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 €28 200 per year and a variable cost of €8 per unit. At what yearly volume Q do both methods cost the same?
FA = €25 000vA = €12FB = €28 200vB = €8
Q = units
2.Break-even analysisHard
A product sells for €23 per unit, with a variable cost of €18 per unit and fixed costs of €10 000 per year. Budgeted sales are 3 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €10 000p = €23v = €18budget = 3 000
MS = %
3.Financial accountingMedium
A project has a positive net present value (NPV) at the company's cost of capital. This means:
- AIt has no risk at all
- BIts reported accounting profit will be positive in every year
- CIt recovers its cost within one year
- DIt earns more than the required return and should add value
4.Financial accountingHard
Under IFRS, how is purchased goodwill treated after acquisition?
- AIt is revalued upwards every year
- BIt is not amortised but tested for impairment at least annually
- CIt is written off against equity immediately
- DIt is amortised over 20 years
3Solutions
1.Break-even analysis
Answer: Q = 800 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 = 28 200 + 8Q
Solve for Q
Q = (28 200 − 25 000)/(12 − 8) = 800
Answer
Q = 800 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
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) = 10 000/5 = 2 000
Margin of safety
MS = (3 000 − 2 000)/3 000·100 = 33.33%
Answer
MS = 33.33%
3.Financial accounting
Answer: D · 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
D · It earns more than the required return and should add value
4.Financial accounting
Answer: B · It is not amortised but tested for impairment at least annually
Why this is the answer
Goodwill has an indefinite life under IFRS. It is allocated to cash-generating units and tested for impairment yearly, or more often if there are signs of impairment.
Answer
B · It is not amortised but tested for impairment at least annually
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