# Cost-Volume-Profit Analysis

 Author John Alvis Pages 141-144

Page 141

Cost-volume-profit (CVP) analysis expands the use of information provided by breakeven analysis. A critical part of CVP analysis is the point where total revenues equal total costs (both fixed and variable costs). At this breakeven point (BEP), a company will experience no income or loss. This BEP can be an initial examination that precedes more detailed CVP analyses.

Cost-volume-profit analysis employs the same basic assumptions as in breakeven analysis. The assumptions underlying CVP analysis are:

The behavior of both costs and revenues in linear throughout the relevant range of activity. (This assumption precludes the concept of volume discounts on either purchased materials or sales.)

Costs can be classified accurately as either fixed or variable.

Changes in activity are the only factors that affect costs.

All units produced are sold (there is no ending finished goods inventory).

When a company sells more than one type of product, the sales mix (the ratio of each product to total sales) will remain constant.

Figure 1

Cost-Volume-Profit Analysis, Production = Sales

In the following discussion, only one product will be assumed. Finding the breakeven point is the initial step in CVP, since it is critical to know whether sales at a given level will at least cover the relevant costs. The breakeven point can be determined with a mathematical equation, using contribution margin, or from a CVP graph. Begin by observing the CVP graph in Figure 1, where the number of units produced equals the number of units sold. This figure illustrates the basic CVP case. Total revenues are zero when output is zero, but grow linearly with each unit sold. However, total costs have a positive base even at zero output, because fixed costs will be incurred even if no units are produced. Such costs may include dedicated equipment or other components of fixed costs. It is important to remember that fixed costs include costs of every kind, including fixed sales salaries, fixed office rent, and fixed equipment depreciation of all types. Variable costs also include all types of variable costs: selling, administrative, and production. Sometimes, the focus is on production to the point where it is easy to overlook that all costs must be classified as either fixed or variable, not merely product costs.

Where the total revenue line intersects the total costs line, breakeven occurs. By drawing a vertical line from this point to the units of output (X) axis, one can determine the number of units to break even.

Page 142

A horizontal line drawn from the intersection to the dollars (Y) axis would reveal the total revenues and total costs at the breakeven point. For units sold above the breakeven point, the total revenue line continues to climb above the total cost line and the company enjoys a profit. For units sold below the breakeven point, the company suffers a loss.

Illustrating the use of a mathematical equation to calculate the BEP requires the assumption of representative numbers. Assume that a company has total annual fixed cost of \$480,000 and that variable costs of all kinds are found to be \$6 per unit. If each unit sells for...