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 €55 per unit with a variable cost of €45 per unit. Fixed costs are €50 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €50 000p = €55v = €45profit = €6 000
Q = units
2.Break-even analysisHard
A product sells for €55 per unit, with a variable cost of €45 per unit and fixed costs of €15 000 per year. Budgeted sales are 1 800 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €15 000p = €55v = €45budget = 1 800
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€0.50
- B€0.05
- C€2.00
- D€5.00
4.Financial accountingHard
The going concern assumption means financial statements are prepared assuming the entity:
- AWill be sold within one year
- BWill make a profit every year
- CWill continue to operate for the foreseeable future
- DHas no debts
3Solutions
1.Break-even analysis
Answer: Q = 5600 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 = 55 − 45 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (50 000 + 6 000)/10 = 5 600
Answer
Q = 5 600 units
2.Break-even analysis
Answer: MS = 16.67 %
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) = 15 000/10 = 1 500
Margin of safety
MS = (1 800 − 1 500)/1 800·100 = 16.67%
Answer
MS = 16.67%
3.Financial accounting
Answer: A · €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
A · €0.50
4.Financial accounting
Answer: C · Will continue to operate for the foreseeable future
Why this is the answer
Unless management intends or must liquidate, assets and liabilities are measured assuming continued operations; material doubts must be disclosed.
Answer
C · Will continue to operate for the foreseeable future
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