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
Integrated marketing communications (IMC) means:
- ACoordinating all communication channels to deliver one consistent message
- BSpending the same budget on each medium
- CUsing only digital channels for advertising
- DMerging the marketing and finance departments
2.Marketing principlesHard
A manufacturer starts selling online directly to consumers at lower prices than its retailers. Retailers complain. What is this?
- AA pull strategy
- BHorizontal channel conflict
- CVertical channel conflict
- DCannibalisation by a rival brand
3.Economics conceptsMedium
Unemployment benefits and progressive income taxes are called automatic stabilisers because they:
- AReduce fluctuations in demand without new government decisions
- BKeep the government budget balanced in every year of the business cycle
- CPrevent all recessions from happening
- DFix the exchange rate automatically
4.Economics conceptsHard
The "convergence hypothesis" from the Solow model predicts that:
- AAll countries will eventually have the same population
- BExchange rates converge to a fixed value
- CPoorer countries with similar fundamentals tend to grow faster than richer ones
- DRich countries always grow faster than poor ones, because they have more capital
5.Financial accountingMedium
A company finds that a machine will last 8 years instead of the 5 originally estimated. Under IAS 8, how is this change applied?
- ABy recognising a large gain in the current year
- BProspectively, by spreading the remaining carrying amount over the new remaining life
- CBy changing the original cost of the machine
- DRetrospectively, by restating all prior years
6.Financial accountingHard
A company sells a software licence together with two years of support for one price. Under IFRS 15, how is revenue recognised?
- ADefer the whole price and recognise it when the two years of support end
- BRecognise half the price in each year without splitting it by obligation
- CAllocate the price using standalone selling prices; recognise the licence at delivery and support over two years
- DRecognise the whole price at once when the customer signs the contract
7.Break-even analysisMedium
A product sells for €49 per unit with a variable cost of €45 per unit. Fixed costs are €10 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €10 000p = €49v = €45profit = €10 000
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €16 with a variable cost of €12; product B sells for €32 with a variable cost of €20. They sell in a fixed mix of 2 units of A for every 3 of B. Fixed costs are €13 200 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €16, vA = €12pB = €32, vB = €20A : B = 2 : 3F = €13 200
Q = units
3Solutions
1.Marketing principles
Answer: A · Coordinating all communication channels to deliver one consistent message
Why this is the answer
IMC aligns advertising, PR, sales promotion, digital and personal selling so they reinforce each other and build a clear brand image.
Answer
A · Coordinating all communication channels to deliver one consistent message
2.Marketing principles
Answer: C · Vertical channel conflict
Why this is the answer
Vertical conflict arises between levels, such as manufacturer and retailer. Horizontal conflict is between firms at the same level, such as two retailers.
Answer
C · Vertical channel conflict
3.Economics concepts
Answer: A · Reduce fluctuations in demand without new government decisions
Why this is the answer
In a downturn tax revenue falls and benefit payments rise automatically, supporting incomes and spending; the reverse happens in a boom.
Answer
A · Reduce fluctuations in demand without new government decisions
4.Economics concepts
Answer: C · Poorer countries with similar fundamentals tend to grow faster than richer ones
Why this is the answer
Capital-poor economies have higher returns to investment, so, given similar saving rates and technology, they should catch up (conditional convergence).
Answer
C · Poorer countries with similar fundamentals tend to grow faster than richer ones
5.Financial accounting
Answer: B · Prospectively, by spreading the remaining carrying amount over the new remaining life
Why this is the answer
Changes in estimates affect the current and future periods only. Prior-period restatement is for changes in policy and corrections of errors.
Answer
B · Prospectively, by spreading the remaining carrying amount over the new remaining life
6.Financial accounting
Answer: C · Allocate the price using standalone selling prices; recognise the licence at delivery and support over two years
Why this is the answer
The licence and support are distinct obligations. The price is split by relative standalone selling prices, and each part is recognised when or as that obligation is satisfied.
Answer
C · Allocate the price using standalone selling prices; recognise the licence at delivery and support over two years
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).
Contribution margin per unit
p − v = 49 − 45 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (10 000 + 10 000)/4 = 5 000
Answer
Q = 5 000 units
8.Break-even analysis
Answer: Q = 1500 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 = €4, cmB = €12
Weighted contribution margin
(2·4 + 3·12)/5 = €8.80
Break-even units
Q = 13 200/8.8 = 1 500
A: 600, B: 900
Answer
Q = 1 500 units
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