our coffee shop is what we pay the baker for them, \$0.30 each. Variable costs can also be very complex; for example, higher sales in one area of our business may increase long distance charges. Labor costs may be fixed for full-time employees, then, as sales increase, some overtime is incurred until additional personnel can be justified.

Generally, an initial break-even analysis focuses on a relatively narrow range of sales volume in which variable costs are simple to calculate. The variable cost in our coffee shop is simply the cost of goods sold. For a pizza delivery operation, it might be the cost of ingredients, and some cost allocated for operation of the delivery vehicle. A general term often used for the difference between selling price and variable cost is “contribution margin,” or the amount that the unit sale contributes to the margin available to pay fixed costs, and generate profit (we hope).

Now let’s take a look at how break-even analysis can be helpful to us. For this example, let’s assume we have determined that the level of fixed costs (salaries, rent, utilities) necessary to run our coffee shop on a monthly basis is \$9,000. In addition, a cup of coffee that we sell for \$1 costs us \$0.25 for the bulk coffee, filters, and water.

The contribution margin of a cup of coffee is, therefore, \$0.75. We can now calculate how many cups of coffee we have to sell to cover our fixed costs:

 Break-Even = (Fixed Costs) / (Contribution Margin) = \$9,000/\$0.75 = 12,000 cups of coffee per month

Let us say, further, that the fixed cost estimate was based on being open 6 days a week, 8 hours a day. This converts roughly to 200 hours a month, so we have to sell 60 cups an hour. This is a cup a minute for every minute we are open.

Does this seem feasible? Let us assume not, and evaluate some options.

(1) Cut fixed expenses

Remember that we are still in the planning stage here, and experience has shown that prospective entrepreneurs almost always underestimate expenses. Let’s pass on this approach.

(2) Raise prices

We could plan on charging \$1.25 per cup from the beginning, for a contribution margin of \$1 per cup. The arithmetic is easy; to cover \$9,000 in fixed expenses we need to sell 9,000 cups of coffee per month. The most important factor here is what the competition is charging.

For the sake of clarity in demonstrating relationships between price, cost, and sales volume, we have considered a simplified version of how a real coffee shop might operate. The market severely constrains the amount we can charge for an ordinary cup of coffee, and a one product shop would have limited appeal.

Let us say we will also offer gourmet coffees, which cost us \$0.50 per cup to brew, at \$2.00 per cup. We will also offer baked goods, which cost us \$0.30 each, at \$1.30. The break-even calculation is now indeterminate, that is, there are an infinite number of solutions without making some additional assumptions.

We will assume that two-thirds of our coffee sales will be regular coffee (call the number of cups R, the remaining third, gourmet coffee, G). Let us further assume that half of all coffee purchasers also buy a pastry (P):

 Contribution Margin (CM) = CM for each product * Units sold = \$0.75*R + \$1.50*G + \$1.00*P But G is half of R, and P is half of R and G combined: = \$0.75*R + \$1.50*(R/2) + \$1.00*(R+G)/2 relating entirely to R: = \$0.75*R + \$0.75*R + \$1.00* (R+(R/2))/2 combining and simplifying: = \$1.50*R + \$1.00*(3*R/4) = \$1.50*R + \$0.75*R = \$2.25*R

Since this must equal fixed costs at break-even: \$2.25*R = \$9000; R = 4000

Relating back to our assumptions, each month we must sell 4000 cups of regular coffee, 2000 cups of gourmet coffee, and 3000 pastries. Does this seem more feasible?

This has been a very brief overview of how breakeven analysis can be used in helping the entrepreneur better understand the relationship of the financial factors involved in measuring the feasibility of a proposed venture. From a preliminary analysis of selling prices that the market will bear, prevailing costs, and reasonable expectations of sales volumes, the entrepreneur can avoid making serious mistakes and may discover significant opportunities.

Wishing you success,

John B. Vinturella, Ph.D.

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