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 €20 000 per year and a variable cost of €12 per unit. Method B, more automated, has fixed costs of €24 000 per year and a variable cost of €8 per unit. At what yearly volume Q do both methods cost the same?
FA = €20 000vA = €12FB = €24 000vB = €8
Q = units
2.Break-even analysisHard
A company sells 1 880 units per month at €20 each, with a variable cost of €15 per unit and fixed costs of €7 500 per month. The variable cost rises by €1 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 1 880p = €20v = €15 → €16F = €7 500
Q = units
3.Financial accountingMedium
Which depreciation method charges the same amount every year?
- AReducing balance
- BStraight-line
- CSum-of-the-years'-digits
- DUnits of production
4.Financial accountingHard
A company issues shares at €5 each with a nominal value of €1. The extra €4 per share is recorded as:
- AA liability
- BShare premium
- CRetained earnings
- DRevenue
3Solutions
1.Break-even analysis
Answer: Q = 1000 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
20 000 + 12Q = 24 000 + 8Q
Solve for Q
Q = (24 000 − 20 000)/(12 − 8) = 1 000
Answer
Q = 1 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
2.Break-even analysis
Answer: Q = 2350 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).
Current profit
Π = 1 880·(20 − 15) − 7 500 = €1 900
New contribution margin per unit
20 − 16 = €4
Units for the same profit
Q = (7 500 + 1 900)/4 = 2 350
Answer
Q = 2 350 units
3.Financial accounting
Answer: B · Straight-line
Why this is the answer
Straight-line spreads the depreciable amount evenly. Reducing balance charges more in early years; units of production follows actual use.
Answer
B · Straight-line
4.Financial accounting
Answer: B · Share premium
Why this is the answer
The amount above nominal value goes to the share premium account in equity; issuing shares is a financing transaction, not income.
Answer
B · Share premium
ExamProblems · examproblems.com/courses/management-accounting