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
A small firm makes premium climbing gear and targets only serious climbers. Which targeting strategy is this?
- AConcentrated (niche) marketing
- BUndifferentiated (mass) marketing
- CMicromarketing for each individual
- DDifferentiated marketing
2.Marketing principlesHard
A company sells printers cheaply but charges high prices for ink cartridges. This is:
- ACaptive product pricing
- BPenetration pricing for both products
- CBundle pricing
- DPsychological pricing
3.Economics conceptsMedium
Unexpectedly high inflation tends to benefit:
- ASavers holding cash
- BPensioners on fixed nominal incomes
- CBorrowers with fixed-rate loans
- DLenders who receive fixed interest payments
4.Economics conceptsHard
Moral hazard arises when:
- AA buyer cannot observe product quality before buying, so low-quality sellers dominate the market
- BTwo firms collude on price
- COne party changes behaviour after a contract because they do not bear the full consequences
- DPrices are too high for poor consumers
5.Financial accountingMedium
Under IAS 16, which cost should be included in the cost of a new machine?
- AStaff training costs after it starts operating
- BInstallation costs needed to get it working
- CRepairs carried out two years later
- DGeneral office overheads for the year
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 full cost of €25 is below €22
- BBuy it, because the full cost of €25 per unit is above €22
- CMake it, because the relevant cost of €20 is below €22
- DBuy it, because fixed costs are always relevant
7.Break-even analysisMedium
A product sells for €38 per unit with a variable cost of €30 per unit. Fixed costs are €12 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €12 000p = €38v = €30profit = €10 000
Q = units
8.Break-even analysisHard
A product sells for €25 per unit, with a variable cost of €15 per unit and fixed costs of €12 000 per year. Budgeted sales are 1 440 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €12 000p = €25v = €15budget = 1 440
MS = %
3Solutions
1.Marketing principles
Answer: A · Concentrated (niche) marketing
Why this is the answer
Concentrated marketing focuses resources on one segment. It builds deep expertise but makes the firm dependent on that segment.
Answer
A · Concentrated (niche) marketing
2.Marketing principles
Answer: A · Captive product pricing
Why this is the answer
Captive product pricing sets a low price for the main product and earns margins on necessary consumables.
Answer
A · Captive product pricing
3.Economics concepts
Answer: C · Borrowers with fixed-rate loans
Why this is the answer
Unexpected inflation reduces the real value of debts, transferring purchasing power from lenders and fixed-income earners to borrowers.
Answer
C · Borrowers with fixed-rate loans
4.Economics concepts
Answer: C · One party changes behaviour after a contract because they do not bear the full consequences
Why this is the answer
Moral hazard is hidden action after the contract, such as an insured driver taking more risks. Adverse selection is hidden information before the contract.
Answer
C · One party changes behaviour after a contract because they do not bear the full consequences
5.Financial accounting
Answer: B · Installation costs needed to get it working
Why this is the answer
Purchase price plus directly attributable costs, such as delivery and installation, are capitalised. Training, later repairs and general overheads are expensed.
Answer
B · Installation costs needed to get it working
6.Financial accounting
Answer: C · 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
C · Make it, because the relevant cost of €20 is below €22
7.Break-even analysis
Answer: Q = 2750 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 = 38 − 30 = €8
Units for the target profit
Q = (F + profit)/(p − v) = (12 000 + 10 000)/8 = 2 750
Answer
Q = 2 750 units
8.Break-even analysis
Answer: MS = 16.67 %
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) = 12 000/10 = 1 200
Margin of safety
MS = (1 440 − 1 200)/1 440·100 = 16.67%
Answer
MS = 16.67%
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