The following standard and actual data relating to an input of 1,200 kgs would help us in identifying the variance.

Output (_O) is in units, Quantities (_Q) are in kgs, Prices (_P) are in monetary value per unit quantity and Costs (_C) are in monetary values.

• Mix of materials.

  Materials have been mixed in a proportion different from the standard.

  Material A 520 kgs instead of 500kgs, Material B 430 kgs instead of 400 kgs and Material C 250 kgs instead of 300 kgs.

  Mix Ratios

  There being a difference in mix can also be identified by using the mix ratios. However, this needs us to calculate the ratios and does not allow conclusion by a straight away comparison of material quantities.

  Standard Quantity Mix Ratio

  SQMR	=	SQA : SQB : SQC
  	=	500 kgs : 400 kgs : 300 kgs
  	=	5 : 4 : 3

  Actual Quantity Mix Ratio

  AQMR	=	AQA : AQB : AQC
  	=	520 kgs : 430 kgs : 250 kgs
  	=	52 : 43 : 25

  AQMR is different from the SQMR

• Yield from materials.

  A total input of 1,200 kgs has yielded an output of 2,400 units as against a standard of 2,500 units.

Why Recalculate Standards?

From the following data, we cannot straightaway say whether there is any variance on account of the mix as well as if the yield is as per the standard.

This is because the actual data pertains to an input of 4,750 kgs as against the standard known for an input of 1,900 kgs.

Comparing the quantities and yield for the actual input of 4,750 kgs with those of the standard input of 1,900 kgs is inappropriate. We cannot say that 2,250 kgs of A were actually used as against a standard of 900 kgs or the actual output/yield is 4,320 kgs as against a standard output of 1,800 kgs.

To be able to make a meaningful comparison straight away, we have to recalculate the standards such that the inputs are the same both in the actual data and the standard data, thereby enabling us to derive variances by comparison.

The comparison becomes meaningful once we obtain the standards for the actual input.

• Mix of materials.

  Materials B and C have been mixed in a proportion different from the standard.

  Material A 2,250 kgs as per standard, Material B 1,950 kgs instead of 2,000 kgs and Material C 550 kgs instead of 500 kgs.

• Yield from materials.

  The input has yielded an output of 4,320 kgs as against a standard of 4,500 kgs.

To find the variance in mix of and yield from material used we need the standard quantity for actual input [SQ(AI)] and the value of the variance we need the standard cost for actual input [SC(AI)] as well as the standard cost of actual quantity [SC(AQ)].

Since standards can be built for any production level we were able to recalculate the standards for the actual input.

The data from the problem obtained as it is, arranged in a working table.

Output (_O) is in units of measurement of output, Quantities (_Q) are in units of measurement of input, Prices (_P) are in monetary value per unit input and Costs (_C) are in monetary values.

Assuming the input and output are in kgs for the purpose of explanations.

The Standard cost data worked out and arranged in the working table.

SC = SQ × SP

Notice that SI ≠ AI i.e. SQ_Mix ≠ AQ_Mix

We ignored other possible calculations like AC = AQ × AP, since we are only trying to recalculate standards primarily quantities and costs.

By Input here we mean the quantity of Mix.

Logic (based on Cost of Material_Mix)

Standard Cost for an Input of 4,750 kgs

Using the data in the illustration above,

It represents the quantity of each material that should have been present in the actual mix had the materials been taken in ratio of standard mix.

• For Each Material Separately

  Standard Quantity of a Material for the Actual Input

  SQ(AI)Mat

  =

  SQMat × AI SI

• For all Materials together

  SQ(AI)Mix	=	SQMix × AI SI
  Or	=	ΣSQ(AI)Mat Sum of the Standard Quantity for Actual Input of Individual Materials
  Or	=	AQMix
  	=	ΣAQMat

  Since SQ(AI)_Mix = AQ_Mix, we don't need to calculate this.

Using the data in the illustration above,

• For each Material separately

  Standard Cost of a Material for the Actual Input

  SC(AI)Mat	=	SCMat × AI SI
  Or	=	SQ(AI)Mat × SPMat

• For all Materials together

  Standard Cost of Mix for Actual Input

  SC(AI)Mix	=	SCMix × AI SI
  Or	=	SQ(AI)Mix × SPMix

  Standard Price of Mix

  SPMix	=	SCMix SQMix
  	=	ΣSCMat ΣSQMat

Using the data in the illustration above,

Alternative

If SQ(AI) and SP are readily available

Consider the data from the illustration above.

• For each Material separately

  AQ_Mat may or may not be equal to AI_Mat for individual materials. But AQ_Mix = AI_Mix.

  For the purpose of this calculation, the input we intend to consider is the actual quantity of input and not the Actual input arrived at by recalculating the total actual input in the standard quantity mix ratio.

  SO(AI)Mat	=	SO(AQ)Mat
  	=	SO × AQMat SQMat

  Note

  Measuring the output for each input material is improbable since the output/yield is relevant to all the inputs together.

  This calculation is intended to give an idea of the possibility. It is not used anywhere in analysing variances.

• For all Materials together

  Since AQ_Mix = AI_Mix, taking either AI or AQ would give the same result for the mix.

  SO(AI)Mix	=	SO × AQMix SQMix
  	=	SO × AI SI

Using the data in the illustration above,

Note

• SO(AQ)_Mix ≠ ΣSO(AQ)_Mat

  The standard output for the actual mix is not equal to the sum of the Standard Outputs for each material separately.

  Each of the SO(AI) represents the total output that could have been achieved, whether we calculate it based on individual materials or the total input.

  Thus the idea that Σ___Mat = ___Mix should not be applied here. The values relating to individual materials do not add up to form the value relating to the mix.

• SO(AQ)_Mix = SO(AQ)_Mat under specific conditions

  The standard output for the actual mix may be equal to the Standard Outputs for a material if the actual material is in the same proportion to the standard material as the actual mix to standard mix.

  AQMix SQMix

  =

  AQMat SQMat

  ⇒ SO × AQMix SQMix

  =

  SO × AQMat SQMat

  ⇒ SO(AQ)_Mix = SO(AQ)_Mat

  From the data in the above illustration

  AQMix SQMix	=	4,750 kgs 1,900 kgs
  	=	2.5

  For Material A

  AQA SQA	=	2,250 kgs 900 kgs
  	=	2.5

  SO(AQ)_Mix = SO(AQ)_A = 4,500 kgs

  For Material B

  AQB SQB	=	1,950 kgs 800 kgs
  	=	2.4375

  SO(AQ)_Mix ≠ SO(AQ)_B
  [4,500 kgs ≠ 4,387.50]

• AQMix

  SQMix

  =

  AQMat

  SQMat

  can also be interpreted as

  SQMat

  SQMix

  =

  AQMat

  AQMix

  The proportion of a material to the mix is the same both in the actuals and standards.

• If the standard quantity mix ratio and the actual quantity mix ratio are the same, then all the materials would satisfy the relation

  AQMat

  AQMix

  =

  SQMat

  SQMix

  .

  In such a case, SO(AQ)_Mix = each of SO(AQ)_Mat

• for each material separately

  The cost of a material type valued at its standard price

  SC(AQ)_Mat = AQ_Mat × SP_Mat

• for all materials together

  The total cost of all material types valued at their standard prices together.

  Standard Cost of Actual Quantity of Mix

  SC(AQ)Mix	=	ΣSC(AQ)Mat Sum of the Standard Costs of Actual (total) Time of Individual Materials
  Or	=	AQMix × SPMix (conditional) Actual Quantity of Mix × Standard Price of Mix This will be true only if the standard quantity mix ratio (SQMR) and the actual quantity mix ratio (AQMR) are the same.

  If SC(AQ)_Mix = AQ_Mix × SP_Mix,

  AQ_Mix × SP_Mix = ΣSC(AQ)_Mat

  SP_Mix is the weighted average of Standard Prices taking standard times (ST) as weights and ΣSC(AQ)_Mat consider actual quantities (AQ). Thus, if SQMR ≠ AQMR, then SC(AQ)_Mix ≠ AQ_Mix × SP_Mix

From the data in the illustration

Verification :

SC(AQ)_Mix ≠ AQ_Mix × SP_Mix

SC(AI) and SC(AQ) are different

SC(AQ) represents that standard cost of actual quantities of materials taking the actual quantities and valuing them at standard prices.

SC(AI) = SC(AQ) if the standard quantity mix ratio and the actual quantity mix ratio are the same.

Using this factor, (AI), the SQ(AI) and from that the SC(AI) can be calculated straight away in the working table. To make these calculations convenient and avoid errors, present this factor also in the working table.

⋇ SC(AI) = SQ(AI) × SP

⋇ SC(AQ) = AQ × SP

Where we need to recalculate the standards we may avoid ascertaining the values for the given standards as the recalculated values are the ones that would be useful.

After recalculating the standards we have Actuals and S_(AI) whose input (Q_Mix) values are the same.