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
A chocolate brand launches an ice cream under the same brand name. This is an example of:
- ACo-branding
- BLine extension
- CPrivate labelling
- DBrand extension
2.Marketing principlesHard
A company sells printers cheaply but charges high prices for ink cartridges. This is:
- APenetration pricing for both products
- BPsychological pricing
- CBundle pricing
- DCaptive product pricing
3.Economics conceptsMedium
A Gini coefficient of 0 indicates:
- AZero economic growth
- BPerfect equality of income
- CPerfect inequality of income
- DZero unemployment
4.Economics conceptsHard
The "Taylor principle" says that, to stabilise inflation, a central bank should respond to a 1 percentage point rise in inflation by:
- ARaising the nominal interest rate by more than 1 percentage point
- BRaising the nominal interest rate, but by less than 1 percentage point
- CCutting the nominal rate
- DKeeping the nominal rate unchanged
5.Financial accountingMedium
Profit for ordinary shareholders is €500,000 and there are 1,000,000 ordinary shares. What are basic earnings per share?
- A€2.00
- B€0.50
- C€5.00
- D€0.05
6.Financial accountingHard
Production exceeds sales this period, so inventory rises. How does absorption costing profit compare with marginal costing profit?
- AMarginal costing profit is higher this period
- BThey are always equal
- CAbsorption costing profit is higher
- DAbsorption costing shows a loss
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €15 000 per year and a variable cost of €10 per unit. Method B, more automated, has fixed costs of €18 000 per year and a variable cost of €7 per unit. At what yearly volume Q do both methods cost the same?
FA = €15 000vA = €10FB = €18 000vB = €7
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €15 with a variable cost of €10; product B sells for €30 with a variable cost of €15. They sell in a fixed mix of 2 units of A for every 3 of B. Fixed costs are €22 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €15, vA = €10pB = €30, vB = €15A : B = 2 : 3F = €22 000
Q = units
3Solutions
1.Marketing principles
Answer: D · Brand extension
Why this is the answer
A brand extension uses an existing brand name in a new category. A line extension adds variants in the same category, such as new flavours.
Answer
D · Brand extension
2.Marketing principles
Answer: D · 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
D · Captive product pricing
3.Economics concepts
Answer: B · 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
B · Perfect equality of income
4.Economics concepts
Answer: A · Raising the nominal interest rate by more than 1 percentage point
Why this is the answer
Only by raising nominal rates more than one-for-one does the real interest rate rise, cooling demand and bringing inflation back down.
Answer
A · Raising the nominal interest rate by more than 1 percentage point
5.Financial accounting
Answer: B · €0.50
Why this is the answer
Basic EPS = €500,000 ÷ 1,000,000 = €0.50 per share. Dividing the share price by EPS gives the P/E ratio.
Answer
B · €0.50
6.Financial accounting
Answer: C · 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
C · Absorption costing profit is higher
7.Break-even analysis
Answer: Q = 1000 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).
Equal total costs
15 000 + 10Q = 18 000 + 7Q
Solve for Q
Q = (18 000 − 15 000)/(10 − 7) = 1 000
Answer
Q = 1 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: Q = 2000 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 = €5, cmB = €15
Weighted contribution margin
(2·5 + 3·15)/5 = €11.00
Break-even units
Q = 22 000/11 = 2 000
A: 800, B: 1 200
Answer
Q = 2 000 units
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