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 €38 per unit with a variable cost of €18 per unit. Fixed costs are €100 000 per month. How many units Q must be sold per month to make a profit of €5 000?
F = €100 000p = €38v = €18profit = €5 000
Q = units
2.Break-even analysisHard
A company sells 1 800 units per month at €26 each, with a variable cost of €20 per unit and fixed costs of €7 200 per month. The variable cost rises by €3 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 800p = €26v = €20 → €23F = €7 200
Q = units
3.Financial accountingMedium
Under IAS 38, how are research and development costs treated?
- AResearch is expensed; development is capitalised only when strict criteria are met
- BResearch is capitalised; development is expensed
- CBoth are always expensed immediately
- DBoth are always capitalised as intangible assets
4.Financial accountingHard
In the indirect method of the cash flow statement, depreciation is:
- AIgnored completely
- BAdded back to net profit because it is a non-cash expense
- CSubtracted from net profit
- DShown in financing activities
3Solutions
1.Break-even analysis
Answer: Q = 5250 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 = 38 − 18 = €20
Units for the target profit
Q = (F + profit)/(p − v) = (100 000 + 5 000)/20 = 5 250
Answer
Q = 5 250 units
2.Break-even analysis
Answer: Q = 3600 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 = 1 800·(26 − 20) − 7 200 = €3 600
New contribution margin per unit
26 − 23 = €3
Units for the same profit
Q = (7 200 + 3 600)/3 = 3 600
Answer
Q = 3 600 units
3.Financial accounting
Answer: A · Research is expensed; development is capitalised only when strict criteria are met
Why this is the answer
Research costs are always expensed. Development costs are capitalised when, for example, technical feasibility, intention, ability and probable future benefits can be shown.
Answer
A · Research is expensed; development is capitalised only when strict criteria are met
4.Financial accounting
Answer: B · Added back to net profit because it is a non-cash expense
Why this is the answer
Starting from profit, non-cash charges like depreciation are added back, and changes in working capital are adjusted.
Answer
B · Added back to net profit because it is a non-cash expense
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