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
Customer lifetime value (CLV) estimates:
- AThe cost of acquiring a new customer through marketing and sales activities
- BThe value of one purchase
- CThe total net profit expected from a customer over the whole relationship
- DThe age of the customer
2.Marketing principlesHard
An airline can buy a certain aircraft model only from one manufacturer, and switching to another model is very costly. In Porter's five forces, what does this mean?
- AHigh bargaining power of buyers
- BHigh bargaining power of suppliers
- CLow bargaining power of suppliers
- DHigh threat of new entrants into the market
3.Economics conceptsMedium
In the short run, a firm in perfect competition should shut down if the market price is below:
- AMarginal revenue
- BAverage variable cost
- CAverage total cost
- DAverage fixed cost
4.Economics conceptsHard
The Lerner index (P − MC)/P for a profit-maximising monopolist equals 1/|PED|. If |PED| = 4, the price is:
- A25% above marginal cost, as a share of price
- B4 times marginal cost
- C75% above marginal cost, as a share of price
- DEqual to marginal cost
5.Financial accountingMedium
Which inventory valuation method assumes the oldest goods are sold first?
- ASpecific identification of each item
- BFIFO (first in, first out)
- CLIFO (last in, first out)
- DWeighted average cost
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 adverse
- B€5,400 adverse
- C€0.40 adverse
- D€400 favourable
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €20 000 per year and a variable cost of €8 per unit. Method B, more automated, has fixed costs of €28 000 per year and a variable cost of €6 per unit. At what yearly volume Q do both methods cost the same?
FA = €20 000vA = €8FB = €28 000vB = €6
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €10 with a variable cost of €5; product B sells for €28 with a variable cost of €20. They sell in a fixed mix of 4 units of A for every 1 of B. Fixed costs are €14 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €10, vA = €5pB = €28, vB = €20A : B = 4 : 1F = €14 000
Q = units
3Solutions
1.Marketing principles
Answer: C · The total net profit expected from a customer over the whole relationship
Why this is the answer
CLV combines purchase frequency, margin, retention and duration (often discounted), guiding acquisition and retention spending.
Answer
C · The total net profit expected from a customer over the whole relationship
2.Marketing principles
Answer: B · High bargaining power of suppliers
Why this is the answer
When suppliers are concentrated and switching is expensive, they can demand higher prices or better terms, reducing industry profitability.
Answer
B · High bargaining power of suppliers
3.Economics concepts
Answer: B · 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
B · Average variable cost
4.Economics concepts
Answer: A · 25% above marginal cost, as a share of price
Why this is the answer
The markup (P − MC)/P = 1/4 = 0.25, so a quarter of the price is a margin above MC; more elastic demand means less market power.
Answer
A · 25% above marginal cost, as a share of price
5.Financial accounting
Answer: B · FIFO (first in, first out)
Why this is the answer
Under FIFO, cost of sales uses the oldest costs and closing inventory reflects recent costs. IFRS does not allow LIFO.
Answer
B · FIFO (first in, first out)
6.Financial accounting
Answer: A · €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
A · €400 adverse
7.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).
Equal total costs
20 000 + 8Q = 28 000 + 6Q
Solve for Q
Q = (28 000 − 20 000)/(8 − 6) = 4 000
Answer
Q = 4 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: Q = 2500 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
(4·5 + 1·8)/5 = €5.60
Break-even units
Q = 14 000/5.6 = 2 500
A: 2 000, B: 500
Answer
Q = 2 500 units
ExamProblems · examproblems.com/courses/business-fundamentals