Lesson 3.3 35 min
Break-even and margin of safety
Break-even hours and revenue, target profit, margin of safety, and how sensitive profit is to volume.
Break-even analysis answers how much a business has to sell before it stops losing money. It uses the two ideas from the previous lessons: fixed costs, and the contribution each unit makes toward them. The full method is often called cost-volume-profit (CVP) analysis.
The equation
Profit = (Contribution per unit × Units) − Fixed costs
Setting profit to zero gives the break-even point.
Break-even units = Fixed costs ÷ Contribution per unit
Break-even revenue = Fixed costs ÷ Contribution margin ratio
Adding a profit target to fixed costs gives the units needed to reach it.
Units for target profit = (Fixed costs + Target profit) ÷ Contribution per unit
Taxes can be handled by converting an after-tax target into a pre-tax one first: divide by one minus the tax rate.
Margin of safety
The margin of safety is how far planned sales can fall before the business reaches break-even.
Margin of safety = (Planned units − Break-even units) ÷ Planned units
A margin of safety of 30% means sales can drop by nearly a third before losses start. Lenders look at this figure, even when they don't call it by name, because it tells them how much bad luck the plan can absorb.
Sensitivity of profit to volume
When fixed costs are high relative to variable costs, a small change in volume causes a large change in profit. One way to measure this is to divide total contribution by profit at the planned volume. A result of 3 means that a 10% rise in volume lifts profit by about 30%, and a 10% fall reduces it by the same proportion. This sensitivity is the reason high-fixed-cost businesses feel very good in strong years and very bad in weak ones.
Assumptions
CVP rests on a set of simplifying assumptions: a constant price, a constant variable cost per unit, fixed costs that stay fixed within the relevant range, and, for multi-product businesses, a constant mix. Each one fails at some point. Use the model to see the shape of the problem and the size of the stakes, and re-run it when any of the inputs change.
Worked case
Hartley's break-even year
Hartley Plumbing has 3 salaried plumbers, each paid for 2,000 hours a year at $38 an hour. It bills labour at $125 an hour. Materials cost it $40 per billable hour on average and are billed to customers at cost plus 30%. Running the vans costs $7 per billable hour in fuel and wear, on top of their fixed leases. The plan for the year is 3,600 billable hours.
Fixed costs are $327,600 a year and each billable hour contributes $130.
| $ | |
|---|---|
| Labour billed | 450,000 |
| Materials billed | 187,200 |
| Revenue | 637,200 |
| Materials at cost | (144,000) |
| Fuel and van wear | (25,200) |
| Contribution margin | 468,000 |
| Fixed costs | (327,600) |
| Operating profit | 140,400 |
Break-even is $327,600 ÷ $130 = 2,520 billable hours, or $446,040 of revenue. The plan of 3,600 hours gives a profit of $140,400 and a margin of safety of 1,080 hours, 30% of planned volume.
The owners want a profit of $117,000 before tax. That needs ($327,600 + $117,000) ÷ $130 = 3,420 billable hours.
At the plan, contribution ÷ profit is $468,000 ÷ $140,400 = 3.33. If billable hours rise 10% to 3,960, profit rises to $187,200, an increase of 33.3%. A 10% shortfall would cut profit by the same amount. Most of Hartley's planning effort should therefore go into keeping its plumbers' hours billable.
Template
Break-even and target profit calculator
Enter fixed costs, price and variable cost per unit (or per hour), planned volume and a target profit. The workbook gives break-even volume and revenue, target volume, margin of safety, the profit sensitivity, and a profit table across volumes. Hartley's plan is loaded.
Download 3-3-break-even.xlsxXLSX, 7 KB, freeExercises
Work these, then open the answers
Hartley's landlord raises rent by $13,000 a year. What is the new break-even in hours?
Answer
($327,600 + 13,000) ÷ 130 = 2,620 hours.
Hartley raises its labour rate to $135 an hour with no change in volume. What are the new contribution per hour and the break-even?
Answer
Contribution rises to $140 per hour. Break-even = 327,600 ÷ 140 = 2,340 hours.
A fourth plumber would add $76,000 to fixed costs (ignore a fourth van). What is the new break-even, and what does it say about the hire?
Answer
Fixed costs become $403,600. Break-even = 403,600 ÷ 130 = 3,104.6, so 3,105 hours. The current plan is 3,600 hours, so the hire only makes sense if the team can sell substantially more billable time, about 585 more billable hours a year just to keep today's profit.
Check
4 questions
Sources
Sources
- Principles of Accounting, Volume 2: Managerial Accounting, OpenStax, Rice University