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
Business Fundamentals: cram pack
Formula sheets, the key method steps for every topic and 8 practice problems, with full solutions at the back.
1Formulas and methods
2Practice problems
1.Marketing principlesMedium
Soft drinks are sold in supermarkets, petrol stations, vending machines and kiosks. Which distribution strategy is this?
- ADirect distribution only
- BExclusive distribution
- CIntensive distribution
- DSelective distribution
2.Marketing principlesHard
A company advertises a product as "eco-friendly" without evidence, while only a minor part is recycled. What is this practice called?
- ACause-related marketing
- BGreen product development
- CSocietal marketing
- DGreenwashing
3.Economics conceptsMedium
Stagflation is a combination of:
- ADeflation and rapid growth
- BHigh growth and falling prices
- CLow inflation and low unemployment
- DHigh inflation and high unemployment with low growth
4.Economics conceptsHard
The Laffer curve illustrates that:
- AHigher tax rates always increase tax revenue
- BLower tax rates always reduce tax revenue, whatever the starting rate
- CTax revenue is unrelated to tax rates
- DBeyond some point, raising tax rates can reduce total tax revenue
5.Financial accountingMedium
A firm buys 200 units at €5 and 300 units at €6, then sells 400 units. Using weighted average cost, what is closing inventory?
- A€600
- B€560
- C€550
- D€500
6.Financial accountingHard
Under the matching principle, the cost of a product warranty sold with goods this year should be:
- AIgnored until the warranty expires
- BRecognised only when a customer actually makes a warranty claim
- CRecorded as revenue
- DEstimated and recognised as an expense in the year of sale
7.Break-even analysisMedium
A company sells 1 280 units at €11 each. The variable cost is €8 per unit and fixed costs are €2 400. Find the degree of operating leverage DOL at this sales level.
Q = 1 280p = €11v = €8F = €2 400
DOL =
8.Break-even analysisHard
A product sells for €50 per unit, with a variable cost of €45 per unit and fixed costs of €20 000 per year. Budgeted sales are 7 200 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €20 000p = €50v = €45budget = 7 200
MS = %
3Solutions
1.Marketing principles
Answer: C · Intensive distribution
Why this is the answer
Intensive distribution suits convenience products that customers buy on impulse and will not search for.
Answer
C · Intensive distribution
2.Marketing principles
Answer: D · Greenwashing
Why this is the answer
Greenwashing uses vague or exaggerated environmental claims. It can mislead consumers, damage trust and break consumer protection rules on unfair commercial practices.
Answer
D · Greenwashing
3.Economics concepts
Answer: D · High inflation and high unemployment with low growth
Why this is the answer
Stagflation combines stagnant output, rising unemployment and high inflation, usually after supply shocks.
Answer
D · High inflation and high unemployment with low growth
4.Economics concepts
Answer: D · Beyond some point, raising tax rates can reduce total tax revenue
Why this is the answer
Very high rates discourage taxed activity or encourage avoidance, so revenue peaks at some rate between 0 and 100%; where that peak lies is debated.
Answer
D · Beyond some point, raising tax rates can reduce total tax revenue
5.Financial accounting
Answer: B · €560
Why this is the answer
Average cost = (€1,000 + €1,800) ÷ 500 = €5.60. Closing inventory = 100 × €5.60 = €560.
Answer
B · €560
6.Financial accounting
Answer: D · Estimated and recognised as an expense in the year of sale
Why this is the answer
A provision for expected warranty costs is recognised when the goods are sold, matching the expense with the related revenue (IAS 37).
Answer
D · Estimated and recognised as an expense in the year of sale
7.Break-even analysis
Answer: DOL = 2.667
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Total contribution margin
CM = 1 280·(11 − 8) = €3 840
Operating profit
Π = 3 840 − 2 400 = €1 440
DOL
DOL = 3 840/1 440 = 2.667
Answer
DOL = 2.667
8.Break-even analysis
Answer: MS = 44.44 %
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) = 20 000/5 = 4 000
Margin of safety
MS = (7 200 − 4 000)/7 200·100 = 44.44%
Answer
MS = 44.44%
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