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 €16 with a variable cost of €8 per unit. Fixed costs are €40 000 per month and profit is taxed at 20%. How many units Q must be sold per month to earn €8 000 after tax?
p = €16v = €8F = €40 000T = 20%after-tax profit = €8 000
Q = units
2.Break-even analysisHard
A product sells for €28 per unit, with a variable cost of €18 per unit and fixed costs of €25 000 per year. Budgeted sales are 3 750 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €25 000p = €28v = €18budget = 3 750
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?
- ABy changing the original cost of the machine
- BProspectively, by spreading the remaining carrying amount over the new remaining life
- CRetrospectively, by restating all prior years
- DBy recognising a large gain in the current year
4.Financial accountingHard
Company P buys 70% of the voting shares of S and gains control. How does P report S in its group accounts?
- AShow one equity-method investment line for its 70% share of S
- BKeep the investment at cost and report only the dividends received from S
- CAdd only 70% of each of S's assets, liabilities, income and expenses
- DConsolidate 100% of S line by line and show a non-controlling interest
3Solutions
1.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).
Pre-tax profit needed
8 000/(1 − 0.2) = €10 000
Units needed
Q = (40 000 + 10 000)/8 = 6 250
Answer
Q = 6 250 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) = 25 000/10 = 2 500
Margin of safety
MS = (3 750 − 2 500)/3 750·100 = 33.33%
Answer
MS = 33.33%
3.Financial accounting
Answer: B · 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
B · Prospectively, by spreading the remaining carrying amount over the new remaining life
4.Financial accounting
Answer: D · Consolidate 100% of S line by line and show a non-controlling interest
Why this is the answer
A subsidiary is consolidated line by line at 100%. The 30% owned by others is shown as a non-controlling interest within equity.
Answer
D · Consolidate 100% of S line by line and show a non-controlling interest
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