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Direct Labor Rate Variance - Cost Accounting

  1. A company reported a direct labor rate variance of $6,160 Favorable for a period. During this period, employees worked 8,800 actual hours. The standard direct labor rate is $18.00 per hour, and the standard hours allowed for the actual output were 8,700 hours. What was the actual wage rate per hour paid to the employees?
    Answer: $17.30 The formula for the direct labor rate variance is (Actual Rate - Standard Rate) × Actual Hours. We can rearrange the formula to solve for the Actual Rate (AR). A favorable variance is treated as a negative value in the formula. Rate Variance=(AR−SR)×AH \text{Rate Variance} = (\text{AR} - \text{SR}) \times \text{AH} −$6,160=(AR−$18.00)×8,800 -\$6,160 = (\text{AR} - \$18.00) \times 8,800 −$6,1608,800=AR−$18.00 \frac{-\$6,160}{8,800} = \text{AR} - \$18.00 −$0.70=AR−$18.00 -\$0.70 = \text{AR} - \$18.00 AR=$18.00−$0.70=$17.30 \text{AR} = \$18.00 - \$0.70 = \$17.30 The information about standard hours (8,700) is irrelevant to this calculation.
  2. A company's standard cost for direct labor includes a base wage of $20.00 per hour plus an allowance for payroll taxes and fringe benefits equal to 25% of the base wage. During the last period, the company incurred a total actual direct labor cost of $104,000 for 4,000 actual hours of work. What is the direct labor rate variance?
    Answer: $4,000 Unfavorable This is a multi-step calculation. First, determine the full standard rate per hour. Standard Rate (SR)=$20.00×(1+0.25)=$25.00 \text{Standard Rate (SR)} = \$20.00 \times (1 + 0.25) = \$25.00 Second, calculate the actual rate per hour. Actual Rate (AR)=Total Actual CostActual Hours=$104,0004,000=$26.00 \text{Actual Rate (AR)} = \frac{\text{Total Actual Cost}}{\text{Actual Hours}} = \frac{\$104,000}{4,000} = \$26.00 Finally, calculate the rate variance. Rate Variance=(AR−SR)×AH=($26.00−$25.00)×4,000=$4,000 Unfavorable \text{Rate Variance} = (\text{AR} - \text{SR}) \times \text{AH} = (\$26.00 - \$25.00) \times 4,000 = \$4,000 \text{ Unfavorable}
  3. A manufacturing company's records for the month show a total direct labor variance of $7,000 unfavorable. The company's standard cost card specifies a rate of $22.00 per direct labor hour. During the month, employees worked 5,200 hours to produce the actual output, for which the standard is 5,000 hours. What was the company's direct labor rate variance for the month?
    Answer: $2,600 Unfavorable The total direct labor variance is the sum of the rate variance and the efficiency variance. The first step is to compute the labor efficiency variance. Efficiency Variance=(Actual Hours−Standard Hours)×Standard Rate \text{Efficiency Variance} = (\text{Actual Hours} - \text{Standard Hours}) \times \text{Standard Rate} Efficiency Variance=(5,200−5,000)×$22.00=200×$22.00=$4,400 Unfavorable \text{Efficiency Variance} = (5,200 - 5,000) \times \$22.00 = 200 \times \$22.00 = \$4,400 \text{ Unfavorable} The second step is to isolate the rate variance. Total Variance=Rate Variance+Efficiency Variance \text{Total Variance} = \text{Rate Variance} + \text{Efficiency Variance} $7,000 U=Rate Variance+$4,400 U \$7,000 \text{ U} = \text{Rate Variance} + \$4,400 \text{ U} Rate Variance=$7,000 U−$4,400 U=$2,600 Unfavorable \text{Rate Variance} = \$7,000 \text{ U} - \$4,400 \text{ U} = \$2,600 \text{ Unfavorable}
  4. A company has a direct labor rate variance that is 5% of the total actual direct labor cost. If the total actual direct labor cost for the period was $210,000 and the variance was unfavorable, what is the value of the direct labor rate variance?
    Answer: $10,000 Unfavorable This question tests the algebraic relationship between actual cost, standard cost, and the variance. Let AC be actual cost and SC_AH be standard cost at actual hours. The rate variance (RV) is AC - SC_AH. The problem states the variance was an unfavorable 5%. This is typically interpreted as the actual rate being 5% over the standard rate, or that the variance is 5% of the standard cost base. Let's use the latter, as it's a common way to express materiality. RV=0.05×SCAH \text{RV} = 0.05 \times \text{SC}_{AH} We also know RV=AC−SCAH \text{RV} = \text{AC} - \text{SC}_{AH} . Substituting this into the first equation: AC−SCAH=0.05×SCAH \text{AC} - \text{SC}_{AH} = 0.05 \times \text{SC}_{AH} AC=1.05×SCAH \text{AC} = 1.05 \times \text{SC}_{AH} We are given AC = $210,000. $210,000=1.05×SCAH \$210,000 = 1.05 \times \text{SC}_{AH} SCAH=$210,0001.05=$200,000 \text{SC}_{AH} = \frac{\$210,000}{1.05} = \$200,000 Now we can find the variance: RV=AC−SCAH=$210,000−$200,000=$10,000 Unfavorable \text{RV} = \text{AC} - \text{SC}_{AH} = \$210,000 - \$200,000 = \$10,000 \text{ Unfavorable}
  5. A company's standards allow for 2.5 direct labor hours per unit at a rate of $16.00 per hour. During a period, 1,000 units were produced. The direct labor efficiency variance was $800 Favorable, and the total actual direct labor payroll was $41,650. What was the direct labor rate variance?
    Answer: $2,450 Unfavorable This problem requires first finding the actual hours (AH) worked. Standard Hours (SH)=1,000 units×2.5 hours/unit=2,500 hours \text{Standard Hours (SH)} = 1,000 \text{ units} \times 2.5 \text{ hours/unit} = 2,500 \text{ hours} Use the efficiency variance formula to find AH. Efficiency Variance=(AH−SH)×SR \text{Efficiency Variance} = (\text{AH} - \text{SH}) \times \text{SR} −$800=(AH−2,500)×$16.00 -\$800 = (\text{AH} - 2,500) \times \$16.00 −$50=AH−2,500  ⟹  AH=2,450 hours -\$50 = \text{AH} - 2,500 \implies \text{AH} = 2,450 \text{ hours} Now, calculate the actual rate (AR). AR=Actual PayrollAH=$41,6502,450=$17.00/hour \text{AR} = \frac{\text{Actual Payroll}}{\text{AH}} = \frac{\$41,650}{2,450} = \$17.00/\text{hour} Finally, calculate the rate variance. Rate Variance=(AR−SR)×AH=($17.00−$16.00)×2,450=$2,450 Unfavorable \text{Rate Variance} = (\text{AR} - \text{SR}) \times \text{AH} = (\$17.00 - \$16.00) \times 2,450 = \$2,450 \text{ Unfavorable}
  6. The direct labor rate variance for a company was $4,000 Unfavorable. The company's employees worked 8,000 actual hours at an average actual wage rate of $22.50 per hour. What is the standard direct labor rate per hour?
    Answer: $22.00 The formula for the direct labor rate variance is (Actual Rate - Standard Rate) × Actual Hours. We can rearrange the formula to solve for the Standard Rate (SR). An unfavorable variance is treated as a positive value. Rate Variance=(AR−SR)×AH \text{Rate Variance} = (\text{AR} - \text{SR}) \times \text{AH} $4,000=($22.50−SR)×8,000 \$4,000 = (\$22.50 - \text{SR}) \times 8,000 $4,0008,000=$22.50−SR \frac{\$4,000}{8,000} = \$22.50 - \text{SR} $0.50=$22.50−SR \$0.50 = \$22.50 - \text{SR} SR=$22.50−$0.50=$22.00 \text{SR} = \$22.50 - \$0.50 = \$22.00
  7. At the end of its fiscal year, a company calculated a $10,000 Favorable direct labor rate variance based on 50,000 actual hours worked. Before closing the books, management finalized a new union contract that included a retroactive pay increase of $0.50 per hour for all hours worked during the year. What is the final direct labor rate variance for the year after accounting for this retroactive pay?
    Answer: $15,000 Unfavorable The original $10,000 Favorable variance means the actual rate paid was lower than the standard rate. The retroactive pay increases the total actual labor cost. The total cost of the retroactive pay is 50,000 hours×$0.50/hour=$25,00050,000 \text{ hours} \times \$0.50/\text{hour} = \$25,000. This represents an unfavorable change to the variance. The final variance is the combination of the original variance and the effect of the retroactive pay. Final Variance=Original Variance+Retroactive Pay Effect \text{Final Variance} = \text{Original Variance} + \text{Retroactive Pay Effect} =$10,000 Favorable+$25,000 Unfavorable = \$10,000 \text{ Favorable} + \$25,000 \text{ Unfavorable} =−$10,000+$25,000=$15,000 Unfavorable = -\$10,000 + \$25,000 = \$15,000 \text{ Unfavorable}
  8. A company budgeted direct labor cost based on a rate of $20.00 per hour for 10,000 hours. The standard cost card, which is used for variance analysis, specifies a rate of $21.00 per hour. The company actually used 9,500 hours at a total cost of $204,250. What is the direct labor rate variance?
    Answer: $4,750 Unfavorable Variance analysis compares actual results to standard costs, not to the static budget. The budgeted rate of $20.00 and budgeted hours of 10,000 are irrelevant information. First, calculate the actual rate (AR). AR=Total Actual CostActual Hours=$204,2509,500=$21.50/hour \text{AR} = \frac{\text{Total Actual Cost}}{\text{Actual Hours}} = \frac{\$204,250}{9,500} = \$21.50/\text{hour} Next, use the standard rate (SR) of $21.00 from the standard cost card to calculate the rate variance. Rate Variance=(AR−SR)×AH=($21.50−$21.00)×9,500=$0.50×9,500=$4,750 Unfavorable \text{Rate Variance} = (\text{AR} - \text{SR}) \times \text{AH} = (\$21.50 - \$21.00) \times 9,500 = \$0.50 \times 9,500 = \$4,750 \text{ Unfavorable}
  9. A company's standards for a product require 4 direct labor hours per unit at a standard rate of $25 per hour. In May, the company produced 1,200 units. The actual labor cost was $117,600 for 4,900 hours of work. What is the direct labor rate variance?
    Answer: $4,900 Favorable To calculate the rate variance, you need the actual rate, standard rate, and actual hours. The information about units produced and standard hours per unit is needed for the efficiency variance but not the rate variance. First, find the actual rate (AR). AR=Total Actual CostActual Hours=$117,6004,900=$24/hour \text{AR} = \frac{\text{Total Actual Cost}}{\text{Actual Hours}} = \frac{\$117,600}{4,900} = \$24/\text{hour} Now, calculate the rate variance. Rate Variance=(AR−SR)×AH=($24−$25)×4,900=−$1×4,900=−$4,900 or $4,900 Favorable \text{Rate Variance} = (\text{AR} - \text{SR}) \times \text{AH} = (\$24 - \$25) \times 4,900 = -\$1 \times 4,900 = -\$4,900 \text{ or } \$4,900 \text{ Favorable}
  10. For the month of July, a company had a total actual direct labor cost of $86,100 for 4,200 hours worked. The direct labor efficiency variance was $5,000 Unfavorable. The standard direct labor rate is $20 per hour. What was the direct labor rate variance for July?
    Answer: $2,100 Unfavorable The rate variance can be calculated directly without using the efficiency variance information, which is a distractor in this case. First, calculate the actual labor rate per hour (AR). AR=Total Actual CostActual Hours=$86,1004,200=$20.50/hour \text{AR} = \frac{\text{Total Actual Cost}}{\text{Actual Hours}} = \frac{\$86,100}{4,200} = \$20.50/\text{hour} Next, use the rate variance formula with the given standard rate (SR) of $20. Rate Variance=(AR−SR)×AH=($20.50−$20.00)×4,200=$0.50×4,200=$2,100 Unfavorable \text{Rate Variance} = (\text{AR} - \text{SR}) \times \text{AH} = (\$20.50 - \$20.00) \times 4,200 = \$0.50 \times 4,200 = \$2,100 \text{ Unfavorable}
  11. A company's controller reported that the total actual direct labor cost for the month was 10% greater than the standard labor cost for the actual hours worked. The company's employees worked 4,000 hours, and the standard rate is $25.00 per hour. What was the direct labor rate variance?
    Answer: $10,000 Unfavorable The direct labor rate variance is the difference between actual labor cost (AR × AH) and the standard labor cost for actual hours worked (SR × AH). First, calculate the standard labor cost for actual hours worked. Standard Cost at Actual Hours=SR×AH=$25.00×4,000=$100,000 \text{Standard Cost at Actual Hours} = \text{SR} \times \text{AH} = \$25.00 \times 4,000 = \$100,000 The problem states that the actual cost was 10% greater than this amount. Actual Cost=$100,000×1.10=$110,000 \text{Actual Cost} = \$100,000 \times 1.10 = \$110,000 The rate variance is the difference between these two values. Rate Variance=Actual Cost−Standard Cost at Actual Hours=$110,000−$100,000=$10,000 Unfavorable \text{Rate Variance} = \text{Actual Cost} - \text{Standard Cost at Actual Hours} = \$110,000 - \$100,000 = \$10,000 \text{ Unfavorable}
  12. A production department has a team of 10 workers who each worked 160 hours during October. The company's standard labor rate is $31.00 per hour. For the month, 8 of the workers earned $4,800 each, and the remaining 2 workers earned $5,920 each. What is the department's direct labor rate variance for October?
    Answer: $640 Unfavorable First, calculate the total actual hours and total actual labor cost. Total Actual Hours=10 workers×160 hours/worker=1,600 hours \text{Total Actual Hours} = 10 \text{ workers} \times 160 \text{ hours/worker} = 1,600 \text{ hours} Total Actual Cost=(8×$4,800)+(2×$5,920)=$38,400+$11,840=$50,240 \text{Total Actual Cost} = (8 \times \$4,800) + (2 \times \$5,920) = \$38,400 + \$11,840 = \$50,240 Second, calculate the weighted-average actual rate. Actual Rate (AR)=$50,2401,600 hours=$31.40/hour \text{Actual Rate (AR)} = \frac{\$50,240}{1,600 \text{ hours}} = \$31.40/\text{hour} Finally, calculate the rate variance. Rate Variance=(AR−SR)×AH=($31.40−$31.00)×1,600=$0.40×1,600=$640 Unfavorable \text{Rate Variance} = (\text{AR} - \text{SR}) \times \text{AH} = (\$31.40 - \$31.00) \times 1,600 = \$0.40 \times 1,600 = \$640 \text{ Unfavorable} Alternatively, calculate the variance for each group and sum them: Group 1 Rate=$4,800/160=$30.00 \text{Group 1 Rate} = \$4,800/160 = \$30.00 Group 2 Rate=$5,920/160=$37.00 \text{Group 2 Rate} = \$5,920/160 = \$37.00 Variance 1=($30−$31)×(8×160)=−$1×1,280=$1,280 F \text{Variance 1} = (\$30-\$31) \times (8 \times 160) = -\$1 \times 1,280 = \$1,280 \text{ F} Variance 2=($37−$31)×(2×160)=$6×320=$1,920 U \text{Variance 2} = (\$37-\$31) \times (2 \times 160) = \$6 \times 320 = \$1,920 \text{ U} Total Variance=$1,920 U+$1,280 F=$640 Unfavorable \text{Total Variance} = \$1,920 \text{ U} + \$1,280 \text{ F} = \$640 \text{ Unfavorable}
  13. Sunset Corporation's direct labor standards are $24.80 per hour. During the month, three different labor categories were used: Category A worked 2,400 hours at $23.60 per hour, Category B worked 1,800 hours at $25.40 per hour, and Category C worked 950 hours at $26.20 per hour. All categories perform the same type of work and are interchangeable according to the production standards. What is the total direct labor rate variance?
    Answer: $530 unfavorable Calculate the variance for each category separately: Category A: ($23.60 - $24.80) × 2,400 = -$1.20 × 2,400 = $2,880 favorable. Category B: ($25.40 - $24.80) × 1,800 = $0.60 × 1,800 = $1,080 unfavorable. Category C: ($26.20 - $24.80) × 950 = $1.40 × 950 = $1,330 unfavorable. Total variance = $2,880 favorable - $1,080 unfavorable - $1,330 unfavorable = $530 unfavorable.
  14. A firm's standard wage rate was revised from $20 to $22 per hour on June 1 due to a new labor law. The accounting department failed to update the standard in the costing system. For June, the system reported a direct labor rate variance of $7,500 Unfavorable based on 5,000 actual hours worked and an actual rate of $21.50 per hour. What is the correct direct labor rate variance for June?
    Answer: $2,500 Favorable The variance should be calculated using the correct, updated standard rate. The system used the old standard rate of $20, which is incorrect. The correct standard rate for June is $22 per hour. The actual rate was $21.50 per hour. Correct Rate Variance=(Actual Rate−Correct Standard Rate)×Actual Hours \text{Correct Rate Variance} = (\text{Actual Rate} - \text{Correct Standard Rate}) \times \text{Actual Hours} =($21.50−$22.00)×5,000 hours = (\$21.50 - \$22.00) \times 5,000 \text{ hours} =−$0.50×5,000=−$2,500 or $2,500 Favorable = -\$0.50 \times 5,000 = -\$2,500 \text{ or } \$2,500 \text{ Favorable} The variance reported by the system ($7,500 U) is based on the outdated standard and is not the correct variance.
  15. The management of a company received a report showing a $5,200 Unfavorable direct labor rate variance and a $5,000 Favorable direct labor efficiency variance. Which of the following scenarios is the most likely single cause for this specific combination of variances?
    Answer: The production manager used higher-skilled, higher-paid workers to operate the machinery. This combination of variances—an unfavorable rate variance and a favorable efficiency variance—is often caused by a trade-off. Using higher-skilled workers than specified in the standard would lead to paying a higher actual wage rate (unfavorable rate variance) but would likely result in completing the work in less time than the standard (favorable efficiency variance). Option A only explains the rate variance. Options B and D would likely cause an unfavorable efficiency variance, which contradicts the data.
  16. A company introduced a new product, and for the initial production run, it utilized 1,000 hours of labor from trainees. The standard cost for this product was based on using experienced workers at a rate of $30 per hour. The trainees were paid $20 per hour. Due to their inexperience, a significant unfavorable labor efficiency variance was recorded. What was the direct labor rate variance for this initial production run?
    Answer: $10,000 Favorable The direct labor rate variance isolates the effect of the wage rate paid. The information about the efficiency variance is a distractor. We compare the actual rate paid to the standard rate for the actual hours worked. Actual Rate (AR)=$20/hour \text{Actual Rate (AR)} = \$20/\text{hour} Standard Rate (SR)=$30/hour \text{Standard Rate (SR)} = \$30/\text{hour} Actual Hours (AH)=1,000 hours \text{Actual Hours (AH)} = 1,000 \text{ hours} Rate Variance=(AR−SR)×AH=($20−$30)×1,000=−$10×1,000=−$10,000 or $10,000 Favorable \text{Rate Variance} = (\text{AR} - \text{SR}) \times \text{AH} = (\$20 - \$30) \times 1,000 = -\$10 \times 1,000 = -\$10,000 \text{ or } \$10,000 \text{ Favorable}
  17. A company's standard direct labor rate is $30 per hour. During March, 2,100 actual direct labor hours were worked. This included 100 hours of overtime, which were paid at time-and-a-half of the employees' base wage rate of $32 per hour. Company policy treats the overtime premium portion of labor cost as part of manufacturing overhead. What is the direct labor rate variance for March?
    Answer: $4,200 Unfavorable The direct labor rate variance formula is (Actual Rate - Standard Rate) × Actual Hours. First, determine the total direct labor cost to be used in the variance calculation. Since the overtime premium is treated as overhead, it must be excluded. Total Labor Cost for Variance Calc.=Actual Hours×Base Wage Rate \text{Total Labor Cost for Variance Calc.} = \text{Actual Hours} \times \text{Base Wage Rate} =2,100 hours×$32/hour=$67,200 = 2,100 \text{ hours} \times \$32/\text{hour} = \$67,200 The actual rate (AR) for the variance calculation is the base rate of $32. Rate Variance=($32.00−$30.00)×2,100 hours=$2.00×2,100=$4,200 Unfavorable \text{Rate Variance} = (\$32.00 - \$30.00) \times 2,100 \text{ hours} = \$2.00 \times 2,100 = \$4,200 \text{ Unfavorable}
  18. A company that uses a standard costing system reported a significant favorable direct labor rate variance for the quarter. Which of the following is the most likely explanation for this variance?
    Answer: The production manager staffed several production lines with newly hired, less-skilled workers, paying them below the standard rate. A favorable direct labor rate variance occurs when the actual wage rate paid is less than the standard wage rate. Hiring less-skilled workers at a lower pay scale than the standard, which is typically based on a blended rate of experienced workers, would result in a lower actual rate and thus a favorable variance. The other options would all lead to an unfavorable rate variance, as the actual rate would be higher than the standard rate.

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