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
Value-based pricing sets prices mainly according to:
- AThe firm's target profit for the year
- BThe cost of making the product plus a mark-up
- CThe prices charged by the cheapest rival
- DCustomers' perception of the product's value
2.Marketing principlesHard
During a major sports tournament, a non-sponsor brand runs ads suggesting a link with the event without paying for official rights. What is this called?
- AAmbush marketing
- BGuerrilla distribution
- CCause-related marketing
- DCo-branding
3.Economics conceptsMedium
A country imposes a tariff on imported steel. Which effect is most likely?
- ADomestic steel prices fall and imports rise
- BThe world price of steel rises sharply for all countries that trade it
- CDomestic steel prices rise and domestic production increases
- DDomestic consumers gain surplus
4.Economics conceptsHard
Moral hazard arises when:
- AOne party changes behaviour after a contract because they do not bear the full consequences
- BPrices are too high for poor consumers
- CTwo firms collude on price
- DA buyer cannot observe product quality before buying, so low-quality sellers dominate the market
5.Financial accountingMedium
Budgeted sales are 1,500 units and the break-even point is 1,000 units. What is the margin of safety?
- A500 units
- B2,500 units
- C1,500 units
- D1,000 units
6.Financial accountingHard
Under the IAS 16 revaluation model, a building is revalued upwards for the first time. Where does the gain go?
- ATo revenue in the income statement
- BTo other comprehensive income and a revaluation surplus in equity
- CTo retained earnings as a realised profit
- DTo a provision on the balance sheet
7.Break-even analysisMedium
A product sells for €19 per unit with a variable cost of €15 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €20 000p = €19v = €15profit = €5 000
Q = units
8.Break-even analysisHard
A company sells 7 500 units at €40 each, with a variable cost of €30 per unit and fixed costs of €50 000. By what percentage %ΔΠ does operating profit change if sales volume falls by 20%?
Q = 7 500p = €40v = €30F = €50 000%ΔQ = −20%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: D · Customers' perception of the product's value
Why this is the answer
Value-based pricing estimates what the offer is worth to buyers. Costs then set a floor, and competitor prices are a reference.
Answer
D · Customers' perception of the product's value
2.Marketing principles
Answer: A · Ambush marketing
Why this is the answer
Ambush marketing tries to gain association with an event without sponsorship. Organisers often protect sponsors through contracts and trademark rules.
Answer
A · Ambush marketing
3.Economics concepts
Answer: C · Domestic steel prices rise and domestic production increases
Why this is the answer
The tariff raises the domestic price, increasing domestic output and government revenue but reducing consumer surplus and creating deadweight losses.
Answer
C · Domestic steel prices rise and domestic production increases
4.Economics concepts
Answer: A · 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
A · One party changes behaviour after a contract because they do not bear the full consequences
5.Financial accounting
Answer: A · 500 units
Why this is the answer
Margin of safety = budgeted sales − break-even sales = 500 units, or one third of budgeted sales.
Answer
A · 500 units
6.Financial accounting
Answer: B · To other comprehensive income and a revaluation surplus in equity
Why this is the answer
Upward revaluations are credited to a revaluation surplus via OCI, unless they reverse an earlier decrease recognised in profit or loss.
Answer
B · To other comprehensive income and a revaluation surplus in equity
7.Break-even analysis
Answer: Q = 6250 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 = 19 − 15 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (20 000 + 5 000)/4 = 6 250
Answer
Q = 6 250 units
8.Break-even analysis
Answer: %ΔΠ = −60 %
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.
Contribution margin and profit
CM = 7 500·10 = €75 000
Π = 75 000 − 50 000 = €25 000
DOL
DOL = 75 000/25 000 = 3
Change in profit
%ΔΠ = 3·(−20%) = −60%
Answer
%ΔΠ = −60%
Check: new profit = 6 000·10 − 50 000 = €10 000.00.
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