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 €50 with a variable cost of €45 per unit. Fixed costs are €20 000 per month and profit is taxed at 25%. How many units Q must be sold per month to earn €6 000 after tax?
p = €50v = €45F = €20 000T = 25%after-tax profit = €6 000
Q = units
2.Break-even analysisHard
A product sells for €32 per unit, with a variable cost of €12 per unit and fixed costs of €100 000 per year. Budgeted sales are 7 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €100 000p = €32v = €12budget = 7 000
MS = %
3.Financial accountingMedium
Operating profit is €120,000 and interest expense is €30,000. What is interest cover?
- A3 times
- B0.25 times
- C4 times
- D90,000 times
4.Financial accountingHard
The standard is 2 labour hours per unit at €20 an hour. 500 units are made in 1,100 hours. What is the labour efficiency variance?
- A€22,000 adverse
- B€2,000 favourable
- C€2,000 adverse
- D€1,000 adverse
3Solutions
1.Break-even analysis
Answer: Q = 5600 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).
Pre-tax profit needed
6 000/(1 − 0.25) = €8 000
Units needed
Q = (20 000 + 8 000)/5 = 5 600
Answer
Q = 5 600 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) = 100 000/20 = 5 000
Margin of safety
MS = (7 000 − 5 000)/7 000·100 = 28.57%
Answer
MS = 28.57%
3.Financial accounting
Answer: C · 4 times
Why this is the answer
€120,000 ÷ €30,000 = 4. The company earns its interest four times over; low cover signals a risk of not meeting interest payments.
Answer
C · 4 times
4.Financial accounting
Answer: C · €2,000 adverse
Why this is the answer
Standard hours = 500 × 2 = 1,000. Extra 100 hours × €20 = €2,000 adverse, because more hours were used than the standard allows.
Answer
C · €2,000 adverse
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