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 laptop comes with a two-year warranty, free delivery and online support. In Kotler's product levels, these belong to the:
- AAugmented product
- BActual product
- CPotential product only
- DCore customer value
2.Marketing principlesHard
During a major sports tournament, a non-sponsor brand runs ads suggesting a link with the event without paying for official rights. What is this called?
- ACo-branding
- BGuerrilla distribution
- CCause-related marketing
- DAmbush marketing
3.Economics conceptsMedium
In the short run, a firm in perfect competition should shut down if the market price is below:
- AAverage total cost
- BAverage variable cost
- CMarginal revenue
- DAverage fixed cost
4.Economics conceptsHard
The principal–agent problem arises when:
- ATwo firms agree to fix prices
- BA buyer and seller have identical information
- CAn agent acting for a principal has different goals and the principal cannot fully monitor them
- DThe government owns a firm
5.Financial accountingMedium
At 31 December, electricity used in December (€800) has not yet been billed. Which year-end entry is correct?
- ADebit accruals, credit electricity expense
- BDebit electricity expense, credit accruals
- CNo entry until the bill arrives
- DDebit prepayments, credit cash
6.Financial accountingHard
A firm has spent €50,000 on market research for a new product and must decide whether to launch it. How should the €50,000 be treated in the decision?
- AIgnored, because it is a sunk cost
- BDeducted from expected sales
- CSpread over the product's expected life
- DAdded to the launch cost
7.Break-even analysisMedium
A product sells for €23 with a variable cost of €8 per unit. Fixed costs are €30 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €9 000 after tax?
p = €23v = €8F = €30 000T = 20%after-tax profit = €9 000
Q = units
8.Break-even analysisHard
A product sells for €33 per unit, with a variable cost of €25 per unit and fixed costs of €32 000 per year. Budgeted sales are 5 200 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €32 000p = €33v = €25budget = 5 200
MS = %
3Solutions
1.Marketing principles
Answer: A · Augmented product
Why this is the answer
The core value is the benefit sought, the actual product is the item with its features and brand, and the augmented product adds services such as warranties and support.
Answer
A · Augmented product
2.Marketing principles
Answer: D · Ambush marketing
Why this is the answer
Ambush marketing tries to gain association with an event without sponsorship. Organisers often protect sponsors through contracts and trademark rules.
Answer
D · Ambush marketing
3.Economics concepts
Answer: B · 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
B · Average variable cost
4.Economics concepts
Answer: C · An agent acting for a principal has different goals and the principal cannot fully monitor them
Why this is the answer
Hidden action and conflicting interests let the agent pursue their own aims; incentive contracts such as performance pay try to align interests.
Answer
C · An agent acting for a principal has different goals and the principal cannot fully monitor them
5.Financial accounting
Answer: B · Debit electricity expense, credit accruals
Why this is the answer
The accrual records December's cost as an expense this year with a current liability, so expenses match the period of use.
Answer
B · Debit electricity expense, credit accruals
6.Financial accounting
Answer: A · Ignored, because it is a sunk cost
Why this is the answer
The research money is spent whichever choice is made, so it is irrelevant. Only future incremental cash flows from launching should be compared.
Answer
A · Ignored, because it is a sunk cost
7.Break-even analysis
Answer: Q = 2750 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
9 000/(1 − 0.2) = €11 250
Units needed
Q = (30 000 + 11 250)/15 = 2 750
Answer
Q = 2 750 units
8.Break-even analysis
Answer: MS = 23.08 %
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) = 32 000/8 = 4 000
Margin of safety
MS = (5 200 − 4 000)/5 200·100 = 23.08%
Answer
MS = 23.08%
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