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 car maker offers separate models and campaigns for students, families and luxury buyers. Which targeting strategy is this?
- AUndifferentiated marketing
- BConcentrated marketing
- CMass customisation of one model
- 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?
- ACutting the price to the lowest in the market
- BWithdrawing the product immediately
- CChanging the distribution to exclusive dealers only
- DRepositioning the brand through new communication and image
3.Economics conceptsMedium
The marginal propensity to consume is:
- AThe average share of total income that households save over a year
- BThe total consumption in an economy
- CThe share of an extra euro of income that is spent on consumption
- DThe interest rate on consumer loans
4.Economics conceptsHard
In the "Battle of the Sexes" coordination game, how many pure-strategy Nash equilibria are there?
- ANone
- BTwo
- CFour
- DOne
5.Financial accountingMedium
Under the accrual basis of accounting, revenue is recognised when:
- ACash is received
- BThe customer pays the invoice, even if goods were delivered earlier
- CIt is earned, whether or not cash has been received
- DThe tax return is filed
6.Financial accountingHard
Budgeted overhead is €200,000 for 40,000 machine hours. Actual hours are 42,000 and actual overhead is €205,000. What is the result?
- AOverhead over-absorbed by €5,000
- BOverhead under-absorbed by €5,000
- COverhead under-absorbed by €10,000
- DOverhead exactly absorbed
7.Break-even analysisMedium
A company sells 7 500 units at €26 each. The variable cost is €18 per unit and fixed costs are €20 000. Find the degree of operating leverage DOL at this sales level.
Q = 7 500p = €26v = €18F = €20 000
DOL =
8.Break-even analysisHard
A product sells for €22 per unit, with a variable cost of €12 per unit and fixed costs of €5 000 per year. Budgeted sales are 750 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €5 000p = €22v = €12budget = 750
MS = %
3Solutions
1.Marketing principles
Answer: D · Differentiated marketing
Why this is the answer
Differentiated marketing targets several segments with different products or messages. It can raise sales but also costs.
Answer
D · Differentiated 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: C · The share of an extra euro of income that is spent on consumption
Why this is the answer
The MPC measures how consumption changes with income; it determines the size of the Keynesian multiplier, 1/(1 − MPC).
Answer
C · The share of an extra euro of income that is spent on consumption
4.Economics concepts
Answer: B · Two
Why this is the answer
Both outcomes where the players choose the same activity are Nash equilibria, so the problem is coordinating on one of them rather than avoiding defection.
Answer
B · Two
5.Financial accounting
Answer: C · It is earned, whether or not cash has been received
Why this is the answer
Accrual accounting records revenue when the performance obligation is satisfied and expenses when incurred, not when cash moves.
Answer
C · It is earned, whether or not cash has been received
6.Financial accounting
Answer: A · Overhead over-absorbed by €5,000
Why this is the answer
Rate = €5 per hour. Absorbed = 42,000 × €5 = €210,000, which exceeds actual €205,000, so €5,000 is over-absorbed and added back to profit.
Answer
A · Overhead over-absorbed by €5,000
7.Break-even analysis
Answer: DOL = 1.5
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 = 7 500·(26 − 18) = €60 000
Operating profit
Π = 60 000 − 20 000 = €40 000
DOL
DOL = 60 000/40 000 = 1.5
Answer
DOL = 1.5
8.Break-even analysis
Answer: MS = 33.33 %
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) = 5 000/10 = 500
Margin of safety
MS = (750 − 500)/750·100 = 33.33%
Answer
MS = 33.33%
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