# 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 Cost Variance ~ MCV

For the output obtained, does the actual cost incurred vary from the standard cost that should have been incurred?

Material Cost Variance is the variance between the standard cost of materials for actual output and the actual cost of materials.

⇒ Material Cost Variance (MCV)

 = SC(AO) − AC Standard Cost for Actual Output − Actual Cost

## Actual Cost

 Based on inputs AC = AQ × AP Based on output = AO × AC/UO

Based on inputs
SC(AO) = SC ×
 AO SO
Based on output
Or = SQ(AO) × SP

## Formula in useful forms

 MCV = SC(AO) − AC Standard Cost for Actual Output − Actual Cost Or = AO × (SC/UO − AC/UO) Actual Output × Difference in Standard and Actual Costs per unit output

## Note

• ×  AO SO
replaces the suffix (AO) in calculations
• Using the formula based on output is prudent when the only data that is available is the data in the formula i.e. SC/UO, AC/UO and the AO.

In other cases where we are required to calculated SC/UO and AC/UO we need the SC and AC data which can be straight away used for finding the MCV.

## For each Material separately

Material Cost variance for a material

 MCVMat = SC(AO)Mat − ACMat Or = AO (SC/UOMat − AC/UOMat)

## For all Materials together

Total Material Cost variance

 TMCV = ΣMCVMat Sum of the variances measured for each material separately

Material Cost variance for the Mix

 MCVMix = SC(AO)Mix − ACMix Or = AO (SC/UOMix − AC/UOMix)

TMCV = MCVMix

# Illustration - Solution

We need to recalculate standards based on AO for finding MCV.
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

MCV = SC(AO) − AC

Material Cost Variance due to

 Material A, MCVA = SC(AO)A − ACA = 32,400 − 36,000 = − 3,600 [Adv] Material B, MCVB = SC(AO)B − ACB = 86,400 − 81,900 = + 4,500 [Fav] Material C, MCVC = SC(AO)C − ACC = 40,800 − 41,800 = − 8,700 [Adv] TMCV or MCVMix = − 7,800 [Adv] Material Mix, MCVMix = SC(AO)Mix − ACMix = 1,59,600 − 1,67,400 = − 7,800 [Adv]

## Alternative - Formula Based on Output

MCV = AO × (SC/UO − AC/UO)

Calculation of SC/UO requires the SC data and AC/UO requires the AC data. When these are available we can straight away use the earlier formula instead of calculating SC/UO and AC/UO.

# Illustration - Solution (without recalculating standards)

Where SO ≠ AO, we can use the adjustment factor
 AO SO
in the formula itself for finding the variance.
• ## Calculating Costs in a working table

Calculate SC and AC 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 AC
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
36,000
81,900
41,800
Total/Mix 1,900 66,500 4,750 1,67,400
Output 1,800
SO
4,320
AO

⋇ SC = SQ × SP

⋇ AC = AQ × AP

MCV = SC × AO SO
− AC
• ## 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
MCV = SQ × AO SO
× SP − AQ × AP
• ## Formula based on outputs

MCV = AO × (SC/UO − AC/UO)

Calculation of SC/UO requires the SC data and AC/UO requires the AC data. When these are available we can straight away use the other formulae instead of calculating SC/UO and AC/UO.

This formula does not require the data from recalculated standards.

# Constituents of Material Cost Variance

Material cost variance is a synthesis of two variances, Material Usage/Quantity Variance and Material Price Variance.
 MCV = SC(AO) − AC Adding and deducting SC(AQ) on the RHS we get MCV = SC(AO) − AC + SC(AQ) − SC(AQ) = [SC(AO) − SC(AQ)] + [SC(AQ) − AC] = Usage Variance + Price Variance = MUV + MPV

# MCV - Miscellaneous aspects

• ## Nature of Variance

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

• SC(AO) ___ AC

## MCVMat

• SC(AO)Mat ___ ACMat

## MCVMix

• SC(AO)Mix ___ ACMix

The variance would be

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

### TMCV

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 each material, for the actual output achieved

Variance Cost incurred 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 Material Cost Variance represents the total difference on account of a number of factors it would not be possible to directly fix the responsibility for the variance. This explains the reason for analysing the variance and segregating it into its constituent parts.

# Formulae based on interrelationship among variances

Material Cost variance can also be obtained from the other variances using the interrelationship among variances.
• MCV = MPV + MQV
• MCV = MPV + MMV + MYV

## Verification

In problem solving, these inter relationships would also help us to verify whether our calculations are correct or not.

Building a table as below would help

Material A Material B Material C Total/Mix
MYV/MSUV
+ MMV

MQV/MUV
+ MPV

MCV − 3,600 + 4,500 − 8,700 − 7,800

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