BUSMGT713 Chap.2 Break-even, margin of safety and target profit
Break-even, margin of safety and target profit
This chapter turns the contribution per unit from Chapter 1 into the cost-volume-profit answers the Week 1 workshop and the practice mid-term ask for. Break-even units come from dividing total fixed costs by contribution per unit, and a fractional answer is rounded up to the next whole unit.
The margin of safety measures how far expected sales sit above break-even, both in units and as a ratio of expected sales, and it reads as the fall in sales a business can absorb before making a loss. Adding a target profit to fixed costs gives the volume needed to earn it.
A guided kayak business carries the method through a cost-volume-profit chart, a price-cut proposal judged on total contribution rather than seat growth, and a sensitivity test in which price, variable cost and fixed cost change one at a time and then together, mirroring the sensitivity example that closes the Week 1 solution. Each result is checked in reverse, so the route from contribution to the final volume stays visible.
What this chapter covers
- 01
Break-even units from fixed costs and contribution per unit
- 02
Break-even revenue and the contribution margin ratio shortcut
- 03
Margin of safety in units, in dollars and as a ratio
- 04
Volume needed for a target profit and how to check it
- 05
Judging a price cut on total contribution
- 06
Sensitivity of break-even to price, variable cost and fixed cost
Worked example · free
Riverbend Kayak Tours: break-even after an 8% lower price
- +2New price = $85 times 0.92 = $78.20, so contribution per seat = $78.20 minus $34 = $44.20.
- +2New break-even = $30,600 divided by $44.20 = 692.3, rounded up to 693 seats, up from 600.
- +2Margin of safety at 900 seats = 900 minus 693 = 207 seats; 207 divided by 900 = 23.0%, down from 33.3%.
Key terms
- Break-even revenue
- Sales in dollars at zero profit, found as break-even units times price or as fixed costs over the contribution margin ratio.
- Margin of safety
- Expected sales less break-even sales, stated in units or dollars, showing the cushion before a loss.
- Target profit
- A profit a manager plans to earn, added to fixed costs before dividing by contribution per unit to find the volume required.
- Sensitivity analysis
- Recalculating a result after changing one assumption, or several, to see which estimate the answer depends on most.
- Cost-volume-profit analysis
- The study of how selling price, variable cost, fixed cost and volume combine to produce profit.
Break-even, margin of safety and target profit FAQ
How do you calculate break-even units?
Divide total fixed costs by contribution per unit, where contribution is selling price minus variable cost per unit. If the result is fractional, round it up, because selling one unit fewer would still leave a loss. The practice mid-term does exactly this, turning 2,333.3 units into 2,334.
What does a margin of safety ratio of 33% mean?
It means expected sales could fall by about a third before the business makes a loss. The ratio is expected sales minus break-even sales, divided by expected sales. A higher ratio means more room for a forecast to be wrong; a low ratio warns that a small shortfall would erase profit.
How do I find the sales needed for a target profit?
Add the target profit to total fixed costs and divide the sum by contribution per unit. Check the answer in reverse: units above break-even multiplied by contribution per unit should equal the target. Round the volume up if the division leaves a fraction, then confirm profit at that volume.
Can I find break-even in dollars without a unit price?
Yes. Compute the contribution margin ratio from total sales and total variable costs, then divide fixed costs by that ratio. The answer is break-even sales value. The Week 1 marginal costing table reports break-even both in units and in sales value, so be ready to give either.
Why does a price cut raise break-even so sharply?
Every dollar removed from price comes straight off contribution per unit, while variable and fixed costs stay put. Because contribution is smaller than price, the percentage fall in contribution is larger than the percentage fall in price, and break-even, being fixed cost divided by contribution, rises by more.
Assessment move
Open every cost-volume-profit question by writing three lines: price, variable cost and contribution per unit, each labelled. Compute break-even, round it up, and prove it by showing revenue equals total cost at that volume. Next, find the margin of safety in units and as a ratio, and say in words what the ratio means. For a target, add it to fixed costs before dividing and check the result in reverse.
Then rehearse change questions: alter one input, recompute contribution, divide again and compare with the base case. Finish with a written recommendation on any proposal, comparing total contribution before and after, and naming the volume at which the proposal stops paying.
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