Chapter 23, Problem 4BP

1

To determine

Compute the direct materials cost variance, including its price and quantity variance.

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:

  $\begin{array}{c}\text{Direct materials price variance}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Actual}\text{Price}-\\ \text{Standard Price}\end{array}\right)\\ \times \text{Actual Quantity}\end{array}\right]\\ =\left[\begin{array}{l}\left(\text{\$4}\text{.25 lb}-\$4.00\text{ lb}\right)\\ \times \text{1,000,000 lbs}\end{array}\right]\\ =\left[\$.25\text{ lb}\times \text{1,000,000 lbs}\right]\\ =\$250,000\text{ U}\end{array}$

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:

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

Compute the direct materials quantity variance:

  $\begin{array}{c}\text{Direct materials quantity variance}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Actual}\text{Quantity}-\\ \text{Standard Quantity}\end{array}\right)\\ \times \text{Standard Price}\end{array}\right]\\ =\left[\begin{array}{l}\left(\begin{array}{l}\text{1,000,000 lbs}-\\ \text{1,050,000 lbs}\end{array}\right)\\ \times \text{\$4}\text{.00 lb}\end{array}\right]\\ =\left[\text{50,000 lbs}\times \text{\$4}\text{.00 lb}\right]\\ =\$200,000\text{F}\end{array}$

Direct materials cost variance is a measure that determines the difference between the estimated cost of the direct material and the actual cost of the direct material purchased.

Calculate the total direct materials cost variance:

$\begin{array}{c}\text{Total direct materials cost variance}\text{=}\left[\begin{array}{l}\text{Direct materials price variance}\left(\text{unfavorable}\right)\\ -\text{Direct materials quantity variance}\left(\text{favorable}\right)\end{array}\right]\\ \text{=}\left[\$250,000-\$200,000\right]\\ \text{=\$50,000 U}\end{array}$

Alternative calculation:

Calculate the total direct materials cost variance:

$\begin{array}{c}\text{Total direct materials cost variance}\text{=}\left[\begin{array}{l}\left(\text{Actual units}\times \text{Actual cost}\right)-\\ \left(\text{Standard units}\times \text{Standard cost}\right)\end{array}\right]\\ \text{=}\left[\begin{array}{l}\left(1,000,000\times \text{\$4}\text{.25}\right)-\\ \left(1,050,000\times \text{\$4}\text{.00}\right)\end{array}\right]\\ =\left[\$4,250,000-\$4,200,000\right]\\ \text{=\$50,000 U}\end{array}$

Conclusion

Hence, the total direct materials cost variance is $50,000 (unfavorable).

2.

To determine

Compute the direct labor cost variance, including its rate variances and efficiency variances.

Explanation of Solution

Direct Labor Rate Variance

The direct labor rate variance is a measure to determine the variation in the estimated cost of the direct labor and the actual cost of the direct labor.

Compute the direct labor rate variance:

$\begin{array}{c}\text{Direct labor rate variance = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Actual direct labor hours used}\\ \times \text{Actual direct labor rate per hour}\end{array}\right)-\\ \left(\begin{array}{l}\text{Actual direct labor hours used}\\ \times \text{Standard direct labor rate per hour}\end{array}\right)\end{array}\right]\\ \text{= }\left[\begin{array}{l}\left(\text{250,000 hours}\times \text{\$7}\text{.75 per hour}\right)-\\ \left(\text{250,000 hours}\times \text{\$8}\text{.00 per hour}\right)\end{array}\right]\\ =\left[\$1,937,500-\$2,000,000\right]\\ =\$62,500\left(\text{favorable}\right)\end{array}$

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:

$\begin{array}{c}\text{Direct labor efficiency variance = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Actual direct labor hours used}\\ \times \text{Standard direct labor rate per hour}\end{array}\right)-\\ \left(\begin{array}{l}\text{Standard direct labor hours used}\\ \times \text{Standard direct labor rate per hour}\end{array}\right)\end{array}\right]\\ \text{= }\left[\begin{array}{l}\left(\text{250,000 hours}\times \text{\$8 per hour}\right)-\\ \left(\text{252,000 hours}\times \text{\$8 per hour}\right)\end{array}\right]\\ =\left[\$2,000,000-\$2,016,000\right]\\ =\$16,000\left(\text{favorable}\right)\end{array}$

Direct labor cost variance is a measure that determines the difference between the estimated cost of the direct labor and the actual cost of the direct labor.

Calculate the total direct labor cost variance:

$\begin{array}{c}\text{Total direct labor cost variance}\text{=}\left[\begin{array}{l}\text{Direct labor rate variance}\left(\text{favorable}\right)\\ \text{+Direct labor efficiency variance}\left(\text{favorable}\right)\end{array}\right]\\ \text{=}\left[\$62,500+\$16,000\right]\\ \text{=\$78,500 F}\end{array}$

Alternative calculation:

Calculate the total direct labor cost variance:

$\begin{array}{c}\text{Total direct labor cost variance}\text{=}\left[\begin{array}{l}\left(\text{Actual hours}\times \text{Actual cost}\right)-\\ \left(\text{Standard hours}\times \text{Standard cost}\right)\end{array}\right]\\ \text{=}\left[\begin{array}{l}\left(250,000\times \text{\$7}\text{.75}\right)-\\ \left(252,000\times \text{\$8}\text{.00}\right)\end{array}\right]\\ =\left[\$1,937,500-\$2,016,000\right]\\ \text{=\$78,500 F}\end{array}$

Conclusion

Hence, the total direct labor cost variance is $78,500 (favorable).

3.

To determine

Compute the overhead controllable variance and volume variance.

Explanation of Solution

Overhead Controllable Variance: Overhead controllable variance is determined by subtracting budgeted overhead to be incurred in standard hours from actual overhead incurred in the standard hours

Compute the overhead controllable variance:

Particulars	Amount ($)
Actual overhead	3,160,000
Less: Budget overhead	(3,276,000)
Overhead controllable variance	$116,000 F

Table (1)

Working notes:

Calculate the amount of actual overhead.

$\begin{array}{c}\text{Actual overhead =}\left(\begin{array}{l}\text{Fixed factory overhead costs }\\ \text{+ Variable factory overhead costs}\end{array}\right)\\ \text{= }\left(\$1,960,000+\$1,200,000\right)\\ =\$3,160,000\end{array}$

Calculate the amount of budgeted overhead.

$\begin{array}{c}\text{Budgeted overhead =}\left(\begin{array}{l}\text{Fixed factory overhead @70\%}\\ \text{+ Variable factory overhead @70\%}\end{array}\right)\\ \text{= }\left(\$2,016,000+\$1,260,000\right)\\ =\$3,276,000\end{array}$

Overhead Volume Variance: Overhead volume variance is determined by multiplying the difference of normal capacity and standard hours with the fixed overhead rate.

Compute the overhead volume variance:

Particulars	Amount ($)
Budgeted fixed overhead cost	2,016,000
Less: Total Fixed overhead applied	1,764,000
Fixed volume overhead variance	$252,000 U

Table (2)

Working notes:

Calculate the amount of fixed overhead applied.

$\begin{array}{c}\text{Fixed overhead applied =}\left(\begin{array}{l}\text{ Factory overhead hours}\times \\ \text{Factory overhead rate per hour}\end{array}\right)\\ =\left(252,000\text{ hours}\times \text{\$7}\right)\\ =\$1,764,000\end{array}$

Conclusion

Hence, the overhead controllable variance is $116,000 F and overhead volume variance is $252,000 U.