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 €14 per unit with a variable cost of €12 per unit. Fixed costs are €8 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €8 000p = €14v = €12profit = €5 000
Q = units
2.Break-even analysisHard
A company sells 2 400 units per month at €33 each, with a variable cost of €18 per unit and fixed costs of €18 000 per month. The variable cost rises by €3 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 2 400p = €33v = €18 → €21F = €18 000
Q = units
3.Financial accountingMedium
A project has a positive net present value (NPV) at the company's cost of capital. This means:
- AIt recovers its cost within one year
- BIt has no risk at all
- CIt earns more than the required return and should add value
- DIts reported accounting profit will be positive in every year
4.Financial accountingHard
Machine hours are scarce. Product X earns €20 contribution and needs 4 hours; product Y earns €15 and needs 2 hours. Which should be made first?
- AY, because it earns €7.50 per hour versus €5 for X
- BEither, because the total contribution is the same
- CX, because it uses more machine time
- DX, because it earns more contribution per unit
3Solutions
1.Break-even analysis
Answer: Q = 6500 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).
Contribution margin per unit
p − v = 14 − 12 = €2
Units for the target profit
Q = (F + profit)/(p − v) = (8 000 + 5 000)/2 = 6 500
Answer
Q = 6 500 units
2.Break-even analysis
Answer: Q = 3000 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 = 2 400·(33 − 18) − 18 000 = €18 000
New contribution margin per unit
33 − 21 = €12
Units for the same profit
Q = (18 000 + 18 000)/12 = 3 000
Answer
Q = 3 000 units
3.Financial accounting
Answer: C · It earns more than the required return and should add value
Why this is the answer
A positive NPV means the present value of inflows exceeds the investment at the required rate, so the project increases shareholder wealth.
Answer
C · It earns more than the required return and should add value
4.Financial accounting
Answer: A · Y, because it earns €7.50 per hour versus €5 for X
Why this is the answer
X earns €20 ÷ 4 = €5 per hour, Y earns €15 ÷ 2 = €7.50 per hour. With a scarce resource, maximise contribution per scarce hour.
Answer
A · Y, because it earns €7.50 per hour versus €5 for X
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