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 €26 with a variable cost of €6 per unit. Fixed costs are €50 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €10 000 after tax?
p = €26v = €6F = €50 000T = 20%after-tax profit = €10 000
Q = units
2.Break-even analysisHard
A company sells 6 250 units at €8 each, with a variable cost of €6 per unit and fixed costs of €5 000. By what percentage %ΔΠ does operating profit change if sales volume falls by 10%?
Q = 6 250p = €8v = €6F = €5 000%ΔQ = −10%
%ΔΠ = %
3.Financial accountingMedium
What is the key difference between absorption costing and marginal costing?
- AAbsorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
- BMarginal costing includes all overheads in inventory; absorption costing excludes them
- CAbsorption costing ignores variable costs
- DMarginal costing is required by IFRS for external reporting
4.Financial accountingHard
When does activity-based costing (ABC) give the biggest improvement over traditional absorption costing?
- AWhen overheads are very small compared with direct costs
- BWhen overheads are large and driven by activities like set-ups rather than volume
- CWhen a firm makes only one standard product
- DWhen all costs are variable with labour hours
3Solutions
1.Break-even analysis
Answer: Q = 3125 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
10 000/(1 − 0.2) = €12 500
Units needed
Q = (50 000 + 12 500)/20 = 3 125
Answer
Q = 3 125 units
2.Break-even analysis
Answer: %ΔΠ = −16.67 %
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 = 6 250·2 = €12 500
Π = 12 500 − 5 000 = €7 500
DOL
DOL = 12 500/7 500 = 1.667
Change in profit
%ΔΠ = 1.667·(−10%) = −16.67%
Answer
%ΔΠ = −16.67%
Check: new profit = 5 625·2 − 5 000 = €6 250.00.
3.Financial accounting
Answer: A · Absorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
Why this is the answer
Under absorption costing each unit carries a share of fixed production overhead. Marginal costing values inventory at variable cost only and expenses fixed costs in the period.
Answer
A · Absorption costing includes fixed production overheads in inventory; marginal costing treats them as period costs
4.Financial accounting
Answer: B · 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
B · When overheads are large and driven by activities like set-ups rather than volume
ExamProblems · examproblems.com/courses/management-accounting