The following standard and actual data relating to an output of 150 units would help us in identifying the variances.

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.

• Quantity of materials.

  440 kgs actual as against a standard of 450 kgs indicating efficiency in using materials.

• Price of materials.

  5 actual as against a standard price of 4 indicating inefficiency in purchasing materials.

• Cost of materials.

  2,200 actual as against a standard cost of 1,800 indicating burden on account of cost of materials.

Why Recalculate Standards?

From the following data, we cannot straightaway say whether the output was obtained at a lesser or greater cost as well as whether the materials have been used efficiently.

This is because the actual data pertains to an output of 210 units as against the standard known for an output of 1,000 units.

Comparing the quantities and costs for the actual output of 210 units with those of the standard output of 1,000 units is inappropriate. We cannot say that 480 kgs were actually used as against a standard of 2,250 kgs or the actual cost is 960 as against a standard cost of 4,500.

However we would be able to say that the materials were acquired at a price of 2 as indicated by the standard. This conclusion can be drawn in spite of the standard output and actual output being different.

To be able to make a meaningful comparison straight away, we have to recalculate the standards such that the outputs 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 output

• Quantity of materials.

  480 kgs actual as against a standard of 472.5 kgs indicating inefficiency in using materials.

• Price of materials.

  2 actual as against a standard price of 2 indicating efficiency in purchasing materials.

  Note that we can draw this conclusion even without recalculating the standards.

• Cost of materials.

  960 actual as against a standard cost 945 indicating a slight burden on account of cost of materials.

To find the variance in quantity of material used we need the standard quantity for actual output [SQ(AO)] and the variance in the cost of materials we need the standard cost for actual output [SC(AO)].

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

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 and loss data worked out and arranged in the working table.

SQIL = SI − SO

AQIL = AI − AO

SC = SQ × SP

Notice that SO ≠ AO.

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

Logic (based on Cost of Material_A)

Standard Cost for an Output of 4,320 kgs

Using the data in the illustration above,

• For each Material separately

  Standard Quantity of a Material for the Actual Output

  SQ(AO)_Mat = SQ_Mat ×

  AO

  SO

• For all Materials together

  Standard Quantity of Mix for Actual Output

  SQ(AO)Mix	=	SQMix × AO SO
  Or	=	ΣSQ(AO)Mat Sum of the Standard Quantity for Actual Output of Individual Materials

Using the data in the illustration above,

• For each Material separately

  Standard Cost of a Material for Actual Output

  SC(AO)Mat	=	SCMat × AO SO
  Or	=	SQ(AO)Mat × SPMat

• For all Materials together

  Standard Cost of Mix for Actual Output

  SC(AO)Mix	=	SCMix × AO SO
  Or	=	SQ(AO)Mix × SPMix

  Standard Price of Mix

  SPMix	=	SCMix SQMix
  	=	ΣSCMat ΣSQMat

Using the data in the illustration above,

Alternative

If SQ(AO) and SP are readily available,

Standard quantity of input loss for the actual output represents the input quantity that would have been lost for the actual output had the materials been used (quantity) as per the standard.

• For each Material separately

  Standard Quantity of input loss for the Actual Output

  SQIL(AO)_Mat = SQIL_Mat ×

  AO

  SO

  Theoretically this measure can be calculated for each material separately. This would be of relevance only in cases where the input loss is being measured for each material separately and not over the mix.

• For all Materials together

  Standard Quantity of input loss of Mix for Actual Output

  SQIL(AO)Mix	=	SQILMix × AO SO
  Or	=	ΣSQIL(AO)Mat Sum of the Standard Quantity of input loss for Actual Output of Individual Materials This would be relevant only when the input loss is being measured for each material separately.

Using the data in the illustration above,

• For each Material separately

  Standard Cost of Input Loss of a Material for Actual Output

  SCIL(AO)Mat	=	SCMat × AO SO
  Or	=	SQIL (AO)Mat × SPMat

• For all Materials together

  Standard Cost of Input Loss of Mix for Actual Output

  SCIL(AO)Mix	=	SCMix × AO SO
  Or	=	SQIL (AO)Mix × SPMix

  Standard Price of Mix

  SPMix	=	SI SQ
  	=	ΣSCMat ΣSQMat

Using the data in the illustration above,

Alternative

If SQIL (AO) and SP are readily available,

The data for the standards based on the actual output is as below.

Using this factor, (AO), the SQ(AO) and SQIL(AO), from that the SC(AO) and SCIL(AO) 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.

3. SC(AO) = SQ(AO) × SP

SP_Mix will be required to calculate SC_Mix and SCIL_Mix directly using a formula, instead of as the sum of the values for the constitutent materials.

5. SO(AO) = AO

7. SCIL(AO) = SQIL(AO) × SP

After recalculating the standards we have Actuals and S_(AO) whose output values are the same.