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 €22 per unit with a variable cost of €12 per unit. Fixed costs are €50 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €50 000p = €22v = €12profit = €2 000
Q = units
2.Break-even analysisHard
A company sells 4 000 units at €32 each, with a variable cost of €20 per unit and fixed costs of €30 000. By what percentage %ΔΠ does operating profit change if sales volume falls by 20%?
Q = 4 000p = €32v = €20F = €30 000%ΔQ = −20%
%ΔΠ = %
3.Financial accountingMedium
When preparing a bank reconciliation, which item explains why the bank statement balance is higher than the cash book balance?
- ACheques issued but not yet presented to the bank
- BBank charges not yet entered in the cash book
- CA direct debit not yet entered in the cash book
- DCash deposited but not yet credited on the bank statement
4.Financial accountingHard
Under IFRS 16, which lease may a lessee choose to expense on a straight-line basis instead of recognising a right-of-use asset?
- AA ten-year lease of a large production machine
- BA lease with a term of 12 months or less
- CAny lease of land and buildings
- DAny lease with monthly payments
3Solutions
1.Break-even analysis
Answer: Q = 5200 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) = (50 000 + 2 000)/10 = 5 200
Answer
Q = 5 200 units
2.Break-even analysis
Answer: %ΔΠ = −53.33 %
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Contribution margin and profit
CM = 4 000·12 = €48 000
Π = 48 000 − 30 000 = €18 000
DOL
DOL = 48 000/18 000 = 2.667
Change in profit
%ΔΠ = 2.667·(−20%) = −53.33%
Answer
%ΔΠ = −53.33%
Check: new profit = 3 200·12 − 30 000 = €8 400.00.
3.Financial accounting
Answer: A · Cheques issued but not yet presented to the bank
Why this is the answer
Unpresented cheques have reduced the cash book but not the bank balance. Outstanding deposits, bank charges and unrecorded direct debits work the other way.
Answer
A · Cheques issued but not yet presented to the bank
4.Financial accounting
Answer: B · A lease with a term of 12 months or less
Why this is the answer
Lessees may elect not to recognise short-term leases (12 months or less) and leases of low-value assets, expensing the payments instead.
Answer
B · A lease with a term of 12 months or less
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