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 for actual output and the standard cost of actual quantity of materials used.

⇒ Material Quantity/Usage Variance (MQV/MUV)

Standard Cost for Actual Output

Standard Cost of Actual Quantity

Formula in useful forms

Note

• ×

  AO

  SO

  replaces the suffix (AO) in calculations
• Finding the costs by building up the working table and using the formula involving costs is the simplest way to find variances.
• The formula involving costs can be used to find the Material Quantity/Usage Variance for individual materials as well as the mix of materials. Appropriate suffix _Mat or _Mix is used in the formula as an indicator.

For each Material separately

Material Quantity/Usage variance for a material

For all Materials together

Total Material Quantity/Usage Variance

Material Quantity/Usage variance for the Mix

TMQV/TMUV = MQV/MUV_Mix, when MQV/MUV_Mix exists.

The Math

Consider the relation, Value (V) = Quantity (Q) × Price (P).

If P is constant,

V = QP

⇒ V₁ = Q₁ × P → (1)

⇒ V₂ = Q₂ × P → (2)

(1) − (2) gives

⇒ V₁ − V₂ = Q₁ × P − Q₂ × P

⇒ V₁ − V₂ = (Q₁ − Q₂) × P

⇒ ΔV = ΔQ × P, where P is a constant

⇒ ΔV ∞ ΔQ

Change in value varies as change in quantity

By taking both prices at standard we are eliminating the effect of difference between the standard price and actual price, thereby leaving only the difference between usage quantities.

⋇ SQIL = SI − SO

⋇ AQIL = AI − AO

⋇ SC(AO) = SQ(AO) × SP

⋇ SO(AO) = AO

⋇ SCIL(AO) = SQIL(AO) × SP

⋇ SC(AQ) = AQ × SP

MQV/MUV = SC(AO) − SC(AQ)

Material Quantity/Usage 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.

  	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

  MQV/MUV

  =

  SC × AO SO − 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

  MUV/MVQ = (SQ ×

  AO

  SO

  − AQ) × SP

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

• Nature of Variance

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

  • SC(AO) ___ SC(AQ)
  • SQ(AO) ___ AQ

  MQV/MUV_Mat

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

  MQV/MUV_Mix

  • SC(AO)_Mix ___ SC(AQ)_Mix
  • SQ(AO)_Mix ___ AQ_Mix (conditional)

    Only when SQMR = AQMR

  The variance would be

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

  TMQV/TMUV

  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.

• Interpretation of the Variance

  For each material, for the output achieved

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

  Similar conclusions can be drawn for the mix based on the mix variance. However, it should be noted that the mix variance is an aggregate of individual variances and as such reflects their net effect.

  Mix variance data would be helpful to get an overall idea only. It would not be as useful as individual variances data in taking corrective actions.

  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.

• Who is answerable for the Variance?

  Since this variance is on account of the quantity of material used being more or less than the standard, the people or department responsible for production can be identified as the ones answerable for this variance.

  This conclusion would be appropriate when there is only type of material in use.

  When there are two or more types of material

  When two or more types of materials are being used for the manufacture of a product, making only the people responsible for production answerable for the variance may not be appropriate as there would be two factors influencing the usage of materials.
  1. the ratio in which the quantities of constituent materials are mixed and
  2. the actual yield from the mix.

  That is the reason, when there are two or more types of material being used, the Quantity/Usage variance is further broken down into two parts called Mix Variance and Yield Variance.

• MQV/MUV = MCV − MPV
• MQV/MUV = MMV + 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