# Material Usage/Quantity Variance

 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.
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 problem data arranged in a working table:

 Quantity(kgs) PriceRs/kg Value/Cost(Rs) Quantity(kgs) PriceRs/kg Value/Cost(Rs) Standard [Production: 9500 units] Actual [Production: 22,800 units] Material A 900 15 13,500 2,250 16 36,000 Material B 800 45 36,000 1,950 42 81,900 Material C 200 85 17,000 550 90 49,500 1,900 66,500 4,750 1,67,400

 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.
⇒ Material Quantity/Usage Variance
= Standard Cost of Standard Quantity for Actual OutputStandard Cost of Actual Quantity

• #### For each Material Separately

MQV/MUVMat = SC of SQMat for AO − SC of AQMat
=
({  AO SO
× SQMat} × SPMat)
− (AQMat × SPMat)
=
({  AO SO
× SQMat} − AQMat) × SPMat)
• #### For all Materials together [Total Material Usage/Quantity Variance :: TMUV/TMQV]

When two or more types of materials are used for the manufacture of a product, the total Material Usage/Quantity variance is the sum of the variances measured for each material separately.

 ⇒ TMUV/TMQV = MUV/MQVA + MUV/MQVB + ....

 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.

• #### Where AO = SO

When AO = SO,  AO SO
becomes 1 thus nullifying its effect, in which case the formula would read as:

For each material separately  MUV/MQV = (SQ × SP) − (AQ × SP) (Or) = (SQ − AQ) × SP

For all materials together  There is no direct formula

• #### MUV/MQV = 0

Material usage/quantity variance for each material would be zero, when the acutal quantity of material used and the standard quantity of material for actual output are the same.
• #### TMUV/TMQV = 0

When more than one type of material is used, the total MUV/MQV may become zero
1. When the MUV/MQV on account of each material is zero, or
2. When the unfavourable variance due to one or more materials is set off by the favourable variance due to one or more other materials.

Therefore, it would not be appropriate to conclude that there is no variance on account of any material just because the total MUV/MQV is zero.

Where the total MUV/MQV is zero, you have to verify individual variances before concluding that all the variances (MUCV's/MQV's) are zero.

 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:

 Quantity(kgs) PriceRs/kg Value/Cost(Rs) Quantity(kgs) PriceRs/kg Value/Cost(Rs) Standard [Production: 9500 units] Actual [Production: 22,800 units] Material A 900 15 13,500 2,250 16 36,000 Material B 800 45 36,000 1,950 42 81,900 Material C 200 85 17,000 550 90 49,500 1,900 66,500 4,750 1,67,400

MUV/MQV =
({
 AO SO
× SQ} − AQ) × SP
Using, MUV/MQVMat =
({
 AO SO
× SQMat} − AQMat) × SPMat

Material Usage/Quantity Variance due to
• Material A =
({
 22,800 units 9,500 units
× 900 kgs} − 2,250 kgs) × Rs. 15/kg
= ({2.4 × 900 kgs} − 2,250 kgs) × Rs. 15/kg
= ({2,160 kgs − 2,250 kgs) × Rs. 15/kg
= ({− 90 kgs) × Rs. 15/kg
= − Rs. 1,350 ⇒ MUV/MQVA = − Rs. 1,350 [Adv]
• Material B =
({
 22,800 units 9,500 units
× 800 kgs} − 1,950 kgs) × Rs. 45/kg
= ({2.4 × 800 kgs} − 1,950 kgs) × Rs. 45/kg
= ({1,920 kgs − 1,950 kgs) × Rs. 45/kg
= ({− 30 kgs) × Rs. 45/kg
= − Rs. 1,350 ⇒ MUV/MQVB = − Rs. 1,350 [Adv]
• Material C =
({
 22,800 units 9,500 units
× 200 kgs} − 550 kgs) × Rs. 85/kg
= ({2.4 × 200 kgs} − 550 kgs) × Rs. 85/kg
= ({480 kgs − 550 kgs) × Rs. 85/kg
= ({− 70 kgs) × Rs. 85/kg
= − Rs. 5,950 ⇒ MUV/MQVC = − Rs. 5,950 [Adv]
Total Material Usage/Quantity Variance ⇒ TMUV/TMQV = − Rs. 8,650 [Adv]

 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.

 Quantity(kgs) PriceRs/kg Value/Cost(Rs) Quantity(kgs) PriceRs/kg Value/Cost(Rs) Standard [Production: 22,800 units] Actual [Production: 22,800 units] Material A 2,160 15 32,400 2,250 16 36,000 Material B 1,920 45 86,400 1,950 42 81,900 Material C 480 85 40,800 550 90 49,500 4,560 1,59,600 4,750 1,67,400

MUV/MQV = (SQ − AQ) × SP [Since AO = SO]

Using MUV/MQVMat = (SQMat − AQMat) × SPMat [Since AO = SO]

Material Usage/Quantity Variance due to
 • Material A = (2,160 kgs − 2,250 kgs) × Rs. 15/kg = − 90 kgs × Rs. 15/kg = − Rs. 1,350 ⇒ MUV/MQVA = − Rs. 1,350 [Adv] • Material B = (1,920 kgs − 1,950 kgs) × Rs. 45/kg = − 30 kgs × Rs. 45/kg = − Rs. 1,350 ⇒ MUV/MQVB = − Rs. 1,350 [Adv] • Material C = (480 kgs − 550 kgs) × Rs. 85/kg = − 70 kgs × Rs. 85/kg = − Rs. 5,950 ⇒ MUV/MQVC = − Rs. 5,950 [Adv] Total Material Usage/Quantity Variance ⇒ TMUV/TMQV = − Rs. 8,650 [Adv]

#### 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 standard

The 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 Inter-relationships among Variances
These formulae can be used both for each material separately as well as for all the materials together.
1. MCV = MPV + MUV/MQV   → (1)
• #### For each Material Separately

 MUV/MQVMat = MCVMat − MPVMat
• #### For all the Materials Together

 TMUV/TMQV = TMCV − TMPV
2. MQV/MUV = MMV + MYV/MSUV   → (2)
• #### For each Material Separately

 MUV/MQVMat = MMVMat + MYVMat
• #### For all the Materials Together

 TMUV/TMQV = TMMV + TMYV

#### Verification

The 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.
 MPV + MUV/MQV = (+ Rs. 850) + (− 8,650) = (− Rs. 7,800) = MCV → We can assume our calculations to be correct.

 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

• #### For each Material Separately

MQV/MUVMat = SC of AO − SC of SO for AI
=
(AO × SP(SO)Mat) − ({  AQMat SQMat
× SO} × SP(SO)Mat)
=
(AO − ({  AQMat SQMat
× SO}) × SP(SO)Mat)

SP(SO)Mat =  SCMat SO
=  SQMat × SPMat SO

• #### For all Materials Together

 There is no direct formula

#### Note:

1. This formula can be used in all cases.

 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:

 Quantity(kgs) PriceRs/kg Value/Cost(Rs) Quantity(kgs) PriceRs/kg Value/Cost(Rs) Standard [Production: 9500 units] Actual [Production: 22,800 units] Material A 900 15 13,500 2,250 16 36,000 Material B 800 45 36,000 1,950 42 81,900 Material C 200 85 17,000 550 90 49,500 1,900 66,500 4,750 1,67,400
Using, SP(SO)Mat =
 SQMat × SPMat SO

• SP(SO)A =
 900 kgs × Rs. 15/kg 9,500 units
⇒ SP(SO)A =
 Rs. 13,500 9,500 units
⇒ SP(SO)A =
Rs.
 27 19
/unit
• SP(SO)B =
 800 kgs × Rs. 45/kg 9,500 units
⇒ SP(SO)B =
 Rs. 36,000 9,500 units
⇒ SP(SO)B =
Rs.
 72 19
/unit
• SP(SO)C =
 200 kgs × Rs. 85/kg 9,500 units
⇒ SP(SO)C =
 Rs. 17,000 9,500 units
⇒ SP(SO)C =
Rs.
 34 19
/unit

Using, MQV/MUVMat =
(AO − {
 AQMat SQMat
× SO}) × SP(SO)Mat

Material Quantity/Usage Variance due to
• Material A =
(22,800 units − {
 2,250 kgs 900 kgs
× 9,500 units}) × Rs.
 27 19
/unit
=
(22,800 units − {2.5 × 9,500 units}) × Rs.
 27 19
/unit
=
(22,800 units − 23,750 units) ×
 Rs. 27 19
/unit
=
(− 950 units) ×
 Rs. 27 19
/unit
⇒ MUV/MQVA = − Rs. 1,350 [Adv]
• Material B =
(22,800 units − {
 1,950 kgs 800 kgs
× 9,500 units}) × Rs.
 72 19
/unit
=
(22,800 units − {2.4375 × 9,500 units}) × Rs.
 72 19
/unit
=
(22,800 units − 23,156.25 units) ×
 Rs. 72 19
/unit
=
(− 356.25 units) ×
 Rs. 72 19
/unit
⇒ MUV/MQVB = − Rs. 1,350 [Adv]
• Material C =
(22,800 units − {
 550 kgs 200 kgs
× 9,500 units}) × Rs.
 34 19
/unit
=
(22,800 units − {2.75 × 9,500 units}) × Rs.
 34 19
/unit
=
(22,800 units − 26,125 units) ×
 Rs. 34 19
/unit
=
(− 3,325 units) ×
 Rs. 34 19
/unit
⇒ MUV/MQVC = − Rs. 5,950 [Adv]
Total Material Usage/Quantity Variance ⇒ TMUV/TMQV = − Rs. 8,650 [Adv]

Note that you get the same values for variances whatever may be the formula you use.

 Author Credit : The Edifier ... Continued Page M:9