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 €30 per unit. Fixed costs are €12 500 per month. How many units Q must be sold per month to make a profit of €10 000?
F = €12 500p = €35v = €30profit = €10 000
Q = units
2.Break-even analysisHard
A product sells for €16 per unit, with a variable cost of €12 per unit and fixed costs of €16 000 per year. Budgeted sales are 7 200 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €16 000p = €16v = €12budget = 7 200
MS = %
3.Financial accountingMedium
A provision is recognised when a company has:
- ACash set aside in a separate account
- BA profit to distribute
- CA possible future loss with no obligation
- DA present obligation from a past event, a probable outflow and a reliable estimate
4.Financial accountingHard
A company's debt-to-equity ratio rises sharply. What does this usually indicate?
- AHigher financial risk because the company relies more on borrowed money
- BThat shareholders invested more money
- CBetter liquidity in the short term
- DHigher profitability
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 = 35 − 30 = €5
Units for the target profit
Q = (F + profit)/(p − v) = (12 500 + 10 000)/5 = 4 500
Answer
Q = 4 500 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) = 16 000/4 = 4 000
Margin of safety
MS = (7 200 − 4 000)/7 200·100 = 44.44%
Answer
MS = 44.44%
3.Financial accounting
Answer: D · A present obligation from a past event, a probable outflow and a reliable estimate
Why this is the answer
Provisions are liabilities of uncertain timing or amount. Possible obligations that do not meet the criteria are disclosed as contingent liabilities.
Answer
D · A present obligation from a past event, a probable outflow and a reliable estimate
4.Financial accounting
Answer: A · Higher financial risk because the company relies more on borrowed money
Why this is the answer
A higher ratio means more leverage: interest and repayments must be met whatever the results, so financial risk rises, although returns to shareholders may also rise.
Answer
A · Higher financial risk because the company relies more on borrowed money
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