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
In Rogers' diffusion of innovations, which group adopts a new product first?
- AInnovators
- BEarly majority
- CLaggards
- DEarly adopters
2.Marketing principlesHard
During a major sports tournament, a non-sponsor brand runs ads suggesting a link with the event without paying for official rights. What is this called?
- AAmbush marketing
- BCause-related marketing
- CCo-branding
- DGuerrilla distribution
3.Economics conceptsMedium
In an oligopoly, firms are typically:
- ACompletely unregulated by competition law
- BA single seller in the market
- CFew and interdependent in their decisions
- DMany and too small to affect the price
4.Economics conceptsHard
Ricardian equivalence suggests that a debt-financed tax cut will:
- AStrongly increase consumption, because households spend most of the tax cut through the multiplier
- BAlways cause inflation
- CHave little effect on spending, because households save to pay expected future taxes
- DReduce interest rates sharply
5.Financial accountingMedium
A company finds that a machine will last 8 years instead of the 5 originally estimated. Under IAS 8, how is this change applied?
- ARetrospectively, by restating all prior years
- BBy changing the original cost of the machine
- CProspectively, by spreading the remaining carrying amount over the new remaining life
- DBy recognising a large gain in the current year
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?
- AThe profit is shown twice, once for each company
- BNothing, because each company is a separate entity
- CThe unrealised profit in inventory is eliminated
- DThe sale is shown as external revenue of the group
7.Break-even analysisMedium
A product sells for €30 per unit with a variable cost of €15 per unit. Fixed costs are €12 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €12 000p = €30v = €15profit = €6 000
Q = units
8.Break-even analysisHard
A product sells for €28 per unit, with a variable cost of €18 per unit and fixed costs of €10 000 per year. Budgeted sales are 1 400 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €10 000p = €28v = €18budget = 1 400
MS = %
3Solutions
1.Marketing principles
Answer: A · Innovators
Why this is the answer
The order is innovators, early adopters, early majority, late majority and laggards. Early adopters are often opinion leaders who influence others.
Answer
A · Innovators
2.Marketing principles
Answer: A · Ambush marketing
Why this is the answer
Ambush marketing tries to gain association with an event without sponsorship. Organisers often protect sponsors through contracts and trademark rules.
Answer
A · Ambush marketing
3.Economics concepts
Answer: C · Few and interdependent in their decisions
Why this is the answer
Oligopolies have a few large firms whose pricing and output decisions affect each other, often analysed with game theory.
Answer
C · Few and interdependent in their decisions
4.Economics concepts
Answer: C · Have little effect on spending, because households save to pay expected future taxes
Why this is the answer
If consumers are forward-looking and see that government borrowing means higher taxes later, they save the tax cut, so aggregate demand barely changes.
Answer
C · Have little effect on spending, because households save to pay expected future taxes
5.Financial accounting
Answer: C · Prospectively, by spreading the remaining carrying amount over the new remaining life
Why this is the answer
Changes in estimates affect the current and future periods only. Prior-period restatement is for changes in policy and corrections of errors.
Answer
C · Prospectively, by spreading the remaining carrying amount over the new remaining life
6.Financial accounting
Answer: C · 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
C · 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 = 30 − 15 = €15
Units for the target profit
Q = (F + profit)/(p − v) = (12 000 + 6 000)/15 = 1 200
Answer
Q = 1 200 units
8.Break-even analysis
Answer: MS = 28.57 %
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).
Break-even quantity
Q = F/(p − v) = 10 000/10 = 1 000
Margin of safety
MS = (1 400 − 1 000)/1 400·100 = 28.57%
Answer
MS = 28.57%
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