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 €19 per unit with a variable cost of €4 per unit. Fixed costs are €18 000 per month. How many units Q must be sold per month to make a profit of €12 000?
F = €18 000p = €19v = €4profit = €12 000
Q = units
2.Break-even analysisHard
A company sells two products. Product A sells for €13 with a variable cost of €8; product B sells for €25 with a variable cost of €10. They sell in a fixed mix of 3 units of A for every 1 of B. Fixed costs are €24 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €13, vA = €8pB = €25, vB = €10A : B = 3 : 1F = €24 000
Q = units
3.Financial accountingMedium
A company is being sued. Its lawyers say losing is possible but not probable. How is this treated under IAS 37?
- AIgnored completely
- BDisclosed as a contingent liability in the notes
- CRecognised as an expense and paid into a reserve
- DRecognised as a provision on the balance sheet
4.Financial accountingHard
Budgeted overhead is €200,000 for 40,000 machine hours. Actual hours are 42,000 and actual overhead is €205,000. What is the result?
- AOverhead under-absorbed by €5,000
- BOverhead under-absorbed by €10,000
- COverhead over-absorbed by €5,000
- DOverhead exactly absorbed
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).
Contribution margin per unit
p − v = 19 − 4 = €15
Units for the target profit
Q = (F + profit)/(p − v) = (18 000 + 12 000)/15 = 2 000
Answer
Q = 2 000 units
2.Break-even analysis
Answer: Q = 3200 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €5, cmB = €15
Weighted contribution margin
(3·5 + 1·15)/4 = €7.50
Break-even units
Q = 24 000/7.5 = 3 200
A: 2 400, B: 800
Answer
Q = 3 200 units
3.Financial accounting
Answer: B · Disclosed as a contingent liability in the notes
Why this is the answer
A possible obligation is not recognised but disclosed, unless the chance of outflow is remote. A probable, measurable outflow would require a provision.
Answer
B · Disclosed as a contingent liability in the notes
4.Financial accounting
Answer: C · Overhead over-absorbed by €5,000
Why this is the answer
Rate = €5 per hour. Absorbed = 42,000 × €5 = €210,000, which exceeds actual €205,000, so €5,000 is over-absorbed and added back to profit.
Answer
C · Overhead over-absorbed by €5,000
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