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?
- AInformation search, need recognition, purchase, evaluation of alternatives, post-purchase behaviour
- BEvaluation of alternatives, need recognition, information search, purchase, post-purchase behaviour
- CPurchase, need recognition, information search, evaluation of alternatives, post-purchase behaviour
- DNeed recognition, information search, evaluation of alternatives, purchase, post-purchase behaviour
2.Marketing principlesHard
In the BCG matrix, a firm has 20% market share and its largest competitor has 40%. What is the firm's relative market share?
- A0.2
- B2.0
- C0.5
- D20%
3.Economics conceptsMedium
A firm has spent €1 million on research for a product that now looks unprofitable. When deciding whether to continue, the €1 million should be:
- ARecovered by raising prices
- BTreated as the opportunity cost of stopping
- CIgnored, because it is a sunk cost
- DAdded to the expected future costs
4.Economics conceptsHard
The J-curve effect describes why, after a depreciation, the trade balance may:
- AImprove immediately and permanently
- BWorsen at first and then improve
- CImprove at first and then worsen
- DRemain unchanged for many years
5.Financial accountingMedium
A company finds that a machine will last 8 years instead of the 5 originally estimated. Under IAS 8, how is this change applied?
- AProspectively, by spreading the remaining carrying amount over the new remaining life
- BBy recognising a large gain in the current year
- CRetrospectively, by restating all prior years
- DBy changing the original cost of the machine
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 adverse
- C€22,000 adverse
- D€2,000 favourable
7.Break-even analysisMedium
A product sells for €13 per unit with a variable cost of €8 per unit. Fixed costs are €25 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €25 000p = €13v = €8profit = €5 000
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €11 with a variable cost of €5; product B sells for €27 with a variable cost of €15. They sell in a fixed mix of 3 units of A for every 2 of B. Fixed costs are €21 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €11, vA = €5pB = €27, vB = €15A : B = 3 : 2F = €21 000
Q = units
3Solutions
1.Marketing principles
Answer: D · 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
D · Need recognition, information search, evaluation of alternatives, purchase, post-purchase behaviour
2.Marketing principles
Answer: C · 0.5
Why this is the answer
Relative market share = 20% ÷ 40% = 0.5. A value below 1 means the firm is not the market leader, placing it on the low-share side of the matrix.
Answer
C · 0.5
3.Economics concepts
Answer: C · Ignored, because it is a sunk cost
Why this is the answer
Sunk costs cannot be recovered and do not change with the decision, so rational choices compare only future costs and benefits.
Answer
C · Ignored, because it is a sunk cost
4.Economics concepts
Answer: B · Worsen at first and then improve
Why this is the answer
In the short run, volumes are slow to adjust while import prices rise immediately, so the balance worsens before the Marshall–Lerner condition takes hold.
Answer
B · Worsen at first and then improve
5.Financial accounting
Answer: A · Prospectively, by spreading the remaining carrying amount over the new remaining life
Why this is the answer
Changes in estimates affect the current and future periods only. Prior-period restatement is for changes in policy and corrections of errors.
Answer
A · Prospectively, by spreading the remaining carrying amount over the new remaining life
6.Financial accounting
Answer: B · €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
B · €2,000 adverse
7.Break-even analysis
Answer: Q = 6000 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 = 13 − 8 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (25 000 + 5 000)/5 = 6 000
Answer
Q = 6 000 units
8.Break-even analysis
Answer: Q = 2500 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 = €6, cmB = €12
Weighted contribution margin
(3·6 + 2·12)/5 = €8.40
Break-even units
Q = 21 000/8.4 = 2 500
A: 1 500, B: 1 000
Answer
Q = 2 500 units
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