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 €23 per unit with a variable cost of €15 per unit. Fixed costs are €32 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €32 000p = €23v = €15profit = €10 000
Q = units
2.Break-even analysisHard
A company sells 2 500 units at €19 each, with a variable cost of €15 per unit and fixed costs of €8 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 12%?
Q = 2 500p = €19v = €15F = €8 000%ΔQ = +12%
%ΔΠ = %
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€600
- C€560
- D€500
4.Financial accountingHard
When does activity-based costing (ABC) give the biggest improvement over traditional absorption costing?
- AWhen a firm makes only one standard product
- BWhen overheads are very small compared with direct costs
- CWhen overheads are large and driven by activities like set-ups rather than volume
- DWhen all costs are variable with labour hours
3Solutions
1.Break-even analysis
Answer: Q = 5250 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 = 23 − 15 = €8
Units for the target profit
Q = (F + profit)/(p − v) = (32 000 + 10 000)/8 = 5 250
Answer
Q = 5 250 units
2.Break-even analysis
Answer: %ΔΠ = 60 %
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.
Contribution margin and profit
CM = 2 500·4 = €10 000
Π = 10 000 − 8 000 = €2 000
DOL
DOL = 10 000/2 000 = 5
Change in profit
%ΔΠ = 5·(+12%) = +60%
Answer
%ΔΠ = +60%
Check: new profit = 2 800·4 − 8 000 = €3 200.00.
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: C · When overheads are large and driven by activities like set-ups rather than volume
Why this is the answer
ABC assigns overheads using cost drivers for each activity. Where products use activities very differently, a single volume-based rate distorts product costs.
Answer
C · When overheads are large and driven by activities like set-ups rather than volume
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