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
In the Boston Consulting Group matrix, a "cash cow" has:
- ALow market share in a high-growth market
- BLow market share in a low-growth market
- CHigh market share in a low-growth market
- DHigh market share in a high-growth market
2.Marketing principlesHard
Which conditions are needed for price discrimination (charging different groups different prices) to work?
- ASegments with different price sensitivity that can be separated, and little reselling between them
- BThe firm must have no fixed costs
- CAll customers must have identical price sensitivity
- DThe product must be sold only in one shop
3.Economics conceptsMedium
In the short run, a firm in perfect competition should shut down if the market price is below:
- AAverage total cost
- BMarginal revenue
- CAverage variable cost
- DAverage fixed cost
4.Economics conceptsHard
The time-inconsistency problem in monetary policy (Kydland and Prescott) is a key argument for:
- AFixing the money supply at zero growth
- BIndependent central banks with a credible commitment to low inflation
- CGovernments setting interest rates directly, especially before elections
- DAbolishing central banks entirely
5.Financial accountingMedium
A company is being sued. Its lawyers say losing is possible but not probable. How is this treated under IAS 37?
- ARecognised as a provision on the balance sheet
- BDisclosed as a contingent liability in the notes
- CRecognised as an expense and paid into a reserve
- DIgnored completely
6.Financial accountingHard
Making a part costs €10 materials, €6 labour and €4 variable overhead, plus €5 of fixed overhead that continues anyway. A supplier offers it at €22. What should the firm do on cost grounds?
- AMake it, because the relevant cost of €20 is below €22
- BBuy it, because fixed costs are always relevant
- CMake it, because the full cost of €25 is below €22
- DBuy it, because the full cost of €25 per unit is above €22
7.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 €10 per unit. Method B, more automated, has fixed costs of €35 000 per year and a variable cost of €6 per unit. At what yearly volume Q do both methods cost the same?
FA = €15 000vA = €10FB = €35 000vB = €6
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €8 with a variable cost of €5; product B sells for €40 with a variable cost of €30. They sell in a fixed mix of 2 units of A for every 1 of B. Fixed costs are €4 800 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €8, vA = €5pB = €40, vB = €30A : B = 2 : 1F = €4 800
Q = units
3Solutions
1.Marketing principles
Answer: C · High market share in a low-growth market
Why this is the answer
Cash cows fund other products. Stars have high share and growth, question marks low share in high growth, dogs low share and low growth.
Answer
C · High market share in a low-growth market
2.Marketing principles
Answer: A · Segments with different price sensitivity that can be separated, and little reselling between them
Why this is the answer
The firm must identify segments with different elasticities, keep them apart (for example with ID or timing) and prevent low-price buyers reselling to others.
Answer
A · Segments with different price sensitivity that can be separated, and little reselling between them
3.Economics concepts
Answer: C · Average variable cost
Why this is the answer
If price covers average variable cost, producing reduces losses by contributing to fixed costs; below AVC, shutting down loses less.
Answer
C · Average variable cost
4.Economics concepts
Answer: B · Independent central banks with a credible commitment to low inflation
Why this is the answer
If the public expects policymakers to inflate later, expectations and inflation rise; delegating policy to an independent, credible central bank reduces this bias.
Answer
B · Independent central banks with a credible commitment to low inflation
5.Financial accounting
Answer: B · Disclosed as a contingent liability in the notes
Why this is the answer
A possible obligation is not recognised but disclosed, unless the chance of outflow is remote. A probable, measurable outflow would require a provision.
Answer
B · Disclosed as a contingent liability in the notes
6.Financial accounting
Answer: A · Make it, because the relevant cost of €20 is below €22
Why this is the answer
Only the €20 of variable cost is avoided by buying; the €5 fixed overhead stays. Making costs €20 versus €22 to buy, so making saves €2 per unit.
Answer
A · Make it, because the relevant cost of €20 is below €22
7.Break-even analysis
Answer: Q = 5000 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 + 10Q = 35 000 + 6Q
Solve for Q
Q = (35 000 − 15 000)/(10 − 6) = 5 000
Answer
Q = 5 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: Q = 900 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €3, cmB = €10
Weighted contribution margin
(2·3 + 1·10)/3 = €5.33
Break-even units
Q = 4 800/5.333 = 900
A: 600, B: 300
Answer
Q = 900 units
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