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
Soft drinks are sold in supermarkets, petrol stations, vending machines and kiosks. Which distribution strategy is this?
- ADirect distribution only
- BExclusive distribution
- CIntensive distribution
- DSelective distribution
2.Marketing principlesHard
A brand surveys only members of its loyalty programme to estimate how satisfied all customers in the market are. What is the main weakness?
- AOnline surveys always give random samples
- BLoyalty members are unable to answer satisfaction surveys honestly
- CThe sample is too large to analyse
- DThe sample is biased and does not represent the whole market
3.Economics conceptsMedium
A Gini coefficient of 0 indicates:
- APerfect equality of income
- BPerfect inequality of income
- CZero unemployment
- DZero economic growth
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
- CPrefer risk when facing gains of any size
- DAlways maximise expected monetary value
5.Financial accountingMedium
A company pays its insurance for next year in advance. How is the payment recorded at the year end?
- AAs an expense of the current year in full
- BAs a prepaid expense (asset)
- CAs revenue
- DAs a liability
6.Financial accountingHard
A company "sells" inventory to a bank and must buy it back later at a higher price, keeping the risks and rewards. How should it be accounted for?
- AAs revenue on the date of transfer
- BAs a secured loan, not a sale
- CAs a contingent asset in the notes
- DAs a gain on disposal of inventory
7.Break-even analysisMedium
A product sells for €45 with a variable cost of €30 per unit. Fixed costs are €15 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €3 000 after tax?
p = €45v = €30F = €15 000T = 20%after-tax profit = €3 000
Q = units
8.Break-even analysisHard
A product sells for €31 per unit, with a variable cost of €25 per unit and fixed costs of €3 000 per year. Budgeted sales are 750 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €3 000p = €31v = €25budget = 750
MS = %
3Solutions
1.Marketing principles
Answer: C · Intensive distribution
Why this is the answer
Intensive distribution suits convenience products that customers buy on impulse and will not search for.
Answer
C · Intensive distribution
2.Marketing principles
Answer: D · The sample is biased and does not represent the whole market
Why this is the answer
Loyalty members are likely to be more satisfied than average and exclude non-customers. Results cannot be generalised to the whole market.
Answer
D · The sample is biased and does not represent the whole market
3.Economics concepts
Answer: A · Perfect equality of income
Why this is the answer
The Gini coefficient ranges from 0 (everyone has the same income) to 1 (one person has all income); higher values mean more inequality.
Answer
A · Perfect equality of income
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: B · As a prepaid expense (asset)
Why this is the answer
The unused part of the payment is an asset (prepayment) and becomes an expense in the period it covers.
Answer
B · As a prepaid expense (asset)
6.Financial accounting
Answer: B · As a secured loan, not a sale
Why this is the answer
Control and risks stay with the company, so the transaction is in substance borrowing secured on inventory. The price difference is an interest cost.
Answer
B · As a secured loan, not a sale
7.Break-even analysis
Answer: Q = 1250 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
3 000/(1 − 0.2) = €3 750
Units needed
Q = (15 000 + 3 750)/15 = 1 250
Answer
Q = 1 250 units
8.Break-even analysis
Answer: MS = 33.33 %
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) = 3 000/6 = 500
Margin of safety
MS = (750 − 500)/750·100 = 33.33%
Answer
MS = 33.33%
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