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
Customer lifetime value (CLV) estimates:
- AThe total net profit expected from a customer over the whole relationship
- BThe age of the customer
- CThe value of one purchase
- DThe cost of acquiring a new customer through marketing and sales activities
2.Marketing principlesHard
A firm launches a cheaper version of its best-selling product. Total sales rise slightly, but sales of the original fall sharply. What has happened?
- AA pull strategy failure
- BBrand dilution by a competitor
- CSuccessful market development into a new segment
- DCannibalisation of the original product's sales
3.Economics conceptsMedium
The law of diminishing marginal returns states that:
- AAdding more of a variable input to a fixed input eventually lowers the extra output per unit added
- BConsumers get less satisfaction as prices rise
- CTotal output always falls as more workers are hired
- DLong-run average costs always fall as output rises
4.Economics conceptsHard
The Laffer curve illustrates that:
- ABeyond some point, raising tax rates can reduce total tax revenue
- BTax revenue is unrelated to tax rates
- CLower tax rates always reduce tax revenue, whatever the starting rate
- DHigher tax rates always increase tax revenue
5.Financial accountingMedium
Under IAS 16, which cost should be included in the cost of a new machine?
- AStaff training costs after it starts operating
- BGeneral office overheads for the year
- CRepairs carried out two years later
- DInstallation costs needed to get it working
6.Financial accountingHard
Machine hours are scarce. Product X earns €20 contribution and needs 4 hours; product Y earns €15 and needs 2 hours. Which should be made first?
- AEither, because the total contribution is the same
- BX, because it earns more contribution per unit
- CY, because it earns €7.50 per hour versus €5 for X
- DX, because it uses more machine time
7.Break-even analysisMedium
A product sells for €38 per unit with a variable cost of €30 per unit. Fixed costs are €16 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €16 000p = €38v = €30profit = €6 000
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €17 with a variable cost of €12; product B sells for €42 with a variable cost of €30. They sell in a fixed mix of 3 units of A for every 2 of B. Fixed costs are €15 600 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €17, vA = €12pB = €42, vB = €30A : B = 3 : 2F = €15 600
Q = units
3Solutions
1.Marketing principles
Answer: A · The total net profit expected from a customer over the whole relationship
Why this is the answer
CLV combines purchase frequency, margin, retention and duration (often discounted), guiding acquisition and retention spending.
Answer
A · The total net profit expected from a customer over the whole relationship
2.Marketing principles
Answer: D · Cannibalisation of the original product's sales
Why this is the answer
Cannibalisation occurs when a new offer mainly takes sales from the firm's existing products. It is a problem if the new product has a lower margin.
Answer
D · Cannibalisation of the original product's sales
3.Economics concepts
Answer: A · 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
A · Adding more of a variable input to a fixed input eventually lowers the extra output per unit added
4.Economics concepts
Answer: A · Beyond some point, raising tax rates can reduce total tax revenue
Why this is the answer
Very high rates discourage taxed activity or encourage avoidance, so revenue peaks at some rate between 0 and 100%; where that peak lies is debated.
Answer
A · Beyond some point, raising tax rates can reduce total tax revenue
5.Financial accounting
Answer: D · 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
D · Installation costs needed to get it working
6.Financial accounting
Answer: C · Y, because it earns €7.50 per hour versus €5 for X
Why this is the answer
X earns €20 ÷ 4 = €5 per hour, Y earns €15 ÷ 2 = €7.50 per hour. With a scarce resource, maximise contribution per scarce hour.
Answer
C · Y, because it earns €7.50 per hour versus €5 for X
7.Break-even analysis
Answer: Q = 2750 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 = 38 − 30 = €8
Units for the target profit
Q = (F + profit)/(p − v) = (16 000 + 6 000)/8 = 2 750
Answer
Q = 2 750 units
8.Break-even analysis
Answer: Q = 2000 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 = €5, cmB = €12
Weighted contribution margin
(3·5 + 2·12)/5 = €7.80
Break-even units
Q = 15 600/7.8 = 2 000
A: 1 200, B: 800
Answer
Q = 2 000 units
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