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 can be made in two ways. Method A has fixed costs of €25 000 per year and a variable cost of €12 per unit. Method B, more automated, has fixed costs of €26 500 per year and a variable cost of €9 per unit. At what yearly volume Q do both methods cost the same?
FA = €25 000vA = €12FB = €26 500vB = €9
Q = units
2.Break-even analysisHard
A product sells for €14 per unit, with a variable cost of €8 per unit and fixed costs of €7 200 per year. Budgeted sales are 1 380 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €7 200p = €14v = €8budget = 1 380
MS = %
3.Financial accountingMedium
Under the accrual basis of accounting, revenue is recognised when:
- AThe tax return is filed
- BCash is received
- CThe customer pays the invoice, even if goods were delivered earlier
- DIt is earned, whether or not cash has been received
4.Financial accountingHard
A firm with spare capacity gets a one-off order at €35 per unit. Variable cost is €30 and full cost including fixed overhead is €42. Assuming no other effects, should it accept?
- ANo, the price is below full cost
- BYes, but only if the price exceeds €42
- CNo, the order makes a €7 loss per unit
- DYes, each unit adds €5 contribution
3Solutions
1.Break-even analysis
Answer: Q = 500 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).
Equal total costs
25 000 + 12Q = 26 500 + 9Q
Solve for Q
Q = (26 500 − 25 000)/(12 − 9) = 500
Answer
Q = 500 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
2.Break-even analysis
Answer: MS = 13.04 %
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) = 7 200/6 = 1 200
Margin of safety
MS = (1 380 − 1 200)/1 380·100 = 13.04%
Answer
MS = 13.04%
3.Financial accounting
Answer: D · It is earned, whether or not cash has been received
Why this is the answer
Accrual accounting records revenue when the performance obligation is satisfied and expenses when incurred, not when cash moves.
Answer
D · It is earned, whether or not cash has been received
4.Financial accounting
Answer: D · Yes, each unit adds €5 contribution
Why this is the answer
Fixed costs do not change, so the order adds €35 − €30 = €5 per unit to profit. Risks such as upsetting regular customers should still be considered.
Answer
D · Yes, each unit adds €5 contribution
ExamProblems · examproblems.com/courses/management-accounting