Question

qs 21 - 8 (algo) direct materials price and quantity variances lo p3
a company reports the following for one of its products:
direct materials standard (3 pounds @ $3 per pound) $9 per unit
actual direct materials used (aq) 270,000 pounds
actual units produced 71,000 units
actual cost of direct materials used $742,500
aq = actual quantity
sq = standard quantity
ap = actual price
sp = standard price
compute the direct materials price and quantity variances and identify each as favorable or unfavorable.

Explanation:

Step1: Calculate the actual price (AP)

The formula for \(AP=\frac{\text{Actual cost of direct materials used}}{\text{Actual quantity (AQ)}}\).
Given that the actual cost of direct materials used is \(\$742,500\) and \(AQ = 270,000\) pounds.
\(AP=\frac{742500}{270000}=\$2.75\) per pound.

Step2: Calculate the direct materials price variance

The formula for direct materials price variance \(=(AP - SP)\times AQ\).
Given \(SP=\$3\) per pound, \(AQ = 270,000\) pounds and \(AP=\$2.75\) per pound.
\((2.75 - 3)\times270000=(- 0.25)\times270000=-\$67,500\) (favorable, since \(AP

Step3: Calculate the standard quantity (SQ)

The formula for \(SQ=\text{Actual units produced}\times\text{Standard pounds per unit}\).
Given actual units produced \(=71,000\) units and standard pounds per unit \( = 3\) pounds.
\(SQ=71000\times3 = 213,000\) pounds.

Step4: Calculate the direct materials quantity variance

The formula for direct materials quantity variance \(=(AQ - SQ)\times SP\).
Given \(AQ = 270,000\) pounds, \(SQ=213,000\) pounds and \(SP = 3\) per pound.
\((270000 - 213000)\times3=57000\times3=\$171,000\) (unfavorable, since \(AQ>SQ\)).

Answer:

• Direct materials price variance: \(-\$67,500\) (favorable)
• Direct materials quantity variance: \(\$171,000\) (unfavorable)