7.4 Variable and Fixed Overhead Variances

In standard costing systems, overhead costs present unique accounting challenges because they represent indirect expenditures that cannot be traced directly to individual output units. To control overhead costs and evaluate operational performance, management accountants decompose overhead variances into distinct components that isolate spending deviations from volume and productivity effects.

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1. Variable Production Overhead Variances

Variable production overheads are indirect manufacturing costs that fluctuate in direct proportion to activity levels—such as machine lubricants, indirect production supplies, and variable factory power. In traditional standard absorption and marginal costing systems, variable overheads are absorbed into production using an hourly activity base, most commonly direct labour hours (DLH) or machine hours (MH).

Because variable overhead is assumed to be incurred per hour worked, the total variable overhead variance is subdivided into two distinct sub-variances:

1. Variable Overhead Expenditure Variance: Evaluates whether the business paid more or less per hour than the standard variable overhead rate.
2. Variable Overhead Efficiency Variance: Evaluates whether the workforce took more or fewer hours than standard to produce the actual output.

Variable Overhead Expenditure Variance

The Variable Overhead Expenditure Variance measures the difference between what the actual hours worked should have cost at the standard variable overhead rate and the actual variable overhead expenditure incurred.

$$\text{Variable Overhead Expenditure Variance} = (\text{Actual Hours Worked} \times \text{Standard Variable Overhead Rate per Hour}) - \text{Actual Variable Overhead Incurred}$$

Alternatively expressed:

$$\text{Variable Overhead Expenditure Variance} = (\text{Standard Variable Overhead Rate} - \text{Actual Variable Overhead Rate}) \times \text{Actual Hours Worked}$$

• Favourable ($F$): Actual variable overhead cost incurred is less than the standard allowance for the actual hours worked.
• Adverse ($A$): Actual variable overhead cost incurred exceeds the standard allowance for the actual hours worked.

Variable Overhead Efficiency Variance

The Variable Overhead Efficiency Variance measures the financial effect of utilizing more or fewer direct labour (or machine) hours than standard to manufacture the actual production volume.

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

• Favourable ($F$): The workforce worked fewer hours than the standard allowance for actual production, thereby consuming fewer variable overhead resources.
• Adverse ($A$): The workforce worked more hours than standard, causing excess variable overhead consumption.

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2. Fixed Production Overhead Variances Under Absorption Costing

Under standard absorption costing, fixed production overheads are treated as product costs and absorbed into inventory units using a predetermined Standard Fixed Overhead Absorption Rate (FOAR):

$$\text{FOAR per Unit} = \frac{\text{Budgeted Fixed Production Overhead}}{\text{Budgeted Output Units}}$$ $$\text{FOAR per Hour} = \frac{\text{Budgeted Fixed Production Overhead}}{\text{Budgeted Direct Labour Hours}}$$

Because fixed overheads are unitized under absorption costing, any divergence between actual fixed costs, budgeted fixed costs, or actual production volumes results in an over- or under-absorption of overhead. The Total Fixed Overhead Variance is exactly equal to the total under- or over-absorbed fixed overhead for the accounting period:

$$\text{Total Fixed Overhead Variance} = \text{Absorbed Fixed Overhead} - \text{Actual Fixed Overhead Incurred}$$

Where:

$$\text{Absorbed Fixed Overhead} = \text{Actual Units Produced} \times \text{FOAR per Unit} = \text{Standard Hours for Actual Output} \times \text{FOAR per Hour}$$

Under absorption costing, this total variance is divided into two primary branches:

1. Fixed Overhead Expenditure Variance
2. Fixed Overhead Volume Variance

Fixed Overhead Expenditure Variance

The expenditure variance measures whether actual fixed spending deviated from budgeted fixed spending. By definition, true fixed costs should not change with production volume within the relevant range; therefore, actual spending is compared directly against the original budget:

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

• Favourable ($F$): Actual fixed overhead spend is less than budgeted fixed overhead spend.
• Adverse ($A$): Actual fixed overhead spend exceeds budgeted fixed overhead spend (e.g., unexpected factory rent increases or higher plant insurance premiums).

Fixed Overhead Volume Variance

The volume variance measures the over- or under-absorption of fixed overhead caused solely by the fact that actual output units differed from budgeted output units:

$$\text{Fixed Overhead Volume Variance} = (\text{Actual Output Units} - \text{Budgeted Output Units}) \times \text{Standard FOAR per Unit}$$

Alternatively expressed in standard hours:

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

• Favourable ($F$): Actual production exceeded budgeted production. More fixed overhead was absorbed into inventory than originally budgeted.
• Adverse ($A$): Actual production was less than budgeted production. The plant failed to absorb its budgeted fixed overhead, resulting in under-absorption.

Subdividing Fixed Overhead Volume Variance: Capacity vs. Efficiency

To provide deeper operational insight, standard absorption costing subdivides the Fixed Overhead Volume Variance into two underlying drivers:

1. Fixed Overhead Capacity Variance: Did the factory operate for more or fewer hours than budgeted?
2. Fixed Overhead Efficiency Variance: Did the workforce convert those operating hours into finished output efficiently?

Fixed Overhead Capacity Variance

The capacity variance measures whether the factory facility had more or less operational working hours available than originally budgeted:

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

• Favourable ($F$): The factory worked more hours than budgeted (e.g., overtime shifts, weekend operations).
• Adverse ($A$): The factory worked fewer hours than budgeted (e.g., machine breakdowns, employee strikes, material shortages, or reduced shifts).

Fixed Overhead Efficiency Variance

The fixed overhead efficiency variance measures the productivity of direct labour during the hours worked, evaluated at the fixed overhead hourly rate:

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

• Favourable ($F$): The workforce completed actual production in fewer hours than standard allowance.
• Adverse ($A$): The workforce took longer than standard allowance to complete actual production.

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3. Fixed Overhead Variances Under Marginal Costing

A critical concept for CIMA BA2 candidates is the contrast between absorption and marginal costing in treating fixed production overheads:

• Under marginal costing, fixed overheads are not unitized and are never absorbed into product cost.
• Fixed overhead is treated strictly as a period cost written off in full against contribution in the period incurred.
• Because fixed costs are not absorbed on a per-unit or per-hour basis, no volume variance, capacity variance, or efficiency variance exists under marginal costing.
• The only fixed overhead variance under marginal costing is the Fixed Overhead Expenditure Variance (Budgeted Fixed Overhead minus Actual Fixed Overhead).

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4. Comprehensive Worked Numerical Master Example

Vanguard Manufacturing Ltd establishes the following standard data for Month 1:

Budgeted Standards

• Budgeted production: 10,000 units
• Standard direct labour hours per unit: 2 direct labour hours
• Total budgeted hours: $10,000 \times 2 = 20,000 \text{ DLH}$
• Budgeted variable production overhead: $80,000
  • Standard variable overhead rate per hour: $\frac{\text{\textdollar}80,000}{20,000} = \text{\textdollar}4.00 \text{ per DLH}$
  • Standard variable overhead rate per unit: $2 \times \text{\textdollar}4.00 = \text{\textdollar}8.00 \text{ per unit}$
• Budgeted fixed production overhead: $60,000
  • Standard fixed overhead absorption rate (FOAR) per hour: $\frac{\text{\textdollar}60,000}{20,000} = \text{\textdollar}3.00 \text{ per DLH}$
  • Standard FOAR per unit: $2 \times \text{\textdollar}3.00 = \text{\textdollar}6.00 \text{ per unit}$

Actual Operational Results for Month 1

• Actual units produced: 9,000 units
• Actual direct labour hours worked: 19,000 DLH
• Actual variable overhead incurred: $77,900
• Actual fixed overhead incurred: $62,500

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Step 1: Calculate Standard Hours Produced

$$\text{Standard Hours for Actual Output} = 9,000 \text{ units} \times 2 \text{ hours} = 18,000 \text{ standard DLH}$$

Step 2: Variable Overhead Variances

1. Variable Overhead Expenditure Variance:

$$\text{Actual Hours Worked} \times \text{Standard VOH Rate} = 19,000 \times \text{\textdollar}4.00 = \text{\textdollar}76,000$$ $$\text{Expenditure Variance} = \text{\textdollar}76,000 - \text{\textdollar}77,900 = -\text{\textdollar}1,900 = \text{\textdollar}1,900 \text{ Adverse } (A)$$

1. Variable Overhead Efficiency Variance:

$$\text{Efficiency Variance} = (18,000 \text{ std hrs} - 19,000 \text{ actual hrs}) \times \text{\textdollar}4.00 = -1,000 \times \text{\textdollar}4.00 = -\text{\textdollar}4,000 = \text{\textdollar}4,000 \text{ Adverse } (A)$$

1. Total Variable Overhead Variance:

$$\text{Standard VOH for Actual Output} = 9,000 \times \text{\textdollar}8.00 = \text{\textdollar}72,000$$ $$\text{Total Variance} = \text{\textdollar}72,000 - \text{\textdollar}77,900 = -\text{\textdollar}5,900 = \text{\textdollar}5,900 \text{ Adverse } (A)$$

• Check: $\text{\textdollar}1,900\text{ (A)} + \text{\textdollar}4,000\text{ (A)} = \text{\textdollar}5,900\text{ (A)}$.

Step 3: Fixed Overhead Variances Under Absorption Costing

1. Fixed Overhead Expenditure Variance:

$$\text{Expenditure Variance} = \text{Budgeted FOH} - \text{Actual FOH} = \text{\textdollar}60,000 - \text{\textdollar}62,500 = -\text{\textdollar}2,500 = \text{\textdollar}2,500 \text{ Adverse } (A)$$

1. Fixed Overhead Volume Variance:

$$\text{Volume Variance} = (9,000 \text{ actual units} - 10,000 \text{ budget units}) \times \text{\textdollar}6.00 = -1,000 \times \text{\textdollar}6.00 = -\text{\textdollar}6,000 = \text{\textdollar}6,000 \text{ Adverse } (A)$$

1. Subdividing the Volume Variance:
   • Capacity Variance:

$$\text{Capacity Variance} = (19,000 \text{ actual hrs} - 20,000 \text{ budget hrs}) \times \text{\textdollar}3.00 = -1,000 \times \text{\textdollar}3.00 = -\text{\textdollar}3,000 = \text{\textdollar}3,000 \text{ Adverse } (A)$$

• Efficiency Variance:

$$\text{Efficiency Variance} = (18,000 \text{ std hrs} - 19,000 \text{ actual hrs}) \times \text{\textdollar}3.00 = -1,000 \times \text{\textdollar}3.00 = -\text{\textdollar}3,000 = \text{\textdollar}3,000 \text{ Adverse } (A)$$

• Reconciliation Check: $\text{\textdollar}3,000\text{ (A)} + \text{\textdollar}3,000\text{ (A)} = \text{\textdollar}6,000\text{ (A)} \text{ Volume Variance}$.

1. Total Fixed Overhead Variance (Under/Over-Absorption):

$$\text{Absorbed Fixed OH} = 9,000 \text{ units} \times \text{\textdollar}6.00 = \text{\textdollar}54,000$$ $$\text{Total Variance} = \text{Absorbed} - \text{Actual} = \text{\textdollar}54,000 - \text{\textdollar}62,500 = -\text{\textdollar}8,500 = \text{\textdollar}8,500 \text{ Under-absorbed } (A)$$

• Check: Expenditure $\text{\textdollar}2,500\text{ (A)} + \text{Volume } \text{\textdollar}6,000\text{ (A)} = \text{\textdollar}8,500\text{ (A)}$.