Chapter 17, Problem 31E

Materials Mix and Yield Variances

John’s Weed-B-Gone yard service sprays lawns to rid them of weeds. John mixes the two chemicals, Weed-X and Pest-O, in proportions depending on the climate and the particular weed problems of the season. A standard mix calls for a gallon of the mixture to combine equal parts of Weed-X and Pest-O. Weed-X has a standard cost of $10 per gallon and Pesto-O has a standard cost of $25 per gallon. Each gallon can treat 100 square yards of lawn. John expects to treat 540,000 square yards of lawn.

For the past season, John treated 648,000 square yards. He used 3,600 gallons of Weed-X and 3,000 gallons of Pest-O. He paid a total of $35,280 for the Weed-X and $72,000 for the Pest-O.

Required

1. a.      Compute the materials price and efficiency variances for the season.
2. b.      Compute the materials mix and yield variances for the season.

To determine

Compute materials price and Materials efficiency variances.

Answer to Problem 31E

The value of materials price variance is $720 F, and Materials efficiency variance is $3,600 U for product Weed-X, and for product Pest-O the materials price variance is $3,000 F, and Materials efficiency variance is $6,000 F.

Explanation of Solution

Materials price variance:

Materials price variance is resultant materials price that has been computed or derived at the end of the accounting period for which the computations are being done.

Materials efficiency variance:

Materials efficiency variance is the resultant Materials efficiency that has been computed or derived at the end of the accounting period for which the computations are being done.

Compute the materials price variance:

Particulars	Weed-X	Pest-O
Materials variance:
Actual $\left(\text{AP×AQ}\right)$	$35,280	$72,000
Standard $\left(\text{SP×AQ}\right)$	$36,000	$75,000
Materials variance $\left(\text{Actual}-\text{Standard}\right)$	$720 F	$3,000 U

Table: (1)

Compute the Materials efficiency variance:

Particulars	Weed-X	Pest-O
Materials mix variance:
Actual $\left(\text{SP×AQ}\right)$	$36,000	$75,000
Standard $\left(\text{SP×ASQ}\right)$	$33,000	$82,500
Materials mix variance $\left(\text{Actual}-\text{Standard}\right)$	$3,000 U	$7,500 F
Materials yield variance:
Actual $\left(\text{SP×ASQ}\right)$	$33,000	$82,500
Standard $\left(\text{SP×SQ}\right)$	$32,400	$81,000
Materials yield variance $\left(\text{Actual}-\text{Standard}\right)$	$600 U	$1,500 U
Materials efficiency variance $\left(\text{Mix variance + Yield variance}\right)$	$3,600 U	$6,000 F

Table: (2)

Measure	Weed-X	Pest-O
AP	$9.80	$24.00
AQ	3,600	3,000
SP	$10.00	$25.00
ASQ	3,300(1)	3,300(2)
SQ	3,240(3)	3,240(4)

Table: (3)

Thus, the value of materials price variance is $720 F and Materials efficiency variance is $3,600 U for product Weed-X, and for product Pest-O the materials price variance is $3,000 F, and Materials efficiency variance is $6,000 F.

Working note 1:

Compute the ASQ for Weed-X:

$\begin{array}{c}\text{ASQ = Ratio of Weed-X }\times \text{Total AQ}\\ \text{=1/2 }\times \text{ 6,600}\\ =3,300\end{array}$

Working note 2:

Compute the ASQ for Pest-O:

$\begin{array}{c}\text{ASQ = Ratio of Beta }\times \text{Total AQ}\\ \text{=1/2 }\times \text{ 6,600}\\ =3,300\end{array}$

Working note 3:

Compute the SQ of Weed-X:

$\begin{array}{c}\text{SQ = Units appropriation in for SP}\times \text{ Acutal output}\\ \text{= 0}\text{.005}\times 648\text{,000}\\ \text{=3,240}\end{array}$

Working note 4:

Compute the SQ of Pest-O:

$\begin{array}{c}\text{SQ = Units appropriation in for SP}\times \text{ Acutal output}\\ \text{= 0}\text{.005}\times 648\text{,000}\\ \text{=3,240}\end{array}$

To determine

Compute materials mix and Materials yield variances.

Answer to Problem 31E

The value of materials mix and Materials yield variances of the product are $3,000 U and $600 U respectively, and the value of materials mix and Materials yield variances of product Pest-O$7,500 and $1,500 respectively.

Explanation of Solution

Materials mix variance:

Materials mix variance is the resultant market Materials mix that has been computed or derived at the end of the accounting period for which the computations are being done for two or more than two products.

Materials yield variance:

Materials yield variance is the resultant difference between the costs of finished goods expected from a specific amount of raw material that has been computed or derived at the end of the accounting period for which the computations are being done.

Compute the materials mix variance and materials yield variance for product Weed-X and Pest-O:

Particulars	Weed-X	Pest-O
Materials mix variance:
Actual $\left(\text{SP×AQ}\right)$	$36,000	$75,000
Standard $\left(\text{SP×ASQ}\right)$	$33,000	$82,500
Materials mix variance $\left(\text{Actual}-\text{Standard}\right)$	$3,000 U	$7,500 F
Materials yield variance:
Actual $\left(\text{SP×ASQ}\right)$	$33,000	$82,500
Standard $\left(\text{SP×SQ}\right)$	$32,400	$81,000
Materials yield variance $\left(\text{Actual}-\text{Standard}\right)$	$600 U	$1,500 U

Table: (4)

Measure	Weed-X	Pest-O
AP	$9.80	$24.00
AQ	3,600	3,000
SP	$10.00	$25.00
ASQ	3,300(1)	3,300(2)
SQ	3,240(3)	3,240(4)

Table: (5)

Thus, the value of materials mix and Materials yield variances of the product are $3,000 U and $600 U respectively, and the value of materials mix and Materials yield variances of product Pest-O $7,500 and $1,500 respectively.