Diamond Company produces a chair that requires 5 yds. of material per unit. The standard price of one yard of material is $7.50. During the month, 8,500 chairs were manufactured, using 43,700 yards at a cost of $7.60. Determine the (a) price variance, (b) quantity variance, and (c) cost variance.
To determine the price variance, quantity variance, and cost variance, we will use the following formulas:
(a) Price variance = (Standard price per unit - Actual price per unit) * Actual quantity
(b) Quantity variance = (Standard quantity per unit - Actual quantity per unit) * Standard price per unit
(c) Cost variance = Price variance + Quantity variance
Given information:
Standard price per yard = $7.50
Actual price per yard = $7.60
Actual quantity = 43,700 yards
Standard quantity per unit = 5 yards
Actual quantity per unit = 43,700 yards / 8,500 chairs
Let's calculate these variances step-by-step.
Step 1: Calculate the standard price per unit.
Standard price per unit = Standard price per yard * Standard quantity per unit
= $7.50 * 5
= $37.50
Step 2: Calculate the actual quantity per unit.
Actual quantity per unit = Actual quantity / Number of units
= 43,700 yards / 8,500 chairs
≈ 5.14 yards
Now, we can calculate the variances.
(a) Price variance = (Standard price per unit - Actual price per unit) * Actual quantity
= ($37.50 - $7.60) * 43,700 yards
= $29.90 * 43,700 yards
≈ $1,305,430
(b) Quantity variance = (Standard quantity per unit - Actual quantity per unit) * Standard price per unit
= (5 - 5.14) * $37.50
= -0.14 * $37.50
≈ -$5.25
(c) Cost variance = Price variance + Quantity variance
= $1,305,430 + (-$5.25)
≈ $1,305,424.75
So, the price variance is approximately $1,305,430, the quantity variance is approximately -$5.25, and the cost variance is approximately $1,305,424.75.
To determine the price variance, quantity variance, and cost variance, we need to compare the actual costs and quantities used with the standard costs and quantities.
(a) Price Variance:
The price variance measures the difference between the actual cost per unit and the standard cost per unit.
To calculate the price variance, we use the formula:
Price Variance = (Actual Quantity x Actual Price) - (Actual Quantity x Standard Price)
Here, the actual quantity used is 43,700 yards, the actual price per yard is $7.60, and the standard price per yard is $7.50.
Price Variance = (43,700 x $7.60) - (43,700 x $7.50)
Price Variance = $332,120 - $327,750
Price Variance = $4,370
Therefore, the price variance is $4,370.
(b) Quantity Variance:
The quantity variance measures the difference between the actual quantity used and the standard quantity allowed.
To calculate the quantity variance, we use the formula:
Quantity Variance = (Actual Quantity - Standard Quantity) x Standard Price
Here, the actual quantity used is 43,700 yards, and the standard quantity allowed (based on manufacturing 8,500 chairs at 5 yds. per unit) is 8,500 x 5 = 42,500 yards. The standard price per yard is $7.50.
Quantity Variance = (43,700 - 42,500) x $7.50
Quantity Variance = 1,200 x $7.50
Quantity Variance = $9,000
Therefore, the quantity variance is $9,000.
(c) Cost Variance:
The cost variance measures the overall difference between the actual cost incurred and the standard cost expected.
To calculate the cost variance, we use the simple formula:
Cost Variance = (Actual Quantity x Actual Price) - (Standard Quantity x Standard Price)
Here, the actual quantity used is 43,700 yards, the actual price per yard is $7.60, the standard quantity based on manufacturing 8,500 chairs at 5 yds. per unit is 8,500 x 5 = 42,500 yards, and the standard price per yard is $7.50.
Cost Variance = (43,700 x $7.60) - (42,500 x $7.50)
Cost Variance = $332,120 - $318,750
Cost Variance = $13,370
Therefore, the cost variance is $13,370.
To summarize:
(a) Price Variance = $4,370
(b) Quantity Variance = $9,000
(c) Cost Variance = $13,370