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
What is a perceptual (positioning) map mainly used for?
- ATo track production costs over time
- BTo show how customers see brands on key attributes compared with competitors
- CTo show where a firm's stores are located
- DTo plan delivery routes for sales staff
2.Marketing principlesHard
A supermarket sells bread below cost to attract shoppers who then buy other, higher-margin items. This is:
- ALoss leader pricing
- BPrice skimming
- CValue-based pricing
- DCost-plus pricing
3.Economics conceptsMedium
The law of diminishing marginal returns states that:
- ATotal output always falls as more workers are hired
- BAdding more of a variable input to a fixed input eventually lowers the extra output per unit added
- CLong-run average costs always fall as output rises
- DConsumers get less satisfaction as prices rise
4.Economics conceptsHard
The "Taylor principle" says that, to stabilise inflation, a central bank should respond to a 1 percentage point rise in inflation by:
- AKeeping the nominal rate unchanged
- BRaising the nominal interest rate, but by less than 1 percentage point
- CCutting the nominal rate
- DRaising the nominal interest rate by more than 1 percentage point
5.Financial accountingMedium
A machine with a carrying amount of €3,000 is sold for €4,000. What is recorded in the income statement?
- AA gain on disposal of €4,000
- BRevenue of €4,000
- CA gain on disposal of €1,000
- DA loss on disposal of €1,000
6.Financial accountingHard
The standard is 2 labour hours per unit at €20 an hour. 500 units are made in 1,100 hours. What is the labour efficiency variance?
- A€1,000 adverse
- B€2,000 favourable
- C€2,000 adverse
- D€22,000 adverse
7.Break-even analysisMedium
A product sells for €28 per unit with a variable cost of €20 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €20 000p = €28v = €20profit = €10 000
Q = units
8.Break-even analysisHard
A company sells 3 750 units per month at €22 each, with a variable cost of €18 per unit and fixed costs of €10 000 per month. The variable cost rises by €2 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 3 750p = €22v = €18 → €20F = €10 000
Q = units
3Solutions
1.Marketing principles
Answer: B · To show how customers see brands on key attributes compared with competitors
Why this is the answer
Perceptual maps plot brands on dimensions that matter to buyers. They reveal crowded positions and possible gaps in the market.
Answer
B · To show how customers see brands on key attributes compared with competitors
2.Marketing principles
Answer: A · Loss leader pricing
Why this is the answer
A loss leader brings traffic into the store. It works when customers buy enough profitable items during the same visit.
Answer
A · Loss leader pricing
3.Economics concepts
Answer: B · Adding more of a variable input to a fixed input eventually lowers the extra output per unit added
Why this is the answer
In the short run, with at least one fixed factor, marginal product eventually falls, which makes marginal cost rise.
Answer
B · Adding more of a variable input to a fixed input eventually lowers the extra output per unit added
4.Economics concepts
Answer: D · Raising the nominal interest rate by more than 1 percentage point
Why this is the answer
Only by raising nominal rates more than one-for-one does the real interest rate rise, cooling demand and bringing inflation back down.
Answer
D · Raising the nominal interest rate by more than 1 percentage point
5.Financial accounting
Answer: C · A gain on disposal of €1,000
Why this is the answer
Gain or loss on disposal = proceeds − carrying amount = €4,000 − €3,000 = €1,000 gain. It is not part of normal revenue.
Answer
C · A gain on disposal of €1,000
6.Financial accounting
Answer: C · €2,000 adverse
Why this is the answer
Standard hours = 500 × 2 = 1,000. Extra 100 hours × €20 = €2,000 adverse, because more hours were used than the standard allows.
Answer
C · €2,000 adverse
7.Break-even analysis
Answer: Q = 3750 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 = 28 − 20 = €8
Units for the target profit
Q = (F + profit)/(p − v) = (20 000 + 10 000)/8 = 3 750
Answer
Q = 3 750 units
8.Break-even analysis
Answer: Q = 7500 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).
Current profit
Π = 3 750·(22 − 18) − 10 000 = €5 000
New contribution margin per unit
22 − 20 = €2
Units for the same profit
Q = (10 000 + 5 000)/2 = 7 500
Answer
Q = 7 500 units
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