Chapter 23, Problem 11E

(1)

To determine

Compute the direct materials price variance and quantity variance and indicate whether it is favorable or unfavorable.

Explanation of Solution

Direct material price variance:

The variation in between actual price and estimated price paid for materials is called material price variance. It is used to determine difference in price paid for material the price that was supposed to be paid for material.

The following formula is used to calculate direct material price variance:

  $\text{Direct materials price variance}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Actual}\text{Price}-\\ \text{Standard Price}\end{array}\right)\\ \times \text{Actual Quantity}\end{array}\right]$

Compute the direct materials price variance and indicate whether it is favorable or unfavorable:

Step 1: Calculate the actual cost of direct materials used.

$\begin{array}{c}\text{Actual cost of direct materials used}=\left(\begin{array}{l}\text{Actual quantity used}\\ \times \text{Actual price}\end{array}\right)\\ =138,000\text{ lbs}\times \$3.75\text{ per lb}\\ =\$517,500\end{array}$

Step 2: Calculate the standard cost of materials used.

$\begin{array}{c}\text{Standard cost of materials used}=\left(\begin{array}{l}\text{Actual quantity used}\\ \times \text{Standard price}\end{array}\right)\\ =\left(\text{138,000}\times \$4\text{ per lb}\right)\\ =\$552,000\end{array}$

Step 3: Calculate the direct materials price variance.

$\begin{array}{c}\text{Direct materials price variance}=\left[\begin{array}{l}\text{Actual cost of direct materials used}\\ -\text{Standard cost of materials used}\end{array}\right]\\ =\$517,500-\$552,000\\ =\$34,500\left(\text{favorable}\right)\end{array}$

Direct material quantity variance:

The variance which is used to compare the actual quantity of materials utilized in production with estimated quantity of materials that is supposed to be used in production and helps to find variation is called material quantity variance.

The following formula is used to calculate direct material quantity variance:

  $\text{Direct materials quantity variance}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Actual}\text{Quantity}-\\ \text{Standard Quantity}\end{array}\right)\\ \times \text{Actual Price}\end{array}\right]$

Compute the direct materials quantity variance and indicate whether it is favorable or unfavorable:

Step 1: Calculate the actual quantity of materials used.

$\begin{array}{c}\text{Actual quantity of materials used}=\left(\begin{array}{l}\text{Actual quantity used }\\ \times \text{Standard price}\end{array}\right)\\ =\left(\text{138,000}\times \$4\text{ per lb}\right)\\ =\$552,000\end{array}$

Step 2: Calculate the standard quantity of materials used.

$\begin{array}{c}\text{Standard quantity of materials used}=\left(\begin{array}{l}\text{Standard quantity }\\ \times \text{Standard price}\end{array}\right)\\ =\left(\text{135,000}\times \$4\text{ per lb}\right)\\ =\$540,000\end{array}$

Working note:

Calculate the standard quantity:

$\begin{array}{c}\text{Standard quantity = }\left(\begin{array}{l}\text{Number of units to produce}\times \\ \text{Price per unit}\end{array}\right)\\ \text{= 9,000 units}\times \text{15 pounds per unit}\\ \text{=\$135,000}\end{array}$

Step 3: Calculate the direct materials quantity variance.

$\begin{array}{c}\text{Direct materials quantity variance}=\left[\begin{array}{l}\text{Actual quantity of direct materials used}\\ -\text{Standard quantity of materials used}\end{array}\right]\\ =\$552,000-\$540,000\\ =\$12,000\left(\text{unfavorable}\right)\end{array}$

Conclusion

Hence, the direct materials price variance is $34,500 (favorable) and direct materials quantity variance is $12,000 (unfavorable).

(2)

To determine

Calculate the direct labor rate variances and efficiency variances and indicate whether it is favorable or unfavorable.

Explanation of Solution

Total Direct Labor Variance

The total direct labor variance is a measure to determine the variation in the standard direct labor and the actual direct labor. This means that the difference between the cost which will be by the standard and the cost which is actually calculated.

Direct Labor Price Variance

The direct labor price variance is a measure that determines the variation in the estimated cost of the direct labor and the actual labor quantity used.

Compute the direct labor rate variances indicate whether it is favorable or unfavorable:

$\begin{array}{c}\text{Direct labor rate variance = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Actual direct labor hours used}\\ \times \text{Actual direct labor rate per hour}\end{array}\right)-\\ \left(\begin{array}{l}\text{Actual direct labor hours used}\\ \times \text{Standard direct laborrate per hour}\end{array}\right)\end{array}\right]\\ \text{= }\left[\begin{array}{l}\left(\text{31,000 hours}\times \text{\$15}\text{.10 per hour}\right)-\\ \left(\text{31,000 hours}\times \text{\$15}\text{.00 per hour}\right)\end{array}\right]\\ =\left[\$468,100-\$465,000\right]\\ =\$3,100\left(\text{unfavorable}\right)\end{array}$

Direct labor efficiency variance is a measure that determines the difference between the estimated labor quantity and the actual labor quantity used.

Compute the direct labor efficiency variance:

$\begin{array}{c}\text{Direct labor efficiency variance = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Actual direct labor hours used}\\ \times \text{Standard direct labor rate per hour}\end{array}\right)-\\ \left(\begin{array}{l}\text{Standard direct labor hours used}\\ \times \text{Standard direct labor rate per hour}\end{array}\right)\end{array}\right]\\ \text{= }\left[\begin{array}{l}\left(\text{31,000 hours}\times \text{\$15 per hour}\right)-\\ \left(\text{27,000 hours}\times \text{\$15 per hour}\right)\end{array}\right]\\ =\left[\$465,000-\$405,000\right]\\ =\$60,000\left(\text{unfavorable}\right)\end{array}$

Working note:

Calculate the standard direct labor hours used:

$\begin{array}{c}\text{Standard direct labor hours used = }\left(\begin{array}{l}\text{Number of units manufactured}\times \\ \text{Total direct labor hours used}\end{array}\right)\\ \text{= 9,000 units}\times 3\text{ hours per unit}\\ \text{=\$27,000}\end{array}$

Conclusion

Hence, the direct labor rate variance is $3,100 (unfavorable) and the direct labor efficiency variance is $60,000 (unfavorable).