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 product costs €60 and sells for €80. What is the profit margin as a percentage of the selling price?
- A20%
- B25%
- C75%
- D33%
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?
- AThe decoy effect
- BCaptive product pricing
- CPenetration pricing
- DPrice skimming
3.Economics conceptsMedium
A firm has spent €1 million on research for a product that now looks unprofitable. When deciding whether to continue, the €1 million should be:
- ARecovered by raising prices
- BIgnored, because it is a sunk cost
- CTreated as the opportunity cost of stopping
- DAdded to the expected future costs
4.Economics conceptsHard
Okun's law describes:
- AThe link between money supply and prices
- BThe relationship between tax rates and revenue
- CA positive relationship between inflation and nominal interest rates over time
- DA negative relationship between output growth and changes in unemployment
5.Financial accountingMedium
A company increases its allowance for doubtful receivables. What is the effect?
- ACash decreases immediately
- BRevenue increases and gross receivables rise by the same amount
- COnly the notes change; no figures move
- DAn expense is recognised and net receivables fall
6.Financial accountingHard
Machine hours are scarce. Product X earns €20 contribution and needs 4 hours; product Y earns €15 and needs 2 hours. Which should be made first?
- AX, because it uses more machine time
- BY, because it earns €7.50 per hour versus €5 for X
- CEither, because the total contribution is the same
- DX, because it earns more contribution per unit
7.Break-even analysisMedium
A company sells 960 units at €28 each. The variable cost is €18 per unit and fixed costs are €8 000. Find the degree of operating leverage DOL at this sales level.
Q = 960p = €28v = €18F = €8 000
DOL =
8.Break-even analysisHard
A company sells two products. Product A sells for €21 with a variable cost of €15; product B sells for €25 with a variable cost of €10. They sell in a fixed mix of 3 units of A for every 1 of B. Fixed costs are €16 500 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €21, vA = €15pB = €25, vB = €10A : B = 3 : 1F = €16 500
Q = units
3Solutions
1.Marketing principles
Answer: B · 25%
Why this is the answer
Profit = €20. Margin = €20 ÷ €80 = 25%. The mark-up on cost is €20 ÷ €60 ≈ 33%.
Answer
B · 25%
2.Marketing principles
Answer: A · 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
A · The decoy effect
3.Economics concepts
Answer: B · Ignored, because it is a sunk cost
Why this is the answer
Sunk costs cannot be recovered and do not change with the decision, so rational choices compare only future costs and benefits.
Answer
B · Ignored, because it is a sunk cost
4.Economics concepts
Answer: D · A negative relationship between output growth and changes in unemployment
Why this is the answer
Okun observed that unemployment falls when real GDP grows faster than its trend rate and rises when growth is below trend.
Answer
D · A negative relationship between output growth and changes in unemployment
5.Financial accounting
Answer: D · An expense is recognised and net receivables fall
Why this is the answer
The increase is charged to profit, and the allowance is deducted from gross receivables, so the balance sheet shows the amount expected to be collected.
Answer
D · An expense is recognised and net receivables fall
6.Financial accounting
Answer: B · Y, because it earns €7.50 per hour versus €5 for X
Why this is the answer
X earns €20 ÷ 4 = €5 per hour, Y earns €15 ÷ 2 = €7.50 per hour. With a scarce resource, maximise contribution per scarce hour.
Answer
B · Y, because it earns €7.50 per hour versus €5 for X
7.Break-even analysis
Answer: DOL = 6
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 = 960·(28 − 18) = €9 600
Operating profit
Π = 9 600 − 8 000 = €1 600
DOL
DOL = 9 600/1 600 = 6
Answer
DOL = 6
8.Break-even analysis
Answer: Q = 2000 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €6, cmB = €15
Weighted contribution margin
(3·6 + 1·15)/4 = €8.25
Break-even units
Q = 16 500/8.25 = 2 000
A: 1 500, B: 500
Answer
Q = 2 000 units
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