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 €38 per unit with a variable cost of €18 per unit. Fixed costs are €30 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €30 000p = €38v = €18profit = €10 000
Q = units
2.Break-even analysisHard
A product sells for €27 per unit, with a variable cost of €15 per unit and fixed costs of €9 600 per year. Budgeted sales are 1 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €9 600p = €27v = €15budget = 1 000
MS = %
3.Financial accountingMedium
Current assets are €300,000, including inventory of €100,000. Current liabilities are €200,000. What is the quick (acid-test) ratio?
- A0.5
- B2.0
- C1.0
- D1.5
4.Financial accountingHard
Making a part costs €10 materials, €6 labour and €4 variable overhead, plus €5 of fixed overhead that continues anyway. A supplier offers it at €22. What should the firm do on cost grounds?
- ABuy it, because fixed costs are always relevant
- BMake it, because the relevant cost of €20 is below €22
- CBuy it, because the full cost of €25 per unit is above €22
- DMake it, because the full cost of €25 is below €22
3Solutions
1.Break-even analysis
Answer: Q = 2000 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 = 38 − 18 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (30 000 + 10 000)/20 = 2 000
Answer
Q = 2 000 units
2.Break-even analysis
Answer: MS = 20 %
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) = 9 600/12 = 800
Margin of safety
MS = (1 000 − 800)/1 000·100 = 20%
Answer
MS = 20%
3.Financial accounting
Answer: C · 1.0
Why this is the answer
Quick ratio = (current assets − inventory) ÷ current liabilities = €200,000 ÷ €200,000 = 1.0. Inventory is excluded because it may be slow to turn into cash.
Answer
C · 1.0
4.Financial accounting
Answer: B · Make it, because the relevant cost of €20 is below €22
Why this is the answer
Only the €20 of variable cost is avoided by buying; the €5 fixed overhead stays. Making costs €20 versus €22 to buy, so making saves €2 per unit.
Answer
B · Make it, because the relevant cost of €20 is below €22
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