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 online advertising, what does CPM mean?
- AClicks per month
- BCost per minute of video viewing
- CCustomers per market
- DCost per thousand impressions
2.Marketing principlesHard
Geoffrey Moore's "chasm" in technology markets refers to the gap between which adopter groups?
- AEarly adopters and the early majority
- BLate majority and laggards
- CInnovators and early adopters
- DEarly majority and late majority
3.Economics conceptsMedium
In country A, 1 car costs 2 tonnes of wheat to produce; in country B, 1 car costs 4 tonnes of wheat. Which statement is correct?
- AB has a comparative advantage in cars and A in wheat
- BA has a comparative advantage in cars and B in wheat
- CA has a comparative advantage in both goods
- DNeither country gains from trade
4.Economics conceptsHard
According to prospect theory (Kahneman and Tversky), people typically:
- AFeel losses more strongly than equal-sized gains
- BTreat losses and gains of the same size as equally important
- CAlways maximise expected monetary value
- DPrefer risk when facing gains of any size
5.Financial accountingMedium
Which error will NOT be revealed by a trial balance?
- AA debit posted without a matching credit
- BA balance copied to the wrong column
- CA wrongly added ledger column
- DA sale left out of the books entirely
6.Financial accountingHard
An asset is impaired when its carrying amount is higher than its:
- ARecoverable amount (the higher of fair value less costs of disposal and value in use)
- BDepreciation charge
- COriginal purchase price
- DResidual value only
7.Break-even analysisMedium
A product sells for €9 with a variable cost of €6 per unit. Fixed costs are €3 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €1 500 after tax?
p = €9v = €6F = €3 000T = 20%after-tax profit = €1 500
Q = units
8.Break-even analysisHard
A company sells 3 200 units at €40 each, with a variable cost of €20 per unit and fixed costs of €40 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 20%?
Q = 3 200p = €40v = €20F = €40 000%ΔQ = +20%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: D · Cost per thousand impressions
Why this is the answer
CPM is the price for 1,000 ad impressions. It suits awareness goals; cost per click (CPC) and cost per acquisition (CPA) tie spending to actions.
Answer
D · Cost per thousand impressions
2.Marketing principles
Answer: A · Early adopters and the early majority
Why this is the answer
Early adopters accept risk for advantage, while the early majority want proven, complete solutions and references. Many products fail to make this transition.
Answer
A · Early adopters and the early majority
3.Economics concepts
Answer: B · A has a comparative advantage in cars and B in wheat
Why this is the answer
A gives up less wheat per car, so it should specialise in cars; B's opportunity cost of wheat (1/4 car) is lower than A's (1/2 car), so B specialises in wheat.
Answer
B · A has a comparative advantage in cars and B in wheat
4.Economics concepts
Answer: A · Feel losses more strongly than equal-sized gains
Why this is the answer
The value function is steeper for losses than for gains and is measured relative to a reference point, explaining behaviour that expected utility theory struggles with.
Answer
A · Feel losses more strongly than equal-sized gains
5.Financial accounting
Answer: D · A sale left out of the books entirely
Why this is the answer
An error of omission leaves both sides unrecorded, so totals still agree. Single-sided postings and addition errors make the trial balance differ.
Answer
D · A sale left out of the books entirely
6.Financial accounting
Answer: A · Recoverable amount (the higher of fair value less costs of disposal and value in use)
Why this is the answer
If the carrying amount exceeds the recoverable amount, the difference is written off as an impairment loss.
Answer
A · Recoverable amount (the higher of fair value less costs of disposal and value in use)
7.Break-even analysis
Answer: Q = 1625 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).
Pre-tax profit needed
1 500/(1 − 0.2) = €1 875
Units needed
Q = (3 000 + 1 875)/3 = 1 625
Answer
Q = 1 625 units
8.Break-even analysis
Answer: %ΔΠ = 53.33 %
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 = 3 200·20 = €64 000
Π = 64 000 − 40 000 = €24 000
DOL
DOL = 64 000/24 000 = 2.667
Change in profit
%ΔΠ = 2.667·(+20%) = +53.33%
Answer
%ΔΠ = +53.33%
Check: new profit = 3 840·20 − 40 000 = €36 800.00.
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