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
Value-based pricing sets prices mainly according to:
- AThe firm's target profit for the year
- BThe cost of making the product plus a mark-up
- CCustomers' perception of the product's value
- DThe prices charged by the cheapest rival
2.Marketing principlesHard
Under the EU General Data Protection Regulation (GDPR), sending marketing emails based on consent requires consent that is:
- AFreely given, specific, informed and unambiguous
- BImplied by pre-ticked boxes
- CAssumed when a customer visits the website
- DGiven once for all future purposes by any company
3.Economics conceptsMedium
Crowding out refers to:
- AOvercrowded public services
- BToo many firms entering a market
- CImports replacing domestic production
- DHigher government borrowing raising interest rates and reducing private investment
4.Economics conceptsHard
A deadweight loss represents:
- ALosses made by firms that are forced to leave the market in the long run
- BThe profit of a monopolist
- CThe tax revenue collected by the government
- DThe loss of total surplus when output differs from the efficient level
5.Financial accountingMedium
An item cost €80. It can be sold for €90, but €20 must be spent to sell it. At what amount is it shown in inventory?
- A€90
- B€80
- C€70
- D€60
6.Financial accountingHard
Machine hours are scarce. Product X earns €20 contribution and needs 4 hours; product Y earns €15 and needs 2 hours. Which should be made first?
- AEither, because the total contribution is the same
- BY, because it earns €7.50 per hour versus €5 for X
- CX, because it uses more machine time
- DX, because it earns more contribution per unit
7.Break-even analysisMedium
A product sells for €23 per unit with a variable cost of €18 per unit. Fixed costs are €25 000 per month. How many units Q must be sold per month to make a profit of €12 000?
F = €25 000p = €23v = €18profit = €12 000
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €21 with a variable cost of €15; product B sells for €32 with a variable cost of €20. They sell in a fixed mix of 2 units of A for every 1 of B. Fixed costs are €7 200 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €21, vA = €15pB = €32, vB = €20A : B = 2 : 1F = €7 200
Q = units
3Solutions
1.Marketing principles
Answer: C · Customers' perception of the product's value
Why this is the answer
Value-based pricing estimates what the offer is worth to buyers. Costs then set a floor, and competitor prices are a reference.
Answer
C · Customers' perception of the product's value
2.Marketing principles
Answer: A · Freely given, specific, informed and unambiguous
Why this is the answer
Consent must be a clear affirmative act; pre-ticked boxes or silence are not valid, and it must be as easy to withdraw as to give.
Answer
A · Freely given, specific, informed and unambiguous
3.Economics concepts
Answer: D · Higher government borrowing raising interest rates and reducing private investment
Why this is the answer
When government borrowing raises interest rates, some private investment is no longer profitable, reducing the net effect of fiscal expansion.
Answer
D · Higher government borrowing raising interest rates and reducing private investment
4.Economics concepts
Answer: D · The loss of total surplus when output differs from the efficient level
Why this is the answer
Deadweight loss is the reduction in combined consumer and producer surplus caused by distortions such as taxes, monopoly or price controls.
Answer
D · The loss of total surplus when output differs from the efficient level
5.Financial accounting
Answer: C · €70
Why this is the answer
NRV = €90 − €20 = €70, which is below cost of €80. Inventory is measured at the lower amount, €70, with a €10 write-down.
Answer
C · €70
6.Financial accounting
Answer: B · Y, because it earns €7.50 per hour versus €5 for X
Why this is the answer
X earns €20 ÷ 4 = €5 per hour, Y earns €15 ÷ 2 = €7.50 per hour. With a scarce resource, maximise contribution per scarce hour.
Answer
B · Y, because it earns €7.50 per hour versus €5 for X
7.Break-even analysis
Answer: Q = 7400 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).
Contribution margin per unit
p − v = 23 − 18 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (25 000 + 12 000)/5 = 7 400
Answer
Q = 7 400 units
8.Break-even analysis
Answer: Q = 900 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €6, cmB = €12
Weighted contribution margin
(2·6 + 1·12)/3 = €8.00
Break-even units
Q = 7 200/8 = 900
A: 600, B: 300
Answer
Q = 900 units
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