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
What is the usual order of stages in the consumer buying decision process?
- AInformation search, need recognition, purchase, evaluation of alternatives, post-purchase behaviour
- BPurchase, need recognition, information search, evaluation of alternatives, post-purchase behaviour
- CEvaluation of alternatives, need recognition, information search, purchase, post-purchase behaviour
- DNeed recognition, information search, evaluation of alternatives, purchase, post-purchase behaviour
2.Marketing principlesHard
Theodore Levitt's "Marketing Myopia" (1960) used US railroads as an example. What was their mistake?
- AThey expanded into too many countries
- BThey spent too much on advertising
- CThey defined their business as railways rather than transportation
- DThey set their prices too low
3.Economics conceptsMedium
A minimum wage set above the equilibrium wage in a competitive labour market is predicted to cause:
- AA surplus of labour (unemployment)
- BNo change in employment
- CA shortage of labour
- DA fall in the wage rate
4.Economics conceptsHard
Using the "rule of 70", an economy growing at 7% per year will double its real GDP in about:
- A70 years
- B7 years
- C49 years
- D10 years
5.Financial accountingMedium
Under the accrual basis of accounting, revenue is recognised when:
- ACash is received
- BThe customer pays the invoice, even if goods were delivered earlier
- CThe tax return is filed
- DIt is earned, whether or not cash has been received
6.Financial accountingHard
The going concern assumption means financial statements are prepared assuming the entity:
- AWill make a profit every year
- BWill be sold within one year
- CHas no debts
- DWill continue to operate for the foreseeable future
7.Break-even analysisMedium
A product sells for €8 with a variable cost of €6 per unit. Fixed costs are €5 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €1 000 after tax?
p = €8v = €6F = €5 000T = 20%after-tax profit = €1 000
Q = units
8.Break-even analysisHard
A product sells for €15 per unit, with a variable cost of €12 per unit and fixed costs of €15 000 per year. Budgeted sales are 7 500 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €15 000p = €15v = €12budget = 7 500
MS = %
3Solutions
1.Marketing principles
Answer: D · Need recognition, information search, evaluation of alternatives, purchase, post-purchase behaviour
Why this is the answer
Buyers recognise a need, look for information, compare options, buy and then judge their satisfaction. Routine purchases may skip stages.
Answer
D · Need recognition, information search, evaluation of alternatives, purchase, post-purchase behaviour
2.Marketing principles
Answer: C · They defined their business as railways rather than transportation
Why this is the answer
Levitt argued firms fail when they focus on their product instead of the customer need it serves. Railroads lost customers to cars, trucks and planes they did not see as rivals.
Answer
C · They defined their business as railways rather than transportation
3.Economics concepts
Answer: A · A surplus of labour (unemployment)
Why this is the answer
At the higher wage more people want to work and firms hire fewer, so labour supplied exceeds labour demanded in the simple competitive model.
Answer
A · A surplus of labour (unemployment)
4.Economics concepts
Answer: D · 10 years
Why this is the answer
The doubling time is approximately 70 divided by the percentage growth rate, so 70 / 7 = 10 years, showing the power of compound growth.
Answer
D · 10 years
5.Financial accounting
Answer: D · It is earned, whether or not cash has been received
Why this is the answer
Accrual accounting records revenue when the performance obligation is satisfied and expenses when incurred, not when cash moves.
Answer
D · It is earned, whether or not cash has been received
6.Financial accounting
Answer: D · Will continue to operate for the foreseeable future
Why this is the answer
Unless management intends or must liquidate, assets and liabilities are measured assuming continued operations; material doubts must be disclosed.
Answer
D · Will continue to operate for the foreseeable future
7.Break-even analysis
Answer: Q = 3125 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
1 000/(1 − 0.2) = €1 250
Units needed
Q = (5 000 + 1 250)/2 = 3 125
Answer
Q = 3 125 units
8.Break-even analysis
Answer: MS = 33.33 %
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) = 15 000/3 = 5 000
Margin of safety
MS = (7 500 − 5 000)/7 500·100 = 33.33%
Answer
MS = 33.33%
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