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 €30 with a variable cost of €18 per unit. Fixed costs are €30 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €6 000 after tax?
p = €30v = €18F = €30 000T = 20%after-tax profit = €6 000
Q = units
2.Break-even analysisHard
A product sells for €18 per unit, with a variable cost of €15 per unit and fixed costs of €15 000 per year. Budgeted sales are 7 500 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €15 000p = €18v = €15budget = 7 500
MS = %
3.Financial accountingMedium
On 1 October a company pays €12,000 rent for the next 12 months. Its year ends on 31 December. What is the rent expense for this year?
- A€1,000
- B€12,000
- C€9,000
- D€3,000
4.Financial accountingHard
Production exceeds sales this period, so inventory rises. How does absorption costing profit compare with marginal costing profit?
- AThey are always equal
- BAbsorption costing shows a loss
- CMarginal costing profit is higher this period
- DAbsorption costing profit is higher
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
6 000/(1 − 0.2) = €7 500
Units needed
Q = (30 000 + 7 500)/12 = 3 125
Answer
Q = 3 125 units
2.Break-even analysis
Answer: MS = 33.33 %
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) = 15 000/3 = 5 000
Margin of safety
MS = (7 500 − 5 000)/7 500·100 = 33.33%
Answer
MS = 33.33%
3.Financial accounting
Answer: D · €3,000
Why this is the answer
October to December is 3 months: 3/12 × €12,000 = €3,000. The remaining €9,000 is a prepayment (asset) at year end.
Answer
D · €3,000
4.Financial accounting
Answer: D · Absorption costing profit is higher
Why this is the answer
Under absorption costing part of this period's fixed overhead sits in closing inventory instead of being expensed, so reported profit is higher when inventory rises.
Answer
D · Absorption costing profit is higher
ExamProblems · examproblems.com/courses/management-accounting