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?
- ASelective distribution
- BDirect distribution only
- CExclusive distribution
- DIntensive distribution
2.Marketing principlesHard
In 1985 Coca-Cola replaced its formula with "New Coke", then brought back the original within months. What is the main marketing lesson?
- AConsumers always prefer the cheapest product
- BBrands should change their formula every year
- CAdvertising cannot influence soft drink sales
- DBlind taste tests can miss consumers' emotional attachment to a brand
3.Economics conceptsMedium
A Nash equilibrium is a situation where:
- AThe players agree to cooperate through a binding contract that maximises their combined total payoff
- BAll players achieve the highest possible total payoff
- CNo player can improve their payoff by changing strategy alone, given the others' strategies
- DOne player has won and the others have lost
4.Economics conceptsHard
Why is the real-world government spending multiplier usually smaller than the simple 1/(1 − MPC)?
- AConsumers never spend extra income
- BGovernments cannot borrow money
- CThe MPC is always above 1
- DTaxes, imports and crowding out leak part of each round of spending
5.Financial accountingMedium
Which error will NOT be revealed by a trial balance?
- AA debit posted without a matching credit
- BA wrongly added ledger column
- CA balance copied to the wrong column
- DA sale left out of the books entirely
6.Financial accountingHard
After the year end, but before the accounts are approved, a customer who owed money at year end goes bankrupt. Under IAS 10 this is:
- AA non-adjusting event, disclosed only
- BAn adjusting event, so receivables are reduced
- CA change in accounting policy
- DIgnored, because it happened after the year end
7.Break-even analysisMedium
A product sells for €53 per unit with a variable cost of €45 per unit. Fixed costs are €6 400 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €6 400p = €53v = €45profit = €2 000
Q = units
8.Break-even analysisHard
A company sells 750 units per month at €35 each, with a variable cost of €25 per unit and fixed costs of €5 000 per month. The variable cost rises by €4 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 750p = €35v = €25 → €29F = €5 000
Q = units
3Solutions
1.Marketing principles
Answer: D · Intensive distribution
Why this is the answer
Intensive distribution suits convenience products that customers buy on impulse and will not search for.
Answer
D · Intensive distribution
2.Marketing principles
Answer: D · Blind taste tests can miss consumers' emotional attachment to a brand
Why this is the answer
Taste tests favoured the new formula, but loyal customers felt something meaningful had been taken away. Brand equity includes emotional and symbolic meaning, not just product attributes.
Answer
D · Blind taste tests can miss consumers' emotional attachment to a brand
3.Economics concepts
Answer: C · No player can improve their payoff by changing strategy alone, given the others' strategies
Why this is the answer
In a Nash equilibrium each strategy is a best response to the others; the outcome need not be efficient, as the Prisoner's Dilemma shows.
Answer
C · No player can improve their payoff by changing strategy alone, given the others' strategies
4.Economics concepts
Answer: D · Taxes, imports and crowding out leak part of each round of spending
Why this is the answer
Income taxes, spending on imports, higher interest rates (crowding out) and saving reduce the extra spending in each round, so the multiplier shrinks.
Answer
D · Taxes, imports and crowding out leak part of each round of spending
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: B · An adjusting event, so receivables are reduced
Why this is the answer
The customer's inability to pay existed at year end, so the accounts are adjusted. A fire after year end would be non-adjusting, because it is a new condition.
Answer
B · An adjusting event, so receivables are reduced
7.Break-even analysis
Answer: Q = 1050 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 = 53 − 45 = €8
Units for the target profit
Q = (F + profit)/(p − v) = (6 400 + 2 000)/8 = 1 050
Answer
Q = 1 050 units
8.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).
Current profit
Π = 750·(35 − 25) − 5 000 = €2 500
New contribution margin per unit
35 − 29 = €6
Units for the same profit
Q = (5 000 + 2 500)/6 = 1 250
Answer
Q = 1 250 units
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