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 €14 per unit with a variable cost of €8 per unit. Fixed costs are €15 000 per month. How many units Q must be sold per month to make a profit of €12 000?
F = €15 000p = €14v = €8profit = €12 000
Q = units
2.Break-even analysisHard
A product sells for €7 per unit, with a variable cost of €4 per unit and fixed costs of €3 600 per year. Budgeted sales are 1 500 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €3 600p = €7v = €4budget = 1 500
MS = %
3.Financial accountingMedium
Revenue is €200,000 and cost of sales is €140,000. What is the gross profit margin?
- A30%
- B60%
- C70%
- D43%
4.Financial accountingHard
A company changes its inventory method from weighted average to FIFO because it gives more relevant information. Under IAS 8, how is this applied?
- ARetrospectively, restating comparative figures as if FIFO had always been used
- BBy recognising the whole effect as income this year
- CIt is not allowed to change inventory methods
- DProspectively, from the date of the change only
3Solutions
1.Break-even analysis
Answer: Q = 4500 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 = 14 − 8 = €6
Units for the target profit
Q = (F + profit)/(p − v) = (15 000 + 12 000)/6 = 4 500
Answer
Q = 4 500 units
2.Break-even analysis
Answer: MS = 20 %
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) = 3 600/3 = 1 200
Margin of safety
MS = (1 500 − 1 200)/1 500·100 = 20%
Answer
MS = 20%
3.Financial accounting
Answer: A · 30%
Why this is the answer
Gross profit = €60,000. Margin = €60,000 ÷ €200,000 = 30%.
Answer
A · 30%
4.Financial accounting
Answer: A · Retrospectively, restating comparative figures as if FIFO had always been used
Why this is the answer
Voluntary policy changes are applied retrospectively where practicable, so comparatives remain consistent. Changes in estimates, by contrast, are applied prospectively.
Answer
A · Retrospectively, restating comparative figures as if FIFO had always been used
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