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 can be made in two ways. Method A has fixed costs of €25 000 per year and a variable cost of €10 per unit. Method B, more automated, has fixed costs of €45 000 per year and a variable cost of €5 per unit. At what yearly volume Q do both methods cost the same?
FA = €25 000vA = €10FB = €45 000vB = €5
Q = units
2.Break-even analysisHard
A company sells two products. Product A sells for €15 with a variable cost of €10; product B sells for €22 with a variable cost of €10. They sell in a fixed mix of 3 units of A for every 2 of B. Fixed costs are €7 800 per month. Find the total number of units Q (A and B together) needed to break even.
pA = €15, vA = €10pB = €22, vB = €10A : B = 3 : 2F = €7 800
Q = units
3.Financial accountingMedium
Net working capital is:
- ACurrent assets minus current liabilities
- BRevenue minus operating expenses
- CNon-current assets minus long-term loans
- DTotal assets minus total liabilities
4.Financial accountingHard
Closing inventory this year is overstated by €10,000 by mistake. What is the effect on profit, if not corrected?
- AProfit is unaffected; only the balance sheet changes
- BOnly this year's profit is understated
- CBoth years' profits are overstated
- DThis year's profit is overstated and next year's understated by €10,000
3Solutions
1.Break-even analysis
Answer: Q = 4000 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).
Equal total costs
25 000 + 10Q = 45 000 + 5Q
Solve for Q
Q = (45 000 − 25 000)/(10 − 5) = 4 000
Answer
Q = 4 000 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
2.Break-even analysis
Answer: Q = 1000 units
Break-even with a sales mix: when products sell in a fixed ratio, use the weighted average contribution margin: weight each product's p − v by its share of units. Break-even units = F/(weighted contribution margin), split again in the mix ratio.
Contribution margins
cmA = €5, cmB = €12
Weighted contribution margin
(3·5 + 2·12)/5 = €7.80
Break-even units
Q = 7 800/7.8 = 1 000
A: 600, B: 400
Answer
Q = 1 000 units
3.Financial accounting
Answer: A · Current assets minus current liabilities
Why this is the answer
Working capital measures the short-term resources available for daily operations: inventory, receivables and cash minus short-term obligations.
Answer
A · Current assets minus current liabilities
4.Financial accounting
Answer: D · 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
D · This year's profit is overstated and next year's understated by €10,000
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