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 "push" promotional strategy focuses on:
- APromoting the product to intermediaries such as wholesalers and retailers
- BCreating end-consumer demand through mass advertising so customers ask retailers for it
- CLowering prices online only
- DUsing word-of-mouth exclusively
2.Marketing principlesHard
Which conditions are needed for price discrimination (charging different groups different prices) to work?
- ASegments with different price sensitivity that can be separated, and little reselling between them
- BAll customers must have identical price sensitivity
- CThe firm must have no fixed costs
- DThe product must be sold only in one shop
3.Economics conceptsMedium
If the ECB raises its main interest rate, the most likely short-term effect is:
- AA fall in the value of the euro
- BAn immediate rise in GDP
- CLower borrowing and spending, reducing inflationary pressure
- DHigher borrowing and spending, which adds to inflationary pressure
4.Economics conceptsHard
Price discrimination by a firm requires that:
- AIt operates in perfect competition
- BIts costs differ for each customer
- CIt has market power, can separate markets and prevent resale
- DAll consumers have identical elasticity of demand and buy the same amount
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€60
- C€80
- D€70
6.Financial accountingHard
Tax rules allow faster depreciation of a machine than the company uses in its accounts. What arises under IAS 12?
- ANo tax effect at all
- BA refund of current tax paid
- CA deferred tax asset
- DA deferred tax liability
7.Break-even analysisMedium
A company sells 1 500 units at €48 each. The variable cost is €45 per unit and fixed costs are €3 600. Find the degree of operating leverage DOL at this sales level.
Q = 1 500p = €48v = €45F = €3 600
DOL =
8.Break-even analysisHard
A company sells two products. Product A sells for €13 with a variable cost of €5; product B sells for €40 with a variable cost of €25. They sell in a fixed mix of 4 units of A for every 1 of B. Fixed costs are €14 100 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €13, vA = €5pB = €40, vB = €25A : B = 4 : 1F = €14 100
Q = units
3Solutions
1.Marketing principles
Answer: A · Promoting the product to intermediaries such as wholesalers and retailers
Why this is the answer
Push strategies use trade promotions and personal selling to channel partners; pull strategies stimulate end-consumer demand so retailers stock the product.
Answer
A · Promoting the product to intermediaries such as wholesalers and retailers
2.Marketing principles
Answer: A · Segments with different price sensitivity that can be separated, and little reselling between them
Why this is the answer
The firm must identify segments with different elasticities, keep them apart (for example with ID or timing) and prevent low-price buyers reselling to others.
Answer
A · Segments with different price sensitivity that can be separated, and little reselling between them
3.Economics concepts
Answer: C · Lower borrowing and spending, reducing inflationary pressure
Why this is the answer
Higher rates make credit more expensive and saving more attractive, reducing demand and inflation; they also tend to strengthen the currency.
Answer
C · Lower borrowing and spending, reducing inflationary pressure
4.Economics concepts
Answer: C · It has market power, can separate markets and prevent resale
Why this is the answer
To charge different prices for the same good, the firm needs market power, the ability to identify groups with different elasticities and to prevent arbitrage.
Answer
C · It has market power, can separate markets and prevent resale
5.Financial accounting
Answer: D · €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
D · €70
6.Financial accounting
Answer: D · A deferred tax liability
Why this is the answer
The tax base falls faster than the carrying amount, creating a taxable temporary difference. The future extra tax is recognised now as a deferred tax liability.
Answer
D · A deferred tax liability
7.Break-even analysis
Answer: DOL = 5
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Total contribution margin
CM = 1 500·(48 − 45) = €4 500
Operating profit
Π = 4 500 − 3 600 = €900
DOL
DOL = 4 500/900 = 5
Answer
DOL = 5
8.Break-even analysis
Answer: Q = 1500 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 = €8, cmB = €15
Weighted contribution margin
(4·8 + 1·15)/5 = €9.40
Break-even units
Q = 14 100/9.4 = 1 500
A: 1 200, B: 300
Answer
Q = 1 500 units
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