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
Ansoff's matrix strategy of selling existing products in new markets is called:
- ADiversification
- BProduct development
- CMarket development
- DMarket penetration
2.Marketing principlesHard
Brand equity in Keller's customer-based model comes mainly from:
- AThe number of factories a company owns
- BThe size of the marketing department
- CThe lowest possible price
- DBrand awareness and strong, favourable and unique brand associations
3.Economics conceptsMedium
The law of diminishing marginal returns states that:
- AAdding more of a variable input to a fixed input eventually lowers the extra output per unit added
- BLong-run average costs always fall as output rises
- CTotal output always falls as more workers are hired
- DConsumers get less satisfaction as prices rise
4.Economics conceptsHard
In the Bertrand model, two firms sell identical products with the same constant marginal cost and compete on price. The equilibrium price is:
- AEqual to marginal cost
- BZero
- CThe monopoly price
- DHalfway between monopoly price and marginal cost
5.Financial accountingMedium
A shop buys 100 units at €10, then 100 units at €12, and then sells 150 units. What is cost of sales using FIFO?
- A€1,650
- B€1,600
- C€1,700
- D€1,500
6.Financial accountingHard
Under IFRS 16, a lessee typically recognises a lease on the balance sheet as:
- ARevenue and inventory
- BA right-of-use asset and a lease liability
- CAn operating expense only, spread evenly over the lease term
- DEquity and a provision
7.Break-even analysisMedium
A product sells for €24 with a variable cost of €4 per unit. Fixed costs are €80 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €32 000 after tax?
p = €24v = €4F = €80 000T = 20%after-tax profit = €32 000
Q = units
8.Break-even analysisHard
A company sells 2 000 units per month at €28 each, with a variable cost of €20 per unit and fixed costs of €6 400 per month. The variable cost rises by €3 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 = €28v = €20 → €23F = €6 400
Q = units
3Solutions
1.Marketing principles
Answer: C · Market development
Why this is the answer
Market penetration: existing products, existing markets; market development: existing products, new markets; product development: new products, existing markets; diversification: new products, new markets.
Answer
C · Market development
2.Marketing principles
Answer: D · Brand awareness and strong, favourable and unique brand associations
Why this is the answer
Customer-based brand equity is the differential effect of brand knowledge (awareness and image) on consumer response to marketing.
Answer
D · Brand awareness and strong, favourable and unique brand associations
3.Economics concepts
Answer: A · Adding more of a variable input to a fixed input eventually lowers the extra output per unit added
Why this is the answer
In the short run, with at least one fixed factor, marginal product eventually falls, which makes marginal cost rise.
Answer
A · Adding more of a variable input to a fixed input eventually lowers the extra output per unit added
4.Economics concepts
Answer: A · Equal to marginal cost
Why this is the answer
Undercutting continues until price equals marginal cost, so even two firms reach the competitive outcome; in Cournot quantity competition, price stays above MC.
Answer
A · Equal to marginal cost
5.Financial accounting
Answer: B · €1,600
Why this is the answer
FIFO: 100 × €10 + 50 × €12 = €1,600. The 50 units left are valued at the latest cost of €12.
Answer
B · €1,600
6.Financial accounting
Answer: B · A right-of-use asset and a lease liability
Why this is the answer
IFRS 16 removed the operating lease distinction for lessees: they recognise a right-of-use asset and a liability for lease payments, except for short-term and low-value leases.
Answer
B · A right-of-use asset and a lease liability
7.Break-even analysis
Answer: Q = 6000 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).
Pre-tax profit needed
32 000/(1 − 0.2) = €40 000
Units needed
Q = (80 000 + 40 000)/20 = 6 000
Answer
Q = 6 000 units
8.Break-even analysis
Answer: Q = 3200 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·(28 − 20) − 6 400 = €9 600
New contribution margin per unit
28 − 23 = €5
Units for the same profit
Q = (6 400 + 9 600)/5 = 3 200
Answer
Q = 3 200 units
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