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 €8 with a variable cost of €6 per unit. Fixed costs are €3 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €1 500 after tax?
p = €8v = €6F = €3 000T = 25%after-tax profit = €1 500
Q = units
2.Break-even analysisHard
A product sells for €35 per unit, with a variable cost of €30 per unit and fixed costs of €2 500 per year. Budgeted sales are 580 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €2 500p = €35v = €30budget = 580
MS = %
3.Financial accountingMedium
Cost of sales is €600,000 and average inventory is €100,000. What is the inventory turnover?
- A16 times a year
- B60 times a year
- C0.17 times a year
- D6 times a year
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?
- ANothing, because each company is a separate entity
- BThe unrealised profit in inventory is eliminated
- CThe sale is shown as external revenue of the group
- DThe profit is shown twice, once for each company
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
1 500/(1 − 0.25) = €2 000
Units needed
Q = (3 000 + 2 000)/2 = 2 500
Answer
Q = 2 500 units
2.Break-even analysis
Answer: MS = 13.79 %
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) = 2 500/5 = 500
Margin of safety
MS = (580 − 500)/580·100 = 13.79%
Answer
MS = 13.79%
3.Financial accounting
Answer: D · 6 times a year
Why this is the answer
€600,000 ÷ €100,000 = 6, so inventory is replaced about every 61 days (365 ÷ 6).
Answer
D · 6 times a year
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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