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
Why might a researcher choose in-depth interviews rather than a large questionnaire?
- ATo produce statistically representative percentages for the market
- BTo survey thousands of people cheaply
- CTo explore customers' motives and feelings in detail
- DTo avoid any interviewer influence
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 rises, because quantity falls proportionally less than price rises
- CRevenue falls to zero, because customers stop buying
- DRevenue falls, because quantity falls proportionally more than price rises
3.Economics conceptsMedium
A minimum wage set above the equilibrium wage in a competitive labour market is predicted to cause:
- AA shortage of labour
- BNo change in employment
- CA surplus of labour (unemployment)
- DA fall in the wage rate
4.Economics conceptsHard
The Fisher effect predicts that, in the long run, a permanent 2 percentage point rise in expected inflation will:
- ARaise real interest rates by about 2 points
- BLower nominal interest rates by about 2 points
- CRaise nominal interest rates by about 2 points, leaving real rates unchanged
- DHave no effect on nominal interest rates, so real interest rates fall by about 2 points
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?
- ARetrospectively, by restating all prior years
- BBy changing the original cost of the machine
- CProspectively, by spreading the remaining carrying amount over the new remaining life
- DBy recognising a large gain in the current year
6.Financial accountingHard
Goodwill arises in a business combination when:
- AThe consideration paid exceeds the fair value of identifiable net assets acquired
- BThe acquired company makes a loss
- CA company has a good reputation
- DAssets are revalued upwards
7.Break-even analysisMedium
A product can be made in two ways. Method A has fixed costs of €30 000 per year and a variable cost of €20 per unit. Method B, more automated, has fixed costs of €38 000 per year and a variable cost of €16 per unit. At what yearly volume Q do both methods cost the same?
FA = €30 000vA = €20FB = €38 000vB = €16
Q = units
8.Break-even analysisHard
A company sells 1 250 units per month at €30 each, with a variable cost of €15 per unit and fixed costs of €7 500 per month. The variable cost rises by €5 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 1 250p = €30v = €15 → €20F = €7 500
Q = units
3Solutions
1.Marketing principles
Answer: C · To explore customers' motives and feelings in detail
Why this is the answer
In-depth interviews give rich, qualitative insight into why people behave as they do. Questionnaires suit measuring how many people think or do something.
Answer
C · To explore customers' motives and feelings in detail
2.Marketing principles
Answer: B · 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
B · Revenue rises, because quantity falls proportionally less than price rises
3.Economics concepts
Answer: C · A surplus of labour (unemployment)
Why this is the answer
At the higher wage more people want to work and firms hire fewer, so labour supplied exceeds labour demanded in the simple competitive model.
Answer
C · A surplus of labour (unemployment)
4.Economics concepts
Answer: C · Raise nominal interest rates by about 2 points, leaving real rates unchanged
Why this is the answer
Lenders demand compensation for expected inflation, so nominal rates move one-for-one with it in the long run while the real rate is set by real factors.
Answer
C · Raise nominal interest rates by about 2 points, leaving real rates unchanged
5.Financial accounting
Answer: C · 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
C · Prospectively, by spreading the remaining carrying amount over the new remaining life
6.Financial accounting
Answer: A · The consideration paid exceeds the fair value of identifiable net assets acquired
Why this is the answer
Goodwill = consideration − fair value of identifiable net assets. Under IFRS it is not amortised but tested for impairment annually.
Answer
A · The consideration paid exceeds the fair value of identifiable net assets acquired
7.Break-even analysis
Answer: Q = 2000 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).
Equal total costs
30 000 + 20Q = 38 000 + 16Q
Solve for Q
Q = (38 000 − 30 000)/(20 − 16) = 2 000
Answer
Q = 2 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
8.Break-even analysis
Answer: Q = 1875 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 = 1 250·(30 − 15) − 7 500 = €11 250
New contribution margin per unit
30 − 20 = €10
Units for the same profit
Q = (7 500 + 11 250)/10 = 1 875
Answer
Q = 1 875 units
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