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 3 750 units at €34 each. The variable cost is €30 per unit and fixed costs are €6 000. Find the degree of operating leverage DOL at this sales level.
Q = 3 750p = €34v = €30F = €6 000
DOL =
2.Break-even analysisHard
A product sells for €14 per unit, with a variable cost of €8 per unit and fixed costs of €30 000 per year. Budgeted sales are 6 250 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €30 000p = €14v = €8budget = 6 250
MS = %
3.Financial accountingMedium
At 31 December, electricity used in December (€800) has not yet been billed. Which year-end entry is correct?
- ADebit prepayments, credit cash
- BDebit accruals, credit electricity expense
- CDebit electricity expense, credit accruals
- DNo entry until the bill arrives
4.Financial accountingHard
A firm has a net profit margin of 5%, asset turnover of 2 and an equity multiplier (assets ÷ equity) of 1.5. Using the DuPont analysis, what is ROE?
- A8.5%
- B15%
- C7.5%
- D10%
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 = 3 750·(34 − 30) = €15 000
Operating profit
Π = 15 000 − 6 000 = €9 000
DOL
DOL = 15 000/9 000 = 1.667
Answer
DOL = 1.667
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) = 30 000/6 = 5 000
Margin of safety
MS = (6 250 − 5 000)/6 250·100 = 20%
Answer
MS = 20%
3.Financial accounting
Answer: C · Debit electricity expense, credit accruals
Why this is the answer
The accrual records December's cost as an expense this year with a current liability, so expenses match the period of use.
Answer
C · Debit electricity expense, credit accruals
4.Financial accounting
Answer: B · 15%
Why this is the answer
ROE = 5% × 2 × 1.5 = 15%. DuPont shows whether returns come from profitability, asset efficiency or leverage.
Answer
B · 15%
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