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?
- ADifferentiated marketing
- BConcentrated marketing
- CUndifferentiated marketing
- DMass customisation of one model
2.Marketing principlesHard
A firm's research shows demand for its product is price inelastic. If costs and competitors stay the same, what does a price rise usually do to revenue?
- ARevenue stays exactly the same
- BRevenue falls to zero, because customers stop buying
- CRevenue falls, because quantity falls proportionally more than price rises
- DRevenue rises, because quantity falls proportionally less than price rises
3.Economics conceptsMedium
A price ceiling set below the equilibrium price typically causes:
- ANo change in the market
- BA surplus
- CAn increase in supply
- DA shortage
4.Economics conceptsHard
In the "Battle of the Sexes" coordination game, how many pure-strategy Nash equilibria are there?
- ANone
- BFour
- CTwo
- DOne
5.Financial accountingMedium
A company increases its allowance for doubtful receivables. What is the effect?
- ACash decreases immediately
- BAn expense is recognised and net receivables fall
- COnly the notes change; no figures move
- DRevenue increases and gross receivables rise by the same amount
6.Financial accountingHard
An asset has a carrying amount of €500,000, fair value less costs of disposal of €380,000 and value in use of €420,000. What impairment loss is recognised?
- A€80,000
- B€0
- C€200,000
- D€120,000
7.Break-even analysisMedium
A product sells for €11 with a variable cost of €6 per unit. Fixed costs are €5 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €1 500 after tax?
p = €11v = €6F = €5 000T = 20%after-tax profit = €1 500
Q = units
8.Break-even analysisHard
A product sells for €38 per unit, with a variable cost of €30 per unit and fixed costs of €16 000 per year. Budgeted sales are 2 400 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €16 000p = €38v = €30budget = 2 400
MS = %
3Solutions
1.Marketing principles
Answer: A · 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
A · Differentiated marketing
2.Marketing principles
Answer: D · Revenue rises, because quantity falls proportionally less than price rises
Why this is the answer
With inelastic demand, the percentage drop in quantity is smaller than the percentage price rise, so total revenue increases.
Answer
D · Revenue rises, because quantity falls proportionally less than price rises
3.Economics concepts
Answer: D · A shortage
Why this is the answer
A binding maximum price raises quantity demanded and lowers quantity supplied, creating excess demand, as with rent control.
Answer
D · A shortage
4.Economics concepts
Answer: C · 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
C · Two
5.Financial accounting
Answer: B · An expense is recognised and net receivables fall
Why this is the answer
The increase is charged to profit, and the allowance is deducted from gross receivables, so the balance sheet shows the amount expected to be collected.
Answer
B · An expense is recognised and net receivables fall
6.Financial accounting
Answer: A · €80,000
Why this is the answer
Recoverable amount = max(€380,000, €420,000) = €420,000. Impairment = €500,000 − €420,000 = €80,000.
Answer
A · €80,000
7.Break-even analysis
Answer: Q = 1375 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
1 500/(1 − 0.2) = €1 875
Units needed
Q = (5 000 + 1 875)/5 = 1 375
Answer
Q = 1 375 units
8.Break-even analysis
Answer: MS = 16.67 %
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) = 16 000/8 = 2 000
Margin of safety
MS = (2 400 − 2 000)/2 400·100 = 16.67%
Answer
MS = 16.67%
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