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 small firm makes premium climbing gear and targets only serious climbers. Which targeting strategy is this?
- AUndifferentiated (mass) marketing
- BMicromarketing for each individual
- CConcentrated (niche) marketing
- DDifferentiated marketing
2.Marketing principlesHard
Research shows young consumers see a long-established brand as old-fashioned, although product quality is good. What is the most suitable strategy?
- AChanging the distribution to exclusive dealers only
- BCutting the price to the lowest in the market
- CWithdrawing the product immediately
- DRepositioning the brand through new communication and image
3.Economics conceptsMedium
The income elasticity of demand for a good is -0.4. The good is:
- AA luxury good
- BAn inferior good
- CA complement
- DA normal necessity
4.Economics conceptsHard
Why does the deadweight loss of a tax grow when the good's demand and supply are more elastic?
- AThe government collects more tax revenue
- BQuantity traded falls more, so more mutually beneficial trades are lost
- CElastic markets have no consumer surplus
- DPrices do not change, so consumers bear the whole burden of the tax instead
5.Financial accountingMedium
Under IAS 16, which cost should be included in the cost of a new machine?
- AInstallation costs needed to get it working
- BRepairs carried out two years later
- CStaff training costs after it starts operating
- DGeneral office overheads for the year
6.Financial accountingHard
A company changes its inventory method from weighted average to FIFO because it gives more relevant information. Under IAS 8, how is this applied?
- ARetrospectively, restating comparative figures as if FIFO had always been used
- BProspectively, from the date of the change only
- CIt is not allowed to change inventory methods
- DBy recognising the whole effect as income this year
7.Break-even analysisMedium
A company sells 1 880 units at €10 each. The variable cost is €6 per unit and fixed costs are €6 000. Find the degree of operating leverage DOL at this sales level.
Q = 1 880p = €10v = €6F = €6 000
DOL =
8.Break-even analysisHard
A company sells two products. Product A sells for €9 with a variable cost of €5; product B sells for €38 with a variable cost of €30. They sell in a fixed mix of 4 units of A for every 1 of B. Fixed costs are €19 200 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €9, vA = €5pB = €38, vB = €30A : B = 4 : 1F = €19 200
Q = units
3Solutions
1.Marketing principles
Answer: C · Concentrated (niche) marketing
Why this is the answer
Concentrated marketing focuses resources on one segment. It builds deep expertise but makes the firm dependent on that segment.
Answer
C · Concentrated (niche) marketing
2.Marketing principles
Answer: D · Repositioning the brand through new communication and image
Why this is the answer
Repositioning changes how the target segment sees the brand, for example with updated design, new messages and channels the younger audience uses.
Answer
D · Repositioning the brand through new communication and image
3.Economics concepts
Answer: B · An inferior good
Why this is the answer
A negative income elasticity means demand falls as income rises, which defines an inferior good; luxuries have income elasticity above 1.
Answer
B · An inferior good
4.Economics concepts
Answer: B · Quantity traded falls more, so more mutually beneficial trades are lost
Why this is the answer
The more responsive buyers and sellers are, the more the tax reduces quantity, and the bigger the triangle of lost surplus; DWL also rises roughly with the square of the tax.
Answer
B · Quantity traded falls more, so more mutually beneficial trades are lost
5.Financial accounting
Answer: A · Installation costs needed to get it working
Why this is the answer
Purchase price plus directly attributable costs, such as delivery and installation, are capitalised. Training, later repairs and general overheads are expensed.
Answer
A · Installation costs needed to get it working
6.Financial accounting
Answer: A · Retrospectively, restating comparative figures as if FIFO had always been used
Why this is the answer
Voluntary policy changes are applied retrospectively where practicable, so comparatives remain consistent. Changes in estimates, by contrast, are applied prospectively.
Answer
A · Retrospectively, restating comparative figures as if FIFO had always been used
7.Break-even analysis
Answer: DOL = 4.947
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 = 1 880·(10 − 6) = €7 520
Operating profit
Π = 7 520 − 6 000 = €1 520
DOL
DOL = 7 520/1 520 = 4.947
Answer
DOL = 4.947
8.Break-even analysis
Answer: Q = 4000 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 = €4, cmB = €8
Weighted contribution margin
(4·4 + 1·8)/5 = €4.80
Break-even units
Q = 19 200/4.8 = 4 000
A: 3 200, B: 800
Answer
Q = 4 000 units
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