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 €16 per unit with a variable cost of €8 per unit. Fixed costs are €40 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €40 000p = €16v = €8profit = €10 000
Q = units
2.Break-even analysisHard
A product sells for €32 per unit, with a variable cost of €30 per unit and fixed costs of €5 000 per year. Budgeted sales are 4 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €5 000p = €32v = €30budget = 4 000
MS = %
3.Financial accountingMedium
A company is being sued. Its lawyers say losing is possible but not probable. How is this treated under IAS 37?
- ARecognised as a provision on the balance sheet
- BIgnored completely
- CDisclosed as a contingent liability in the notes
- DRecognised as an expense and paid into a reserve
4.Financial accountingHard
In the indirect method of the cash flow statement, depreciation is:
- AAdded back to net profit because it is a non-cash expense
- BIgnored completely
- CSubtracted from net profit
- DShown in financing activities
3Solutions
1.Break-even analysis
Answer: Q = 6250 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 = 16 − 8 = €8
Units for the target profit
Q = (F + profit)/(p − v) = (40 000 + 10 000)/8 = 6 250
Answer
Q = 6 250 units
2.Break-even analysis
Answer: MS = 37.5 %
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) = 5 000/2 = 2 500
Margin of safety
MS = (4 000 − 2 500)/4 000·100 = 37.5%
Answer
MS = 37.5%
3.Financial accounting
Answer: C · Disclosed as a contingent liability in the notes
Why this is the answer
A possible obligation is not recognised but disclosed, unless the chance of outflow is remote. A probable, measurable outflow would require a provision.
Answer
C · Disclosed as a contingent liability in the notes
4.Financial accounting
Answer: A · Added back to net profit because it is a non-cash expense
Why this is the answer
Starting from profit, non-cash charges like depreciation are added back, and changes in working capital are adjusted.
Answer
A · Added back to net profit because it is a non-cash expense
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