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 €57 per unit with a variable cost of €45 per unit. Fixed costs are €6 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €6 000p = €57v = €45profit = €6 000
Q = units
2.Break-even analysisHard
A product sells for €21 per unit, with a variable cost of €6 per unit and fixed costs of €75 000 per year. Budgeted sales are 6 500 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €75 000p = €21v = €6budget = 6 500
MS = %
3.Financial accountingMedium
Net working capital is:
- ARevenue minus operating expenses
- BTotal assets minus total liabilities
- CCurrent assets minus current liabilities
- DNon-current assets minus long-term loans
4.Financial accountingHard
After the year end, but before the accounts are approved, a customer who owed money at year end goes bankrupt. Under IAS 10 this is:
- AAn adjusting event, so receivables are reduced
- BIgnored, because it happened after the year end
- CA non-adjusting event, disclosed only
- DA change in accounting policy
3Solutions
1.Break-even analysis
Answer: Q = 1000 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 = 57 − 45 = €12
Units for the target profit
Q = (F + profit)/(p − v) = (6 000 + 6 000)/12 = 1 000
Answer
Q = 1 000 units
2.Break-even analysis
Answer: MS = 23.08 %
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) = 75 000/15 = 5 000
Margin of safety
MS = (6 500 − 5 000)/6 500·100 = 23.08%
Answer
MS = 23.08%
3.Financial accounting
Answer: C · Current assets minus current liabilities
Why this is the answer
Working capital measures the short-term resources available for daily operations: inventory, receivables and cash minus short-term obligations.
Answer
C · Current assets minus current liabilities
4.Financial accounting
Answer: A · An adjusting event, so receivables are reduced
Why this is the answer
The customer's inability to pay existed at year end, so the accounts are adjusted. A fire after year end would be non-adjusting, because it is a new condition.
Answer
A · An adjusting event, so receivables are reduced
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