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 company sells printers cheaply but charges high prices for ink cartridges. This is:
- ABundle pricing
- BPenetration pricing for both products
- CCaptive product pricing
- DPsychological pricing
3.Economics conceptsMedium
The price of a good rises by 10% and quantity demanded falls by 20%. The price elasticity of demand is:
- A-0.5, so demand is elastic
- B-2, so demand is inelastic
- C-2, so demand is elastic
- D-0.5, so demand is inelastic
4.Economics conceptsHard
Purchasing power parity (PPP) suggests that, in the long run, exchange rates adjust so that:
- AInterest rates are equal in all countries
- BThe same basket of goods costs the same in different countries
- CTrade balances are always zero
- DEvery currency ends up having the same nominal value as the US dollar
5.Financial accountingMedium
Which error will NOT be revealed by a trial balance?
- AA wrongly added ledger column
- BA sale left out of the books entirely
- CA debit posted without a matching credit
- DA balance copied to the wrong column
6.Financial accountingHard
Production exceeds sales this period, so inventory rises. How does absorption costing profit compare with marginal costing profit?
- AThey are always equal
- BAbsorption costing shows a loss
- CMarginal costing profit is higher this period
- DAbsorption costing profit is higher
7.Break-even analysisMedium
A product sells for €22 per unit with a variable cost of €12 per unit. Fixed costs are €50 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €50 000p = €22v = €12profit = €5 000
Q = units
8.Break-even analysisHard
A product sells for €16 per unit, with a variable cost of €6 per unit and fixed costs of €50 000 per year. Budgeted sales are 5 750 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €50 000p = €16v = €6budget = 5 750
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: C · Captive product pricing
Why this is the answer
Captive product pricing sets a low price for the main product and earns margins on necessary consumables.
Answer
C · Captive product pricing
3.Economics concepts
Answer: C · -2, so demand is elastic
Why this is the answer
PED = -20% / 10% = -2; since the absolute value is above 1, demand is elastic.
Answer
C · -2, so demand is elastic
4.Economics concepts
Answer: B · The same basket of goods costs the same in different countries
Why this is the answer
PPP is based on the law of one price: if a good is cheaper in one country, arbitrage should push exchange rates towards equalising prices, though transport costs and non-traded goods limit this.
Answer
B · The same basket of goods costs the same in different countries
5.Financial accounting
Answer: B · 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
B · A sale left out of the books entirely
6.Financial accounting
Answer: D · Absorption costing profit is higher
Why this is the answer
Under absorption costing part of this period's fixed overhead sits in closing inventory instead of being expensed, so reported profit is higher when inventory rises.
Answer
D · Absorption costing profit is higher
7.Break-even analysis
Answer: Q = 5500 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 = 22 − 12 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (50 000 + 5 000)/10 = 5 500
Answer
Q = 5 500 units
8.Break-even analysis
Answer: MS = 13.04 %
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) = 50 000/10 = 5 000
Margin of safety
MS = (5 750 − 5 000)/5 750·100 = 13.04%
Answer
MS = 13.04%
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