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 €38 per unit with a variable cost of €18 per unit. Fixed costs are €50 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €50 000p = €38v = €18profit = €10 000
Q = units
2.Break-even analysisHard
A company sells two products. Product A sells for €13 with a variable cost of €10; product B sells for €42 with a variable cost of €30. They sell in a fixed mix of 2 units of A for every 1 of B. Fixed costs are €10 800 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €13, vA = €10pB = €42, vB = €30A : B = 2 : 1F = €10 800
Q = units
3.Financial accountingMedium
Under IAS 16, which cost should be included in the cost of a new machine?
- AStaff training costs after it starts operating
- BInstallation costs needed to get it working
- CGeneral office overheads for the year
- DRepairs carried out two years later
4.Financial accountingHard
Tax rules allow faster depreciation of a machine than the company uses in its accounts. What arises under IAS 12?
- ANo tax effect at all
- BA deferred tax asset
- CA refund of current tax paid
- DA deferred tax liability
3Solutions
1.Break-even analysis
Answer: Q = 3000 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 = 38 − 18 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (50 000 + 10 000)/20 = 3 000
Answer
Q = 3 000 units
2.Break-even analysis
Answer: Q = 1800 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 = €3, cmB = €12
Weighted contribution margin
(2·3 + 1·12)/3 = €6.00
Break-even units
Q = 10 800/6 = 1 800
A: 1 200, B: 600
Answer
Q = 1 800 units
3.Financial accounting
Answer: B · Installation costs needed to get it working
Why this is the answer
Purchase price plus directly attributable costs, such as delivery and installation, are capitalised. Training, later repairs and general overheads are expensed.
Answer
B · Installation costs needed to get it working
4.Financial accounting
Answer: D · A deferred tax liability
Why this is the answer
The tax base falls faster than the carrying amount, creating a taxable temporary difference. The future extra tax is recognised now as a deferred tax liability.
Answer
D · A deferred tax liability
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