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 can be made in two ways. Method A has fixed costs of €25 000 per year and a variable cost of €18 per unit. Method B, more automated, has fixed costs of €40 000 per year and a variable cost of €12 per unit. At what yearly volume Q do both methods cost the same?
FA = €25 000vA = €18FB = €40 000vB = €12
Q = units
2.Break-even analysisHard
A company sells two products. Product A sells for €13 with a variable cost of €5; product B sells for €30 with a variable cost of €15. They sell in a fixed mix of 3 units of A for every 2 of B. Fixed costs are €54 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €13, vA = €5pB = €30, vB = €15A : B = 3 : 2F = €54 000
Q = units
3.Financial accountingMedium
A firm buys 200 units at €5 and 300 units at €6, then sells 400 units. Using weighted average cost, what is closing inventory?
- A€600
- B€500
- C€550
- D€560
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?
- A10%
- B7.5%
- C8.5%
- D15%
3Solutions
1.Break-even analysis
Answer: Q = 2500 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).
Equal total costs
25 000 + 18Q = 40 000 + 12Q
Solve for Q
Q = (40 000 − 25 000)/(18 − 12) = 2 500
Answer
Q = 2 500 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
2.Break-even analysis
Answer: Q = 5000 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €8, cmB = €15
Weighted contribution margin
(3·8 + 2·15)/5 = €10.80
Break-even units
Q = 54 000/10.8 = 5 000
A: 3 000, B: 2 000
Answer
Q = 5 000 units
3.Financial accounting
Answer: D · €560
Why this is the answer
Average cost = (€1,000 + €1,800) ÷ 500 = €5.60. Closing inventory = 100 × €5.60 = €560.
Answer
D · €560
4.Financial accounting
Answer: D · 15%
Why this is the answer
ROE = 5% × 2 × 1.5 = 15%. DuPont shows whether returns come from profitability, asset efficiency or leverage.
Answer
D · 15%
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