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 €22 with a variable cost of €18 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 = €22v = €18F = €6 000T = 25%after-tax profit = €3 000
Q = units
2.Break-even analysisHard
A company sells 750 units per month at €35 each, with a variable cost of €25 per unit and fixed costs of €5 000 per month. The variable cost rises by €4 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 750p = €35v = €25 → €29F = €5 000
Q = units
3.Financial accountingMedium
An item cost €80. It can be sold for €90, but €20 must be spent to sell it. At what amount is it shown in inventory?
- A€80
- B€60
- C€70
- D€90
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?
- AProspectively, from the date of the change only
- BIt is not allowed to change inventory methods
- CRetrospectively, restating comparative figures as if FIFO had always been used
- DBy recognising the whole effect as income this year
3Solutions
1.Break-even analysis
Answer: Q = 2500 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)/4 = 2 500
Answer
Q = 2 500 units
2.Break-even analysis
Answer: Q = 1250 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).
Current profit
Π = 750·(35 − 25) − 5 000 = €2 500
New contribution margin per unit
35 − 29 = €6
Units for the same profit
Q = (5 000 + 2 500)/6 = 1 250
Answer
Q = 1 250 units
3.Financial accounting
Answer: C · €70
Why this is the answer
NRV = €90 − €20 = €70, which is below cost of €80. Inventory is measured at the lower amount, €70, with a €10 write-down.
Answer
C · €70
4.Financial accounting
Answer: C · 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
C · Retrospectively, restating comparative figures as if FIFO had always been used
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