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 €15 000 per year and a variable cost of €8 per unit. Method B, more automated, has fixed costs of €16 600 per year and a variable cost of €6 per unit. At what yearly volume Q do both methods cost the same?
FA = €15 000vA = €8FB = €16 600vB = €6
Q = units
2.Break-even analysisHard
A product sells for €20 per unit, with a variable cost of €12 per unit and fixed costs of €32 000 per year. Budgeted sales are 4 600 units. Find the margin of safety MS as a percentage of budgeted sales.
F = €32 000p = €20v = €12budget = 4 600
MS = %
3.Financial accountingMedium
Profit for ordinary shareholders is €500,000 and there are 1,000,000 ordinary shares. What are basic earnings per share?
- A€5.00
- B€0.05
- C€0.50
- D€2.00
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€400 adverse
- B€400 favourable
- C€5,400 adverse
- D€0.40 adverse
3Solutions
1.Break-even analysis
Answer: Q = 800 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
15 000 + 8Q = 16 600 + 6Q
Solve for Q
Q = (16 600 − 15 000)/(8 − 6) = 800
Answer
Q = 800 units
Below this volume method A is cheaper; above it the automated method B is cheaper.
2.Break-even analysis
Answer: MS = 13.04 %
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) = 32 000/8 = 4 000
Margin of safety
MS = (4 600 − 4 000)/4 600·100 = 13.04%
Answer
MS = 13.04%
3.Financial accounting
Answer: C · €0.50
Why this is the answer
Basic EPS = €500,000 ÷ 1,000,000 = €0.50 per share. Dividing the share price by EPS gives the P/E ratio.
Answer
C · €0.50
4.Financial accounting
Answer: A · €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
A · €400 adverse
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