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 company sells 1 800 units at €47 each. The variable cost is €45 per unit and fixed costs are €3 000. Find the degree of operating leverage DOL at this sales level.
Q = 1 800p = €47v = €45F = €3 000
DOL =
2.Break-even analysisHard
A company sells 3 750 units per month at €20 each, with a variable cost of €15 per unit and fixed costs of €12 500 per month. The variable cost rises by €2 per unit and the price stays the same. How many units Q must now be sold per month to keep the same profit?
Q = 3 750p = €20v = €15 → €17F = €12 500
Q = units
3.Financial accountingMedium
A provision is recognised when a company has:
- AA possible future loss with no obligation
- BA profit to distribute
- CCash set aside in a separate account
- DA present obligation from a past event, a probable outflow and a reliable estimate
4.Financial accountingHard
A company changes its inventory method from weighted average to FIFO because it gives more relevant information. Under IAS 8, how is this applied?
- AProspectively, from the date of the change only
- BBy recognising the whole effect as income this year
- CRetrospectively, restating comparative figures as if FIFO had always been used
- DIt is not allowed to change inventory methods
3Solutions
1.Break-even analysis
Answer: DOL = 6
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Total contribution margin
CM = 1 800·(47 − 45) = €3 600
Operating profit
Π = 3 600 − 3 000 = €600
DOL
DOL = 3 600/600 = 6
Answer
DOL = 6
2.Break-even analysis
Answer: Q = 6250 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 = 3 750·(20 − 15) − 12 500 = €6 250
New contribution margin per unit
20 − 17 = €3
Units for the same profit
Q = (12 500 + 6 250)/3 = 6 250
Answer
Q = 6 250 units
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: C · Retrospectively, restating comparative figures as if FIFO had always been used
Why this is the answer
Voluntary policy changes are applied retrospectively where practicable, so comparatives remain consistent. Changes in estimates, by contrast, are applied prospectively.
Answer
C · Retrospectively, restating comparative figures as if FIFO had always been used
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