# 5.5 Cost-Volume-Profit Analysis In Planning

#### Cost-volume-profit (CVP) analysis

Companies use cost-volume-profit (CVP) analysis (also called break-even analysis) to determine what affects changes in their selling prices, costs, and/or volume will have on profits in the short run. A careful and accurate cost-volume-profit (CVP) analysis requires knowledge of costs and their fixed or variable behavior as volume changes.

A cost-volume-profit chart is a graph that shows the relationships among sales, costs, volume, and profit. Look at illustration below.  The illustration shows a cost-volume-profit chart for Video Productions, a company that produces DVDs. Each DVD sells for $20. The variable cost per DVD is$12, and the fixed costs per month are $40,000. The total cost line represents the fixed costs of$40,000 plus $12 per unit. Thus, if Video Productions produces and sells 6,000 DVDs, the company's total costs are$112,000, made up of $40,000 fixed costs and$ 72,000 total variable costs ($72,000 =$ 12 per unit X 6,000 units produced and sold).

The total revenue line shows how revenue increases as volume increases. Total revenue is $120,000 for sales of 6,000 tapes ($ 20 per unit X 6,000 units sold). In the chart, we demonstrate the effect of volume on revenue, costs, and net income, for a particular price, variable cost per unit, and fixed cost per period.

At each volume, one can estimate the company's profit or loss. For example, at a volume of 6,000 units, the profit is $8,000. We can find the net income either by constructing an income statement or using the profit equation. The contribution margin income statement gives the following results for a volume of 6,000 units:  Revenue$120,000 Less: variable costs 72,000 Contribution margin $48,000 Less: Fixed costs 40,000 Net income$ 8,000
We have introduced a new term in this income statement—the contribution margin. The contribution margin is the amount by which revenue exceeds the variable costs of producing that revenue. We can calculate it on a per unit or total sales volume basis. On a per unit basis, the contribution margin for Video Productions is $8 (the selling price of$20 minus the variable cost per unit of $12).  Contribution Margin = Sales - Variable Cost The contribution margin indicates the amount of money remaining after the company covers its variable costs. This remainder contributes to the coverage of fixed costs and to net income. In Video Production's income statement, the$ 48,000 contribution margin covers the $40,000 fixed costs and leaves$ 8,000 in net income.

You can also calculate a contribution margin ratio by using the following formula:

 Contribution Margin RATIO  = Sales - Variable Cost Sales
Watch this video to see more about contribution margin and how it can be used in business.

Profit equation The profit equation is just like the income statement, except it presents the analysis in a slightly different form. According to the profit equation:

Net income = Revenue - Total variable costs - Fixed costs

For Video Productions, the profit equation looks like this:

Net income = $120,000 −$ 72,000 − $40,000 Net income =$ 8,000

The CVP chart above shows cost data for Video Productions in a relevant range of output from 500 to 10,000 units. Recall the relevant range is the range of production or sales volume over which the basic cost behavior assumptions hold true. For volumes outside these ranges, costs behave differently and alter the assumed relationships. For example, if Video Productions produced and sold more than 10,000 units per month, it might be necessary to increase plant capacity (thus incurring additional fixed costs) or to work extra shifts (thus incurring overtime charges and other inefficiencies). In either case, the assumed cost relationships would no longer be valid.

The contribution margin income statement is used quite frequently since it separates fixed and variable costs to allow a company to see what it can directly change and what it cannot change.  This video will give you an example of the why and how to do a contribution margin income statement.