- For the month of May, a company reported a direct labor efficiency variance of $15,000 unfavorable. The standard direct labor rate is $25.00 per hour, and the standard is 0.5 direct labor hours per unit. If 4,000 actual direct labor hours were worked in May, how many units were actually produced?
Answer: 6,800 units
First, use the efficiency variance formula to solve for the total standard hours (SH) allowed. The formula is (Actual Hours - Standard Hours) × Standard Rate = Efficiency Variance. Plugging in the given values: (4,000 - SH) × $25.00 = $15,000. Solving for SH: 4,000 - SH = $15,000 / $25.00 = 600 hours. Therefore, SH = 4,000 - 600 = 3,400 hours. Second, use the standard hours per unit to find the number of units produced: Total Standard Hours / Standard Hours per Unit = 3,400 hours / 0.5 hours/unit = 6,800 units.
- A company's total direct labor variance was $5,000 favorable for a period. During this time, 8,000 actual hours were worked to produce output that had a standard of 8,500 hours. The standard direct labor rate is $25.00 per hour. What was the actual rate paid per hour?
Answer: $25.94
This requires a three-step calculation. First, find the labor efficiency variance: (AH - SH) × SR = (8,000 - 8,500) × $25.00 = -500 × $25.00 = -$12,500, or $12,500 F. Second, find the labor rate variance using the total variance formula: Total Var = Rate Var + Eff. Var. So, -$5,000 = Rate Var + (-$12,500). This gives Rate Var = $7,500, or $7,500 U. Third, use the rate variance to find the actual rate (AR): (AR - SR) × AH = $7,500. So, (AR - $25.00) × 8,000 = $7,500. AR - $25.00 = $0.9375. AR = $25.9375, or $25.94.
- A company has determined that its unfavorable labor rate variance of $10,000 is comprised of two effects: $7,000 due to a new union contract and $3,000 due to using a higher mix of senior-level employees. The standard rate was $25 per hour, and 5,000 actual hours were worked. What was the portion of the average actual wage rate attributable to the change in labor mix?
Answer: $0.60 per hour
The question asks for the per-hour effect of the labor mix change. The total variance due to the mix change is given as $3,000. To find the per-hour impact, this amount should be divided by the total actual hours worked. Per-hour effect = Variance from mix / Actual Hours = $3,000 / 5,000 hours = $0.60 per hour. The other information, such as the union contract effect and the standard rate, is provided to test the ability to isolate the relevant data.
- A company's direct labor efficiency variance for March was $12,000 favorable. The controller noted that this variance amount was exactly 10% of the total standard direct labor cost for the units produced in March. If the standard direct labor rate is $20 per hour, how many actual hours were worked?
Answer: 5,400 hours
This is a multi-step problem. First, find the total standard cost. Since the $12,000 favorable variance is 10% of the standard cost, the total standard cost is $12,000 / 0.10 = $120,000. Second, find the total standard hours (SH) allowed: Total Standard Cost / Standard Rate = $120,000 / $20/hr = 6,000 hours. Third, use the efficiency variance formula to find actual hours (AH): (AH - SH) × SR = Efficiency Variance. (AH - 6,000) × $20 = -$12,000. Divide by $20: AH - 6,000 = -600. Therefore, AH = 6,000 - 600 = 5,400 hours.
- A company produced 8,000 units during a period in which 14,750 actual direct labor hours were worked. The direct labor efficiency variance was $22,500 favorable, and the standard rate is $18.00 per hour. The production manager credited a new training program for the improved performance. What is the standard number of direct labor hours allowed per unit?
Answer: 2.0000 hours
First, solve for the total standard hours (SH) allowed for the actual output. The efficiency variance formula is (AH - SH) × SR = Eff. Var. A favorable variance is negative. So, (14,750 - SH) × $18.00 = -$22,500. Divide both sides by $18.00: 14,750 - SH = -1,250. Therefore, SH = 14,750 + 1,250 = 16,000 hours. Second, divide the total standard hours by the number of units produced to find the standard hours per unit: 16,000 hours / 8,000 units = 2.0 hours per unit.
- To improve product quality, a company replaced its workforce with higher-skilled technicians. The original labor standard was 4.0 hours per unit at $20.00 per hour. The new technicians are paid $23.00 per hour and have reduced the actual time to produce a unit to 3.5 hours. For a period in which 1,000 units were produced, what was the total direct labor variance?
Answer: $500 Unfavorable
This is a multi-step problem requiring calculation of total standard cost and total actual cost. First, calculate the total standard cost based on the original standard: 1,000 units × 4.0 hours/unit × $20.00/hour = $80,000. Next, calculate the total actual cost with the new technicians: 1,000 units × 3.5 hours/unit × $23.00/hour = $80,500. The total direct labor variance is the difference between actual cost and standard cost: $80,500 - $80,000 = $500 Unfavorable.
- A company incurred a total direct labor variance of $2,000 unfavorable. The standard is 2.0 hours per unit at $15.00 per hour. During the period, the company produced 1,000 units, and the actual wage rate paid was 10% higher than the standard rate. How many actual direct labor hours were worked?
Answer: 1,939 hours
This requires solving for actual hours (AH) using the total variance formula. First, determine the known values: Standard Hours (SH) = 1,000 units × 2.0 hrs/unit = 2,000 hrs. Standard Rate (SR) = $15.00/hr. Actual Rate (AR) = $15.00 × 1.10 = $16.50/hr. Total Variance = (AR × AH) - (SR × SH). Plugging in the values: $2,000 = ($16.50 × AH) - ($15.00 × 2,000). $2,000 = $16.50 × AH - $30,000. $32,000 = $16.50 × AH. Solving for AH: AH = $32,000 / $16.50 ≈ 1,939 hours.
- A company's direct labor rate variance was $9,750 unfavorable. The standard labor rate is $15.00 per hour, and investigation revealed that the actual rate paid was exactly 10% higher than this standard rate. Based on this information, what was the actual number of direct labor hours worked?
Answer: 6,500 hours
This problem requires two steps. First, calculate the actual rate (AR). The standard rate (SR) is $15.00, and the AR is 10% higher: AR = $15.00 × 1.10 = $16.50. Second, use the rate variance formula to solve for actual hours (AH): (AR - SR) × AH = Rate Variance. Plugging in the values: ($16.50 - $15.00) × AH = $9,750. This simplifies to $1.50 × AH = $9,750. Solving for AH: AH = $9,750 / $1.50 = 6,500 hours.
- For the period just ended, a company's total actual direct labor cost was $158,400. The total standard direct labor cost allowed for the units produced was $150,000. If the direct labor rate variance was $6,600 unfavorable, what was the direct labor efficiency variance?
Answer: $1,800 Unfavorable
First, calculate the total direct labor variance, which is the difference between total actual cost and total standard cost: $158,400 - $150,000 = $8,400 Unfavorable. The total variance is the sum of the rate and efficiency variances. We can set up the equation: Total Variance = Rate Variance + Efficiency Variance. $8,400 U = $6,600 U + Efficiency Variance. Solving for the efficiency variance: Efficiency Variance = $8,400 - $6,600 = $1,800 Unfavorable.
- A manufacturing company's controller reported a favorable direct labor rate variance of $11,250 and an unfavorable direct labor efficiency variance of $24,000 for the most recent period. The company incurred a total actual direct labor cost of $261,250 for 12,500 actual hours worked. What is the standard direct labor rate per hour?
Answer: $21.80
The solution requires working backwards from the direct labor rate variance. First, calculate the actual rate (AR) per hour: $261,250 / 12,500 hours = $20.90 per hour. The direct labor rate variance formula is (Actual Rate - Standard Rate) × Actual Hours. A favorable variance means the actual rate is less than the standard rate. The equation is ($20.90 - SR) × 12,500 = -$11,250. Solving for the standard rate (SR): $20.90 - SR = -$11,250 / 12,500 = -$0.90. Therefore, SR = $20.90 + $0.90 = $21.80.
- A company's standard cost card specifies 0.40 direct labor hours per unit at a rate of $22.00 per hour. During July, 20,000 units were produced. The direct labor payroll was $182,300 for 8,500 hours of work. What was the direct labor rate variance for July?
Answer: $4,700 Favorable
The rate variance calculation does not use standard hours or production volume. The rate variance formula is: (Actual Rate × Actual Hours) - (Standard Rate × Actual Hours) = Total Actual Payroll - (Standard Rate × Actual Hours) = $182,300 - ($22.00 × 8,500 hours) = $182,300 - $187,000 = -$4,700, which is $4,700 Favorable.
- A company has a standard of 3 direct labor hours per unit at $20 per hour. For the most recent period, the direct labor efficiency variance was $30,000 unfavorable. During this period, the direct labor rate variance was $12,500 favorable. If 5,000 units were produced, what was the total actual direct labor cost?
Answer: $317,500
First, find the standard hours (SH): 5,000 units × 3 hrs/unit = 15,000 hrs. Second, find the actual hours (AH) using the efficiency variance: (AH - SH) × SR = $30,000. (AH - 15,000) × $20 = $30,000. AH - 15,000 = 1,500. So, AH = 16,500 hours. Third, find the actual rate (AR) using the rate variance: (AR - SR) × AH = -$12,500. (AR - $20) × 16,500 = -$12,500. AR - $20 ≈ -$0.7576. AR ≈ $19.2424. Finally, calculate total actual cost: AR × AH = $19.2424 × 16,500 = $317,500. Alternatively, Total Variance = 30,000 U - 12,500 F = 17,500 U. Standard Cost = 15,000 hrs * $20 = $300,000. Actual Cost = Standard Cost + Total Variance = $300,000 + $17,500 = $317,500.
- A project's labor standard was 4,800 hours at a standard rate of $30 per hour. The project required 5,000 actual direct labor hours to complete, of which 800 hours were overtime paid at 150% of the regular rate. The company treats all labor costs, including overtime premiums, as direct labor. What is the direct labor rate variance for the project?
Answer: $12,000 Unfavorable
First, calculate the total actual labor cost. Regular pay: 4,200 hours × $30/hr = $126,000. Overtime pay: 800 hours × ($30/hr × 1.5) = 800 hours × $45/hr = $36,000. Total actual cost = $126,000 + $36,000 = $162,000. Second, calculate the average actual rate (AR): $162,000 / 5,000 total hours = $32.40/hr. Finally, calculate the rate variance: (AR - SR) × AH = ($32.40 - $30.00) × 5,000 hours = $2.40 × 5,000 = $12,000 Unfavorable.
- A company has a direct labor rate variance of $5,000 unfavorable and a direct labor efficiency variance of $4,000 favorable. Which of the following scenarios is the most likely explanation for this combination of variances?
Answer: The company hired highly skilled, more expensive workers who completed the work in less time than standard.
An unfavorable rate variance means the actual labor rate was higher than standard. A favorable efficiency variance means the actual hours worked were less than the standard hours allowed. The scenario in B (hiring highly skilled, more expensive workers who work faster) directly explains both of these outcomes: higher cost per hour (U rate variance) and less time required (F efficiency variance).
- At the start of the year, a standard of 2.5 labor hours per unit at $16 per hour was established. After one month, an engineering review concluded the time standard was too loose and should be 2.2 hours per unit. For performance evaluation in the second month, which variance should be reported if 1,000 units were made using 2,300 actual hours?
Answer: $1,600 Unfavorable Efficiency Variance
For performance evaluation, variances should be calculated against the most accurate and current standard. The revised standard of 2.2 hours per unit is the appropriate benchmark. First, calculate the standard hours (SH) allowed for actual production: 1,000 units × 2.2 hours/unit = 2,200 hours. Then, calculate the efficiency variance: (Actual Hours - Standard Hours) × Standard Rate = (2,300 - 2,200) × $16 = 100 × $16 = $1,600 Unfavorable.
- A company planned to produce 10,000 units, with a standard of 2 direct labor hours per unit at $18 per hour. Actual production was 11,000 units, and the company incurred a total direct labor cost of $418,000 for 23,000 actual hours. What is the direct labor efficiency variance?
Answer: $18,000 Unfavorable
The efficiency variance must be based on the standard hours allowed for actual production, not planned production. The planned production of 10,000 units is irrelevant information. First, calculate standard hours (SH) for actual output: 11,000 units × 2 hours/unit = 22,000 hours. Then, calculate the efficiency variance: (Actual Hours - Standard Hours) × Standard Rate = (23,000 - 22,000) × $18 = 1,000 × $18 = $18,000 Unfavorable.
- A company that uses a standard costing system had a favorable labor efficiency variance of $9,600. The standard labor rate was $24 per hour. The labor rate variance was $12,000 unfavorable, which was determined to be 20% of the actual labor payroll. What were the actual hours worked?
Answer: 2,000 hours
First, calculate the total actual payroll. Since the rate variance ($12,000 unfavorable) is 20% of the actual payroll: Actual Payroll = $12,000 ÷ 0.20 = $60,000. Second, use the rate variance formula: Rate Variance = Actual Payroll - (Standard Rate × Actual Hours). $12,000 = $60,000 - ($24 × AH). Solving: $24 × AH = $48,000. Therefore, AH = 2,000 hours.
