... From Page M:7 
A Problem  
900 kgs of Material A @ Rs. 15 per kg, 800 kgs of Material B @ Rs. 45/kg and 200 kgs of Material C @ Rs. 85 per kg were planned to be purchased/used for manufacturing 9,500 units. 2,250 kgs of Material A @ Rs. 16 per kg, 1,950 kgs of Material B @ Rs. 42/kg and 550 kgs of Material C @ Rs. 90 per kg were purchased/used actually for manufacturing 22,800 units.
The problem data arranged in a working table:
What is the variation in total cost on account of efficient/inefficient usage of materials? This information is provided by the material usage/quantity variance.

The Formulae » Material Quantity/Usage Variance (MQV/MUV)  
That part of the variance in the total cost of materials on account of a variation in the usage of materials i.e difference between the standard rate at which material quantities are to be used (i.e. the standard quantities for actual output) and the actual rate at which they have been used (i.e. the actual quantities). It is a part of the Material Cost Variance.
It is the difference between the Standard Cost of Standard Quantity for Actual Output and the Standard Cost of Actual Quantity of materials.

MQV/MUV » Formula interpretation  
This formula can be used in all cases i.e. both when the actual output and the standard output are equal as well as not equal. When the actual output and the standard output are different, AO/SO works as a correction factor to readjust the standard quantity to standard quantity for actual Output.

Solution [Using the data as it is]  
For working out problems with the data considered as it has been given without having to do any recalculations, use the above formulae (which are capable of being used in all cases)
Consider the working table above:
Material Usage/Quantity Variance due to

Solution [Using recalculated data]  
Where you find that the SO ≠ AO, you may alternatively recalculate the standard to make the SO = AO and use the figures relating to the recalculated standard in the working table. In such a case, the formulae that you use would look simpler (without the adjustment factor AO/SO).
From the data relating to the problem, it is evident that AO ≠ SO. Thus we recalculate the standard data for Actual Output [Refer to the calculations]. Consider the recalculated standard data and the actual data arranged in a working table.
MUV/MQV = (SQ − AQ) × SP [Since AO = SO] Using MUV/MQV_{Mat} = (SQ_{Mat} − AQ_{Mat}) × SP_{Mat} [Since AO = SO] Material Usage/Quantity Variance due to
Note:This formula can be used only when the standard output and the actual output are the same.You don't need to recalculate the standardThe formula with the adjustment factor AO/SO can be used in all cases i.e. both when AO = SO and AO ≠ SO. Therefore, you don't need to rebuild the working table by recalculating the standards for the purpose of finding the variances.Check:The same problem was solved in both the cases above. The only difference being that in the second case, the data was considered by recalculating the Standard for Actual Output to make AO = SO. 
Formulae using Interrelationships among Variances  
These formulae can be used both for each material separately as well as for all the materials together.
VerificationThe interrelationships between variances would also be useful in verifying whether our calculations are correct or not. After calculating the three variances we can verify whether MUV/MQV and MPV add up to MCV or not. If MUV/MQV + MPV = MCV we can assume our calculations to be correct.We used the same set of data in all the explanations. Using the figures obtained for verification.

Who is held responsible for the Variance?  
Since this variance is on account of the quantity used being more or less than the standard, the people or department responsible for production can be held responsible for this variance.
When there are two or more types of materials being used for the manufacture of a product making only the people responsible for production may not be appropriate as there would be two factors influencing the usage of materials in such a case. One, the ratio in which the constitutent materials are mixed and two the actual yield from the materials. That is the reason the Quantity/Usage variance is further broken down into two parts called Mix Variance and Yield Variance (only in cases where there are two or more types of material being used for the manufacture of the product). 
Alternative Formula  
Material Usage/Quantity Variance is the difference between the "Standard Cost of Actual Output" and the "Standard Cost of Standard Output for Actual Input".
Material Usage/Quantity Variance = Standard Cost of Actual Output − Standard Cost of Standard Output for Actual Input
Note:

Solution [Using the data as it is]  
For working out problems with the data consider as it has been given without having to do any recalculations, use the above formulae (which are capable of being used in all cases)
Consider the working table above:
Material Quantity/Usage Variance due to
Note that you get the same values for variances whatever may be the formula you use. 
Author Credit : The Edifier  ... Continued Page M:9 