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
Why might a researcher choose in-depth interviews rather than a large questionnaire?
- ATo explore customers' motives and feelings in detail
- BTo survey thousands of people cheaply
- CTo produce statistically representative percentages for the market
- DTo avoid any interviewer influence
2.Marketing principlesHard
A campaign costs €50,000. Each extra unit sold gives €25 contribution. How many extra units must it sell to break even?
- A500 units
- B2,000 units
- C1,250 units
- D20,000 units
3.Economics conceptsMedium
In the short run, a firm in perfect competition should shut down if the market price is below:
- AAverage variable cost
- BMarginal revenue
- CAverage fixed cost
- DAverage total cost
4.Economics conceptsHard
A monopolist maximises profit where:
- AAverage cost is at its minimum
- BMarginal revenue equals marginal cost
- CPrice equals marginal cost
- DTotal revenue is at its maximum
5.Financial accountingMedium
Revenue is €200,000 and cost of sales is €140,000. What is the gross profit margin?
- A30%
- B43%
- C70%
- D60%
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€400 favourable
- B€5,400 adverse
- C€400 adverse
- D€0.40 adverse
7.Break-even analysisMedium
A product sells for €16 per unit with a variable cost of €6 per unit. Fixed costs are €15 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €15 000p = €16v = €6profit = €10 000
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €20 with a variable cost of €15; product B sells for €18 with a variable cost of €10. They sell in a fixed mix of 3 units of A for every 1 of B. Fixed costs are €4 600 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €20, vA = €15pB = €18, vB = €10A : B = 3 : 1F = €4 600
Q = units
3Solutions
1.Marketing principles
Answer: A · To explore customers' motives and feelings in detail
Why this is the answer
In-depth interviews give rich, qualitative insight into why people behave as they do. Questionnaires suit measuring how many people think or do something.
Answer
A · To explore customers' motives and feelings in detail
2.Marketing principles
Answer: B · 2,000 units
Why this is the answer
€50,000 ÷ €25 = 2,000 extra units. Marketers use this to judge whether a campaign's sales uplift is realistic.
Answer
B · 2,000 units
3.Economics concepts
Answer: A · Average variable cost
Why this is the answer
If price covers average variable cost, producing reduces losses by contributing to fixed costs; below AVC, shutting down loses less.
Answer
A · Average variable cost
4.Economics concepts
Answer: B · Marginal revenue equals marginal cost
Why this is the answer
Profit is maximised where MR = MC. For a monopolist, price is above MR, so P > MC, causing a deadweight loss.
Answer
B · Marginal revenue equals marginal cost
5.Financial accounting
Answer: A · 30%
Why this is the answer
Gross profit = €60,000. Margin = €60,000 ÷ €200,000 = 30%.
Answer
A · 30%
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 = 2500 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 = 16 − 6 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (15 000 + 10 000)/10 = 2 500
Answer
Q = 2 500 units
8.Break-even analysis
Answer: Q = 800 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 = €8
Weighted contribution margin
(3·5 + 1·8)/4 = €5.75
Break-even units
Q = 4 600/5.75 = 800
A: 600, B: 200
Answer
Q = 800 units
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