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
Psychographic segmentation divides customers by:
- AAge and income only
- BCountry and climate
- CLifestyle, values and personality
- DPurchase frequency only
2.Marketing principlesHard
A firm uses different prices for the same seat on a flight depending on demand and booking time. This is:
- ADynamic pricing (yield management)
- BCost-plus pricing
- CPsychological pricing with .99 endings
- DCaptive product pricing
3.Economics conceptsMedium
In perfect competition in the long run, firms earn:
- AMonopoly profits
- BLarge economic profits
- CLosses forever
- DZero economic profit
4.Economics conceptsHard
Under a fixed exchange rate with free capital movement, a country:
- AMust have a budget surplus
- BLoses control of independent monetary policy
- CCannot trade with other countries
- DCan set any interest rate it likes
5.Financial accountingMedium
Under IAS 16, which cost should be included in the cost of a new machine?
- AGeneral office overheads for the year
- BInstallation costs needed to get it working
- CStaff training costs after it starts operating
- DRepairs carried out two years later
6.Financial accountingHard
An investor holds 30% of a company's shares and has significant influence but not control. How is the investment usually accounted for in group accounts?
- AUsing the equity method as an associate
- BAs a joint operation with line-by-line sharing
- CBy full consolidation as a subsidiary
- DAt cost with no changes ever
7.Break-even analysisMedium
A product sells for €55 per unit with a variable cost of €45 per unit. Fixed costs are €20 000 per month. How many units Q must be sold per month to make a profit of €12 000?
F = €20 000p = €55v = €45profit = €12 000
Q = units
8.Break-even analysisHard
A product sells for €24 per unit, with a variable cost of €12 per unit and fixed costs of €24 000 per year. Budgeted sales are 2 400 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €24 000p = €24v = €12budget = 2 400
MS = %
3Solutions
1.Marketing principles
Answer: C · Lifestyle, values and personality
Why this is the answer
Psychographic segmentation looks at attitudes, interests, values and lifestyles; behavioural segmentation uses usage and loyalty.
Answer
C · Lifestyle, values and personality
2.Marketing principles
Answer: A · Dynamic pricing (yield management)
Why this is the answer
Dynamic pricing adjusts prices to demand, time and capacity to maximise revenue, common in airlines and hotels.
Answer
A · Dynamic pricing (yield management)
3.Economics concepts
Answer: D · Zero economic profit
Why this is the answer
Profits attract entry and losses cause exit until price equals minimum average cost and economic profit is zero.
Answer
D · Zero economic profit
4.Economics concepts
Answer: B · Loses control of independent monetary policy
Why this is the answer
A country cannot simultaneously have a fixed exchange rate, free capital flows and an independent monetary policy; it must give up one of the three.
Answer
B · Loses control of independent monetary policy
5.Financial accounting
Answer: B · Installation costs needed to get it working
Why this is the answer
Purchase price plus directly attributable costs, such as delivery and installation, are capitalised. Training, later repairs and general overheads are expensed.
Answer
B · Installation costs needed to get it working
6.Financial accounting
Answer: A · Using the equity method as an associate
Why this is the answer
Under IAS 28 the investment starts at cost and is adjusted for the investor's share of the associate's profits or losses, less dividends received.
Answer
A · Using the equity method as an associate
7.Break-even analysis
Answer: Q = 3200 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 = 55 − 45 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (20 000 + 12 000)/10 = 3 200
Answer
Q = 3 200 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) = 24 000/12 = 2 000
Margin of safety
MS = (2 400 − 2 000)/2 400·100 = 16.67%
Answer
MS = 16.67%
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