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The price variance is calculated as follows: (Actual Price ? Standard Price) × Actual Quantity. Since the purchase price variance is required, the price to use for the actual price is the price per unit of the units purchased instead of the price per unit of the units used; and the actual quantity is the number of units purchased. This price variance is incorrect because the figure used in the formula is not the actual quantity of units purchased but is instead the standard quantity for the planned production (26,000 units x 3 pounds per unit). The quantity variance is calculated as follows: (Actual Quantity ? Standard Quantity for Actual Output ) × Standard Price. The actual quantity is the actual quantity used, not the quantity purchased. The standard quantity is the standard quantity allowed for the actual output. This quantity variance is incorrect because it uses the standard quantity allowed for the planned production (26,000 × 3 pounds) instead of the standard quantity allowed for the actual production.
The purchase price variance is calculated as follows: (Actual Price ? Standard Price) × Actual Quantity. Since the purchase price variance is required, the price to use for the actual price is the price per unit of the units purchased instead of the price per unit of the units used; and the actual quantity is the number of units purchased , not the number of units that were put into production. The actual price is $3.96 per pound ($297,000 ÷ 75,000). The standard price is $4.00 per pound. The actual quantity purchased is 75,000 pounds. The purchase price variance is ($3.96 ? $4.00) × 75,000 = $(3,000) favorable. The quantity variance is calculated as follows: (Actual Quantity ? Standard Quantity for Actual Output ) × Standard Price. The actual quantity is the actual quantity used , not the quantity purchased. The standard quantity is the standard quantity allowed for the actual output. The actual quantity is 70,000. The standard quantity allowed for the actual level of output is 69,000 pounds (3 lb.× 23,000 units). The standard price is $4. Hence, the quantity variance is (70,000 ? 69,000) × $4 = $4,000 unfavorable.
The quantity variance is incorrect because it is calculated as (the actual quantity purchased of 75,000 minus the actual quantity used of 70,000) multiplied by the standard price per unit of $4. The correct formula to use for the quantity variance is (Actual Quantity ? Standard Quantity for Actual Output ) × Standard Price. The actual quantity is the actual quantity used , not the quantity purchased. The standard quantity is the standard quantity allowed for the actual output.
The purchase price variance is incorrect because it is calculated using the quantity used in production instead of the quantity purchased. When a question asks for the purchase price variance, the actual quantity to use is the quantity purchased, and the actual price is the actual price per unit for the quantity purchased.