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 2 000 units at €14 each. The variable cost is €6 per unit and fixed costs are €8 000. Find the degree of operating leverage DOL at this sales level.
Q = 2 000p = €14v = €6F = €8 000
DOL =
2.Break-even analysisHard
A product sells for €14 per unit, with a variable cost of €12 per unit and fixed costs of €1 600 per year. Budgeted sales are 1 440 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €1 600p = €14v = €12budget = 1 440
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€500
- B€550
- C€560
- D€600
4.Financial accountingHard
Budgeted overhead is €200,000 for 40,000 machine hours. Actual hours are 42,000 and actual overhead is €205,000. What is the result?
- AOverhead over-absorbed by €5,000
- BOverhead exactly absorbed
- COverhead under-absorbed by €10,000
- DOverhead under-absorbed by €5,000
3Solutions
1.Break-even analysis
Answer: DOL = 2
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 = 2 000·(14 − 6) = €16 000
Operating profit
Π = 16 000 − 8 000 = €8 000
DOL
DOL = 16 000/8 000 = 2
Answer
DOL = 2
2.Break-even analysis
Answer: MS = 44.44 %
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) = 1 600/2 = 800
Margin of safety
MS = (1 440 − 800)/1 440·100 = 44.44%
Answer
MS = 44.44%
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: A · Overhead over-absorbed by €5,000
Why this is the answer
Rate = €5 per hour. Absorbed = 42,000 × €5 = €210,000, which exceeds actual €205,000, so €5,000 is over-absorbed and added back to profit.
Answer
A · Overhead over-absorbed by €5,000
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