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
Soft drinks are sold in supermarkets, petrol stations, vending machines and kiosks. Which distribution strategy is this?
- ASelective distribution
- BIntensive distribution
- CExclusive distribution
- DDirect distribution only
2.Marketing principlesHard
Brand equity in Keller's customer-based model comes mainly from:
- AThe lowest possible price
- BThe number of factories a company owns
- CThe size of the marketing department
- DBrand awareness and strong, favourable and unique brand associations
3.Economics conceptsMedium
In perfect competition in the long run, firms earn:
- AMonopoly profits
- BZero economic profit
- CLarge economic profits
- DLosses forever
4.Economics conceptsHard
For a normal good, when its price falls, the substitution effect and income effect:
- ABoth decrease the quantity demanded
- BCancel out exactly
- CWork in opposite directions
- DBoth increase the quantity demanded
5.Financial accountingMedium
Under IAS 38, how are research and development costs treated?
- AResearch is expensed; development is capitalised only when strict criteria are met
- BBoth are always capitalised as intangible assets
- CBoth are always expensed immediately
- DResearch is capitalised; development is expensed
6.Financial accountingHard
Over three years a company reports rising profits while operating cash flow keeps falling. What should an analyst suspect?
- AProfits may be driven by aggressive accruals, such as rising receivables or capitalised costs
- BDepreciation must have been too high
- CThe company has very high earnings quality
- DThe company must have repaid all its loans
7.Break-even analysisMedium
A company sells 2 400 units at €42 each. The variable cost is €30 per unit and fixed costs are €18 000. Find the degree of operating leverage DOL at this sales level.
Q = 2 400p = €42v = €30F = €18 000
DOL =
8.Break-even analysisHard
A product sells for €27 per unit, with a variable cost of €25 per unit and fixed costs of €8 000 per year. Budgeted sales are 5 200 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €8 000p = €27v = €25budget = 5 200
MS = %
3Solutions
1.Marketing principles
Answer: B · Intensive distribution
Why this is the answer
Intensive distribution suits convenience products that customers buy on impulse and will not search for.
Answer
B · Intensive distribution
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: B · Zero economic profit
Why this is the answer
Profits attract entry and losses cause exit until price equals minimum average cost and economic profit is zero.
Answer
B · Zero economic profit
4.Economics concepts
Answer: D · Both increase the quantity demanded
Why this is the answer
The substitution effect always favours the cheaper good, and for a normal good the higher real income also raises demand, so both effects reinforce each other.
Answer
D · Both increase the quantity demanded
5.Financial accounting
Answer: A · Research is expensed; development is capitalised only when strict criteria are met
Why this is the answer
Research costs are always expensed. Development costs are capitalised when, for example, technical feasibility, intention, ability and probable future benefits can be shown.
Answer
A · Research is expensed; development is capitalised only when strict criteria are met
6.Financial accounting
Answer: A · Profits may be driven by aggressive accruals, such as rising receivables or capitalised costs
Why this is the answer
A widening gap between profit and operating cash flow often signals working capital build-up or aggressive recognition, suggesting low earnings quality.
Answer
A · Profits may be driven by aggressive accruals, such as rising receivables or capitalised costs
7.Break-even analysis
Answer: DOL = 2.667
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Total contribution margin
CM = 2 400·(42 − 30) = €28 800
Operating profit
Π = 28 800 − 18 000 = €10 800
DOL
DOL = 28 800/10 800 = 2.667
Answer
DOL = 2.667
8.Break-even analysis
Answer: MS = 23.08 %
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) = 8 000/2 = 4 000
Margin of safety
MS = (5 200 − 4 000)/5 200·100 = 23.08%
Answer
MS = 23.08%
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