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 sells for €28 per unit with a variable cost of €20 per unit. Fixed costs are €40 000 per month. How many units Q must be sold per month to make a profit of €12 000?
F = €40 000p = €28v = €20profit = €12 000
Q = units
2.Break-even analysisHard
A product sells for €24 per unit, with a variable cost of €18 per unit and fixed costs of €4 800 per year. Budgeted sales are 1 120 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €4 800p = €24v = €18budget = 1 120
MS = %
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€550
- B€500
- C€560
- D€600
4.Financial accountingHard
A firm has spent €50,000 on market research for a new product and must decide whether to launch it. How should the €50,000 be treated in the decision?
- ASpread over the product's expected life
- BIgnored, because it is a sunk cost
- CDeducted from expected sales
- DAdded to the launch cost
3Solutions
1.Break-even analysis
Answer: Q = 6500 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).
Contribution margin per unit
p − v = 28 − 20 = €8
Units for the target profit
Q = (F + profit)/(p − v) = (40 000 + 12 000)/8 = 6 500
Answer
Q = 6 500 units
2.Break-even analysis
Answer: MS = 28.57 %
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) = 4 800/6 = 800
Margin of safety
MS = (1 120 − 800)/1 120·100 = 28.57%
Answer
MS = 28.57%
3.Financial accounting
Answer: C · €560
Why this is the answer
Average cost = (€1,000 + €1,800) ÷ 500 = €5.60. Closing inventory = 100 × €5.60 = €560.
Answer
C · €560
4.Financial accounting
Answer: B · Ignored, because it is a sunk cost
Why this is the answer
The research money is spent whichever choice is made, so it is irrelevant. Only future incremental cash flows from launching should be compared.
Answer
B · Ignored, because it is a sunk cost
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