Problem 16 - Accounting

Question

The following data relate to factory overhead cost for the production of 5,000 computers: \(\begin{array}{llr}\text { Actual: } & \text { Variable factory overhead } & \$ 125,000 \\ & \text { Fixed factory overhead } & 34,000 \\ \text { Standard: } & 5,000 \text { hrs. at } \$ 30 & 150,000\end{array}\) If productive capacity of \(100 \%\) was 8,000 hours and the factory overhead cost budgeted at the level of 5,000 standard hours was \(\$ 162,750\), determine the variable factory overhead controllable variance, fixed factory overhead volume variance, and total factory overhead cost variance. The fixed factory overhead rate was \(\$ 4.25\) per hour.

Step-by-Step Solution

Answer

The variable factory overhead controllable variance is -$25,000 (unfavorable), the fixed factory overhead volume variance is $12,750 (unfavorable), and the total factory overhead cost variance is -$3,750 (favorable).

Step 1: Calculate Variable Factory Overhead Controllable Variance

The Variable Factory Overhead Controllable Variance is calculated by subtracting the standard cost from the actual cost. The formula is: \[ \text{Variable Factory Overhead Controllable Variance} = \text{Actual Variable Factory Overhead} - \text{Standard Variable Factory Overhead} \] Using the provided data:\[ = \\(125,000 - \\)150,000 = -\$25,000 \] This is unfavorable because the actual cost is less than the standard.

Step 2: Calculate Fixed Factory Overhead Volume Variance

The Fixed Factory Overhead Volume Variance compares the budgeted fixed overhead based on standard hours used versus the actual hours worked. The formula is: \[ \text{Fixed Factory Overhead Volume Variance} = (\text{Standard Hours} - \text{Actual Hours}) \times \text{Fixed Factory Overhead Rate} \] Given that the fixed overhead is planned at 8,000 hours capacity and only 5,000 hours were used (productive capacity of 100%:\[ = (8,000 - 5,000) \times 4.25 = 3,000 \times 4.25 = \$12,750 \] This is unfavorable because the hours used are significantly less than budgeted.

Step 3: Calculate Total Factory Overhead Cost Variance

The Total Factory Overhead Cost Variance is the overall difference between actual factory overhead and the budgeted factory overhead at the level of standard hours. The formula is: \[ \text{Total Factory Overhead Cost Variance} = \text{Actual Total Overhead} - \text{Budgeted Overhead} \]Calculate Actual Total Overhead:\[ \text{Actual Total Overhead} = \\(125,000 + \\)34,000 = \\(159,000 \]Budgeted Overhead at Standard Hours is given as:\[ = \\)162,750 \]The Total Variance is:\[ = \\(159,000 - \\)162,750 = -\$3,750 \]This is favorable because actual costs are less than budgeted.

Key Concepts

Variable Factory Overhead Controllable Variance

When analyzing factory overhead, it's essential to understand the concept of "Variable Factory Overhead Controllable Variance." This variance helps manufacturing businesses evaluate how well they are managing variable costs which usually vary with production levels, such as indirect materials and utility costs. The controllable variance is the difference between the actual variable overhead costs incurred and the standard variable overhead costs expected based on a certain level of output. Essentially, this variance tells us how effectively the management controlled the variable overhead costs during production. For example, using the given data:

• Actual Variable Overhead: $125,000
• Standard Variable Overhead: $150,000
• Variable Factory Overhead Controllable Variance = Actual - Standard = $125,000 - $150,000 = -$25,000

This -$25,000 variance is unfavorable, indicating that the actual overhead was less than the standard. Although at first glance this appears beneficial, it could suggest issues like under-utilization of resources or inefficiencies that need addressing. Understanding this metric allows businesses to control costs better and streamline operations, leading to improved profitability.

Fixed Factory Overhead Volume Variance

The "Fixed Factory Overhead Volume Variance" is crucial when evaluating factory overhead, especially fixed overheads that remain constant regardless of production volumes, such as salaries of permanent staff or lease payments. This variance specifically examines the impact of production levels on fixed costs.It quantifies the difference in overhead costs caused by the volume of production, calculated using the formula:\[ \text{Fixed Factory Overhead Volume Variance} = (\text{Standard Hours} - \text{Actual Hours}) \times \text{Fixed Factory Overhead Rate} \]In our scenario:

• Standard Hours: 8,000 (planned operating capacity)
• Actual Hours: 5,000
• Fixed Overhead Rate: \(4.25 per hour
• Variance: (8,000 - 5,000) \times 4.25 = \)12,750

This $12,750 unfavorable variance implies that the plant did not operate at full capacity, leading to inefficiencies and higher per-unit costs. Addressing these inefficiencies can help improve resource utilization and profitability.

Total Factory Overhead Cost Variance

The "Total Factory Overhead Cost Variance" serves as a comprehensive summary of both variable and fixed overhead variances, providing a snapshot of overall cost control efficiency in manufacturing.By comparing actual overhead costs to the budgeted costs, businesses gain insight into how closely they adhere to planned spending, helping pinpoint resource management successes or issues.To calculate this:\[ \text{Total Factory Overhead Cost Variance} = \text{Actual Total Overhead} - \text{Budgeted Overhead} \]From our data:

• Actual Total Overhead (Variable + Fixed): \(125,000 + \)34,000 = \(159,000
• Budgeted Overhead: \)162,750
• Total Variance: \(159,000 - \)162,750 = -\(3,750

This is a favorable variance, signifying that the company spent \)3,750 less than the budgeted overhead. While spending less is generally positive, it's crucial to ensure that quality and operational efficiency were maintained, as reductions in spending should not compromise these areas.Regular analysis of these variances helps businesses optimize cost management, reinforce their financial health, and achieve their strategic goals.