variance-analysis-price-volume-decomposition

# Price / Volume Decomposition (+3)

## Price / Volume Decomposition


The most fundamental variance decomposition. Used for revenue, cost of goods, and any metric that can be expressed as Price x Volume.

**Formula:**
```
Total Variance = Actual - Budget (or Prior)

Volume Effect  = (Actual Volume - Budget Volume) x Budget Price
Price Effect   = (Actual Price - Budget Price) x Actual Volume
Mix Effect     = Residual (interaction term), or allocated proportionally

Verification:  Volume Effect + Price Effect = Total Variance
               (when mix is embedded in the price/volume terms)
```

**Three-way decomposition (separating mix):**
```
Volume Effect = (Actual Volume - Budget Volume) x Budget Price x Budget Mix
Price Effect  = (Actual Price - Budget Price) x Budget Volume x Actual Mix
Mix Effect    = Budget Price x Budget Volume x (Actual Mix - Budget Mix)
```

**Example — Revenue variance:**
- Budget: 10,000 units at $50 = $500,000
- Actual: 11,000 units at $48 = $528,000
- Total variance: +$28,000 favorable
  - Volume effect: +1,000 units x $50 = +$50,000 (favorable — sold more units)
  - Price effect: -$2 x 11,000 units = -$22,000 (unfavorable — lower ASP)
  - Net: +$28,000


## Rate / Mix Decomposition


Used when analyzing blended rates across segments with different unit economics.

**Formula:**
```
Rate Effect = Sum of (Actual Volume_i x (Actual Rate_i - Budget Rate_i))
Mix Effect  = Sum of (Budget Rate_i x (Actual Volume_i - Expected Volume_i at Budget Mix))
```

**Example — Gross margin variance:**
- Product A: 60% margin, Product B: 40% margin
- Budget mix: 50% A, 50% B → Blended margin 50%
- Actual mix: 40% A, 60% B → Blended margin 48%
- Mix effect explains 2pp of margin compression


## Headcount / Compensation Decomposition


Used for analyzing payroll and people-cost variances.

```
Total Comp Variance = Actual Compensation - Budget Compensation

Decompose into:
1. Headcount variance    = (Actual HC - Budget HC) x Budget Avg Comp
2. Rate variance         = (Actual Avg Comp - Budget Avg Comp) x Budget HC
3. Mix variance          = Difference due to level/department mix shift
4. Timing variance       = Hiring earlier/later than planned (partial-period effect)
5. Attrition impact      = Savings from unplanned departures (partially offset by backfill costs)
```


## Spend Category Decomposition


Used for operating expense analysis when price/volume is not applicable.

```
Total OpEx Variance = Actual OpEx - Budget OpEx

Decompose by:
1. Headcount-driven costs    (salaries, benefits, payroll taxes, recruiting)
2. Volume-driven costs       (hosting, transaction fees, commissions, shipping)
3. Discretionary spend       (travel, events, professional services, marketing programs)
4. Contractual/fixed costs   (rent, insurance, software licenses, subscriptions)
5. One-time / non-recurring  (severance, legal settlements, write-offs, project costs)
6. Timing / phasing          (spend shifted between periods vs plan)
```