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 do many firms invest in customer retention and relationship marketing?
- ALoyal customers always accept any price rise
- BKeeping existing customers is usually cheaper than winning new ones
- CRetention removes the need for any advertising
- DNew customers are never profitable
2.Marketing principlesHard
A company advertises a product as "eco-friendly" without evidence, while only a minor part is recycled. What is this practice called?
- AGreen product development
- BGreenwashing
- CCause-related marketing
- DSocietal marketing
3.Economics conceptsMedium
The marginal propensity to consume is:
- AThe share of an extra euro of income that is spent on consumption
- BThe interest rate on consumer loans
- CThe total consumption in an economy
- DThe average share of total income that households save over a year
4.Economics conceptsHard
The "paradox of thrift" suggests that if all households try to save more during a recession:
- AInterest rates will rise sharply
- BInflation will increase
- CInvestment and growth will rise immediately
- DTotal income may fall, so total saving does not rise
5.Financial accountingMedium
Fixed costs are €20,000, the selling price is €50 and the variable cost is €30 per unit. What is the break-even point?
- A667 units
- B2,000 units
- C400 units
- D1,000 units
6.Financial accountingHard
The standard is 2 labour hours per unit at €20 an hour. 500 units are made in 1,100 hours. What is the labour efficiency variance?
- A€2,000 adverse
- B€22,000 adverse
- C€1,000 adverse
- D€2,000 favourable
7.Break-even analysisMedium
A product sells for €23 with a variable cost of €20 per unit. Fixed costs are €3 600 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €1 500 after tax?
p = €23v = €20F = €3 600T = 20%after-tax profit = €1 500
Q = units
8.Break-even analysisHard
A company sells 10 000 units at €27 each, with a variable cost of €12 per unit and fixed costs of €60 000. By what percentage %ΔΠ does operating profit change if sales volume rises by 20%?
Q = 10 000p = €27v = €12F = €60 000%ΔQ = +20%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: B · Keeping existing customers is usually cheaper than winning new ones
Why this is the answer
Acquiring customers is often more expensive than keeping them, and loyal customers tend to buy more and recommend the firm, raising lifetime value.
Answer
B · Keeping existing customers is usually cheaper than winning new ones
2.Marketing principles
Answer: B · Greenwashing
Why this is the answer
Greenwashing uses vague or exaggerated environmental claims. It can mislead consumers, damage trust and break consumer protection rules on unfair commercial practices.
Answer
B · Greenwashing
3.Economics concepts
Answer: A · The share of an extra euro of income that is spent on consumption
Why this is the answer
The MPC measures how consumption changes with income; it determines the size of the Keynesian multiplier, 1/(1 − MPC).
Answer
A · The share of an extra euro of income that is spent on consumption
4.Economics concepts
Answer: D · Total income may fall, so total saving does not rise
Why this is the answer
Higher saving reduces consumption and aggregate demand, lowering income; with lower income, aggregate saving may end up no higher, as Keynes argued.
Answer
D · Total income may fall, so total saving does not rise
5.Financial accounting
Answer: D · 1,000 units
Why this is the answer
Contribution per unit = €50 − €30 = €20. Break-even = €20,000 ÷ €20 = 1,000 units.
Answer
D · 1,000 units
6.Financial accounting
Answer: A · €2,000 adverse
Why this is the answer
Standard hours = 500 × 2 = 1,000. Extra 100 hours × €20 = €2,000 adverse, because more hours were used than the standard allows.
Answer
A · €2,000 adverse
7.Break-even analysis
Answer: Q = 1825 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).
Pre-tax profit needed
1 500/(1 − 0.2) = €1 875
Units needed
Q = (3 600 + 1 875)/3 = 1 825
Answer
Q = 1 825 units
8.Break-even analysis
Answer: %ΔΠ = 33.33 %
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 = 10 000·15 = €150 000
Π = 150 000 − 60 000 = €90 000
DOL
DOL = 150 000/90 000 = 1.667
Change in profit
%ΔΠ = 1.667·(+20%) = +33.33%
Answer
%ΔΠ = +33.33%
Check: new profit = 12 000·15 − 60 000 = €120 000.00.
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