MA.7:5.1 - Locate the aggregate difference
A constructed material-consumption account planned 100 accepted units, two material units per accepted unit and a price of 3 per material unit. Planned cost was 100 × 2 × 3 = 600.
The actual comparable account has 120 accepted units, 2.5 material units per accepted unit and a price of 4. Actual cost is 120 × 2.5 × 4 = 1,200, a difference of 600.
Using the stated order volume, usage, then price:
| Component | Calculation | Amount |
|---|---|---|
| Volume at planned usage and price | (120 − 100) × 2 × 3 | 120 |
| Usage at actual volume and planned price | 120 × (2.5 − 2) × 3 | 180 |
| Price at actual volume and usage | 120 × 2.5 × (4 − 3) | 300 |
| Total difference | 120 + 180 + 300 | 600 |
The decomposition is complete arithmetically. It does not establish that the extra 0.5 material units were waste. If the actual workload included a different product mix legitimately requiring more material, the comparison needs that distinction. If the mix is unchanged and adequate records identify failed attempts, the process question becomes more specific. A changed measuring convention would instead require repairing the account.
Another valid decomposition order can assign interaction amounts differently. Retain the chosen convention rather than using a component’s exact size as independent evidence of causal responsibility.