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 €15 000 per year and a variable cost of €12 per unit. Method B, more automated, has fixed costs of €19 000 per year and a variable cost of €8 per unit. At what yearly volume Q do both methods cost the same?
FA = €15 000vA = €12FB = €19 000vB = €8
Q = units
2.Break-even analysisHard
A product sells for €33 per unit, with a variable cost of €30 per unit and fixed costs of €7 500 per year. Budgeted sales are 3 130 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €7 500p = €33v = €30budget = 3 130
MS = %
3.Financial accountingMedium
Operating profit is €120,000 and interest expense is €30,000. What is interest cover?
- A0.25 times
- B90,000 times
- C3 times
- D4 times
4.Financial accountingHard
A company "sells" inventory to a bank and must buy it back later at a higher price, keeping the risks and rewards. How should it be accounted for?
- AAs a gain on disposal of inventory
- BAs a secured loan, not a sale
- CAs revenue on the date of transfer
- DAs a contingent asset in the notes
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
15 000 + 12Q = 19 000 + 8Q
Solve for Q
Q = (19 000 − 15 000)/(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: MS = 20.13 %
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) = 7 500/3 = 2 500
Margin of safety
MS = (3 130 − 2 500)/3 130·100 = 20.13%
Answer
MS = 20.13%
3.Financial accounting
Answer: D · 4 times
Why this is the answer
€120,000 ÷ €30,000 = 4. The company earns its interest four times over; low cover signals a risk of not meeting interest payments.
Answer
D · 4 times
4.Financial accounting
Answer: B · As a secured loan, not a sale
Why this is the answer
Control and risks stay with the company, so the transaction is in substance borrowing secured on inventory. The price difference is an interest cost.
Answer
B · As a secured loan, not a sale
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