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 the usual order of stages in the consumer buying decision process?
- ANeed recognition, information search, evaluation of alternatives, purchase, post-purchase behaviour
- BEvaluation of alternatives, need recognition, information search, purchase, post-purchase behaviour
- CInformation search, need recognition, purchase, evaluation of alternatives, post-purchase behaviour
- DPurchase, need recognition, information search, evaluation of alternatives, post-purchase behaviour
2.Marketing principlesHard
A company launches a product that is easy to copy, with highly price-sensitive buyers and strong economies of scale. Which launch pricing strategy fits best?
- APenetration pricing
- BCaptive product pricing
- CPrestige pricing
- DPrice skimming
3.Economics conceptsMedium
Both supply and demand for a good increase. What can we say for certain about the new equilibrium?
- ABoth price and quantity rise
- BPrice rises, but the change in quantity is uncertain
- CBoth price and quantity fall
- DQuantity rises, but the change in price is uncertain
4.Economics conceptsHard
In the Mundell–Fleming model with perfect capital mobility and a floating exchange rate:
- ABoth policies are equally effective
- BBoth policies have no effect on output
- CMonetary policy is effective but fiscal policy is largely ineffective
- DFiscal policy is effective, but monetary policy is largely ineffective
5.Financial accountingMedium
Which error will NOT be revealed by a trial balance?
- AA balance copied to the wrong column
- BA wrongly added ledger column
- CA sale left out of the books entirely
- DA debit posted without a matching credit
6.Financial accountingHard
In the indirect method of the cash flow statement, depreciation is:
- ASubtracted from net profit
- BAdded back to net profit because it is a non-cash expense
- CIgnored completely
- DShown in financing activities
7.Break-even analysisMedium
A company sells 4 500 units at €22 each. The variable cost is €18 per unit and fixed costs are €6 000. Find the degree of operating leverage DOL at this sales level.
Q = 4 500p = €22v = €18F = €6 000
DOL =
8.Break-even analysisHard
A company sells 1 880 units at €10 each, with a variable cost of €4 per unit and fixed costs of €9 000. By what percentage %ΔΠ does operating profit change if sales volume falls by 8%?
Q = 1 880p = €10v = €4F = €9 000%ΔQ = −8%
%ΔΠ = %
3Solutions
1.Marketing principles
Answer: A · Need recognition, information search, evaluation of alternatives, purchase, post-purchase behaviour
Why this is the answer
Buyers recognise a need, look for information, compare options, buy and then judge their satisfaction. Routine purchases may skip stages.
Answer
A · Need recognition, information search, evaluation of alternatives, purchase, post-purchase behaviour
2.Marketing principles
Answer: A · Penetration pricing
Why this is the answer
Low prices build share quickly, lower unit costs through scale and discourage imitators. Skimming suits unique products with buyers who are less sensitive to price.
Answer
A · Penetration pricing
3.Economics concepts
Answer: D · Quantity rises, but the change in price is uncertain
Why this is the answer
Both shifts raise quantity, but the demand shift raises price while the supply shift lowers it, so the price effect depends on their relative size.
Answer
D · Quantity rises, but the change in price is uncertain
4.Economics concepts
Answer: C · Monetary policy is effective but fiscal policy is largely ineffective
Why this is the answer
Under floating rates, fiscal expansion causes appreciation that crowds out net exports, while monetary expansion causes depreciation that boosts output; under fixed rates the result is reversed.
Answer
C · Monetary policy is effective but fiscal policy is largely ineffective
5.Financial accounting
Answer: C · A sale left out of the books entirely
Why this is the answer
An error of omission leaves both sides unrecorded, so totals still agree. Single-sided postings and addition errors make the trial balance differ.
Answer
C · A sale left out of the books entirely
6.Financial accounting
Answer: B · Added back to net profit because it is a non-cash expense
Why this is the answer
Starting from profit, non-cash charges like depreciation are added back, and changes in working capital are adjusted.
Answer
B · Added back to net profit because it is a non-cash expense
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 = 4 500·(22 − 18) = €18 000
Operating profit
Π = 18 000 − 6 000 = €12 000
DOL
DOL = 18 000/12 000 = 1.5
Answer
DOL = 1.5
8.Break-even analysis
Answer: %ΔΠ = −39.58 %
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.
Contribution margin and profit
CM = 1 880·6 = €11 280
Π = 11 280 − 9 000 = €2 280
DOL
DOL = 11 280/2 280 = 4.947
Change in profit
%ΔΠ = 4.947·(−8%) = −39.58%
Answer
%ΔΠ = −39.58%
Check: new profit = 1 730·6 − 9 000 = €1 377.60.
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