# Material Variances
## Variance Tree
```
Total Material Cost Variance
|
┌──────────────┴──────────────┐
Price Usage
Variance Variance
|
┌─────────┴─────────┐
Mix Yield
Variance Variance
```
## Notation
| Symbol | Meaning |
|---|---|
| SQAO | Standard Quantity of RM for Actual Output produced |
| AQAO (or AQ) | Actual Quantity of RM used for actual output |
| SP | Standard Price per unit of raw material |
| AP | Actual Price paid per unit of raw material |
| RSQ | Revised Standard Quantity — Actual total quantity used, redistributed across materials as per the standard mix |
## Formulas
1. Total Material Cost Variance
$$\text{TMCV} = (\text{SQAO} \times \text{SP}) - (\text{AQAO} \times \text{AP})$$
Or equivalently:
$$= (\text{SQ/unit} \times \text{AO} \times \text{SP}) - (\text{AQ/unit} \times \text{AO} \times \text{AP})$$
2. Material Price Variance (MPV)
$$\text{MPV} = (\text{SP} - \text{AP}) \times \text{AQ}$$
Tests: Did we pay more / less per kg than planned?
3. Material Usage Variance (MUV)
$$\text{MUV} = (\text{SQAO} - \text{AQAO}) \times \text{SP}$$
Tests: Did we use more / less material than the standard allows for the actual output?
4. Material Mix Variance (MMV) — only when 2+ materials are used
$$\text{MMV} = (\text{RSQ} - \text{AQ}) \times \text{SP}$$
Tests: Did we deviate from the standard proportion of materials?
5. Material Yield Variance (MYV)
$$\text{MYV} = (\text{SQAO} - \text{RSQ}) \times \text{SP}$$
Tests: Did the input mix yield more / less output than expected?
## Verification (Reconciliation)
- MPV + MUV = TMCV
- MMV + MYV = MUV
## How to Compute RSQ
If two materials A and B are mixed in standard ratio 60:40, and the actual total quantity used (A + B) is 1,000 kg:
- RSQ of A = 60% × 1,000 = 600 kg
- RSQ of B = 40% × 1,000 = 400 kg
RSQ keeps total actual input but assumes standard proportion.