# Quantity Variances Vs. Rate Variances

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You need to know if your production and manufacturing facilities are making the most efficient use of their time and materials for the cost expended. The goal is be efficient to maximize profit potential. You can analyze the quantity variance compared to the rate variances for a given period of time. The difference will tell the tale.

## Quantity and Rate Variance Formulas

Begin to compute your company's quantity variance using the following accounting formula: actual quantity of input multiplied by actual price. In other words, the amount of materials purchased at the beginning of the month (or other time period) and the price per unit for the material. An example from the text of Managerial Accounting provides an illustration for a manufacturing facility: 6,500 pounds x \$3.80 per pound. This equals \$24,700.

Compute your company's rate variance using this formula: actual quantity of input multiplied by standard price. Using the above example, the 6,500 pounds of material purchased would typically cost your company \$4 per pound instead of \$3.80. Reflect that in your rate variance and you will arrive at \$26,000.

## Computing Price Variance

After using the quantity variance formula and the rate variance formula you can now compute the price variance this way: \$26,000 minus \$24,700 equals a price variance of \$1,300. In other words, you have a favorable rate variance because your cost was less than it normally would have been for the same amount of material purchased. Next, you need to analyze how your price variance stacks up against your quantity variance to see if your company has been working efficiently or not.

## Computing Quantity Variance

Computing your quantity variance involves one more formula: standard quantity output instead of actual output -- multiplied at the standard price. While our imaginary scenario reflects 6,500 pounds of material, your company might normally produce the same quantity with only 6,000 pounds of material. This would reflect a waste of 500 pounds, unnecessarily, in manufacturing. The quantity variance addresses that discrepancy. The 6,000 pounds x \$4 per pound equals \$24,000. Comparing the actual quantity cost at the standard price you normally pay (\$26,000) to the cost that should have been incurred for the correct amount of material needed for the job (\$24,000) reflects a \$2,000 negative difference.

## Significance

Compare the price variance total of \$1,300 to the quantity variance of \$2,000 and you arrive at a total variance of \$700. It is important to note that the \$1,300 price variance represented a positive number, as this was a profit from paying less for materials. The \$2,000 number, however, was a negative number, as it represented wasted material costs of that amount. Therefore, after deducting your profit of \$1,300 from your excess expense of \$2,000, you are still left with a negative balance of \$700 for the project analyzed.

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