Material Mix Variance

... From Page M:8
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 proportion in which the materials are mixed
Standard Proportion :: 900 kgs : 800 kgs : 200 kgs i.e. 9 : 8 : 2
Actual Proportion :: 2,250 kgs : 1,950 kgs : 550 kgs i.e. 45 : 39 : 11
What is the variation in total cost on account of variation in the proportion in which the materials are mixed?
This information is provided by Material Mix Variance.
The problem data arranged in a working table:

Standard
[Production: 9500 units]
Actual
[Production: 22,800 units]
Quantity
(kgs)
Price
Rs/kg
Value/Cost
(Rs)
Quantity
(kgs)
Price
Rs/kg
Value/Cost
(Rs)
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
Total 1,900   66,500 4,750   1,67,400

The Formulae » Material Mix Variance (MMV)  
 
Material Mix Variance is that part of the variance in the total cost of materials on account of a variation between the standard mix (standard proportion in which material quantities are to be mixed) and the actual mix (proportion in which they are actually mixed). It is a part of the Material Usage/Quantity Variance or a Sub-Part of the Material Cost Variance.

It is the difference between the Standard Cost of Standard Quantity for Actual Input (Actual Quantity of Mix) and the Standard Cost of Actual Quantity of materials.
⇒ Material Mix Variance = Standard Cost of Standard Quantity for Actual MixStandard Cost of Actual Quantity

  • For each Material Separately

    MMV = SC of SQ for AM − SC of AQ
    =
    ({
    AQMix
    SQMix
    × SQMat} × SPMat)(AQMat × SPMat)
    =
    ({
    AQ(AM)
    SQ(SM)
    × SQ} − AQ) × SP)
  • For all Materials together [Total Material Mix Variance :: TMMV]

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

    ⇒ TMMV = MMVA + MMV B + ....

    Direct Formula

    There is no direct formula for calculating the total mix variance

MMV » Formula interpretation  
 
This formula can be used in all cases i.e. when AQMix = SQMix or AQMix ≠ SQMix. When AQMix and SQMix are different, AQMix/SQMix works as an adjustment factor to readjust the Standard Quantity to Standard Quantity for Actual Input.
  • Where AQMix = SQMix

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

    For each material separately
    MMV = (SQ × SP) − (AQ × SP)
    (Or) = (SQ − AQ) SP

    For all materials together
    There is no direct formula

    Caution:

    The formula for Material Usage/Quantity Variance where AO = SO also reads the same. Though they look the same, the condition under which they can be used is different. In case of MUV/MQV, the condition being SO = AO and in case of MMV it is SQMix = AQMix.
  • MMV = 0

    MMV for each material would be zero, when the proportion of the quantity of material to the quantity of mix is the
    same both in the standards as well as actuals. i.e. when
    SQMat
    SQMix
    =
    AQMat
    AQMix

    Where there is only one material being used, there is no meaning in thinking of the Material Mix Variance.

    Where MMV = 0, the total usage/quantity variance is nothing but Yield Variance.
    MUV/MQV = MMV + MYV
    = 0 + MYV
    = MYV

  • TMMV = 0

    When more than one type of material is used, the total MMV may become zero
    1. When the MMV on account of each material is zero, or
    2. When the proportion of materials inter-se between them both as per the standard and the actual is the same. SQA : SQB : SQC : ... = AQA : AQB : AQC : ...
    3. 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 MMV is zero.

    Where the total MMV is zero, you have to verify individual variances before concluding that all the variances MMV'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:

Standard
[Production: 9500 units]
Actual
[Production: 22,800 units]
Quantity
(kgs)
Price
Rs/kg
Value/Cost
(Rs)
Quantity
(kgs)
Price
Rs/kg
Value/Cost
(Rs)
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
Total 1,900   66,500 4,750   1,67,400

Using,
MMV =
({
AQMix
SQMix
× SQMat} − AQMat) × SPMat
Material Mix Variance due to
• Material A =
({
4,750 units
1,900 units
× 900 kgs} − 2,250 kgs) × Rs. 15/kg
= ({2.5 × 900 kgs) − 2,250 kgs) × Rs. 15/kg
= (2,250 kgs − 2,250 kgs) × Rs. 15/kg
= (0) × Rs. 15/kg ⇒ MMVA = Nil [None]
Material B =
({
4,750 units
1,900 units
× 800 kgs} − 1,950 kgs) × Rs. 45/kg
= ({2.5 × 800 kgs} − 1,950 kgs) × Rs. 45/kg
= (2,000 kgs − 1,950 kgs) × Rs. 45/kg
= (+ 50 kgs) × Rs. 45/kg ⇒ MMVB = + Rs. 2,250 [Fav]
Material C =
({
4,750 units
1,900 units
× 200 kgs} − 550 kgs) × Rs. 85/kg
= ({2.5 × 200 kgs} − 550 kgs) × Rs. 85/kg
= (500kgs − 550 kgs) × Rs. 85/kg
= (− 50 kgs) × Rs. 85/kg ⇒ MMVC = − Rs. 4,250 [Adv]
Total Material Mix Varaince = − Rs. 2,000 [Adv]

Solution [Using recalculated data]  
 
Where you find that the SQMix ≠ AQMix, you may alternatively recalculate the standard to make the SQMix = AQMix 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 AQMix/SQMix).

From the data relating to the problem, it is evident that SQMix ≠ AQMix. Thus we recalculate the standard data for Actual Input [Refer to the calculations].

Consider the recalculated standard data and the actual data arranged in a working table.

Standard
[Production: 23,750 units]
Actual
[Production: 22,800 units]
Quantity
(kgs)
Price
Rs/kg
Value/Cost
(Rs)
Quantity
(kgs)
Price
Rs/kg
Value/Cost
(Rs)
Material A 2,250 15 33,750 2,250 16 36,000
Material B 2,000 45 90,000 1,950 42 81,900
Material C 500 85 42,500 550 90 49,500
Total 4,750   1,66,250 4,750   1,67,400

Using MMV = (SQMat − AQMat) SPMat [Since AQMix = SQMix]

Material Mix Variance due to
• Material A = (2,250 kgs − 2,250 kgs) × Rs. 15/kg
= (0 kgs) × Rs. 15/kg ⇒ MMVA = Nil [None]
Material B = (2,000 kgs − 1,950 kgs) × Rs. 45/kg
= (+ 50 kgs) × Rs. 45 ⇒ MMVB = + Rs. 2,250 [Fav]
Material C = (500 kgs − 550 kgs) × Rs. 85/kg
= (− 50 kgs) × Rs. 85 ⇒ MMVC = − Rs. 4,250 [Adv]
= Total Material Mix Variance = − Rs. 2,000 [Adv]

Note:

This formula can be used only when AQMix = SQMix

You don't need to recalculate the standard

The formula with the adjustment factor AQMix/SQMix can be used in all cases i.e. both when AQMix = SQMix and AQMix ≠ SQMix. 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 Input to make AQMix = SQMix.

Formulae using Inter-relationships among Variances  
 
These formulae can be used both for each material separately as well as for all the mateirals together
  1. MUV/MQV = MMV + MYV   ⇒ (1)
    • For each Material Separately

      MMVMat = MUV/MQVMat − MYVMat
    • For All Materials Together

      TMMV = TMUV/TMQV − TMYV
  2. MCV = MPV + MMV + MYV/MSUV   ⇒ (2)
    • For each Material Separately

      MMVMat = MCVMat − MPVMat − MYV/MSUVMat
    • For All Materials Together

      TMMV = TMCV − TMPV − TMYV/TMSUV

Who is held responsible for the Variance?  
 
Since this variance is on account of the variation in the ratio in which the constituent materials are mixed, the actual ratio being different from the standard ratio, the people or department responsible for authorising the usage and mixing of component materials for production can be held responsible for this variance.
Author Credit : The Edifier ... Continued Page M:10

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