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 €48 per unit with a variable cost of €45 per unit. Fixed costs are €6 000 per month. How many units Q must be sold per month to make a profit of €6 000?
F = €6 000p = €48v = €45profit = €6 000
Q = units
2.Break-even analysisHard
A product sells for €26 per unit, with a variable cost of €6 per unit and fixed costs of €24 000 per year. Budgeted sales are 2 160 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €24 000p = €26v = €6budget = 2 160
MS = %
3.Financial accountingMedium
Under the accrual basis of accounting, revenue is recognised when:
- AThe customer pays the invoice, even if goods were delivered earlier
- BCash is received
- CThe tax return is filed
- DIt is earned, whether or not cash has been received
4.Financial accountingHard
A company issues shares at €5 each with a nominal value of €1. The extra €4 per share is recorded as:
- ARetained earnings
- BShare premium
- CRevenue
- DA liability
3Solutions
1.Break-even analysis
Answer: Q = 4000 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 = 48 − 45 = €3
Units for the target profit
Q = (F + profit)/(p − v) = (6 000 + 6 000)/3 = 4 000
Answer
Q = 4 000 units
2.Break-even analysis
Answer: MS = 44.44 %
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) = 24 000/20 = 1 200
Margin of safety
MS = (2 160 − 1 200)/2 160·100 = 44.44%
Answer
MS = 44.44%
3.Financial accounting
Answer: D · It is earned, whether or not cash has been received
Why this is the answer
Accrual accounting records revenue when the performance obligation is satisfied and expenses when incurred, not when cash moves.
Answer
D · It is earned, whether or not cash has been received
4.Financial accounting
Answer: B · Share premium
Why this is the answer
The amount above nominal value goes to the share premium account in equity; issuing shares is a financing transaction, not income.
Answer
B · Share premium
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