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 company sells 2 500 units at €33 each. The variable cost is €25 per unit and fixed costs are €8 000. Find the degree of operating leverage DOL at this sales level.
Q = 2 500p = €33v = €25F = €8 000
DOL =
2.Break-even analysisHard
A company sells 1 000 units at €32 each, with a variable cost of €20 per unit and fixed costs of €9 600. By what percentage %ΔΠ does operating profit change if sales volume rises by 5%?
Q = 1 000p = €32v = €20F = €9 600%ΔQ = +5%
%ΔΠ = %
3.Financial accountingMedium
Under IAS 16, which cost should be included in the cost of a new machine?
- ARepairs carried out two years later
- BInstallation costs needed to get it working
- CGeneral office overheads for the year
- DStaff training costs after it starts operating
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:
- AA change in accounting policy
- BAn adjusting event, so receivables are reduced
- CA non-adjusting event, disclosed only
- DIgnored, because it happened after the year end
3Solutions
1.Break-even analysis
Answer: DOL = 1.667
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Total contribution margin
CM = 2 500·(33 − 25) = €20 000
Operating profit
Π = 20 000 − 8 000 = €12 000
DOL
DOL = 20 000/12 000 = 1.667
Answer
DOL = 1.667
2.Break-even analysis
Answer: %ΔΠ = 25 %
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Contribution margin and profit
CM = 1 000·12 = €12 000
Π = 12 000 − 9 600 = €2 400
DOL
DOL = 12 000/2 400 = 5
Change in profit
%ΔΠ = 5·(+5%) = +25%
Answer
%ΔΠ = +25%
Check: new profit = 1 050·12 − 9 600 = €3 000.00.
3.Financial accounting
Answer: B · Installation costs needed to get it working
Why this is the answer
Purchase price plus directly attributable costs, such as delivery and installation, are capitalised. Training, later repairs and general overheads are expensed.
Answer
B · Installation costs needed to get it working
4.Financial accounting
Answer: B · 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
B · An adjusting event, so receivables are reduced
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