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 6 000 units at €8 each. The variable cost is €4 per unit and fixed costs are €16 000. Find the degree of operating leverage DOL at this sales level.
Q = 6 000p = €8v = €4F = €16 000
DOL =
2.Break-even analysisHard
A company sells 5 000 units per month at €24 each, with a variable cost of €18 per unit and fixed costs of €12 000 per month. The variable cost rises by €1 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 5 000p = €24v = €18 → €19F = €12 000
Q = units
3.Financial accountingMedium
A company increases its allowance for doubtful receivables. What is the effect?
- ARevenue increases and gross receivables rise by the same amount
- BAn expense is recognised and net receivables fall
- CCash decreases immediately
- DOnly the notes change; no figures move
4.Financial accountingHard
Goodwill arises in a business combination when:
- AThe acquired company makes a loss
- BAssets are revalued upwards
- CA company has a good reputation
- DThe consideration paid exceeds the fair value of identifiable net assets acquired
3Solutions
1.Break-even analysis
Answer: DOL = 3
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 = 6 000·(8 − 4) = €24 000
Operating profit
Π = 24 000 − 16 000 = €8 000
DOL
DOL = 24 000/8 000 = 3
Answer
DOL = 3
2.Break-even analysis
Answer: Q = 6000 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).
Current profit
Π = 5 000·(24 − 18) − 12 000 = €18 000
New contribution margin per unit
24 − 19 = €5
Units for the same profit
Q = (12 000 + 18 000)/5 = 6 000
Answer
Q = 6 000 units
3.Financial accounting
Answer: B · An expense is recognised and net receivables fall
Why this is the answer
The increase is charged to profit, and the allowance is deducted from gross receivables, so the balance sheet shows the amount expected to be collected.
Answer
B · An expense is recognised and net receivables fall
4.Financial accounting
Answer: D · The consideration paid exceeds the fair value of identifiable net assets acquired
Why this is the answer
Goodwill = consideration − fair value of identifiable net assets. Under IFRS it is not amortised but tested for impairment annually.
Answer
D · The consideration paid exceeds the fair value of identifiable net assets acquired
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