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 €15 per unit. Method B, more automated, has fixed costs of €26 000 per year and a variable cost of €13 per unit. At what yearly volume Q do both methods cost the same?
FA = €25 000vA = €15FB = €26 000vB = €13
Q = units
2.Break-even analysisHard
A product sells for €25 per unit, with a variable cost of €20 per unit and fixed costs of €5 000 per year. Budgeted sales are 1 200 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €5 000p = €25v = €20budget = 1 200
MS = %
3.Financial accountingMedium
Retained earnings represent:
- AThe share price
- BMoney owed to shareholders
- CCash kept in the bank
- DAccumulated profits that have not been paid out as dividends
4.Financial accountingHard
The standard price of material is €5 per kg. The company buys 1,000 kg for €5,400. What is the material price variance?
- A€0.40 adverse
- B€400 adverse
- C€5,400 adverse
- D€400 favourable
3Solutions
1.Break-even analysis
Answer: Q = 500 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 + 15Q = 26 000 + 13Q
Solve for Q
Q = (26 000 − 25 000)/(15 − 13) = 500
Answer
Q = 500 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
2.Break-even analysis
Answer: MS = 16.67 %
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) = 5 000/5 = 1 000
Margin of safety
MS = (1 200 − 1 000)/1 200·100 = 16.67%
Answer
MS = 16.67%
3.Financial accounting
Answer: D · Accumulated profits that have not been paid out as dividends
Why this is the answer
Retained earnings are cumulative net profits minus dividends; they are part of equity, not a pile of cash.
Answer
D · Accumulated profits that have not been paid out as dividends
4.Financial accounting
Answer: B · €400 adverse
Why this is the answer
Standard cost of 1,000 kg = €5,000; actual cost = €5,400. Paying more than standard gives a €400 adverse price variance.
Answer
B · €400 adverse
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