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
A firm competes across a broad market by having the lowest costs in its industry and passing savings on as low prices. Which Porter generic strategy is this?
- AMarket development
- BDifferentiation
- CDifferentiation focus
- DCost leadership
2.Marketing principlesHard
In Rogers' diffusion curve, roughly what share of adopters are laggards?
- A2.5%
- B13.5%
- C34%
- D16%
3.Economics conceptsMedium
Education generates benefits for society beyond the individual student. Without intervention, the market will likely:
- AProvide exactly the efficient amount of education, as prices reflect all benefits
- BOver-provide education compared with the social optimum
- CUnder-provide education compared with the social optimum
- DStop providing education altogether
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
- CReduce interest rates sharply
- DHave little effect on spending, because households save to pay expected future taxes
5.Financial accountingMedium
Which costs are relevant when making a business decision?
- AFuture cash flows that differ between the alternatives
- BCosts already paid for the project
- CAllocated fixed overheads that do not change with the decision
- DAll costs in last year's income statement
6.Financial accountingHard
Tax rules allow faster depreciation of a machine than the company uses in its accounts. What arises under IAS 12?
- ANo tax effect at all
- BA deferred tax asset
- CA deferred tax liability
- DA refund of current tax paid
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €10 000 per year and a variable cost of €15 per unit. Method B, more automated, has fixed costs of €25 000 per year and a variable cost of €9 per unit. At what yearly volume Q do both methods cost the same?
FA = €10 000vA = €15FB = €25 000vB = €9
Q = units
8.Break-even analysisHard
A product sells for €50 per unit, with a variable cost of €45 per unit and fixed costs of €25 000 per year. Budgeted sales are 9 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €25 000p = €50v = €45budget = 9 000
MS = %
3Solutions
1.Marketing principles
Answer: D · Cost leadership
Why this is the answer
Cost leadership seeks the lowest cost position in a broad market. Differentiation offers unique value at a premium; focus strategies target a narrow segment.
Answer
D · Cost leadership
2.Marketing principles
Answer: D · 16%
Why this is the answer
Innovators 2.5%, early adopters 13.5%, early majority 34%, late majority 34% and laggards 16%, based on a normal distribution of adoption time.
Answer
D · 16%
3.Economics concepts
Answer: C · Under-provide education compared with the social optimum
Why this is the answer
Private decisions ignore external benefits, so output is below the socially optimal level; subsidies or public provision can raise it.
Answer
C · Under-provide education compared with the social optimum
4.Economics concepts
Answer: D · 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
D · Have little effect on spending, because households save to pay expected future taxes
5.Financial accounting
Answer: A · Future cash flows that differ between the alternatives
Why this is the answer
Relevant costs are future, incremental cash flows. Sunk costs, committed costs and unchanged allocated overheads are ignored.
Answer
A · Future cash flows that differ between the alternatives
6.Financial accounting
Answer: C · A deferred tax liability
Why this is the answer
The tax base falls faster than the carrying amount, creating a taxable temporary difference. The future extra tax is recognised now as a deferred tax liability.
Answer
C · A deferred tax liability
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).
Equal total costs
10 000 + 15Q = 25 000 + 9Q
Solve for Q
Q = (25 000 − 10 000)/(15 − 9) = 2 500
Answer
Q = 2 500 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: MS = 44.44 %
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) = 25 000/5 = 5 000
Margin of safety
MS = (9 000 − 5 000)/9 000·100 = 44.44%
Answer
MS = 44.44%
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