Having gained an understanding of various cost behaviors, we can now expand our discussion to include the relationships among costs (both manufacturing costs and operating expenses), revenue, and operating income as follows:

**Revenue – Variable Costs – Fixed Costs = Operating Income**

This basic relationship set s the stage for introducing cost-volume-profit analysis. a widely used management planning tool. Cost-volume-profit analysis is often called breake Ven analysis. in reference to the point at which total revenue exactly equals, total cost. The break-even point may be defined as the level of activity at which operating income is equal to ztfV. Its computation often serves as a starting point in decisions involving cost-volume-profit relationships.

Before we proceed with an illustration, one last point must be emphasized. The term profit in cost-volume-profit analysis refers to operating income, not net income. This is because income taxes and non operating gains and lose. do not possess the characteristics of variable costs ‘or fixed costs Cost-volume-profit analysis tells managers very little about cash flow effects. Revenue, for example, could be either cash sales or accounts receivable sales; However, cash flow information can be Important In CVP analysis when an activity that causes cash to vary significantly is a cost driver. Consider a company seiling two products. Product A iS,primarily cash-based sales and product B results in long-term holdings of outstanding accounts receivable balances. Managers may decide to include a cost in product Bis CVP analysis representing the lost opportunity to earn a return on the cash tied up in the accounts receivable balance.

**Cost-Volume-Profit Analysis: An Illustration**

Assume that ProGlide Skate Company manufactures high-quality in-line skates. The company currently sells its product to wholesale distributors in California, Washington, and Oregon. Because of the rapid growth in the popularity of in-line skates, the company is considering distributing to several East Coast wholesalers as well. Although wholesale prices vary depending on the quantity of skates purchased by a distributor, revenue consistently averages $90 per pair of skates sold. ProGlide’s monthly operating statistics are shown below.

**Preparing and Using a Cost-Volume-Profit Graph**

The cost-volume-profit (or- break-even) graph on the following page is based on ProGlide’s cost and revenue statistics. The graph shows the reader, at a glance; the break even point in units and in dollars.

The horizontal ‘axis represents the activity base, which for ProGlide is pairs of skates sold per month. Since the company is not equipped to manufacture more than 1,500 units, per month, this is assumed to be the upper limit of the relevant range. The vertical axis of the graph represents dollars of revenue and costs corresponding to various levels of unit sales activity. The steps in .drawing this graph are as follows

1. Draw the total revenue line. This line runs from $0 to $135,000 in total revenue, which is the maximum revenue that the company can currently generate, given its monthly production capacity of 1,500 units. Note that the slope of the total revenue line equals the average selling price per unit of $90.

2. Draw the fixed cost line. This is a horizontal line representing a constant $37,800 . monthly fixed cost at all volumes within the company’s relevant range of activity.

3. Draw the total cost line. Starting where the fixed cost lme intercepts the vertical axis at $37,800, the total cost line wil] rise by $54,000 to a total cost of $91,800. This is the total cost the company expects to incur, given its monthly production capacity of 1,500 units. Note that, for a~y level of activity, the distance from the fixed cost line to the total cost line represents the company’s total variable cost and that the slope of the total cost line’ equals the company’s variable cost per unit of $36. Thus; for each additional pair of skates that the company sells, its total cost will increase by

$36. c

4. Label the point at which the revenue line intersects the total cost line as the break even point. Note that ProGlide’s break-even point is at 700 units, which corresponds to $63,000 in total revenue.

If ProGlide is able to operate at its monthly capacity of 1,500 units its monthly operating income will amount to $43,200 ($135,000 in revenue, less $91,800 in total costs).

**Contribution Margin: A Key Relationship**

We have shown that variable costs change in direct proportiori to revenue. Thus the generation of an additional dollar of revenue will result in an additional amount of variable cost. The operating data for ProG\ide (Rage 833) indicate that variable costs account for 40% of every sales dollar. In ‘other words, for every $1 in revenue that the company earns, it can expect to incur 40 cents in variable costs. The remaining 60 cents is called the **contributlen margin**.

Contribution margin may be expressed as a percentage of revenue, asa total dollar amount for the period (total revenue less total variable expenses), or as ,the contribution margin per unit (unit sales price less the variable cost per unit). For example, the average contribution margin per pair of skates sold by ProGlide is $54, computed as follows:

**How Many Units Must We Sell?**

The concept of contribution margin provides a quick means of determining the unit sales volume required for a business to break even or earn any desired level of operating income. Knowing the break-even sales volume cari be of vital importance. especially to companies deciding whether to introduce a new product line. build a new plant. or in some cases, remain in business

To illustrate the relationship between sales volume and contribution margin. assume that we want to compute how many pairs of skates ProGlide must sell in a month to break even. From the cost-volume-profit graph on page 834. we can see that the answer is 700 units. We will oow prove that this is so. At the break-even point, the company must generate a total contribution exactly equal to its fixed costs. The data on page 833 show that monthly fixed costs amount to $37,800. Given-a contribution margin of $54 from each pair of skates. the company must sell 700 pairs per month to break even, as follows

This reasoning can be taken one step further to find not only the unit sales volume needed to break even but also the unit sales volume needed to achieve (IIi.\’ desired level oj operating income. The following formula enables us to do this

For example. how many pairs of skates must ProGlide sell in order to earn a monthly operating income of $5,4oo