Calculate material variances from the above data

Working table populated with the information that can be obtained as it is from the problem data

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 rest of the information that we make use of in problem solving is filled through calculations.

It is the difference between the Standard Cost of Standard Quantity for Actual Input and the Standard Cost of Actual Quantity.

⇒ Material Mix Variance (MMV)

Standard Cost of Actual Input

Standard Cost of Actual Quantity

Formula in useful forms

Note

• Material Mix Variance is a part of Material Usage Variance whose calculations are based on the gross input before deducting any losses and as such the Material Mix Variance should also be based on gross input.

  Thus, actual input (AI) in the formulae is gross input AQ_Mix.

• ×

  AI

  SI

  replaces the suffix (AI) in calculations.

For each Material Separately

Material Mix Variance

For all Materials together

Total Material Mix Variance

Material Mix variance for the Mix

TMMV = MMV_Mix, when MMV_Mix exists.

⋇ SQIL = SI − SO

⋇ AQIL = AI − AO

⋇ SC(AI) = SQ(AI) × SP

⋇ SCIL(AO) = SQIL(AO) × SP

⋇ SC(AQ) = AQ × SP

MMV = SC(AI) − SC(AQ)

Material Mix Variance due to

Alternative

• Calculating Costs in a working table

  Calculate SC and SC(AQ) based on the given data in a working table and then use formulae based on costs.

  Working Table

  	Standard			Actual
  	for SO
  	SQ	SP	SC	AQ	AP	SC(AQ)
  Material A Material B Material C	900 800 200	15 45 85	13,500 36,000 17,000	2,250 1,950 550	16 42 90	33,750 87,750 46,750
  Total/Mix	1,900		66,500	4,750		1,68,250
  Output	1,800 SO			4,320 AO

  ⋇ SC = SQ × SP

  ⋇ SC(AQ) = AQ × SP

  MMV

  =

  SC × AI SI − SC(AQ)

• Using Formula with Quantities and Prices

  Using the quantity and price data from the working table built using the problem data we may do all the working in the formula itself if we expand the formula using the relation cost = quantity × price.

  Working Table

  	Standard		Actual
  	for SO
  	SQ	SP	AQ	AP
  Material A Material B Material C	900 800 200	15 45 85	2,250 1,950 550	16 42 90
  Total/Mix	1,900		4,750
  Output	1,800 SO		4,320 AO

  MMV

  =

  (SQ × AI SI − AQ) × SP

  Since this formula involves the term AQ × SP and SQMR ≠ AQMR, it cannot be used for calculating the variance for the mix.

• MUV vs MMV

  Variance	Formula	Measures Variation in
  MUV MMV	SC(AO) − SC(AQ) SC(AI) − SC(AQ)	Quantity of Material used Material Quantity Mix Ratios

• Nature of Variance

  Based on the relations derived from the formulae for calculating MMV, we can identify the nature of Variance

  • SC(AI) ___ SC(AQ)
  • SQ(AI) ___ AQ

  MMV_Mat

  • SC(AI)_Mat ___ SC(AQ)_Mat
  • SQ(AI)_Mat ___ AQ_Mat

  MMV_Mix

  • SC(AI)_Mix ___ SC(AQ)_Mix

  The variance would be

  • zero when =
  • Positive when >
  • Negative when <

  We do not draw such a conclusion based on SQ(AI)_Mix ___ AQ_Mix as they both are the same.

  TMMV

  Variance of Mix and Total Variance are the same.

  Variance_Mix provides a method to find the total variance through calculations instead of by just adding up individual variances.

• Where there is only one material being used, there is no meaning in thinking of the Material Mix Variance. TMMV = 0 as well as MMV_Mat = 0 in such a case.

• Interpretation of the Variance

  For each material, for the input used

  Variance	Quantity input is	indicating
  None	as per standard	efficiency
  Positive	lesser than standard	efficiency
  Negative	greater than standard	inefficiency

  Using a material lesser than the standard is considered efficiency only in terms of cost.

  To conclude that using a lesser quantity is efficiency in general may not be appropriate as it results in other materials being used in higher quantities. Changing the mix ratio may affect the quality of the output also.

  Similar conclusions can be drawn for the mix based on the mix variance. The value of mix variance should not be viewed in isolation as it is an aggregate of individual variances and as such reflects their net effect.

  Mix variance data would be helpful to get an overall idea. In terms of cost, the mix variance data would give an immediate understanding of the gain/loss on account of variation in ratio of quantity mix. In taking corrective actions both the mix as well as individual variances should be considered.

  Eg: When the Total Variance is zero, we cannot conclude that the cost incurred on all materials is as per standard, as it might have been zero on account of

  1. each material variance being zero, or
  2. the unfavourable variance due to one or more materials is set off by the favourable variance due to one or more other materials.

     If the total variance is zero on account of this reason, it would be wrong to conclude that the SQMR and AQMR are the same.

• Who is answerable 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 would be made answerable for this variance.

• Conclusions based on Mix Ratios

  If the Standard Mix Ratio (SMR) and the Actual Mix Ratio (AMR) are the same, then there is no Mix variance either for individual materials or for the total mix.

  SQMR and AQMR being different is an indicator of existence of mix variance relating to individual materials.

  Standard Quantity Mix Ratio ~ SQMR

  A : B : C	=	900 kgs : 800 kgs : 200 kgs
  	=	9 : 8 : 2
  	=	9 19 : 8 19 : 2 19   [= AQA AQMix : AQB AQMix : AQC AQMix ]
  	=	0.474 : 0.421 : 0.105 (approximately)

  Actual quantity Mix Ratio ~ AQMR

  A : B : C	=	2,250 kgs : 1,950 kgs : 550 kgs
  	=	45 : 39 : 11
  	=	45 95 : 39 95 : 11 95   [= SQA SQMix : SQB SQMix : SQC SQMix ]
  	=	0.474 : 0.411 : 0.116 (approximately)

  We will be able to tell which materials are causing the variance by comparing the terms of the ratio.

  • AQMR value = SQMR value

    No variance since Materials have been taken in the same proportion as the standard

  • AQMR value < SQMR value

    Materials have been taken in a lesser proportion compared to the standard resulting in a negative variance

  • AQMR value > SQMR value

    Materials have been taken in a greater proportion compared to the standard resulting in a negative variance

  	AQMR		SQMR	Variance
  Material A Material B Material C	0.474 0.411 0.116	= < >	0.474 0.421 0.105	None Positive Negative

  Alternative 1

  Standard Quantity Mix Ratio ~ SQMR

  A : B : C	=	900 kgs : 800 kgs : 200 kgs
  	=	9 : 8 : 2
  		Multiplying all terms with AI SI , i.e. 2.5. To make it a whole number, 5, multiply with 2 (2.5 × 2) Use this number, 5, to derive the terms in the next step
  	=	45 : 40 : 10

  We get values as whole numbers

  Actual Quantity Mix Ratio ~ AQMR

  A : B : C	=	2,250 kgs : 1,950 kgs : 550 kgs
  	=	45 : 39 : 11

  	AQMR		SQMR	Variance
  Material A Material B Material C	45 39 11	= < >	45 40 10	None Positive Negative

  Alternative 2

  Comparing the proportion of AQ to SQ with (AI) value.

  (AI) = 2.5

  AQA SQA	=	2,250 kgs 900 kgs
  	=	2.5
  	=	(AI)
  		No Variance

  AQA SQA	=	1,950 kgs 800 kgs
  	=	2.4375
  	<	(AI)
  		Positive Variance

  AQC SQC	=	550 kgs 200 kgs
  	=	2.75
  	>	(AI)
  		Negative Variance

• MMV = MUV/MQV − MYV/MSUV
• MMV = MCV − MPV − MYV/MSUV

Verification

Building a table as below would help

By including a column for formula, this format would also work as the simplest format for calculating and presenting variances after building the working table