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
Which pricing method adds a fixed percentage to the cost of a product?
- ACost-plus pricing
- BDynamic pricing
- CValue-based pricing
- DCompetitive pricing
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 house of brands
- BA branded house
- CA private label strategy
- DCo-branding
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
- CNeither country gains from trade
- DA has a comparative advantage in both goods
4.Economics conceptsHard
The Laffer curve illustrates that:
- ABeyond some point, raising tax rates can reduce total tax revenue
- BTax revenue is unrelated to tax rates
- CLower tax rates always reduce tax revenue, whatever the starting rate
- DHigher tax rates always increase tax revenue
5.Financial accountingMedium
Net working capital is:
- ACurrent assets minus current liabilities
- BNon-current assets minus long-term loans
- CTotal assets minus total liabilities
- DRevenue minus operating expenses
6.Financial accountingHard
The standard price of material is €5 per kg. The company buys 1,000 kg for €5,400. What is the material price variance?
- A€0.40 adverse
- B€400 favourable
- C€400 adverse
- D€5,400 adverse
7.Break-even analysisMedium
A product sells for €17 per unit with a variable cost of €15 per unit. Fixed costs are €4 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €4 000p = €17v = €15profit = €2 000
Q = units
8.Break-even analysisHard
A company sells 2 000 units per month at €22 each, with a variable cost of €20 per unit and fixed costs of €2 000 per month. The variable cost rises by €1 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 2 000p = €22v = €20 → €21F = €2 000
Q = units
3Solutions
1.Marketing principles
Answer: A · Cost-plus pricing
Why this is the answer
Cost-plus pricing is simple but ignores customer willingness to pay; value-based pricing starts from the value perceived by customers.
Answer
A · Cost-plus pricing
2.Marketing principles
Answer: A · 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
A · A house of brands
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 · Beyond some point, raising tax rates can reduce total tax revenue
Why this is the answer
Very high rates discourage taxed activity or encourage avoidance, so revenue peaks at some rate between 0 and 100%; where that peak lies is debated.
Answer
A · Beyond some point, raising tax rates can reduce total tax revenue
5.Financial accounting
Answer: A · Current assets minus current liabilities
Why this is the answer
Working capital measures the short-term resources available for daily operations: inventory, receivables and cash minus short-term obligations.
Answer
A · Current assets minus current liabilities
6.Financial accounting
Answer: C · €400 adverse
Why this is the answer
Standard cost of 1,000 kg = €5,000; actual cost = €5,400. Paying more than standard gives a €400 adverse price variance.
Answer
C · €400 adverse
7.Break-even analysis
Answer: Q = 3000 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 = 17 − 15 = €2
Units for the target profit
Q = (F + profit)/(p − v) = (4 000 + 2 000)/2 = 3 000
Answer
Q = 3 000 units
8.Break-even analysis
Answer: Q = 4000 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 = 2 000·(22 − 20) − 2 000 = €2 000
New contribution margin per unit
22 − 21 = €1
Units for the same profit
Q = (2 000 + 2 000)/1 = 4 000
Answer
Q = 4 000 units
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