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
Positioning refers to:
- AThe geographical location of the company
- BWhere products are physically placed on shop shelves and in store displays
- CThe order of products in a catalogue
- DHow a brand is perceived relative to competitors in customers' minds
2.Marketing principlesHard
A firm's research shows demand for its product is price inelastic. If costs and competitors stay the same, what does a price rise usually do to revenue?
- ARevenue falls, because quantity falls proportionally more than price rises
- BRevenue stays exactly the same
- CRevenue rises, because quantity falls proportionally less than price rises
- DRevenue falls to zero, because customers stop buying
3.Economics conceptsMedium
Unemployment benefits and progressive income taxes are called automatic stabilisers because they:
- APrevent all recessions from happening
- BFix the exchange rate automatically
- CKeep the government budget balanced in every year of the business cycle
- DReduce fluctuations in demand without new government decisions
4.Economics conceptsHard
In the Bertrand model, two firms sell identical products with the same constant marginal cost and compete on price. The equilibrium price is:
- AHalfway between monopoly price and marginal cost
- BEqual to marginal cost
- CThe monopoly price
- DZero
5.Financial accountingMedium
Revenue is €200,000 and cost of sales is €140,000. What is the gross profit margin?
- A43%
- B30%
- C70%
- D60%
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:
- ARises because interest is fixed
- BFalls by exactly 20% as well
- CFalls by a larger percentage
- DFalls by a smaller percentage
7.Break-even analysisMedium
A company sells 15 000 units at €23 each. The variable cost is €20 per unit and fixed costs are €15 000. Find the degree of operating leverage DOL at this sales level.
Q = 15 000p = €23v = €20F = €15 000
DOL =
8.Break-even analysisHard
A product sells for €20 per unit, with a variable cost of €15 per unit and fixed costs of €5 000 per year. Budgeted sales are 1 250 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €5 000p = €20v = €15budget = 1 250
MS = %
3Solutions
1.Marketing principles
Answer: D · How a brand is perceived relative to competitors in customers' minds
Why this is the answer
Positioning defines the distinctive place a brand wants to occupy in the target customers' minds, based on benefits and differences from rivals.
Answer
D · How a brand is perceived relative to competitors in customers' minds
2.Marketing principles
Answer: C · Revenue rises, because quantity falls proportionally less than price rises
Why this is the answer
With inelastic demand, the percentage drop in quantity is smaller than the percentage price rise, so total revenue increases.
Answer
C · Revenue rises, because quantity falls proportionally less than price rises
3.Economics concepts
Answer: D · Reduce fluctuations in demand without new government decisions
Why this is the answer
In a downturn tax revenue falls and benefit payments rise automatically, supporting incomes and spending; the reverse happens in a boom.
Answer
D · Reduce fluctuations in demand without new government decisions
4.Economics concepts
Answer: B · Equal to marginal cost
Why this is the answer
Undercutting continues until price equals marginal cost, so even two firms reach the competitive outcome; in Cournot quantity competition, price stays above MC.
Answer
B · Equal to marginal cost
5.Financial accounting
Answer: B · 30%
Why this is the answer
Gross profit = €60,000. Margin = €60,000 ÷ €200,000 = 30%.
Answer
B · 30%
6.Financial accounting
Answer: C · 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
C · Falls by a larger percentage
7.Break-even analysis
Answer: DOL = 1.5
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 = 15 000·(23 − 20) = €45 000
Operating profit
Π = 45 000 − 15 000 = €30 000
DOL
DOL = 45 000/30 000 = 1.5
Answer
DOL = 1.5
8.Break-even analysis
Answer: MS = 20 %
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) = 5 000/5 = 1 000
Margin of safety
MS = (1 250 − 1 000)/1 250·100 = 20%
Answer
MS = 20%
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