The formula for calculating the materials price variance is (AP ? SP) × AQ. The actual price for raw materials was $105,000 ÷ 35,000 units in inventory, or $3.00 per unit. The standard price is $2.50 per unit of raw materials ($60,000 ÷ 12,000 units actually produced ÷ 2 units of materials per unit produced). The Actual Quantity in the formula is the actual quantity of the raw materials that were used in producing the 12,000 finished units. It is not the actual quantity of product produced, nor is it the standard quantity of materials for the actual quantity produced. So to calculate the price variance, we need to know how many units of materials were actually used in production, and the question does not tell us that. However, it does tell us that there was an unfavorable quantity variance. So to figure out how many units of materials were actually used, we first have to work out the quantity variance, which the question says is an unfavorable $2,500, to solve for the AQ in that formula. The quantity variance formula is (AQ ? SQ) × SP. Since the question tells us that the materials standard is two units of raw materials for each unit produced, we know that the standard quantity of materials for 12,000 units was 24,000 units. The actual quantity we do not know yet. The standard price was $2.50 per unit of raw material ($60,000 standard allowed ÷ 12,000 units actually produced ÷ 2 units of materials per unit produced). Therefore, our formula is: (AQ ? 24,000) × 2.50 = 2,500 Solving for AQ, we get AQ = 25,000, as follows: 2.5AQ ? 60,000 = 2,500 2.5AQ = 62,500 AQ = 25,000 Now, we can put the actual quantity of materials used into the materials price variance formula and calculate the materials price variance. (AP ? SP) × AQ ($3.00 ? $2.50) × 25,000 = $12,500 Unfavorable
This answer results from using the actual quantity of units produced as the AQ in the materials price variance formula, instead of the actual quantity of materials used. See the correct answer for a complete explanation.
$2,500 Unfavorable is the quantity variance, which is given in the question.
This answer results from using the standard amount of materials for the actual quantity produced as the AQ in the materials price variance formula, instead of the actual quantity of materials used. See the correct answer for a complete explanation.
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