# Illustration - Problem

1,800 kgs of a product are planned to be produced using 900 kgs of Material A @ 15 per kg, 800 kgs of Material B @ 45/kg and 200 kgs of Material C @ 85 per kg at a total cost of 66,500. 4,320 kgs of the product were manufactured using 2,250 kgs of Material A @ 16 per kg, 1,950 kgs of Material B @ 42/kg and 550 kgs of Material C @ 90 per kg.

Calculate material variances from the above data

# Working Table

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

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

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.

# Formulae - Material Yield Variance (using Loss Measured based on Inputs)

What is the variation in total cost on account of the actual input loss being different from the standard input loss for actual output?

Material Yield Variance is the difference between the Standard Cost of Loss for Actual Output and the Standard Cost of Actual Loss

⇒ Material Yield/Sub-Usage Variance (MYV/MSUV)

 = SCIL(AO) − SC(AQIL) Standard Cost of Input Loss for Actual Output − Standard Cost of Actual Quantity of Input Loss

## Standard Cost of Input Loss for Actual Output

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

Standard Quantity of Input Loss for Actual Output × Standard Price of Mix

## Standard Cost of Actual Input Loss

SC(AQIL) = SC ×
 AQIL SQIL
= AQIL × SPMix

Actual Quantity of Input Loss × Standard Price of Mix

## Formula in useful forms

 MYV/MSUV = SCIL(AO) − SC(AQIL) Standard Cost of Input Loss for Actual Output − Standard Cost of Actual Quantity of Input Loss Or = [SQIL(AO) − AQIL] × SPMix Difference between Standard Quantity of Loss for Actual Output and Actual Quantity of Loss × Standard Price of Loss

# Illustration - Solution

We need to recalculate standards based on AO for finding MYV/MSUV using losses.
Working Table with recalculated standards
Standard Actual
for SO for AO
SQ SP SQ(AO) SC(AO) AQ AP AC
Factor 2.4
Material A
Material B
Material C
900
800
200
15
45
85
2,160
1,920
480
32,400
86,400
40,800
2,250
1,950
550
16
42
90
36,000
81,900
41,800
Total/Mix 1,900 4,560 1,59,600 4,750 1,67,400
Input Loss 100 240 8,400 430 15,050
Output 1,800
SO
4,320
SO(AO)
4,320
AO

⋇ SQIL = SI − SO

⋇ AQIL = AI − AO

(AO) =
 AO SO
=
 4,320 1,800
= 2.4
SQ(AO) = SQ ×
 AO SO
= SQ × 2.4

⋇ SC(AO) = SQ(AO) × SP

SPMix =
 SC(AO)Mix SQ(AO)Mix

⋇ SO(AO) = AO

SQIL(AO) = SQIL ×
 AO SO
= SQIL × 2.4

⋇ SCIL(AO) = SQIL(AO) × SP

MYV/MSUV = SCIL(AO) − SC(AQIL)

Material Yield Variance due to

 Material Mix, MYV/MSUVMix = SCIL(AO) − SC(AQIL) = 8,400 − 15,050 = − 6,650 [Adv]

## Alternative

Where MYV/MSUV is the only variance to be found, we may avoid calculating the cost/value data in the working table and use the formula involving quantities and prices.

MYV/MSUV = [SQIL(AO) − AQIL] × SPMix

Material Yield Variance due to

 Material Mix, MYV/MSUVMix = [SQIL(AO) − AQIL] × SPMix = [240 kgs − 430 kgs] × 35/kg = − 190 kgs × 35/kg = − 6,650 [Adv]

### Note

We can only identify the MYV/MSUV based on losses for all the materials together as the loss is measured over all materials and not for individual material.

The yield variance calculated with the formula SC(AO)− SC(AI) would also give the same result.

# MYV/MSUV with Losses - Miscellaneous Aspects

• ## 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.

• ## Ascertaining Output using Loss Data

Where input and output are of the same units, the data relating to output can be ascertained using input and loss data.
• ### Standard Output ~ SO

 = SI − SQILMix Standard Input − Standard Quantity of Input Loss of Mix
• ### Actual Output ~ AO

 = AI − AQILMix Actual Input − Actual Quantity of Input Loss of Mix

SI = SQMix and AI = AQMix

• ## Nature of Variance

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

• SCIL(AO) ___ SC(AQIL)
• SQIL(AO) ___ AQIL

## MYV/MSUVMat

• SCIL(AO)Mat ___ SC(AQIL)Mat
• SQIL(AO)Mat ___ AQILMat

## MYV/MSUVMix

• SCIL(AO)Mix ___ SC(AQIL)Mix
• SQIL(AO)Mix ___ AQILMix

The variance would be

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

### TMYV/MSUV

Variance of Mix and Total Variance are the same.

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

• ## Interpretation of the Variance

For the material mix, for the output achieved

Variance Input Loss is indicating
None as per standard efficiency
Positive lesser than standard efficiency
Negative greater than standard inefficiency

Similar conclusions can be drawn for the individual materials based on individual quantities input. However, it should be noted that the output is a result of the mix and measuring the influence of individual materials in quantitative terms is inappropriate.

The individual variances data would be of little help in taking corrective actions.