Cost-volume-profit analysis
Cost-volume-profit (CVP) analysis shows how changes in sales volume, prices, and costs affect profit. It answers questions such as how much must we sell to break even.
Contribution margin per unit and ratio
Contribution margin per unit = selling price - variable cost per unit. The contribution margin ratio = contribution margin / sales. If a product sells for 50 dollars with variable costs of 30, the contribution margin is 20 dollars per unit and the ratio is 40%: each sales dollar contributes 40 cents to fixed costs and profit.
Break-even point
The break-even point is where total revenue equals total costs and profit is zero. Break-even units = fixed costs / contribution margin per unit. Break-even sales dollars = fixed costs / contribution margin ratio. With fixed costs of 100,000 and a 20-dollar contribution margin, break-even is 5,000 units, or 250,000 dollars of sales.
Target profit
To find the volume needed for a target profit, add the target to fixed costs: required units = (fixed costs + target profit) / contribution margin per unit. In the example, a profit of 40,000 dollars requires (100,000 + 40,000) / 20 = 7,000 units.
Margin of safety
The margin of safety is how far sales can fall before the business makes a loss: actual (or budgeted) sales minus break-even sales. As a percentage, margin of safety ratio = margin of safety / actual sales. A higher margin of safety means lower risk.
Operating leverage
Operating leverage measures how sensitive operating income is to changes in sales. Businesses with high fixed costs and low variable costs, such as airlines and software firms, have high operating leverage: profits rise quickly when sales grow but fall quickly when sales drop. Degree of operating leverage = contribution margin / operating income.
Sales mix
When a business sells several products, the break-even point depends on the sales mix, the proportion of each product sold. A shift toward products with higher contribution margins lowers the break-even point; a shift toward lower-margin products raises it. A weighted-average contribution margin is used for multi-product CVP.
Assumptions and limits
CVP analysis assumes a linear relationship within the relevant range: constant selling prices, constant variable cost per unit, fixed costs that do not change, a constant sales mix, and no change in inventory levels. Real businesses are messier, so CVP results are estimates to guide, not dictate, decisions.
Worked example
A café sells coffee at 4 dollars with variable costs of 1.50 per cup. Fixed costs are 5,000 dollars per month. Contribution margin = 2.50 per cup; break-even = 5,000 / 2.50 = 2,000 cups. If it sells 2,800 cups, operating income = 800 x 2.50 = 2,000 dollars, and the margin of safety is 800 cups, about 29% of sales.
Key takeaways
Contribution margin per unit is price minus variable cost; the ratio is contribution margin over sales. Break-even units = fixed costs / contribution margin per unit; add target profit to fixed costs to find required volume. Margin of safety measures the cushion above break-even. High fixed costs create high operating leverage, magnifying profit swings. Sales mix affects multi-product break-even. CVP relies on simplifying assumptions within the relevant range.
Flashcard
Price - variable cost per unit
Check your understanding
Fixed costs are 60,000 dollars, price is 25 dollars, and variable cost is 13 dollars per unit. What is the break-even point in units?