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 €27 per unit with a variable cost of €25 per unit. Fixed costs are €8 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €8 000p = €27v = €25profit = €2 000
Q = units
2.Break-even analysisHard
A product sells for €57 per unit, with a variable cost of €45 per unit and fixed costs of €12 000 per year. Budgeted sales are 1 500 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €12 000p = €57v = €45budget = 1 500
MS = %
3.Financial accountingMedium
A company finds that a machine will last 8 years instead of the 5 originally estimated. Under IAS 8, how is this change applied?
- AProspectively, by spreading the remaining carrying amount over the new remaining life
- BBy recognising a large gain in the current year
- CBy changing the original cost of the machine
- DRetrospectively, by restating all prior years
4.Financial accountingHard
Closing inventory this year is overstated by €10,000 by mistake. What is the effect on profit, if not corrected?
- ABoth years' profits are overstated
- BThis year's profit is overstated and next year's understated by €10,000
- CProfit is unaffected; only the balance sheet changes
- DOnly this year's profit is understated
3Solutions
1.Break-even analysis
Answer: Q = 5000 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 = 27 − 25 = €2
Units for the target profit
Q = (F + profit)/(p − v) = (8 000 + 2 000)/2 = 5 000
Answer
Q = 5 000 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) = 12 000/12 = 1 000
Margin of safety
MS = (1 500 − 1 000)/1 500·100 = 33.33%
Answer
MS = 33.33%
3.Financial accounting
Answer: A · Prospectively, by spreading the remaining carrying amount over the new remaining life
Why this is the answer
Changes in estimates affect the current and future periods only. Prior-period restatement is for changes in policy and corrections of errors.
Answer
A · Prospectively, by spreading the remaining carrying amount over the new remaining life
4.Financial accounting
Answer: B · This year's profit is overstated and next year's understated by €10,000
Why this is the answer
Higher closing inventory reduces cost of sales, raising this year's profit. Next year opening inventory is too high, increasing cost of sales and lowering profit by the same amount.
Answer
B · This year's profit is overstated and next year's understated by €10,000
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