Material Variance

Material Cost

In general

Value = Quantity × Price

For materials

Cost of Materials

From this we can see that the material cost is influenced by two factors,

1. The quantity of material used;
2. The price at which the materials are acquired.

Illustration for explanation

Consider the following data relating to the standard costs and the actual costs incurred in relation to the manufacture of a product. This data is referred to in all the explanations below

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.

Note

• The Price in total row is derived using the relation

  Value

  Quantity

• Price/unit input (standard)

  =	66,500 1,900 kgs
  =	35/kg

• Price/kg (actual)

  	=	1,67,400 4,750 kgs
  	=	3,348 95 /kg
  Or	=	35.2421/kg

  In using this in calculations, use fractional value if it is simple. Otherwise use the decimal number with substantial number of digits after the decimal.

Identities

SQ_A for standard quantity of material A, AQ_Mix for total quantity of actual mix (all the materials together) etc.

Mix

• Quantity of Mix indicates quantity of all the materials taken together.
• Cost of Mix indicates cost of all the materials taken together.
• Price of Mix indicates the weighted average price of all the material prices taking quantities as weights.

We will go through the explanation for the terms below.

Standard

• A basis for comparison
• The ideal in terms of which something can be judged
• a reference point against which other things can be evaluated
• criterion

The following terms involving standards are relevant to this topic.

• Standard Quantity ~ SQ

  The quantity of material required for manufacturing the product.

  It may be expressed for one or more units of output.

  1. Standard Material required for producing 1 unit is 10 kg.
  2. Standard output is 120 units and the material required for the same is 1,200 kg.

  • Standard Quantity of Material ~ SQ_Mat

    The quantity of each distinct type of material

  • Standard Quantity of Mix

    The quantity of all types of materials together

    SQMix

    =

    ΣSQMat Sum of the Standard Quantities of Individual Materials

    Where there is only one material SQ_Mix = SQ_Mat.

  From the data in the illustration

  SQA	=	900 kgs
  SQB	=	800 kgs
  SQC	=	200 kgs
  SQMix	=	1,900 kgs

• Standard Input

  The total quantity of materials input as per standards.

  SI	=	ΣSQMat
  	=	SQMix

  From the data in the illustration

  SI	=	SQMix
  	=	1,900 kgs

• Standard Mix Ratio

  Where there are two or more materials involved in the production process, Standard Mix Ratio indicates the ratio in which the component materials are to be mixed if the production process is carried on according to plans.

  This ratio can be for the quantities or for costs of materials used.

  Standard Quantity Mix Ratio

  SQMR

  =

  SQMat1 : SQMat2 : ... Ratio of Standard Quantities of Individual Materials

  Standard Cost Mix Ratio

  SCMR	=	SCMat1 : SCMat2 : ...
  Or	=	SQMat1 × SPMat1 : SQMat2 × SPMat2 : ...
  		Ratio of Standard Costs of Individual Materials

  From the data in the illustration,

  SQMR	=	SQA : SQB : SQC
  	=	900 kgs : 800 kgs : 200 kgs
  	=	9 : 8 : 2
  SCMR	=	SCA : SCB : SCC
  	=	13,500 : 36,000 : 17,000
  	=	27 : 72 : 34

• Standard Price

  The price at which the materials used in the production process are to be acquired.

  • Standard Price of Material ~ SP_Mat

    The price of each type of material

  • Standard Price of Mix

    The weighted average standard price of all types of materials taking quantities as weights.

    SPMix	=	SQMat1 × SPMat1 + SQMat2 × SPMat2 + ... SQMat1 + SQMat2 + ...
    	=	Σ(SQMat × SPMat) ΣSQMat
    	=	ΣSCMat ΣSQMat
    	=	SCMix SQMix

    Where there is only one material SP_Mix = SP_Mat.

    From the data in the illustration

    SP_A = 15/kg
    SP_B = 45/kg
    SP_C = 85/kg

    SPMix	=	66,500 1,900 kg
    	=	35/kg

• Standard Cost of Materials

  The cost of materials to be incurred on manufacturing the standard output.

  It is the value of standard quantity of materials taken at the standard price.

  SC

  =

  SQ × SP Standard Quantity × Standard Price

  • Standard Cost of Material

    The cost of each type of material distinctly

    SCMat

    =

    SQMat × SPMat

  • Standard Cost of Mix

    The standard cost of all types of materials together

    SCMix	=	SQMix × SPMix Standard Quantity of Mix × Standard Price of Mix
    Or	=	ΣSCMat Sum of the Standard Costs of Individual Materials

    Where there is only one material SC_Mix = SC_Mat.

  From the data in the illustration

  SCA	=	SQA × SPA
  	=	900 kgs × 15/kg	=	13,500
  SCB	=	SQB × SPB
  	=	800 kgs × 45/kg	=	36,000
  SCC	=	SQC × SPC
  	=	200 kgs × 85/kg	=	17,000
  SCMix			=	66,500
  SCMix	=	SQMix × SPMix
  	=	1,900 kgs × 35/kg	=	66,500

• Standard Output/Production ~ SO

  It is the output to be achieved using the standard quantity of materials.

  From the data in the illustration

  SO = 1,800 kgs

  Input and Output need not be in the same terms

  The input and output may or may not be in the same units.

  • Different Units

    The Standard Quantity of Materials required for producing 1 unit of DEXAR are 20 tons of AMY and 15 tons of TRE.

    Here the input (in tons) and output (in units) are in different terms.

  • Same Units

    The Actual Quantity of Materials used for producing 9 tons of SUFTRA is 12 tons comprising of 5 tons of Chemical A, 4 tons of Chemical B and 3 tons of Material Z.

    Here the input (in tons) and the output (in tons) are in the same terms.

• Standard Cost for Unit Output/Yield

  The standard cost incurred per unit output

  =	Standard Cost Standard Output

  ⇒ SC/UO

  =

  SC SO

  SC/UO ≡ SC/UY. Output is also addressed to as yield.

  • for each Material separately

    SC/UOMat

    =

    SCMat SO

    Since after mixing up the input materials, each material loses its individual identity, measuring SC/UO_Mat is not rational.

  • for all Materials together

    The standard cost incurred per unit output over all the materials taken together.

    SC/UOMix

    =

    SCMix SO

  From the data in the illustration,

  SC/UOA	=	SCA SO
  	=	13,500 1,800 kgs
  	=	27 19 /kg

  SC/UOB	=	SCB SO
  	=	36,000 1,800 kgs
  	=	72 19 /kg

  SC/UOC	=	SCC SO
  	=	17,000 1,800 kgs
  	=	34 19 /kg

  SC/UOMix	=	SCMix SO
  	=	66,500 1,800 kgs
  	=	7/kg

When there are losses

• Standard Quantity of Input Loss ~ SQIL

  It is the inupt lost in achieving the output. It may be expressed as an absolute figure of as a % of input.
  • Of the total input of 4,000 kgs, 250 kgs will be lost in achieving the output.
  • 10% of the input would be lost in processing.

• Loss of Mix

  In dealing with losses in calculating material variances we consider loss of mix and not of individual materials. This amounts to assuming that the losses are being ascertained after the materials are mixed up for the purposes of production.

  For being capable of identifying the loss for individual materials, the production process should be such that the materials are processed individually till the point where the losses are ascertained. Losses should be ascertained and then the net quantities are to be combined to form the material mix.

• Standard Output (from loss data)

  Where input and output are expressed in the same units and loss is expressed in input terms, we will be able to calculate the output.

  Standard Output ~ SO

  =	SI − SQIL Standard Input − Standard Quantity of Input Loss

  SI = SQ_Mix

• Standard Cost of Input Loss

  It is the cost incurred on the input loss quantity.

  It is obtained by valuing the input loss quantity at the standard price.

  SCIL

  =

  SQIL × SP Standard Quantity of Input Loss × Standard Price

  For the mix of materials

  SCIL_Mix

  = SQIL_Mix × SP_Mix

• Actual Quantity of Materials ~ AQ

  The quantity of material actually used in the manufacture of the product.

  It may be expressed for one or more units of output.

  1. Actual Material used for producing 1 kg of the product is 18 units.
  2. 2,450 tons of the material have been used in producing an output of 8 million units.

  • Actual Quantity of Material ~ AQ_Mat

    The quantity of each type of material

  • Actual Quantity of Mix

    The quantity of all types of materials together

    AQMix

    =

    ΣAQMat Sum of the Actual Quantities of Individual Materials

    Where there is only one material AQ_Mix = AQ_Mat.

  From the data in the illustration

  AQA	=	2,250 kgs
  AQB	=	1,950 kgs
  AQC	=	550 kgs
  AQMix	=	4,750 kgs

• Actual Input

  The total quantity of materials actually input.

  AI	=	ΣAQMat
  	=	AQMix

  From the data in the illustration

  AI	=	AQMix
  	=	4,750 kgs

• Actual Mix Ratios

  Where there are two or more materials involved in the production process, Actual Mix Ratio indicates the ratio in which the component materials are actually mixed.

  This ratio can be for the quantities or for costs of materials used.

  Actual Quantity Mix Ratio

  AQMR

  =

  AQMat1 : AQMat2 : ... Ratio of Actual Quantities of Individual Materials

  Actual Cost Mix Ratio

  ACMR	=	ACMat1 : ACMat2 : ...
  Or	=	AQMat1 × APMat1 : AQMat2 × APMat2 : ...
  		Ratio of Actual Costs of Individual Materials

  From the data in the illustration,

  AQMR	=	AQA : AQB : AQC
  	=	2,250 kgs : 1,950 kgs : 550 kgs
  	=	45 : 39 : 11
  ACMR	=	ACA : ACB : ACC
  	=	36,000 : 81,900 : 41,800
  	=	40 : 91 : 55

• Actual Price (of Materials Input) ~ AP

  The price at which the materials used in the production process are acquired.

  Cost and Value

  By Price we mean price based on the value of materials used and not just the cost of purchase. Value would also include the direct expenses incurred before bringing the material into the store or more specifically to the production area.

  Where there are no direct expenses relating to materials, value would be the purchase price itself.

  • Actual Price of Material ~ AP_Mat

    The price of each type of material

  • Actual Price of Mix

    The weighted average actual price of all types of materials taking quantities as weights.

    APMix	=	AQMat1 × APMat1 + AQMat2 × APMat2 + ... AQMat1 + AQMat2 + ...
    	=	Σ(AQMat × APMat) ΣAQMat
    	=	ΣACMat ΣAQMat
    	=	ACMix AQMix

    Where there is only one material AP_Mix = AP_Mat.

  From the data in the illustration

  AP_A = 15/kg
  AP_B = 45/kg
  AP_C = 85/kg

  ARMix	=	ACMix AQMix
  	=	1,67,400 4,750 kg
  	=	3,348 95 /kg (Or) 35.2421/kg

• Actual Cost

  The actual cost of materials incurred for manufacturing the actual output.

  It is the value of actual quantity of materials taken at the actual price.

  AC

  =

  AQ × AP Actual Quantity × Actual Price

  • Actual Cost of Material

    The cost of each type of material distinctly.

    ACMat

    =

    AQMat × APMat

  • Actual Cost of Mix

    The actual cost of all types of materials together

    ACMix	=	AQMix × APMix Actual Quantity of Mix × Actual Price of Mix
    Or	=	ΣACMat Sum of the Actual Costs of Individual Materials

    Where there is only one material AC_Mix = AC_Mat.

  From the data in the illustration

  ACA	=	AQA × APA
  	=	2,250 kgs × 16/kg	=	36,000
  ACB	=	AQB × APB
  	=	1,950 kgs × 42/kg	=	81,900
  ACC	=	AQC × APC
  	=	550 kgs × 90/kg	=	41,800
  ACMix			=	1,67,400
  ACMix	=	AQMix × APMix
  	=	4,750 kgs × 3,348 95 /kg	=	1,67,400

  Note

  In calculations use fractions where it is a simple one to reduce the need for corrections on account of approximations. Alternatively take more digits after the decimal.

  35.2421 × 4,750 = 1,67,399.975

• Actual Output/Production ~ AO

  It is the output achieved using the actual quantity of materials.

  From the data in the illustration

  AO = 4,320 kgs

  Input and Output need not be in the same terms

  The input and output may or may not be in the same units.

  • Different Units

    The Actual Quantity of Materials required for producing 1 unit of DEXAR are 20 tons of AMY and 15 tons of TRE.

    Here the input (in tons) and output (in units) are in different terms.

  • Same Units

    The Actual Quantity of Materials used for producing 9 tons of SUFTRA is 12 tons comprising of 5 tons of Chemical A, 4 tons of Chemical B and 3 tons of Material Z.

    Here the input (in tons) and the output (in tons) are in the same terms.

• Actual Cost of Output/Yield per unit

  The actual cost incurred per unit output.

  AC/UO	=	Actual Cost Actual Output
  	=	AC AO

  Output is also addressed to as yield. As such ACY/U ≡ AC/UO.

  for each Material separately

  AC/UOMat

  =

  ACMat AO

  Since after mixing up the input materials, each material loses its individual identity, measuring AC/UO_Mat is not rational.

  for all Materials together

  The actual cost incurred per unit output over all the materials taken together.

  AC/UOMix

  =

  ACMix AO

  From the data in the illustration,

  AC/UOMix	=	ACMix AO
  	=	1,67,400 4,320 kgs
  	=	837 114 /kg
  Or	=	7.342/kg

When there are losses

• Actual Quantity of Input Loss ~ AQIL

  It is the inupt lost in achieving the output. It may be expressed as an absolute figure of as a % of input.
  • Of the total input of 5,000 kgs, 350 kgs are lost in achieving the output.
  • 8% of the input is lost in processing.

• Loss of Mix

  In dealing with losses in calculating material variances we consider loss of mix and not of individual materials. This amounts to assuming that the losses are being ascertained after the materials are mixed up for the purposes of production.

• Actual Output (from loss data)

  Where input and output are expressed in the same units and loss is expressed in input terms, we will be able to calculate the output.

  Actual Output ~ AO

  =	AI − AQIL Actual Input − Actual Quantity of Input Loss

  AI = AQ_Mix

• Standard Cost of Input Loss

  It is the standard cost of actual input loss quantity.

  It is obtained by valuing the actual input loss quantity at the standard price.

  SC(ACIL)

  =

  AQIL × SP Actual Quantity of Input Loss × Standard Price

  For the mix of materials

  ACILMix

  =

  AQILMix × SPMix

Budget

• a depiction of a future activity in quantitative terms.

1. Production Budget

   A Production Budget indicates the production that is planned to be achieved over a future period through a production process.

2. Material Budget

   A Material Budget indicates the quantity of materials required for the production that is planned to be achieved over a future period through a production process.

3. Cash Budget

   A cash budget indicates the inflow and outflow of cash over a certain future period.

4. Expenditure Budget

   An expenditure budget indicates the expenditure that is to be incurred over the budget period.

Budgeted

• relates to a budget

By the term Budgeted Data in this topic, we mean the data pertaining to a specified budget indicating a level of activity that has been planned to be achieved.

The following terms involving budgets are relevant to this topic.

• Budgeted Output/Production ~ BO

  The output that is planned to be achieved during a period through the production process.

• Budgeted Quantity

  The standard quantity of materials to be input into the production process for achieving the budgeted output.

  BQ

  =

  SQ/UO × BO Standard Quantity of Materials for unit output × Budgeted Output

• Budgeted Price

  Budgets are prepared as per standards. As such Budgeted Price is nothing but standard price.

  BP = SP

• Budgeted Cost

  The cost of materials to be incurred for manufacturing the budgeted output. It is the value of budgeted quantity of materials taken at the standard price.

  BC

  =

  BQ × SP Budgeted Quantity × Standard Price

Examples

1. Budgeted Output is the output that is planned to be achieved by the organisation in a given period/process and Standard Output is that output for which the standards are expressed.
2. Standard Cost gives an idea of how much each unit of the product should cost under normal circumstances. Budget Cost gives an idea of the cost that should be incurred for bringing out the budget quantity of output (over a certain period or in a certain process) under normal circumstances.

We use the terms Budgeted and Standard synonymously at times, but they would not be the same in all cases.

For analysing material variances, we need standards

Budgets are always as per the standard

Since budgeted data is standard data for a particular production level we do not need separate data for the standard when the budgeted data is known.

SO = BO

SO ≠ BO