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?
- APurchase, need recognition, information search, evaluation of alternatives, post-purchase behaviour
- BNeed recognition, information search, evaluation of alternatives, purchase, post-purchase behaviour
- CEvaluation of alternatives, need recognition, information search, purchase, post-purchase behaviour
- DInformation search, need recognition, purchase, evaluation of alternatives, post-purchase behaviour
2.Marketing principlesHard
A manufacturer starts selling online directly to consumers at lower prices than its retailers. Retailers complain. What is this?
- AHorizontal channel conflict
- BCannibalisation by a rival brand
- CVertical channel conflict
- DA pull strategy
3.Economics conceptsMedium
In the short run, a firm in perfect competition should shut down if the market price is below:
- AMarginal revenue
- BAverage total cost
- CAverage variable cost
- DAverage fixed cost
4.Economics conceptsHard
In the Solow growth model, sustained long-run growth in output per worker comes from:
- AA higher saving rate alone
- BTechnological progress
- CGovernment budget deficits
- DPopulation growth
5.Financial accountingMedium
When preparing a bank reconciliation, which item explains why the bank statement balance is higher than the cash book balance?
- AA direct debit not yet entered in the cash book
- BCheques issued but not yet presented to the bank
- CCash deposited but not yet credited on the bank statement
- DBank charges not yet entered in the cash book
6.Financial accountingHard
Under the matching principle, the cost of a product warranty sold with goods this year should be:
- AIgnored until the warranty expires
- BRecorded as revenue
- CRecognised only when a customer actually makes a warranty claim
- DEstimated and recognised as an expense in the year of sale
7.Break-even analysisMedium
A product sells for €14 with a variable cost of €6 per unit. Fixed costs are €16 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €8 000 after tax?
p = €14v = €6F = €16 000T = 20%after-tax profit = €8 000
Q = units
8.Break-even analysisHard
A product sells for €40 per unit, with a variable cost of €30 per unit and fixed costs of €50 000 per year. Budgeted sales are 5 750 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €50 000p = €40v = €30budget = 5 750
MS = %
3Solutions
1.Marketing principles
Answer: B · 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
B · Need recognition, information search, evaluation of alternatives, purchase, post-purchase behaviour
2.Marketing principles
Answer: C · Vertical channel conflict
Why this is the answer
Vertical conflict arises between levels, such as manufacturer and retailer. Horizontal conflict is between firms at the same level, such as two retailers.
Answer
C · Vertical channel conflict
3.Economics concepts
Answer: C · Average variable cost
Why this is the answer
If price covers average variable cost, producing reduces losses by contributing to fixed costs; below AVC, shutting down loses less.
Answer
C · Average variable cost
4.Economics concepts
Answer: B · Technological progress
Why this is the answer
A higher saving rate raises the steady-state level of output per worker but not its long-run growth rate; only technological progress produces continuous growth.
Answer
B · Technological progress
5.Financial accounting
Answer: B · Cheques issued but not yet presented to the bank
Why this is the answer
Unpresented cheques have reduced the cash book but not the bank balance. Outstanding deposits, bank charges and unrecorded direct debits work the other way.
Answer
B · Cheques issued but not yet presented to the bank
6.Financial accounting
Answer: D · Estimated and recognised as an expense in the year of sale
Why this is the answer
A provision for expected warranty costs is recognised when the goods are sold, matching the expense with the related revenue (IAS 37).
Answer
D · Estimated and recognised as an expense in the year of sale
7.Break-even analysis
Answer: Q = 3250 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
8 000/(1 − 0.2) = €10 000
Units needed
Q = (16 000 + 10 000)/8 = 3 250
Answer
Q = 3 250 units
8.Break-even analysis
Answer: MS = 13.04 %
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) = 50 000/10 = 5 000
Margin of safety
MS = (5 750 − 5 000)/5 750·100 = 13.04%
Answer
MS = 13.04%
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