Cost Accounting — Cost-Volume-Profit (CVP) Analysis: Break-Even Point and Operating Leverage

The last chapter of cost accounting covers the most basic tool for using cost information in profit planning: cost-volume-profit (CVP) analysis. It combines the cost behavior of chapter 1 with the contribution margin of chapter 12. Extending it to multiple products, after-tax targets and uncertainty is covered in Managerial Accounting chapter 3.

1. Contribution margin

Contribution margin is sales minus variable costs — the amount that “contributes” to recovering fixed costs and earning a profit.

Contribution margin and operating profit

\begin{aligned}\text{Unit contribution margin} &= p - v \\ \text{Contribution margin ratio} &= \frac{p - v}{p} \\ \text{Operating profit} &= (p - v) \times Q - F\end{aligned}

p is the selling price, v the variable cost per unit, Q the quantity sold and F fixed costs.

Company BG’s product sells for ₩50,000 per unit, variable cost is ₩30,000 and annual fixed costs are ₩10 million. Unit contribution margin is ₩20,000 and the contribution margin ratio is 40%.

2. Break-even point and target profit

The break-even point is the quantity at which operating profit is zero.

Q_{BEP} = \frac{F}{p - v} = \frac{1{,}000}{2} = 500\text{ units}, \qquad S_{BEP} = \frac{F}{\text{CM ratio}} = \frac{1{,}000}{0.4} = 2{,}500

In units of ₩10,000, break-even sales are ₩25 million. To earn a target operating profit of ₩4 million, contribution margin must cover both fixed costs and the target.

Q = \frac{F + \text{Target profit}}{p - v} = \frac{1{,}000 + 400}{2} = 700\text{ units}

Operating profit by quantity sold (unit: ₩10,000)
Units sold	Sales	Variable costs	Contribution margin	Fixed costs	Operating profit
400	2,000	1,200	800	1,000	−200
500	2,500	1,500	1,000	1,000	0
700	3,500	2,100	1,400	1,000	400
800	4,000	2,400	1,600	1,000	600

Beyond break-even, each additional unit sold raises operating profit by the ₩20,000 contribution margin.

3. Margin of safety and operating leverage

The margin of safety is how far current sales exceed break-even sales. At 800 units, the margin of safety is $800 - 500 = 300$ units and the margin of safety ratio $300 / 800 = 37.5\%$ : sales can fall by up to 37.5% before a loss arises.

The degree of operating leverage (DOL) is the multiple of the percentage change in operating profit to the percentage change in sales.

Degree of operating leverage

\text{DOL} = \frac{\text{Contribution margin}}{\text{Operating profit}} = \frac{1{,}600}{600} ≈ 2.67 = \frac{1}{\text{Margin of safety ratio}}

At 800 units, a 10% increase in sales raises operating profit by about 26.7%. The larger the share of fixed costs, the larger the DOL.

If sales actually rise to 880 units (a 10% increase), operating profit is $880 \times 2 - 1{,}000 = 760$ (₩7.6 million), 26.7% more than ₩6 million. DOL becomes very large near break-even and shrinks as volume grows.

4. Choosing a cost structure

Installing automated equipment to make the same product raises fixed costs and lowers variable costs. Comparing the current structure (fixed costs ₩10 million, variable cost ₩30,000) with an automated one (fixed costs ₩16 million, variable cost ₩20,000), the two give equal profit where $1{,}000 + 3Q = 1{,}600 + 2Q$ , i.e. $Q = 600$ units. If you are confident of selling more than 600 units, automation is better; if sales are uncertain, the structure with lower fixed costs is safer. The automated structure’s break-even point is higher, at $1{,}600 / 3 ≈ 533$ units.

Check your understanding

Company BH’s contribution margin ratio is 30%, its annual fixed costs are ₩24 million and this year’s sales are ₩100 million. What are break-even sales, the margin of safety ratio and the degree of operating leverage? If sales fall by 8% next year, by what percentage does operating profit fall?

Break-even sales are $2{,}400 / 0.3 = 8{,}000$ (₩80 million). The margin of safety is ₩20 million, a ratio of 20%. Operating profit is $10{,}000 \times 30\% - 2{,}400 = 600$ (₩6 million) and DOL is $3{,}000 / 600 = 5$ . An 8% fall in sales cuts operating profit by $8\% \times 5 = 40\%$ , to ₩3.6 million. Check: at sales of ₩92 million, operating profit is $9{,}200 \times 30\% - 2{,}400 = 360$ (₩3.6 million).

References

Charles Horngren, Srikant Datar and Madhav Rajan, Cost Accounting: A Managerial Emphasis, ch. 3
Ray Garrison, Eric Noreen and Peter Brewer, Managerial Accounting, ch. 5
Robert Kaplan and Anthony Atkinson, Advanced Management Accounting, ch. 2