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
Positioning refers to:
- AHow a brand is perceived relative to competitors in customers' minds
- BThe order of products in a catalogue
- CThe geographical location of the company
- DWhere products are physically placed on shop shelves and in store displays
2.Marketing principlesHard
Procter and Gamble sells Pampers, Ariel and Gillette under separate brand names, not under the company name. Which brand architecture is this?
- AA branded house
- BA private label strategy
- CA house of brands
- DCo-branding
3.Economics conceptsMedium
The price of a good rises by 10% and quantity demanded falls by 20%. The price elasticity of demand is:
- A-2, so demand is elastic
- B-0.5, so demand is elastic
- C-2, so demand is inelastic
- 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:
- ATrade balances are always zero
- BEvery currency ends up having the same nominal value as the US dollar
- CThe same basket of goods costs the same in different countries
- DInterest rates are equal in all countries
5.Financial accountingMedium
A company increases its allowance for doubtful receivables. What is the effect?
- AAn expense is recognised and net receivables fall
- BCash decreases immediately
- COnly the notes change; no figures move
- DRevenue increases and gross receivables rise by the same amount
6.Financial accountingHard
Inventory days are 60, receivable days 45 and payable days 30. What is the cash conversion (operating) cycle?
- A105 days
- B135 days
- C15 days
- D75 days
7.Break-even analysisMedium
A product sells for €45 per unit with a variable cost of €25 per unit. Fixed costs are €80 000 per month. How many units Q must be sold per month to make a profit of €20 000?
F = €80 000p = €45v = €25profit = €20 000
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €8 with a variable cost of €5; product B sells for €22 with a variable cost of €10. They sell in a fixed mix of 5 units of A for every 2 of B. Fixed costs are €23 400 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €8, vA = €5pB = €22, vB = €10A : B = 5 : 2F = €23 400
Q = units
3Solutions
1.Marketing principles
Answer: A · How a brand is perceived relative to competitors in customers' minds
Why this is the answer
Positioning defines the distinctive place a brand wants to occupy in the target customers' minds, based on benefits and differences from rivals.
Answer
A · How a brand is perceived relative to competitors in customers' minds
2.Marketing principles
Answer: C · A house of brands
Why this is the answer
A house of brands gives each product its own identity, so brands can target different segments and problems with one do not spread easily. A branded house, like Virgin, uses one master brand.
Answer
C · A house of brands
3.Economics concepts
Answer: A · -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
A · -2, so demand is elastic
4.Economics concepts
Answer: C · 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
C · The same basket of goods costs the same in different countries
5.Financial accounting
Answer: A · An expense is recognised and net receivables fall
Why this is the answer
The increase is charged to profit, and the allowance is deducted from gross receivables, so the balance sheet shows the amount expected to be collected.
Answer
A · An expense is recognised and net receivables fall
6.Financial accounting
Answer: D · 75 days
Why this is the answer
60 + 45 − 30 = 75 days between paying suppliers and collecting cash from customers. A shorter cycle needs less working capital finance.
Answer
D · 75 days
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 = 45 − 25 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (80 000 + 20 000)/20 = 5 000
Answer
Q = 5 000 units
8.Break-even analysis
Answer: Q = 4200 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 = €3, cmB = €12
Weighted contribution margin
(5·3 + 2·12)/7 = €5.57
Break-even units
Q = 23 400/5.571 = 4 200
A: 3 000, B: 1 200
Answer
Q = 4 200 units
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