# Labour Variances

## Variance Tree

```

Total Labour Cost Variance

┌─────────────┴─────────────┐

Rate Efficiency

Variance Variance

┌──────────────┼──────────────┐

Idle Time Mix Yield

Variance Variance Variance

```

## Notation

Symbol	Meaning
SHAQ	Standard Hours for Actual Quantity (output) produced
AH	Actual Hours for actual output
AHP	Actual Hours Paid
AHW	Actual Hours Worked
SR	Standard Rate per hour
AR	Actual Rate paid per hour
RSH	Revised Standard Hours — Actual hours worked, redistributed as per the standard mix of labour grades

## Formulas

1. Total Labour Cost Variance

$$\text{TLCV} = (\text{SHAQ} \times \text{SR}) - (\text{AH} \times \text{AR})$$

2. Labour Rate Variance (LRV) — use Actual Hours Paid (AHP)

$$\text{LRV} = (\text{SR} - \text{AR}) \times \text{AHP}$$

Tests: Did we pay a higher / lower wage rate than planned?

3. Labour Efficiency Variance (LEV) — use Actual Hours Worked (AHW)

$$\text{LEV} = (\text{SHAQ} - \text{AHW}) \times \text{SR}$$

Tests: Did workers take more / less time than standard allows?

4. Idle Time Variance (ITV) — always Adverse (cost of paid-but-not-worked time)

$$\text{ITV} = (\text{AHW} - \text{AHP}) \times \text{SR}$$

Or stated as: Idle Hours × SR (Adverse)

5. Labour Mix Variance (LMV) — when 2+ grades of labour

$$\text{LMV} = (\text{RSH} - \text{AHW}) \times \text{SR}$$

6. Labour Yield (Sub-Efficiency) Variance (LYV)

$$\text{LYV} = (\text{SHAQ} - \text{RSH}) \times \text{SR}$$

## Reconciliation

## Critical Distinction: AHP vs. AHW

Rate Variance uses AHP because workers are paid for hours, including idle hours.
Efficiency Variance uses AHW because efficiency is measured against actual productive time.
The difference (AHP − AHW) is Idle Time, and creates the Idle Time Variance.

Worked example

### Example 1

Example: Standard: 100 units × 3 hrs/unit = 300 SHAQ @ ₹20/hr = ₹6,000.

Actual: 100 units produced; workers paid for 350 hrs @ ₹22/hr = ₹7,700; out of which 20 hrs were idle (so AHW = 330).

⚠️ Common exam mistakes

Using AHP in the Efficiency Variance — this double-counts idle time. Always use AHW for efficiency, AHP for rate.
Treating Idle Time Variance as possibly Favourable — it is always Adverse by definition (idle = paid but unproductive).
Forgetting that Idle Time Variance only appears when AHP ≠ AHW — if all paid hours were worked, no idle time variance arises and LRV + LEV = TLCV directly.
In mix problems, computing RSH from standard total hours rather than from actual hours worked. RSH must total AHW.
Omitting F/A labels in answers, or computing variances as percentages instead of currency.

Reference:

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