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 €28 each. The variable cost is €25 per unit and fixed costs are €6 000. Find the degree of operating leverage DOL at this sales level.
Q = 2 500p = €28v = €25F = €6 000
DOL =
2.Break-even analysisHard
A product sells for €35 per unit, with a variable cost of €30 per unit and fixed costs of €20 000 per year. Budgeted sales are 6 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €20 000p = €35v = €30budget = 6 000
MS = %
3.Financial accountingMedium
On 1 October a company pays €12,000 rent for the next 12 months. Its year ends on 31 December. What is the rent expense for this year?
- A€12,000
- B€9,000
- C€3,000
- D€1,000
4.Financial accountingHard
A company's debt-to-equity ratio rises sharply. What does this usually indicate?
- AHigher profitability
- BThat shareholders invested more money
- CBetter liquidity in the short term
- DHigher financial risk because the company relies more on borrowed money
3Solutions
1.Break-even analysis
Answer: DOL = 5
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·(28 − 25) = €7 500
Operating profit
Π = 7 500 − 6 000 = €1 500
DOL
DOL = 7 500/1 500 = 5
Answer
DOL = 5
2.Break-even analysis
Answer: MS = 33.33 %
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) = 20 000/5 = 4 000
Margin of safety
MS = (6 000 − 4 000)/6 000·100 = 33.33%
Answer
MS = 33.33%
3.Financial accounting
Answer: C · €3,000
Why this is the answer
October to December is 3 months: 3/12 × €12,000 = €3,000. The remaining €9,000 is a prepayment (asset) at year end.
Answer
C · €3,000
4.Financial accounting
Answer: D · Higher financial risk because the company relies more on borrowed money
Why this is the answer
A higher ratio means more leverage: interest and repayments must be met whatever the results, so financial risk rises, although returns to shareholders may also rise.
Answer
D · Higher financial risk because the company relies more on borrowed money
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