Chapter 9, Problem 1PA

Shasta Fixture Company manufactures faucets in a small manufacturing facility. The faucets are made from brass. Manufacturing has 70 employees. Each employee presently provides 38 hours of labor per week. Information about a production week is as follows:

Instructions

Determine (a) the standard cost per unit for direct materials and direct labor; (b) the direct materials price variance, direct materials quantity variance, and total direct materials cost variance; and (c) the direct labor rate variance, direct labor time variance, and total direct labor cost variance.

To determine

Compute the following:

1. a. The standard cost per unit for direct materials, and direct labor.
2. b. The direct materials price variance, the direct materials quantity variance, and the total direct materials cost variance, and
3. c. The direct labor rate variance, direct labor time variance, and total direct labor cost variance.

Explanation of Solution

Direct material variances:

The difference between the actual material cost per unit and the standard material cost per unit for the direct material purchased is known as direct material cost variance. The direct material variance can be classified as follows:

• v Direct materials price variance.
• v Direct materials quantity variance.

Direct labor variances:

The difference between the actual labor cost in the production and the standard labor cost for actual production is known as direct labor cost variance. The direct labor variance can be classified as follows:

• v Labor rate variance.
• v Labor time variance.

1. a. Compute the standard cost per unit for direct materials, and direct labor.

Particulars	Standard materials and labor cost per faucet
Direct materials (1)	$4.50
Direct labor (2)	$10.00
	$14.50

Table (1)

Therefore, the standard cost per unit for direct materials, and direct labor is $14.50.

Working note (1):

Compute the amount of direct materials:

$\begin{array}{c}\left(\begin{array}{l}\text{Standard direct }\\ \text{materials cost}\end{array}\right)=\text{Standard price per lb}\text{.}\times \text{Standard number of lb}\text{.}\\ =\text{\$1}\text{.80}\times 2.\text{50 lbs}\text{.}\\ =\text{\$4}\text{.50}\end{array}$

Working note (2):

Compute the amount of direct labor:

$\begin{array}{c}\left(\begin{array}{l}\text{Standard direct labor}\\ \text{cost}\end{array}\right)=\left(\begin{array}{l}\text{Standard wage per hour}\times \text{Standard labor time}\\ \text{ per minute}\end{array}\right)\\ =\$20.00\times \frac{30\text{minutes}}{60\text{minutes}}\\ =\$10.00\end{array}$

1. b. Compute the direct materials price variance, the direct materials quantity variance, and the total direct materials cost variance
2. Ø Ascertain the direct materials price variance.

$\begin{array}{c}\text{Direct materials price variance = }\left[\left(\begin{array}{l}\text{Actual price}-\\ \text{Standard price}\end{array}\right)\text{× Actual quantity}\right]\\ =\left[\begin{array}{l}\left(\text{\$1}\text{.95}\text{per lb}\text{.}-\text{\$1}\text{.80 per lb}\text{.}\right)\\ \text{×13,000 lbs}\text{.}\end{array}\right]\\ \text{=\$}\text{0}\text{.15×13,000 lbs}\text{.}\\ \text{=\$1,950}\end{array}$

Hence, the direct materials price variance is $1,950, and it is an unfavorable variance, since the actual price is more than the standard price.

• Ø Ascertain the direct materials quantity.

$\begin{array}{c}\left[\begin{array}{l}\text{Direct materials }\\ \text{quantity variance}\end{array}\right]\text{ = }\left[\left(\begin{array}{l}\text{Actual quantity}-\\ \text{Standard quantity (3)}\end{array}\right)\text{× Standard price}\right]\\ =\left[\left(13,000\text{lbs}\text{.}-12,500\text{lbs}\text{.}\right)\text{× \$1}\text{.80}\text{per lb}\text{.}\right]\\ \text{=\$}500\times \text{\$1}\text{.80}\\ \text{=\$900}\end{array}$

Working note (3):

Compute the standard quantity:

$\begin{array}{c}\text{Standard quantity=}\left(\begin{array}{l}\text{Number of faucets produced}\times \text{Standard}\\ \text{number of lb}\text{.}\end{array}\right)\\ =5,000\text{units}\times 2.\text{5}\text{lbs}\text{.}\\ \text{=12,500}\text{lbs}\text{.}\end{array}$

Hence, the quantity variance is $900, and it is an Unfavorable variance. Since the actual quantity is more than the standard quantity.

• Ø Ascertain the total direct materials cost variance.

$\begin{array}{c}\text{Total direct materials cost variance = }\left(\begin{array}{l}\text{Direct materials price variance +}\\ \text{Direct materials quantity variance}\end{array}\right)\\ \text{= \$1,950}+\text{\$900}\\ \text{=\$2,850}\end{array}$

Hence, the total direct materials cost variance is $2,850, and it is an unfavorable variance, since both the direct materials price variance and the direct materials quantity variance are unfavorable.

1. c. Compute the direct labor rate variance, direct labor time variance, and total direct labor cost variance:
   • Ø Ascertain the direct labor rate variance.

$\begin{array}{c}\text{Direct labor rate variance = }\left[\left(\begin{array}{l}\text{Actual rate per hour}-\\ \text{Standard rate per hour}\end{array}\right)\times \text{Actual hours (4)}\right]\\ =\left[\left(\text{\$18}\text{.75}-\text{\$20}\text{.00}\right)\times \text{2,660 hours}\right]\\ \text{=\$}-1.25\times \text{2,660 hours}\\ \text{=\$}\left(3,325\right)\end{array}$

Working note (4):

Compute the actual labor hours:

$\begin{array}{c}\text{Actual labor hours=}\left(\begin{array}{l}\text{Number of employees}\times \text{Number}\\ \text{of labor hours per week}\end{array}\right)\\ =70\text{employees}\times \text{38}\text{hours}\\ =2\text{,660}\text{hours}\end{array}$

The direct labor rate variance is $(3,325) and it is a favorable variance, since the actual rate per hour is lesser than the standard rate per hour.

• Ø Ascertain the direct labor time variance.

$\begin{array}{c}\begin{array}{l}\text{Direct labor }\\ \text{time variance}\end{array}\}\text{ = }\left[\left(\begin{array}{l}\text{Actual direct labor hours (4)}-\\ \text{Standard direct labor hours (5)}\end{array}\right)\times \text{Standard rate per hour}\right]\\ =\left[\left(2,660\text{hours}-2,500\text{ hours}\right)\times \text{\$20}\text{.00 per hour}\right]\\ \text{=}\left[\text{160 hours}\times \text{\$20}\text{.00}\text{per hour}\right]\\ \text{=\$3,200}\end{array}$

Working note (5):

Compute the standard direct labor hours:

$\begin{array}{c}\left(\begin{array}{l}\text{Standard direct }\\ \text{labor hours}\end{array}\right)=\left(\begin{array}{l}\text{Number of faucets produced}\times \\ \text{Standard labor time per minute}\end{array}\right)\\ =5,000\text{units}\times \frac{30\text{minutes}}{60\text{minutes}}\\ =2,500\text{hours}\end{array}$

The direct labor time variance is $3,200 and it is an unfavorable variance, since the actual direct labor hour is more than the standard direct labor hour.

• Ø Ascertain the total direct labor cost time variance.

$\begin{array}{c}\text{Total direct labor cost variance = }\left(\begin{array}{l}\text{Direct labor rate variance +}\\ \text{Direct labor time variance}\end{array}\right)\\ \text{= \$(3,325)+\$3,200}\\ \text{=\$}\left(125\right)\end{array}$

The direct labor cost variance is $(125) and it is a favorable variance, since the direct labor rate variance is lesser than the direct labor time variance.