Break-even analysis
- Contribution margin
- CM = p − v
- Break-even quantity
- QBE = FC/(p − v)
- Target profit
- Q = (FC + profit)/(p − v)
- Profit
- π = (p − v)·Q − FC
- Margin of safety
- (Q − QBE)/Q
Management Accounting: cram pack
Formula sheets, the key method steps for every topic and 4 practice problems, with full solutions at the back.
1Formulas and methods
2Practice problems
1.Break-even analysisMedium
A product sells for €17 with a variable cost of €12 per unit. Fixed costs are €6 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €3 000 after tax?
p = €17v = €12F = €6 000T = 25%after-tax profit = €3 000
Q = units
2.Break-even analysisHard
A product sells for €20 per unit, with a variable cost of €15 per unit and fixed costs of €6 000 per year. Budgeted sales are 1 560 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €6 000p = €20v = €15budget = 1 560
MS = %
3.Financial accountingMedium
Fixed costs are €20,000, the selling price is €50 and the variable cost is €30 per unit. What is the break-even point?
- A667 units
- B1,000 units
- C2,000 units
- D400 units
4.Financial accountingHard
In the indirect method of the cash flow statement, depreciation is:
- ASubtracted from net profit
- BAdded back to net profit because it is a non-cash expense
- CIgnored completely
- DShown in financing activities
3Solutions
1.Break-even analysis
Answer: Q = 2000 units
Cost-volume-profit: each unit sold earns a contribution margin, price minus variable cost per unit. Profit = Q·(p − v) − F, where F is the fixed cost. At the break-even point profit is zero, so Q = F/(p − v).
Pre-tax profit needed
3 000/(1 − 0.25) = €4 000
Units needed
Q = (6 000 + 4 000)/5 = 2 000
Answer
Q = 2 000 units
2.Break-even analysis
Answer: MS = 23.08 %
Cost-volume-profit: each unit sold earns a contribution margin, price minus variable cost per unit. Profit = Q·(p − v) − F, where F is the fixed cost. At the break-even point profit is zero, so Q = F/(p − v).
Break-even quantity
Q = F/(p − v) = 6 000/5 = 1 200
Margin of safety
MS = (1 560 − 1 200)/1 560·100 = 23.08%
Answer
MS = 23.08%
3.Financial accounting
Answer: B · 1,000 units
Why this is the answer
Contribution per unit = €50 − €30 = €20. Break-even = €20,000 ÷ €20 = 1,000 units.
Answer
B · 1,000 units
4.Financial accounting
Answer: B · Added back to net profit because it is a non-cash expense
Why this is the answer
Starting from profit, non-cash charges like depreciation are added back, and changes in working capital are adjusted.
Answer
B · Added back to net profit because it is a non-cash expense
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