Chapter 21, Problem 4PSB

1.

To determine

The direct materials cost variance, price variance and quantity variance.

Explanation of Solution

Given,

The actual material used is 1,000,000 lbs.
The standard quantity of materials for actual production is 1,050,000 lbs.
The actual price is $4.25 per lb.
The standard price is $4.00 per lb.

Calculation of direct material cost variance:

Particulars	Amount ($)
Actual units at actual cost $\left(1,000,000\times \$4.25\right)$	4,250,000
Standard units at standard cost $\left(1,050,000\times \$4.00\right)$	4,200,000
Direct material cost variance	50,000 (unfavorable)

Table(1)

The direct material cost variance is $50,000 (unfavorable).

Calculation of direct material price variance:

The formula to calculate the direct material price variance is,

   $\begin{array}{c}\text{Direct}\text{material}\text{price}\text{variance}=\text{Actual}\text{quantity}\\ \times \left(\text{Actual}\text{price}-\text{Standard}\text{price}\right)\end{array}$

Substitute 1,000,000 lb. for the actual quantity, $4.25 for the actual price and $4 for the standard price in the above formula.

   $\begin{array}{c}\text{Direct}\text{material}\text{price}\text{variance}=1,000,000\text{lb}\times \left(\$4.25-\$4.00\right)\text{per}\text{lb}\\ =1,000\text{,000}\text{lb}\times \left(\$0.25\right)\text{per}\text{lb}\\ =\text{\$250,000}\text{U}\end{array}$

The direct material price variance is $250,000 (unfavorable).

Calculation of direct material quantity variance:

The formula to calculate the direct material quantity variance is,

   $\begin{array}{c}\text{Direct}\text{material}\text{quantity}\text{variance}=\left(\text{Actual}\text{quantity}-\text{Standard}\text{quantity}\right)\\ \times \text{Standard}\text{price}\end{array}$

Substitute 1,000,000 lb for the actual quantity, 1,050,000 lb for standard quantity and $4.00 for standard price in the above formula.

   $\begin{array}{c}\text{Direct}\text{material}\text{quantity}\text{variance}=\left(1,050,000-1,000,000\right)\text{lb}\times \$4\text{per}\text{lb}\\ \text{=50,000}\text{lb}\times \text{\$4}\text{.00}\text{per}\text{lb}\\ \text{=\$200,000}\text{U}\end{array}$

The direct material quantity variance is $200,000 (unfavorable).

Hence, the direct material cost variance, price variance and quantity variance is $50,000 (unfavorable), $250,000 (unfavorable) and $200,000 (unfavorable).

2.

To determine

The direct labor cost, rate and efficiency variances.

Explanation of Solution

Given,
The actual hours used is 250,000 hours.
The standard hours for actual production are 252,000 hours.
The actual rate is $7.75 per hour.
The standard rate is $8.00 per hour.

Calculation of direct labor cost variance:

Particulars	Amount ($)
Actual hours at actual cost $\left(250,000\text{hours}\times \$7.75\right)$	1,937,500
Standard hours at standard cost $\left(252,000\times \$8.00\right)$	2,016,000
Direct labor cost variance	78,500 (favorable)

Table(2)

The direct labor cost variance is $78,500 (favorable).

Calculation of direct labor rate variance:

The formula to calculate the direct labor rate variance is,

   $\begin{array}{c}\text{Direct}\text{labor}\text{rate}\text{variance}=\text{Actual}\text{hours}\\ \times \left(\text{Actual}\text{rate}-\text{Standard}\text{rate}\right)\end{array}$

Substitute 250,000 hours for the actual hours, $7.75 for the actual rate and $8 for the standard rate in the above formula.

   $\begin{array}{c}\text{Direct}\text{labor}\text{rate}\text{variance}=250,000\text{hours}\times \left(\$7.75-\$8.00\right)\text{per}\text{lb}\\ =250\text{,000}\text{hours}\times \left(\$0.25\right)\text{per}\text{lb}\\ =\text{\$62,500}\text{F}\end{array}$

The direct labor rate variance is $62,500 (favorable).

Calculation of direct labor efficiency variance:

The formula to calculate the direct labor efficiency variance is,

   $\begin{array}{c}\text{Direct}\text{labor}\text{efficiency}\text{variance}=\left(\text{Actual}\text{hours}-\text{Standard}\text{hours}\right)\\ \times \text{Standard}\text{rate}\end{array}$

Substitute 250,000 for the actual hours, 252,000 for standard hours and $8.00 for standard rate in the above formula.

   $\begin{array}{c}\text{Direct}\text{labor}\text{efficiency}\text{variance}=\left(250,000-252,000\right)\text{hours}\times \$8\text{per}\text{hour}\\ =\left(2,000\right)\text{hours}\times \text{\$8}\text{.00}\text{per}\text{hour}\\ =\text{\$16,000}\text{F}\end{array}$

The direct labor efficiency variance is $16,000 (favorable).

Hence, the direct labor cost variance, rate variance and efficiency variance is $78,500 (favorable), $62,500 (favorable) and $16,000 (favorable).

3.

To determine

The overhead controllable and volume variances.

Explanation of Solution

Calculation of the overhead controllable variance:

Particulars	Amount ($)
Actual overhead incurred ($1,960,000+$1,200,000)	3,160,000
Budgeted overhead (from flexible budget)	3,276,000
Controllable overhead variance	116,000 (favorable)

Table(3)

The overhead controllable variance is $116,000 (favorable).

Calculation of the fixed overhead volume variance:

Particulars	Amount ($)
Budgeted fixed overhead(at 80% capacity)	2,016,000
Fixed overhead $\left(252,000\text{hours}\times \text{\$7}\right)$	1,764,000
Fixed overhead volume variance	252,000 (unfavorable)

Table(4)

The fixed overhead volume variance is $252,000 (unfavorable).

Thus, the overhead controllable variance is $116,000 (favorable) and the fixed overhead volume variance is $252,000 (unfavorable).