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 company sells 3 600 units at €50 each. The variable cost is €45 per unit and fixed costs are €6 000. Find the degree of operating leverage DOL at this sales level.
Q = 3 600p = €50v = €45F = €6 000
DOL =
2.Break-even analysisHard
A product sells for €9 per unit, with a variable cost of €4 per unit and fixed costs of €10 000 per year. Budgeted sales are 2 300 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €10 000p = €9v = €4budget = 2 300
MS = %
3.Financial accountingMedium
Profit for ordinary shareholders is €500,000 and there are 1,000,000 ordinary shares. What are basic earnings per share?
- A€2.00
- B€5.00
- C€0.50
- D€0.05
4.Financial accountingHard
A parent sold goods to its subsidiary at a profit, and the subsidiary still holds them at year end. What must happen on consolidation?
- AThe sale is shown as external revenue of the group
- BThe unrealised profit in inventory is eliminated
- CThe profit is shown twice, once for each company
- DNothing, because each company is a separate entity
3Solutions
1.Break-even analysis
Answer: DOL = 1.5
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Total contribution margin
CM = 3 600·(50 − 45) = €18 000
Operating profit
Π = 18 000 − 6 000 = €12 000
DOL
DOL = 18 000/12 000 = 1.5
Answer
DOL = 1.5
2.Break-even analysis
Answer: MS = 13.04 %
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) = 10 000/5 = 2 000
Margin of safety
MS = (2 300 − 2 000)/2 300·100 = 13.04%
Answer
MS = 13.04%
3.Financial accounting
Answer: C · €0.50
Why this is the answer
Basic EPS = €500,000 ÷ 1,000,000 = €0.50 per share. Dividing the share price by EPS gives the P/E ratio.
Answer
C · €0.50
4.Financial accounting
Answer: B · The unrealised profit in inventory is eliminated
Why this is the answer
Intra-group sales and purchases are cancelled, and profit on goods still held in the group is removed from inventory and group profit until sold outside.
Answer
B · The unrealised profit in inventory is eliminated
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