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 €35 per unit with a variable cost of €20 per unit. Fixed costs are €22 500 per month. How many units Q must be sold per month to make a profit of €12 000?
F = €22 500p = €35v = €20profit = €12 000
Q = units
2.Break-even analysisHard
A product sells for €40 per unit, with a variable cost of €20 per unit and fixed costs of €40 000 per year. Budgeted sales are 3 000 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €40 000p = €40v = €20budget = 3 000
MS = %
3.Financial accountingMedium
A machine with a carrying amount of €3,000 is sold for €4,000. What is recorded in the income statement?
- AA gain on disposal of €1,000
- BRevenue of €4,000
- CA gain on disposal of €4,000
- DA loss on disposal of €1,000
4.Financial accountingHard
Under IFRS 15, revenue is recognised:
- AWhen (or as) the entity satisfies a performance obligation by transferring control to the customer
- BAt the end of the financial year
- COnly when cash is received
- DWhen the contract is signed
3Solutions
1.Break-even analysis
Answer: Q = 2300 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 = 35 − 20 = €15
Units for the target profit
Q = (F + profit)/(p − v) = (22 500 + 12 000)/15 = 2 300
Answer
Q = 2 300 units
2.Break-even analysis
Answer: MS = 33.33 %
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).
Break-even quantity
Q = F/(p − v) = 40 000/20 = 2 000
Margin of safety
MS = (3 000 − 2 000)/3 000·100 = 33.33%
Answer
MS = 33.33%
3.Financial accounting
Answer: A · A gain on disposal of €1,000
Why this is the answer
Gain or loss on disposal = proceeds − carrying amount = €4,000 − €3,000 = €1,000 gain. It is not part of normal revenue.
Answer
A · A gain on disposal of €1,000
4.Financial accounting
Answer: A · When (or as) the entity satisfies a performance obligation by transferring control to the customer
Why this is the answer
The steps: identify the contract, identify performance obligations, determine the price, allocate it, and recognise revenue as each obligation is satisfied.
Answer
A · When (or as) the entity satisfies a performance obligation by transferring control to the customer
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