A. Because the actual and budgeted hours were the same, there was no direct labor efficiency variance. The formula is: (AQ - SQ) × SP or (Actual Hours - Standard Hours for Actual Output) × Standard Rate. We know that the company maintained the direct labor standard of 45 minutes, or .75 of an hour per unit, throughout the month. The standard labor hour rate is $12 per hour, calculated as follows: 9,000 units planned × .75 of an hour per unit = total hours planned of 6,750. A total cost of $81,000 was planned, so therefore, the standard hourly rate must be $81,000 ÷ 6,750, or $12 per hour.
The Standard Hours for the Actual Output is .75 × 8,500, or 6,375 hours. Since we are told that the direct labor standard was maintained, the Actual Hours must be the same as the Standard Hours, or 6,375.
Putting the numbers into the formula, we get (6,375 - 6,375) × $12 = 0. However, it is not really necessary to go through all those calculations. Because the problem states that the direct labor standard was maintained throughout the period, we can know that the direct labor efficiency variance must be zero.
B. This problem does not give enough information to enable calculation of a materials usage variance. The materials quantity, or usage, variance is the difference between the actual quantity of materials that were used for the actual output and the standard quantity of materials for the actual output, multiplied by the standard price per unit of direct materials. The problem does not give us either the standard quantity or the actual quantity of materials per unit of output. Nor does it give us the standard price per unit of direct materials. We are given only the standard price for the total direct materials per unit of finished product. The standard price for direct materials per unit of finished product is not the same thing as the standard price per unit of direct materials.
Therefore, we have no way of telling whether the actual quantity used was different from the quantity planned for the output; and we have no way of telling whether the actual price per unit of direct materials was different from the planned price per unit. By dividing the actual material cost by the actual number of units produced and the planned materials costs by the planned number of units, we can determine that the actual direct materials cost was $15 per finished unit of product and the planned direct materials cost was also $15 per finished unit of product, so we know that the total direct materials variance (price and quantity) was zero. However, that could consist of any variances at all for price and quantity that would net to zero.
Since there is just not enough information given in this problem to permit a calculation of the materials usage variance (or the materials price variance, either), it cannot be said that the material usage variance was $7,500 favorable.
C. Because the budgeted and actual hours were the same, there was no direct labor efficiency variance. The formula is: (AQ - SQ) × SP or (Actual Hours - Standard Hours for Actual Output) × Standard Rate. We know that the company maintained the direct labor standard of 45 minutes, or .75 of an hour per unit, throughout the month. The standard labor hour rate is $12 per hour, calculated as follows: 9,000 units planned × .75 of an hour per unit = total hours planned of 6,750. A total cost of $81,000 was planned, so therefore, the standard hourly rate must be $81,000 ÷ 6,750, or $12 per hour.
The Standard Hours for the Actual Output is .75 × 8,500, or 6,375 hours. Since we are told that the direct labor standard was maintained, the Actual Hours must be the same as the Standard Hours, or 6,375.
Putting the numbers into the formula, we get (6,375 - 6,375) × $12 = 0. However, it is not really necessary to go through all those calculations. Because the problem states that the direct labor standard was maintained throughout the period, we can know that the direct labor efficiency variance must be zero.
D. The direct labor price variance is calculated (AP - SP) × AQ or (Actual Rate - Standard Rate) × Actual Hours. The standard labor rate per hour is $12, calculated as follows: the labor standard is 45 minutes per unit, or .75 of an hour. 9,000 units were planned, so total planned hours was .75 × 9,000 or 6,750 hours. Total planned cost was $81,000, so the standard cost per hour was $81,000 ÷ 6,750 hours, or $12 per hour.
The actual labor rate was $12.20, calculated as follows: The labor standard of 45 minutes per unit or .75 of an hour per unit was maintained. 8,500 units were actually produced, so the total actual hours was .75 × 8,500 or 6,375 hours. Total actual cost was $77,775, so the actual cost per hour (the actual rate) was $77,775 ÷ 6,375 hours, or $12.20 per hour.
Putting the numbers into the formula, we get ($12.20 - $12.00) × 6,375 = $1,275 Unfavorable.
