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 €27 per unit with a variable cost of €12 per unit. Fixed costs are €75 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €75 000p = €27v = €12profit = €6 000
Q = units
2.Break-even analysisHard
A company sells 1 500 units per month at €10 each, with a variable cost of €4 per unit and fixed costs of €6 000 per month. The variable cost rises by €1 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 500p = €10v = €4 → €5F = €6 000
Q = units
3.Financial accountingMedium
Which error will NOT be revealed by a trial balance?
- AA sale left out of the books entirely
- BA wrongly added ledger column
- CA debit posted without a matching credit
- DA balance copied to the wrong column
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 change in accounting policy
- BA non-adjusting event, disclosed only
- CAn adjusting event, so receivables are reduced
- DIgnored, because it happened after the year end
3Solutions
1.Break-even analysis
Answer: Q = 5400 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 = 27 − 12 = €15
Units for the target profit
Q = (F + profit)/(p − v) = (75 000 + 6 000)/15 = 5 400
Answer
Q = 5 400 units
2.Break-even analysis
Answer: Q = 1800 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 = 1 500·(10 − 4) − 6 000 = €3 000
New contribution margin per unit
10 − 5 = €5
Units for the same profit
Q = (6 000 + 3 000)/5 = 1 800
Answer
Q = 1 800 units
3.Financial accounting
Answer: A · A sale left out of the books entirely
Why this is the answer
An error of omission leaves both sides unrecorded, so totals still agree. Single-sided postings and addition errors make the trial balance differ.
Answer
A · A sale left out of the books entirely
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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