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# Break-Even Analysis

The Weatherhead School of Management, part of Case Western Reserve University, provides a succinct definition of break-even analysis on its Web site of the same name: "On the surface, break-even analysis is a tool to calculate at which sales volume the variable and fixed costs of producing your product will be recovered. Another way to look at it is that the break-even point is the point at which your product stops costing you money to produce and sell, and starts to generate a profit for your company." They continue to say that break-even analysis can also be used to solve other management problems, including setting prices, "targeting optimal variable/fixed cost combinations," and evaluating the best strategies to follow.

The basic formula for break-even analysis, sometimes abbreviated as BEA, is as follows:

BEQ = FC / (P-VC)

Where BEQ = Break-even quantity

FC = Total fixed costs

P = Average price per unit, and

VC = Variable costs per unit.

Fixed costs are costs that never change no matter how much or little a company produces: administrative salaries, rent or mortgage payments, insurance, interest on borrowed funds, and similar costs sometimes also labeled fixed overhead. Variable costs are directly tied to product manufacturing or service provision: direct labor, raw materials, sales commissions, delivery expenses, and more.

In the formula shown above, BEQ, the "quantity," refers to a single unit sold, whatever it might be. It may be a product like a teddy-bear (including its packaging) or something more complicated such a "carpet cleaning job" (including travel to and from the site). BEQ always refers to the actual entity sold (teddy-bear or carpet cleaning job) rather than something that goes into the entity (e.g., teddy-bear stuffing or vacuum cleaner bags). BEQ is the entity the company puts a price on, "the unit." Total sales of this unit, divided by the number of units sold, produces P, the average price. All costs associated with the unit, divided by number of units sold, yields VC, the cost per unit. Note that fixed cost is not included in VC.

Price per unit less variable cost per unit produces a surplus if the price is set correctly. In accounting terminology, this is called the "contribution margin." It is the amount the sale of each unit contributes to the ultimate profitability of a corporation. When enough such chunks of contribution have been produced to equal fixed costs, the business has reached its break-even point. It isn't profitable yet, but all of the overhead has been "absorbed."

Supposing that fixed costs are \$150,000. Price per unit is \$85 and variable cost per unit is \$75. The contribution margin will then be \$10. Fixed cost divided by \$10 results in 15,000. Therefore this company must sell 15,000 units just to break even. The next unit sold thereafter is the first contribution to profit. This company must sell 15,001 units to make a tiny profit of \$10.

This example illustrates how changes can affect break-even. Fixed costs can be lowered, price can be increased, variable costs can be shaved. Conversely, if variable costs rise and cannot be lowered, contribution margin will sink and break-even will require more salesunless, for example, price is hiked or the company moves to cheaper space and lowers its rent substantially.

## DIFFICULTIES AND APPLICABILITY

BEA is easiest to use in situations where the product or service is uniform and variable costs can be very clearly calculated and assigned to the "unit." Significant analytical problems arise with complexity. In a medical practice, for example, the "unit" may be easy to determine: it is a single patient-visit to the practice. But variable cost associated with every visit will vary with the patient's condition, needs, medical insurance policies, the payments those policies cover depending on the diagnosis, the percentage of charges the patient must pay directly, and the variable costs of collecting that contribution. Administrative personnel dealing with insurance companies must maintain exacting records to tie their time not only to patients but to specific visits by each patient. Doctors, similarly, must be meticulous in dividing time between administrative duties (fixed costs) and patient-related activities (variable costs); these activities often extend beyond the visit itself, e.g., to time spent reviewing test results or studying recent literature on a disease or medication. Very substantial data must be gathered over a long time to arrive at precise data. Unless this is done, the break-even analysis will be too broad to serve informed management decisions.

An example of the difficulties is presented by Merry J. McBryde-Foster writing in Nursing Economics about BEA as practiced in a hypothetical nurse-managed center. "[P]rices for visits will vary according to the type of visit billed," writes McBryde-Foster. "The variable costs of visits will vary according to the type of visit." She shows how, in this hypothetical center, contribution margins for each type of visit must be calculated using Current Procedural Terminology (CPT) codes. CPT was developed by the American Medical Association and is a complex structure that frequently changes based on Medicare Payment Schedules.

Similar difficulties arise in many contracting businesses where the size and complexity of the contractwhich is the "unit"and the great variability of inputs make it very difficult to produce a single number that means break-even.

Despite these difficulties, BEA is universally applicable. Attempts to apply it will bring out deficiencies in accounting and cost-tracking practices and will indirectly improve the management of the business.

## BIBLIOGRAPHY

Bohinc, Michael A. "Math for Contractors or Yes, Your Teacher Was Correct: All too often, hard-working contractors are shortchanging themselves by making mistakes in math and accounting." Plumbing & Mechanical. October 2004.

Hilton, Ronald W. Managerial Accounting. McGraw-Hill, 1991.

LeFever, Steve and Laurie Owen. "Break Even, Part II: Know thy costs and manage the 'creepers'." Jewelers Circular Keystone. January 2005.

McBryde-Foster, Merry J. "Break-Even Analysis in a Nurse-Managed Center." Nursing Economics. January-February 2005.

Peterson, Ken W. "Break-Even Analysis Boosts Dealer Profitability." Kitchen & Bath Design News. March 2005.

Hillstrom, Northern Lights

updated by Darnay, ECDI

# Break-Even Analysis

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