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 €16 per unit with a variable cost of €4 per unit. Fixed costs are €48 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €48 000p = €16v = €4profit = €6 000
Q = units
2.Break-even analysisHard
A company sells 7 500 units per month at €21 each, with a variable cost of €18 per unit and fixed costs of €15 000 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 = 7 500p = €21v = €18 → €19F = €15 000
Q = units
3.Financial accountingMedium
A company increases its allowance for doubtful receivables. What is the effect?
- ARevenue increases and gross receivables rise by the same amount
- BAn expense is recognised and net receivables fall
- COnly the notes change; no figures move
- DCash decreases immediately
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?
- AAny lease of land and buildings
- BAny lease with monthly payments
- CA lease with a term of 12 months or less
- DA ten-year lease of a large production machine
3Solutions
1.Break-even analysis
Answer: Q = 4500 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 = 16 − 4 = €12
Units for the target profit
Q = (F + profit)/(p − v) = (48 000 + 6 000)/12 = 4 500
Answer
Q = 4 500 units
2.Break-even analysis
Answer: Q = 11250 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 = 7 500·(21 − 18) − 15 000 = €7 500
New contribution margin per unit
21 − 19 = €2
Units for the same profit
Q = (15 000 + 7 500)/2 = 11 250
Answer
Q = 11 250 units
3.Financial accounting
Answer: B · An expense is recognised and net receivables fall
Why this is the answer
The increase is charged to profit, and the allowance is deducted from gross receivables, so the balance sheet shows the amount expected to be collected.
Answer
B · An expense is recognised and net receivables fall
4.Financial accounting
Answer: C · 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
C · A lease with a term of 12 months or less
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