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 €13 with a variable cost of €8 per unit. Fixed costs are €5 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €1 500 after tax?
p = €13v = €8F = €5 000T = 25%after-tax profit = €1 500
Q = units
2.Break-even analysisHard
A company sells 1 250 units per month at €15 each, with a variable cost of €12 per unit and fixed costs of €1 500 per month. The variable cost rises by €1 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 1 250p = €15v = €12 → €13F = €1 500
Q = units
3.Financial accountingMedium
A shop buys 100 units at €10, then 100 units at €12, and then sells 150 units. What is cost of sales using FIFO?
- A€1,600
- B€1,500
- C€1,650
- D€1,700
4.Financial accountingHard
An asset has a carrying amount of €500,000, fair value less costs of disposal of €380,000 and value in use of €420,000. What impairment loss is recognised?
- A€0
- B€200,000
- C€120,000
- D€80,000
3Solutions
1.Break-even analysis
Answer: Q = 1400 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
1 500/(1 − 0.25) = €2 000
Units needed
Q = (5 000 + 2 000)/5 = 1 400
Answer
Q = 1 400 units
2.Break-even analysis
Answer: Q = 1875 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 = 1 250·(15 − 12) − 1 500 = €2 250
New contribution margin per unit
15 − 13 = €2
Units for the same profit
Q = (1 500 + 2 250)/2 = 1 875
Answer
Q = 1 875 units
3.Financial accounting
Answer: A · €1,600
Why this is the answer
FIFO: 100 × €10 + 50 × €12 = €1,600. The 50 units left are valued at the latest cost of €12.
Answer
A · €1,600
4.Financial accounting
Answer: D · €80,000
Why this is the answer
Recoverable amount = max(€380,000, €420,000) = €420,000. Impairment = €500,000 − €420,000 = €80,000.
Answer
D · €80,000
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