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 avoid any interviewer influence
- BTo survey thousands of people cheaply
- CTo explore customers' motives and feelings in detail
- DTo produce statistically representative percentages for the market
2.Marketing principlesHard
A cinema sells small popcorn for €4 and large for €8. Adding a medium size at €7.50 makes many more people buy the large. Which effect is this?
- APrice skimming
- BPenetration pricing
- CThe decoy effect
- DCaptive product pricing
3.Economics conceptsMedium
A negative externality occurs when:
- AConsumers pay more for a product than it costs the firm to produce
- BThe government taxes a product
- CA firm makes a loss
- DA third party bears a cost not paid by the producer or consumer
4.Economics conceptsHard
According to the quantity theory of money (MV = PY), if velocity and real output are constant, a 5% rise in the money supply leads to:
- AAbout a 5% rise in the price level
- BA 5% fall in velocity
- CNo change in prices
- DAbout a 5% rise in real output
5.Financial accountingMedium
Profit for ordinary shareholders is €500,000 and there are 1,000,000 ordinary shares. What are basic earnings per share?
- A€0.05
- B€0.50
- C€2.00
- D€5.00
6.Financial accountingHard
Two firms have the same operating profit, but one is financed mostly by debt. When operating profit falls by 20%, the highly geared firm's net profit:
- AFalls by a smaller percentage
- BRises because interest is fixed
- CFalls by exactly 20% as well
- DFalls by a larger percentage
7.Break-even analysisMedium
A product sells for €10 per unit with a variable cost of €6 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €20 000?
F = €20 000p = €10v = €6profit = €20 000
Q = units
8.Break-even analysisHard
A company sells 6 400 units at €31 each, with a variable cost of €25 per unit and fixed costs of €24 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 8%?
Q = 6 400p = €31v = €25F = €24 000%ΔQ = +8%
%ΔΠ = %
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: C · The decoy effect
Why this is the answer
A decoy is an option that is slightly worse than the target, making the target look like good value by comparison. Choices depend on the set of options shown.
Answer
C · The decoy effect
3.Economics concepts
Answer: D · A third party bears a cost not paid by the producer or consumer
Why this is the answer
Negative externalities lead to overproduction relative to the social optimum; Pigouvian taxes or tradeable permits can correct them.
Answer
D · A third party bears a cost not paid by the producer or consumer
4.Economics concepts
Answer: A · About a 5% rise in the price level
Why this is the answer
With V and Y constant, M and P move proportionally, so prices rise about 5%. This is the classical view of money neutrality in the long run.
Answer
A · About a 5% rise in the price level
5.Financial accounting
Answer: B · €0.50
Why this is the answer
Basic EPS = €500,000 ÷ 1,000,000 = €0.50 per share. Dividing the share price by EPS gives the P/E ratio.
Answer
B · €0.50
6.Financial accounting
Answer: D · Falls by a larger percentage
Why this is the answer
Fixed interest stays the same, so any change in operating profit causes a bigger percentage change in profit for shareholders. This is financial risk.
Answer
D · Falls by a larger percentage
7.Break-even analysis
Answer: Q = 10000 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 = 10 − 6 = €4
Units for the target profit
Q = (F + profit)/(p − v) = (20 000 + 20 000)/4 = 10 000
Answer
Q = 10 000 units
8.Break-even analysis
Answer: %ΔΠ = 21.33 %
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.
Contribution margin and profit
CM = 6 400·6 = €38 400
Π = 38 400 − 24 000 = €14 400
DOL
DOL = 38 400/14 400 = 2.667
Change in profit
%ΔΠ = 2.667·(+8%) = +21.33%
Answer
%ΔΠ = +21.33%
Check: new profit = 6 912·6 − 24 000 = €17 472.00.
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