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Managerial Accounting Unit 5: Cost-Volume-Profit and Break-Even Analysis

CVP analysis uses contribution margin to answer how many units a company must sell to break even or hit a profit goal. It is one of the most tested topics in managerial accounting.

Covers: Break-even in units and dollars, Target profit (pretax and after-tax), Margin of safety, Operating leverage, Multiproduct break-even and sales mix, CVP graph and assumptions, What-if analysis of price, cost and volume changes

Study guide

Cost-volume-profit (CVP) analysis studies how price, volume, variable cost, fixed cost and sales mix affect profit. Its core equation is profit = (price - variable cost per unit) × units - fixed costs, or profit = CM per unit × Q - F. The break-even point is where profit is zero, so break-even units = F ÷ CM per unit and break-even sales dollars = F ÷ CM ratio. For example, with fixed costs of $96,000 and a unit CM of $16, break-even is 6,000 units. Each unit sold beyond break-even adds its full CM to profit, because fixed costs are already covered.

To find the volume needed for a target profit, add the target to fixed costs: units = (F + target profit) ÷ CM per unit, or dollars = (F + target profit) ÷ CM ratio. If the target is stated after taxes, first convert it to pretax income by dividing by (1 - tax rate). The margin of safety is how far sales can drop before a loss: actual sales - break-even sales, or as a percentage, that difference ÷ actual sales. What-if analysis applies the same equation to proposed changes. A price cut, a new ad campaign or a wage increase can each be judged by its effect on total CM and fixed costs.

Operating leverage measures how sensitive income is to changes in sales. The degree of operating leverage (DOL) = CM ÷ operating income at a given sales level, and % change in income = DOL × % change in sales. Firms with high fixed costs and low variable costs have high operating leverage: profits climb quickly when sales grow but fall just as quickly when they shrink. DOL is highest near break-even and declines as sales rise. A neat link: the margin of safety percentage equals 1 ÷ DOL. Choosing between automation and labor-intensive production is really a choice about operating leverage and risk.

Most firms sell several products. Multiproduct CVP assumes a constant sales mix and uses a weighted-average CM. In units, build a package matching the mix (for example, 3 of A and 1 of B), find the CM per package, and divide fixed costs by it. In dollars, weight each product's CM ratio by its share of sales. If the mix shifts toward low-margin products, the average CM falls and break-even rises even when total sales hold. CVP also assumes linear revenue and costs in the relevant range, constant prices and unit variable costs, and production equal to sales. Results are only as good as these assumptions.

Key ideas

• Break-even is where total CM equals fixed costs and operating income is zero.
• Use CM per unit for answers in units and the CM ratio for answers in dollars.
• Target profit is added to fixed costs; after-tax targets must first be divided by (1 - tax rate).
• Margin of safety measures the cushion between actual and break-even sales.
• DOL = CM ÷ operating income, and it multiplies percentage changes in sales into income changes.
• Multiproduct break-even uses a weighted-average CM based on a constant sales mix.
• CVP assumes linear costs and revenues within the relevant range.

Formulas and rules

Common mistakes

• Dividing fixed costs by price or variable cost instead of contribution margin.
• Using the CM ratio when the question asks for units, or CM per unit when it asks for dollars.
• Adding an after-tax profit target directly without converting it to pretax income.
• Dividing margin of safety by break-even sales instead of actual sales.
• Using a simple average of CM ratios instead of a sales-mix-weighted average.

Before the test, make sure you can

• Calculate break-even in units and in sales dollars.
• Calculate the units or sales needed to earn a pretax or after-tax target profit.
• Compute margin of safety in dollars, units and percent.
• Calculate degree of operating leverage and use it to predict income changes.
• Find multiproduct break-even using a package or weighted-average CM ratio.
• Evaluate what-if changes in price, variable cost, fixed cost and volume.
• State the assumptions of CVP and explain how violating them affects results.

Words to know

Cost-volume-profit (CVP) analysis

Analysis of how price, volume, costs and mix affect profit.

Break-even point

The sales level at which total revenue equals total cost and profit is zero.

Break-even in units

Fixed costs divided by contribution margin per unit.

Break-even in sales dollars

Fixed costs divided by the contribution margin ratio.

Target profit analysis

Finding the sales needed to earn a desired profit: (fixed costs + target) ÷ CM.

Margin of safety

The excess of actual or budgeted sales over break-even sales.

Operating leverage

The extent to which a firm uses fixed costs in its cost structure, magnifying profit changes.

Degree of operating leverage

Contribution margin divided by operating income at a given sales level.

Cost structure

The relative mix of fixed and variable costs in an organization.

Sales mix

The relative proportions in which a company's products are sold.

Weighted-average CM

The average contribution margin per unit or ratio, weighted by the sales mix.

CVP graph

A chart of total revenue and total cost lines showing break-even where they cross.

Indifference point

The volume at which two cost structures yield the same total cost or profit.

Incremental analysis

Evaluating a change by looking only at the revenues and costs that change.

Sample practice questions

30 more questions like these, from level 1 to 5, are in the practice set.