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
Which of these is one of Porter's five competitive forces?
- AThe level of inflation
- BThe political stability of a country
- CThe firm's brand awareness
- DThe threat of substitute products
2.Marketing principlesHard
Cognitive dissonance after an expensive purchase can be reduced by:
- AReassuring follow-up communication and good after-sales service
- BStopping all communication with the customer so the purchase is forgotten
- CRemoving the warranty
- DRaising the price further
3.Economics conceptsMedium
A sharp rise in world oil prices leading to higher inflation is an example of:
- ADeflation
- BDemand-pull inflation
- CDisinflation
- DCost-push inflation
4.Economics conceptsHard
Ricardian equivalence suggests that a debt-financed tax cut will:
- AAlways cause inflation
- BStrongly increase consumption, because households spend most of the tax cut through the multiplier
- CHave little effect on spending, because households save to pay expected future taxes
- DReduce interest rates sharply
5.Financial accountingMedium
Which inventory valuation method assumes the oldest goods are sold first?
- ASpecific identification of each item
- BLIFO (last in, first out)
- CFIFO (first in, first out)
- DWeighted average cost
6.Financial accountingHard
After the year end, but before the accounts are approved, a customer who owed money at year end goes bankrupt. Under IAS 10 this is:
- AIgnored, because it happened after the year end
- BAn adjusting event, so receivables are reduced
- CA non-adjusting event, disclosed only
- DA change in accounting policy
7.Break-even analysisMedium
A product sells for €22 per unit with a variable cost of €12 per unit. Fixed costs are €12 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €12 000p = €22v = €12profit = €5 000
Q = units
8.Break-even analysisHard
A company sells two products. Product A sells for €18 with a variable cost of €10; product B sells for €22 with a variable cost of €10. They sell in a fixed mix of 2 units of A for every 3 of B. Fixed costs are €52 000 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €18, vA = €10pB = €22, vB = €10A : B = 2 : 3F = €52 000
Q = units
3Solutions
1.Marketing principles
Answer: D · The threat of substitute products
Why this is the answer
The five forces are rivalry among competitors, threat of new entrants, threat of substitutes, and the bargaining power of buyers and of suppliers.
Answer
D · The threat of substitute products
2.Marketing principles
Answer: A · Reassuring follow-up communication and good after-sales service
Why this is the answer
Post-purchase dissonance is reduced when companies confirm the decision, for example through thank-you messages, reviews, support and guarantees.
Answer
A · Reassuring follow-up communication and good after-sales service
3.Economics concepts
Answer: D · Cost-push inflation
Why this is the answer
Higher input costs shift aggregate supply to the left, raising prices and possibly lowering output; demand-pull inflation comes from excess aggregate demand.
Answer
D · Cost-push inflation
4.Economics concepts
Answer: C · Have little effect on spending, because households save to pay expected future taxes
Why this is the answer
If consumers are forward-looking and see that government borrowing means higher taxes later, they save the tax cut, so aggregate demand barely changes.
Answer
C · Have little effect on spending, because households save to pay expected future taxes
5.Financial accounting
Answer: C · FIFO (first in, first out)
Why this is the answer
Under FIFO, cost of sales uses the oldest costs and closing inventory reflects recent costs. IFRS does not allow LIFO.
Answer
C · FIFO (first in, first out)
6.Financial accounting
Answer: B · An adjusting event, so receivables are reduced
Why this is the answer
The customer's inability to pay existed at year end, so the accounts are adjusted. A fire after year end would be non-adjusting, because it is a new condition.
Answer
B · An adjusting event, so receivables are reduced
7.Break-even analysis
Answer: Q = 1700 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 = 22 − 12 = €10
Units for the target profit
Q = (F + profit)/(p − v) = (12 000 + 5 000)/10 = 1 700
Answer
Q = 1 700 units
8.Break-even analysis
Answer: Q = 5000 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 = €8, cmB = €12
Weighted contribution margin
(2·8 + 3·12)/5 = €10.40
Break-even units
Q = 52 000/10.4 = 5 000
A: 2 000, B: 3 000
Answer
Q = 5 000 units
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