Process costing and equivalence numbers
For mass production of one product, divide costs by output. For similar varieties, equivalence numbers weight the output.
Formulas
- Simple: cost per unit = total cost / output
- Two-stage: production cost / units made + admin and selling / units sold
- Equivalence numbers: equivalent units = Σ output × factor; cost per unit = cost per equivalent unit × factor
Your turn
Three problems on this topic. Amounts with or without thousands separators, a point for pence.
Task
A waterworks (one product, no stock) had total costs of £693,400.00 for 10,000 m³ in the year. Work out the cost per m³ and the price with a 14% profit mark-up.
Cost per m³ in £
Price per m³ in £
Amounts like 12,500 or 12500.50; percentages as a number (12.5). Round to the penny or 2 decimal places.
Worked example
7,900 units were made and 6,700 sold; the rest goes into stock. Production costs £451,564.00, administration and selling costs £84,554.00. Use two-stage process costing.
Worked solution
- 1.Production cost per unit = £451,564.00 / 7,900 (units made) = £57.16
- 2.Admin and selling per unit = £84,554.00 / 6,700 (units sold) = £12.62
- 3.Total cost per unit = £57.16 + £12.62 = £69.78
- 4.Stock increase = 1,200 × £57.16 = £68,592.00
Typical mistake: Spreading administration and selling costs over units made instead of units sold.
A brewery makes three varieties. Total costs are £497,500.00. Allocate them with equivalence numbers (variety A is the base).
| Variety | Output (hl) | Equivalence number |
|---|---|---|
| A | 4,600 | 1.0 |
| B | 5,500 | 1.2 |
| C | 5,900 | 0.8 |
Worked solution
- 1.Equivalent units = 4,600 × 1.0 + 5,500 × 1.2 + 5,900 × 0.8 = 15,920
- 2.Cost per equivalent unit = £497,500.00 / 15,920 = £31.25
- 3.Variety B: £31.25 × 1.2 = £37.50 per hl
- 4.Variety C: £31.25 × 0.8 × 5,900 = £147,500.00
Typical mistake: Dividing total cost by total output instead of by equivalent units.
Frequently asked questions
When is two-stage costing needed?
When units made and units sold differ, i.e. stock is built up or run down.