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 produce statistically representative percentages for the market
- BTo survey thousands of people cheaply
- CTo explore customers' motives and feelings in detail
- DTo avoid any interviewer influence
2.Marketing principlesHard
In the SERVQUAL gap model, the "knowledge gap" (gap 1) is the difference between:
- AWhat customers expect and what managers think customers expect
- BThe service standards set by managers and the service actually delivered
- CThe price paid and the cost of providing the service
- DThe service delivered and what advertising promised
3.Economics conceptsMedium
If demand for a product is price inelastic, a price increase will:
- AReduce quantity demanded to zero
- BIncrease total revenue
- CLeave total revenue unchanged
- DDecrease total revenue
4.Economics conceptsHard
A regulator forces a natural monopoly to set price equal to marginal cost. The likely problem is that:
- AConsumers face a shortage, because demand exceeds supply at that price
- BThe firm makes very large profits
- COutput falls below the monopoly level
- DThe firm makes a loss because average cost is above marginal cost
5.Financial accountingMedium
A machine with a carrying amount of €3,000 is sold for €4,000. What is recorded in the income statement?
- AA gain on disposal of €4,000
- BA gain on disposal of €1,000
- CRevenue of €4,000
- DA loss on disposal of €1,000
6.Financial accountingHard
A parent sold goods to its subsidiary at a profit, and the subsidiary still holds them at year end. What must happen on consolidation?
- ANothing, because each company is a separate entity
- BThe unrealised profit in inventory is eliminated
- CThe sale is shown as external revenue of the group
- DThe profit is shown twice, once for each company
7.Break-even analysisMedium
A product sells for €25 per unit with a variable cost of €20 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 = €25v = €20profit = €2 000
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €8 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 €12 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €8, vA = €5pB = €28, vB = €20A : B = 4 : 1F = €12 000
Q = units
3Solutions
1.Marketing principles
Answer: C · 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
C · To explore customers' motives and feelings in detail
2.Marketing principles
Answer: A · What customers expect and what managers think customers expect
Why this is the answer
Gap 1 arises when managers misread expectations, often due to poor research. Other provider gaps cover standards, delivery and communication, which together create the customer gap.
Answer
A · What customers expect and what managers think customers expect
3.Economics concepts
Answer: B · Increase total revenue
Why this is the answer
With inelastic demand the percentage fall in quantity is smaller than the percentage price rise, so price × quantity rises.
Answer
B · Increase total revenue
4.Economics concepts
Answer: D · The firm makes a loss because average cost is above marginal cost
Why this is the answer
With falling average cost, marginal cost is below average cost, so marginal cost pricing does not cover total costs; subsidies or average cost pricing are alternatives.
Answer
D · The firm makes a loss because average cost is above marginal cost
5.Financial accounting
Answer: B · A gain on disposal of €1,000
Why this is the answer
Gain or loss on disposal = proceeds − carrying amount = €4,000 − €3,000 = €1,000 gain. It is not part of normal revenue.
Answer
B · A gain on disposal of €1,000
6.Financial accounting
Answer: B · The unrealised profit in inventory is eliminated
Why this is the answer
Intra-group sales and purchases are cancelled, and profit on goods still held in the group is removed from inventory and group profit until sold outside.
Answer
B · The unrealised profit in inventory is eliminated
7.Break-even analysis
Answer: Q = 1200 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 = 25 − 20 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (4 000 + 2 000)/5 = 1 200
Answer
Q = 1 200 units
8.Break-even analysis
Answer: Q = 3000 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 = €3, cmB = €8
Weighted contribution margin
(4·3 + 1·8)/5 = €4.00
Break-even units
Q = 12 000/4 = 3 000
A: 2 400, B: 600
Answer
Q = 3 000 units
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