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
The Net Promoter Score (NPS) is based on the question:
- AHow old are you?
- BHow likely are you to recommend us to a friend or colleague?
- CHow much did you pay?
- DWhere did you buy the product?
2.Marketing principlesHard
A software firm offers a free basic version and charges for premium features. Which metric is most critical for this freemium model's revenue?
- AThe number of competitors' free users
- BThe number of printed brochures distributed
- CThe price of the free version
- DThe conversion rate from free users to paying users
3.Economics conceptsMedium
A country imposes a tariff on imported steel. Which effect is most likely?
- ADomestic steel prices rise and domestic production increases
- BThe world price of steel rises sharply for all countries that trade it
- CDomestic consumers gain surplus
- DDomestic steel prices fall and imports rise
4.Economics conceptsHard
The Laffer curve illustrates that:
- AHigher tax rates always increase tax revenue
- BTax revenue is unrelated to tax rates
- CLower tax rates always reduce tax revenue, whatever the starting rate
- DBeyond some point, raising tax rates can reduce total tax revenue
5.Financial accountingMedium
When preparing a bank reconciliation, which item explains why the bank statement balance is higher than the cash book balance?
- ACash deposited but not yet credited on the bank statement
- BBank charges not yet entered in the cash book
- CA direct debit not yet entered in the cash book
- DCheques issued but not yet presented to the bank
6.Financial accountingHard
A company's debt-to-equity ratio rises sharply. What does this usually indicate?
- AThat shareholders invested more money
- BHigher financial risk because the company relies more on borrowed money
- CBetter liquidity in the short term
- DHigher profitability
7.Break-even analysisMedium
A product sells for €9 with a variable cost of €4 per unit. Fixed costs are €25 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €10 000 after tax?
p = €9v = €4F = €25 000T = 20%after-tax profit = €10 000
Q = units
8.Break-even analysisHard
A product sells for €60 per unit, with a variable cost of €45 per unit and fixed costs of €60 000 per year. Budgeted sales are 7 200 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €60 000p = €60v = €45budget = 7 200
MS = %
3Solutions
1.Marketing principles
Answer: B · How likely are you to recommend us to a friend or colleague?
Why this is the answer
NPS = % promoters (9–10) minus % detractors (0–6) on a 0–10 recommendation scale.
Answer
B · How likely are you to recommend us to a friend or colleague?
2.Marketing principles
Answer: D · The conversion rate from free users to paying users
Why this is the answer
Freemium revenue depends on attracting many free users and converting a share of them to paid plans, while keeping the cost of serving free users low.
Answer
D · The conversion rate from free users to paying users
3.Economics concepts
Answer: A · Domestic steel prices rise and domestic production increases
Why this is the answer
The tariff raises the domestic price, increasing domestic output and government revenue but reducing consumer surplus and creating deadweight losses.
Answer
A · Domestic steel prices rise and domestic production increases
4.Economics concepts
Answer: D · Beyond some point, raising tax rates can reduce total tax revenue
Why this is the answer
Very high rates discourage taxed activity or encourage avoidance, so revenue peaks at some rate between 0 and 100%; where that peak lies is debated.
Answer
D · Beyond some point, raising tax rates can reduce total tax revenue
5.Financial accounting
Answer: D · 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
D · Cheques issued but not yet presented to the bank
6.Financial accounting
Answer: B · Higher financial risk because the company relies more on borrowed money
Why this is the answer
A higher ratio means more leverage: interest and repayments must be met whatever the results, so financial risk rises, although returns to shareholders may also rise.
Answer
B · Higher financial risk because the company relies more on borrowed money
7.Break-even analysis
Answer: Q = 7500 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
10 000/(1 − 0.2) = €12 500
Units needed
Q = (25 000 + 12 500)/5 = 7 500
Answer
Q = 7 500 units
8.Break-even analysis
Answer: MS = 44.44 %
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) = 60 000/15 = 4 000
Margin of safety
MS = (7 200 − 4 000)/7 200·100 = 44.44%
Answer
MS = 44.44%
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