11.3 Direct Labour & Overhead Variances

Direct Labour & Overhead Variances

Core Principle: Labour and overhead variances examine operational throughput speed, wage rate management, idle plant capacity, and fixed overhead absorption. When idle time occurs, standard costing strictly segregates hours paid from hours worked to avoid distorting efficiency measurements. Under absorption costing, fixed overhead variances fulfill a dual purpose: explaining cost deviations against budget and reconciling the periodic under- or over-absorption of factory overhead.

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1. Direct Labour Variances: Total, Rate, Idle Time & Efficiency

The total direct labour variance isolates whether the actual workforce cost was higher or lower than the standard flexed labour allowance for the units manufactured. In environments subject to unproductive downtime, the total variance splits into three distinct components:

                               Direct Labour Total Variance
                     ┌──────────────────────┼──────────────────────┐
                     ▼                      ▼                      ▼
           Labour Rate Variance    Idle Time Variance    Labour Efficiency Variance
            (Wage Rate Shifts)    (Unproductive Hours)     (Speed of Actual Work)
            [Based on AH Paid]     [Always ADVERSE]         [Based on AH Worked]

A. Direct Labour Total Variance

The total variance compares the standard labour cost of actual production achieved with the actual direct labour payroll incurred:

$$\text{Direct Labour Total Variance} = (\text{Standard Hours for Actual Output} \times \text{Standard Rate}) - \text{Actual Labour Cost}$$ $$\text{Direct Labour Total Variance} = (SH \times SR) - (AH_{\text{paid}} \times AR)$$

B. Direct Labour Rate Variance

The Labour Rate Variance measures the difference between the standard hourly wage rate and the actual hourly rate paid, applied across all actual hours paid:

$$\text{Direct Labour Rate Variance} = (\text{Standard Rate} - \text{Actual Rate}) \times \mathbf{\text{Actual Hours Paid}}$$ $$\text{Direct Labour Rate Variance} = (AH_{\text{paid}} \times SR) - \text{Actual Labour Cost}$$

• If $\text{Actual Rate} < \text{Standard Rate} \implies \mathbf{\text{Favourable (F)}}$
• If $\text{Actual Rate} > \text{Standard Rate} \implies \mathbf{\text{Adverse (A)}}$

Operational Causes of Labour Rate Variances:

• Adverse: Unscheduled overtime paid at premium rates to meet rush deadlines; deployment of higher-skilled, higher-wage workers on routine jobs; national wage increases or cost-of-living adjustments exceeding budget expectations.
• Favourable: Hiring lower-skilled trainees or apprentices at lower wage rates; reduction in overtime premiums; lower-than-anticipated wage settlements.

C. Idle Time Variance

Idle time arises when direct production workers are present and paid, but unable to produce output due to external or internal disruptions (e.g., machine breakdowns, power grid blackouts, raw material delivery delays, or waiting for work orders).

$$\mathbf{\text{Idle Time Variance}} = (\text{Actual Hours Worked} - \text{Actual Hours Paid}) \times \text{Standard Rate} = -(\text{Idle Hours}) \times \mathbf{\text{Standard Rate}}$$

D. Direct Labour Efficiency Variance

The Labour Efficiency Variance measures the productivity of the workforce during the hours they were actively working. It compares the standard hours allowed for the output achieved against the actual hours worked (excluding idle time), valued at the standard rate:

$$\text{Direct Labour Efficiency Variance} = (\mathbf{\text{Standard Hours for Actual Output}} - \mathbf{\text{Actual Hours Worked}}) \times \mathbf{\text{Standard Rate}}$$ $$\text{Direct Labour Efficiency Variance} = (SH - AH_{\text{worked}}) \times SR$$

• If $\text{Actual Hours Worked} < \text{Standard Hours} \implies \mathbf{\text{Favourable (F)}}$ (Workforce worked faster than standard)
• If $\text{Actual Hours Worked} > \text{Standard Hours} \implies \mathbf{\text{Adverse (A)}}$ (Workforce took longer than standard)

Mathematical Check and Reconciliation:

$$\text{Direct Labour Total Variance} = \text{Labour Rate Variance} + \text{Idle Time Variance} + \text{Labour Efficiency Variance}$$

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2. Variable Production Overhead Variances

Variable production overheads (e.g., indirect factory materials, machine lubricants, consumable tools, and factory power) are assumed to vary directly with activity. In standard costing, variable overhead is usually absorbed using direct labour hours or machine hours. Total variable overhead variance decomposes into Expenditure and Efficiency:

                      Variable Overhead Total Variance
                     ┌────────────────┴────────────────┐
                     ▼                                 ▼
       Variable Overhead Expenditure       Variable Overhead Efficiency
     (Hourly Spending Rate Variance)       (Linked to Labour Productivity)
          [Based on AH Worked]                 [Based on (SH - AH) × Rate]

A. Variable Overhead Total Variance

$$\text{Variable Overhead Total Variance} = (\text{Standard Hours for Actual Output} \times \text{Standard Variable OAR}) - \text{Actual Variable Overhead Cost}$$

B. Variable Overhead Expenditure Variance

The Expenditure Variance measures whether the business paid more or less per hour of active operation than the standard variable overhead rate:

$$\text{Variable Overhead Expenditure Variance} = (AH_{\text{worked}} \times \text{Standard Variable OAR}) - \text{Actual Variable Overhead Cost}$$ $$\text{Variable Overhead Expenditure Variance} = (\text{Standard Variable OAR} - \text{Actual Variable OAR}) \times AH_{\text{worked}}$$

C. Variable Overhead Efficiency Variance

The Efficiency Variance measures the variable overhead cost caused by worker productivity deviations. If workers are inefficient and take longer to produce goods, the factory consumes extra power, lighting, and lubricants:

$$\text{Variable Overhead Efficiency Variance} = (\mathbf{\text{Standard Hours for Actual Output}} - \mathbf{\text{Actual Hours Worked}}) \times \mathbf{\text{Standard Variable OAR}}$$ $$\text{Variable Overhead Efficiency Variance} = (SH - AH_{\text{worked}}) \times \text{Standard Variable OAR}$$

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3. Fixed Production Overhead Variances (Absorption Costing)

Fixed production overheads (e.g., factory rent, business property taxes, plant depreciation, supervisor salaries) do not fluctuate with short-term changes in production output. However, under standard absorption costing, fixed overheads are absorbed into product units via a predetermined fixed overhead absorption rate (FOAR). This accounting mechanism creates two distinct variance dimensions: spending against budget and output volume absorption.

A. Fixed Overhead Total Variance (Under/Over Absorption)

The total variance represents the total under- or over-absorption of fixed production overhead for the period:

$$\text{Fixed Overhead Total Variance} = \text{Absorbed Fixed Overhead} - \text{Actual Fixed Overhead}$$ $$\text{Absorbed Fixed Overhead} = \text{Actual Units Produced} \times \text{Standard Fixed OAR per Unit}$$ $$\text{Absorbed Fixed Overhead} = \text{Standard Hours for Actual Output} (SH) \times \text{Standard Fixed OAR per Hour}$$

• If $\text{Absorbed} > \text{Actual} \implies \mathbf{\text{Favourable (F)}} \quad \text{(Over-absorption)}$
• If $\text{Absorbed} < \text{Actual} \implies \mathbf{\text{Adverse (A)}} \quad \text{(Under-absorption)}$

B. The Two-Way Split: Expenditure and Volume Variances

                      Fixed Overhead Total Variance
                     ┌──────────────┴──────────────┐
                     ▼                             ▼
       Fixed Overhead Expenditure      Fixed Overhead Volume
     (Budgeted vs. Actual Spending)   (Absorbed Output vs. Budget)

1. Fixed Overhead Expenditure Variance

The Expenditure Variance measures the absolute difference between the original budgeted fixed overhead and the actual fixed overhead incurred:

$$\mathbf{\text{Fixed Overhead Expenditure Variance}} = \mathbf{\text{Budgeted Fixed Overhead}} - \mathbf{\text{Actual Fixed Overhead}}$$

• If $\text{Actual Spending} < \text{Budgeted} \implies \mathbf{\text{Favourable (F)}}$
• If $\text{Actual Spending} > \text{Budgeted} \implies \mathbf{\text{Adverse (A)}}$

2. Fixed Overhead Volume Variance

The Volume Variance measures the overhead absorbed by producing more or fewer units than originally budgeted:

$$\text{Fixed Overhead Volume Variance} = (\text{Actual Output Units} - \text{Budgeted Output Units}) \times \mathbf{\text{Standard Fixed OAR per Unit}}$$ $$\text{Fixed Overhead Volume Variance} = (\text{Standard Hours for Actual Output} - \text{Budgeted Hours}) \times \mathbf{\text{Standard Fixed OAR per Hour}}$$

• If $\text{Actual Output} > \text{Budgeted Output} \implies \mathbf{\text{Favourable (F)}}$
• If $\text{Actual Output} < \text{Budgeted Output} \implies \mathbf{\text{Adverse (A)}}$

C. The Advanced Three-Way / Four-Way Split: Capacity and Efficiency

To pinpoint why actual volume differed from budget, the Fixed Overhead Volume Variance is subdivided into Capacity and Efficiency:

$$\mathbf{\text{Fixed Overhead Volume Variance}} = \mathbf{\text{Capacity Variance}} + \mathbf{\text{Efficiency Variance}}$$

1. Fixed Overhead Capacity Variance:

Measures whether the factory worked more or fewer hours than budgeted (plant utilization):

$$\text{Fixed Overhead Capacity Variance} = (\mathbf{\text{Actual Hours Worked}} - \mathbf{\text{Budgeted Hours}}) \times \mathbf{\text{Standard Fixed OAR per Hour}}$$

• If $\text{Actual Hours Worked} > \text{Budgeted Hours} \implies \mathbf{\text{Favourable (F)}}$
• If $\text{Actual Hours Worked} < \text{Budgeted Hours} \implies \mathbf{\text{Adverse (A)}}$

2. Fixed Overhead Efficiency Variance:

Measures whether the workforce transformed active hours worked into output at faster or slower rates than standard:

$$\text{Fixed Overhead Efficiency Variance} = (\mathbf{\text{Standard Hours for Actual Output}} - \mathbf{\text{Actual Hours Worked}}) \times \mathbf{\text{Standard Fixed OAR per Hour}}$$

• If $SH > AH_{\text{worked}} \implies \mathbf{\text{Favourable (F)}}$
• If $SH < AH_{\text{worked}} \implies \mathbf{\text{Adverse (A)}}$

Fixed Overhead under Marginal Costing

Under Standard Marginal Costing, fixed overheads are not absorbed into products or inventory. Therefore, there is NO volume variance, NO capacity variance, and NO efficiency variance. The only fixed overhead variance recognized under marginal costing is the Fixed Overhead Expenditure Variance.

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4. Comprehensive Integrated Numerical Example: Labour and Overhead Variances

Scenario: Sterling Industrial Equipment Ltd manufactures a heavy-duty hydraulic pump, Pump Titan. The standard cost profile and monthly operating budget for June are established as follows:

Budgeted Standards:

• Budgeted monthly production and sales: 1,000 pumps
• Direct Labour Standard: 5.0 direct labour hours per pump at a standard rate of $20.00 per hour ($100.00 per pump).
• Budgeted Direct Labour Hours: $1,000 \text{ pumps} \times 5.0 \text{ hours} = \mathbf{5,000 \text{ hours}}$
• Variable Production Overhead: Absorbed at $8.00 per direct labour hour ($40.00 per pump).
• Budgeted Variable Overhead: $5,000 \text{ hours} \times \text{\textdollar}8.00 = \mathbf{\text{\textdollar}40,000}$
• Budgeted Fixed Production Overhead: $60,000 per month
• Standard Fixed Overhead Absorption Rate (FOAR): $\text{FOAR per Hour} = \frac{\$60,000}{5,000 \text{ hours}} = \mathbf{\$12.00 \text{ per direct labour hour}}$ $\text{FOAR per Unit} = 5.0 \text{ hours} \times \$12.00 = \mathbf{\$60.00 \text{ per pump}}$

Actual Results for June:

• Actual Production Output: 1,100 pumps
• Direct Labour Hours Paid: 5,600 hours at a total gross cost of $117,600 (Actual Rate = $\frac{\text{\textdollar}117,600}{5,600} = \text{\textdollar}21.00$ per hour).
• Direct Labour Hours Worked: 5,350 hours
• Unproductive Idle Time: 250 hours (caused by a regional electrical grid outage).
• Actual Variable Production Overhead: $45,475
• Actual Fixed Production Overhead: $63,500

Step 1: Calculate Direct Labour Variances

1. Standard Hours for Actual Output:

   $$\mathbf{SH} = 1,100 \text{ pumps} \times 5.0 \text{ hours} = \mathbf{5,500 \text{ hours}}$$

2. Direct Labour Rate Variance:

   $$\text{Rate Variance} = (\text{Standard Rate} - \text{Actual Rate}) \times \text{Actual Hours Paid}$$ $$\text{Rate Variance} = (\$20.00 - \$21.00) \times 5,600 \text{ hours} = -\$1.00 \times 5,600 = -\$5,600 \implies \mathbf{\$5,600 \text{ Adverse (A)}}$$

3. Idle Time Variance:

   $$\text{Idle Time Variance} = -(\text{Idle Hours}) \times \text{Standard Rate}$$ $$\text{Idle Time Variance} = -(5,600 \text{ paid} - 5,350 \text{ worked}) \times \$20.00 = -250 \text{ hours} \times \$20.00 = -\$5,000 \implies \mathbf{\$5,000 \text{ Adverse (A)}}$$

4. Direct Labour Efficiency Variance:

   $$\text{Efficiency Variance} = (SH - AH_{\text{worked}}) \times \text{Standard Rate}$$ $$\text{Efficiency Variance} = (5,500 \text{ hours} - 5,350 \text{ hours}) \times \$20.00 = +150 \text{ hours} \times \$20.00 = +\$3,000 \implies \mathbf{\$3,000 \text{ Favourable (F)}}$$

5. Direct Labour Total Variance Check:

   $$\text{Standard Cost of Actual Output} (5,500 \text{ hours} \times \$20.00) = \$110,000$$ $$\text{Actual Labour Cost Incurred} = \$117,600$$ $$\text{Total Labour Variance} = \$110,000 - \$117,600 = -\$7,600 \implies \mathbf{\$7,600 \text{ Adverse (A)}}$$ $$\text{Reconciliation:} \quad -\$5,600 \text{ (Rate A)} - \$5,000 \text{ (Idle A)} + \$3,000 \text{ (Effic F)} = \mathbf{-\$7,600 \text{ (Total A)}}$$

Step 2: Calculate Variable Overhead Variances

1. Standard Variable Overhead for Actual Output:

   $$5,500 \text{ standard hours} \times \$8.00 = \mathbf{\$44,000}$$

2. Variable Overhead Expenditure Variance:

   $$\text{Expenditure Variance} = (AH_{\text{worked}} \times \text{Std Rate}) - \text{Actual Cost}$$ $$\text{Expenditure Variance} = (5,350 \text{ hours} \times \$8.00) - \$45,475 = \$42,800 - \$45,475 = -\$2,675 \implies \mathbf{\$2,675 \text{ Adverse (A)}}$$

3. Variable Overhead Efficiency Variance:

   $$\text{Efficiency Variance} = (SH - AH_{\text{worked}}) \times \text{Std Variable OAR}$$ $$\text{Efficiency Variance} = (5,500 \text{ hours} - 5,350 \text{ hours}) \times \$8.00 = +150 \text{ hours} \times \$8.00 = +\$1,200 \implies \mathbf{\$1,200 \text{ Favourable (F)}}$$

4. Variable Overhead Total Variance Check:

   $$\text{Total Variable Overhead Variance} = \$44,000 - \$45,475 = -\$1,475 \implies \mathbf{\$1,475 \text{ Adverse (A)}}$$ $$\text{Reconciliation:} \quad -\$2,675 \text{ (Expend A)} + \$1,200 \text{ (Effic F)} = \mathbf{-\$1,475 \text{ (Total A)}}$$

Step 3: Calculate Fixed Overhead Variances (Absorption Costing)

1. Fixed Overhead Absorbed:

   $$\text{Absorbed Overhead} = 1,100 \text{ actual units} \times \$60.00 \text{ per unit} = \mathbf{\$66,000}$$

   (Alternatively: $5,500 \text{ SH} \times \text{\textdollar}12.00 = \text{\textdollar}66,000$).

2. Fixed Overhead Total Variance (Net Over-Absorption):

   $$\text{Total Variance} = \text{Absorbed Fixed Overhead} - \text{Actual Fixed Overhead}$$ $$\text{Total Variance} = \$66,000 - \$63,500 = +\$2,500 \implies \mathbf{\$2,500 \text{ Favourable (F)}} \quad \text{(Over-absorbed)}$$

3. The Two-Way Decomposition:

   • Fixed Overhead Expenditure Variance: $$\text{Expenditure Variance} = \text{Budgeted Fixed Overhead} - \text{Actual Fixed Overhead}$$ $$\text{Expenditure Variance} = \$60,000 - \$63,500 = -\$3,500 \implies \mathbf{\$3,500 \text{ Adverse (A)}}$$
   • Fixed Overhead Volume Variance: $$\text{Volume Variance} = (\text{Actual Output} - \text{Budget Output}) \times \text{Fixed OAR per Unit}$$ $$\text{Volume Variance} = (1,100 \text{ units} - 1,000 \text{ units}) \times \$60.00 = +100 \text{ units} \times \$60.00 = +\$6,000 \implies \mathbf{\$6,000 \text{ Favourable (F)}}$$
   • Check 2-Way: $-\text{\textdollar}3,500 \text{ (Expend A)} + \text{\textdollar}6,000 \text{ (Volume F)} = \mathbf{+\text{\textdollar}2,500 \text{ Favourable (F)}}$.

4. The Sub-Division of Volume Variance (Capacity vs. Efficiency):

   • Fixed Overhead Capacity Variance: $$\text{Capacity Variance} = (AH_{\text{worked}} - \text{Budgeted Hours}) \times \text{Fixed OAR per Hour}$$ $$\text{Capacity Variance} = (5,350 \text{ hours} - 5,000 \text{ hours}) \times \$12.00 = +350 \text{ hours} \times \$12.00 = +\$4,200 \implies \mathbf{\$4,200 \text{ Favourable (F)}}$$
   • Fixed Overhead Efficiency Variance: $$\text{Efficiency Variance} = (SH - AH_{\text{worked}}) \times \text{Fixed OAR per Hour}$$ $$\text{Efficiency Variance} = (5,500 \text{ hours} - 5,350 \text{ hours}) \times \$12.00 = +150 \text{ hours} \times \$12.00 = +\$1,800 \implies \mathbf{\$1,800 \text{ Favourable (F)}}$$
   • Check Volume Split: $\text{\textdollar}4,200 \text{ (Capacity F)} + \text{\textdollar}1,800 \text{ (Efficiency F)} = \mathbf{+\text{\textdollar}6,000 \text{ (Volume F)}}$.

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5. Master Summary Table of Basic Cost Variances