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
Management Accounting: cram pack
Formula sheets, the key method steps for every topic and 4 practice problems, with full solutions at the back.
1Formulas and methods
2Practice problems
1.Break-even analysisMedium
A product sells for €20 per unit with a variable cost of €12 per unit. Fixed costs are €40 000 per month. How many units Q must be sold per month to make a profit of €12 000?
F = €40 000p = €20v = €12profit = €12 000
Q = units
2.Break-even analysisHard
A company sells two products. Product A sells for €20 with a variable cost of €15; product B sells for €23 with a variable cost of €15. They sell in a fixed mix of 2 units of A for every 1 of B. Fixed costs are €14 400 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €20, vA = €15pB = €23, vB = €15A : B = 2 : 1F = €14 400
Q = units
3.Financial accountingMedium
Trade receivables are €50,000 and annual credit sales are €365,000. What are the receivable days?
- A73 days
- B7.3 days
- C50 days
- D36.5 days
4.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:
- AA non-adjusting event, disclosed only
- BIgnored, because it happened after the year end
- CAn adjusting event, so receivables are reduced
- DA change in accounting policy
3Solutions
1.Break-even analysis
Answer: Q = 6500 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 = 20 − 12 = €8
Units for the target profit
Q = (F + profit)/(p − v) = (40 000 + 12 000)/8 = 6 500
Answer
Q = 6 500 units
2.Break-even analysis
Answer: Q = 2400 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 = €8
Weighted contribution margin
(2·5 + 1·8)/3 = €6.00
Break-even units
Q = 14 400/6 = 2 400
A: 1 600, B: 800
Answer
Q = 2 400 units
3.Financial accounting
Answer: C · 50 days
Why this is the answer
€50,000 ÷ €365,000 × 365 = 50 days. This is the average time customers take to pay.
Answer
C · 50 days
4.Financial accounting
Answer: C · 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
C · An adjusting event, so receivables are reduced
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