Problem 10 - Accounting

Question

The Freedom Clothes Company produced 18,000 units during June of the current year. The Cutting Department used 3,500 direct labor hours at an actual rate of \(12.10 per hour. The Sewing Department used 5,800 direct labor hours at an actual rate of \)11.80 per hour. Assume there were no work in process inventories in either department at the beginning or end of the month. The standard labor rate is $12.00. The standard labor time for the Cutting and Sewing departments is 0.20 hour and 0.30 hour per unit, respectively a. Determine the direct labor rate and time variance for the (1) Cutting Department and (2) Sewing Department. b. Interpret your results.

Step-by-Step Solution

Answer

Cutting: Rate variance = $350 U, Time variance = $1,200 F. Sewing: Rate variance = $1,160 F, Time variance = $4,800 U. Cutting demonstrated cost overages and labor efficiency; Sewing showed cost savings but inefficiency.

Step 1: Calculate Total Standard Hours for Cutting Department

The standard time for the Cutting Department is 0.20 hours per unit. With 18,000 units produced, the total standard hours is: \ \[ \text{Standard Hours (Cutting)} = 18,000 \times 0.20 = 3,600 \text{ hours} \]

Step 2: Calculate Total Standard Hours for Sewing Department

The standard time for the Sewing Department is 0.30 hours per unit. With 18,000 units produced, the total standard hours is: \ \[ \text{Standard Hours (Sewing)} = 18,000 \times 0.30 = 5,400 \text{ hours} \]

Step 3: Calculate Direct Labor Rate Variance for Cutting Department

The direct labor rate variance is calculated by comparing the actual labor cost to the expected (standard) labor cost. For the Cutting Department: \ \[ \text{Rate Variance (Cutting)} = (\text{Actual Rate} - \text{Standard Rate}) \times \text{Actual Hours} \ = (12.10 - 12.00) \times 3,500 = 0.10 \times 3,500 = 350 \text{ (unfavorable)} \]

Step 4: Calculate Direct Labor Rate Variance for Sewing Department

Similarly, for the Sewing Department: \ \[ \text{Rate Variance (Sewing)} = (\text{Actual Rate} - \text{Standard Rate}) \times \text{Actual Hours} \ = (11.80 - 12.00) \times 5,800 = -0.20 \times 5,800 = -1,160 \text{ (favorable)} \]

Step 5: Calculate Direct Labor Time Variance for Cutting Department

The time variance measures the efficiency of labor usage. For the Cutting Department: \ \[ \text{Time Variance (Cutting)} = (\text{Actual Hours} - \text{Standard Hours}) \times \text{Standard Rate} \ = (3,500 - 3,600) \times 12.00 = -100 \times 12.00 = -1,200 \text{ (favorable)} \]

Step 6: Calculate Direct Labor Time Variance for Sewing Department

For the Sewing Department, the calculation is: \ \[ \text{Time Variance (Sewing)} = (\text{Actual Hours} - \text{Standard Hours}) \times \text{Standard Rate} \ = (5,800 - 5,400) \times 12.00 = 400 \times 12.00 = 4,800 \text{ (unfavorable)} \]

Step 7: Interpret Results

The Cutting Department had an unfavorable rate variance, indicating higher labor costs than expected, but a favorable time variance, showing efficiency in labor usage. The Sewing Department had a favorable rate variance, indicating lower labor costs, but an unfavorable time variance, suggesting inefficiency in labor usage.

Key Concepts

Labor Rate Variance

Labor rate variance is a key concept in productivity and cost management. It helps identify whether the actual wages paid to workers differ from the standard hourly wages set by the organization. This variance is calculated to understand the financial impact of any deviation.
In the exercise, both the Cutting and Sewing Departments have different outcomes. For the Cutting Department, the actual hourly wage was $12.10 compared to the standard rate of $12.00, resulting in an unfavorable variance of $350. This means the department paid more in wages than expected. Conversely, the Sewing Department paid an actual rate of $11.80, resulting in a favorable variance of $1,160, meaning they spent less on labor costs than expected.

• Unfavorable rate variance: actual wages > standard rate → extra cost
• Favorable rate variance: actual wages < standard rate → cost saving

Understanding labor rate variance helps departments manage their labor costs effectively and encourages cost-saving measures where possible.

Labor Time Variance

Labor time variance is another critical component of variance analysis, focusing on the efficiency of labor utilization. It shows the difference between actual labor hours used and the expected standard hours.
In the case of the Cutting Department, the actual hours used were 3,500 compared to the standard hours of 3,600, leading to a favorable time variance of $1,200. This indicates efficient use of labor, as fewer hours were needed than planned. On the other hand, the Sewing Department used 5,800 hours compared to a standard of 5,400, resulting in an unfavorable time variance of $4,800.

• Favorable time variance: actual < standard hours → efficiency
• Unfavorable time variance: actual > standard hours → inefficiency

By analyzing labor time variance, companies can seek ways to improve workforce efficiency and productivity.

Standard Hours Calculation

Calculating standard hours involves determining the expected time needed to produce a certain number of units. This calculation sets benchmarks for labor efficiency and cost management.
In this exercise, the standard labor time for the Cutting Department is 0.20 hours per unit, and for the Sewing Department, it’s 0.30 hours per unit. To find the total standard hours, you multiply the standard time per unit by the total units produced, which is 18,000 in this case.

• Cutting Department: \[18,000 imes 0.20 = 3,600 \ ext{hours}\]
• Sewing Department: \[18,000 imes 0.30 = 5,400 \ ext{hours}\]

Understanding how to calculate standard hours is essential for setting realistic goals and managing labor efficiency.

Manufacturing Efficiency Analysis

Manufacturing efficiency analysis involves examining how well a manufacturing process uses resources, particularly labor. It combines rate and time variances to assess overall productivity.
In this exercise, the Cutting Department displayed both favorable time and an unfavorable rate variance. This means that while they had efficient labor usage, they incurred higher costs for the hours worked. The reverse was true for the Sewing Department, which had unfavorable time but favorable rate variance, indicating inefficiency in time usage but lower wage costs.
By balancing these variances, companies can aim to reduce unnecessary labor costs while maximizing productivity. Efficiency analysis is an ongoing process that helps highlight areas for improvement and strategies for cost optimization.