# 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 Mix Variance ~ MMV

What is the variation in the total cost on account of the actual quantity mix ratio being different from the standard quantity mix ratio?

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)

 = SC(AI) − SC(AQ) Standard Cost for Actual Input − Standard Cost of Actual Quantity

SC(AI) = SC ×
 AI SI
Or = SQ(AI) × SP

## Standard Cost of Actual Quantity

 SC(AQ) = AQ × SP

## Formula in useful forms

 MMV = SC(AI) − SC(AQ) Standard Cost for Actual Input − Standard Cost of Actual Quantity Or = [SQ(AI) − AQ] × SP Difference between Standard Quantity for Actual Input and Actual Quantity × Standard Price

## 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 AQMix.

• ×  AI SI
replaces the suffix (AI) in calculations.

## For each Material Separately

Material Mix Variance

 MMVMat = SC(AI)Mat − SC(AQ)Mat Or = [SQ(AI)Mat − AQMat] × SPMat

## For all Materials together

Total Material Mix Variance

 TMMV = ΣMMVMat Sum of the variances measured for each material separately

Material Mix variance for the Mix

 MMVMix = SC(AI)Mix − SC(AQ)Mix = [SQ(AI)Mix − AQMix] × SPMix (conditional) This formula can be used for the mix only when the actual quantity mix ratio is the same as the standard quantity mix ratio.

TMMV = MMVMix, when MMVMix exists.

# Illustration - Solution

We need to recalculate standards based on AI for finding MMV.
Working Table with recalculated standards
Standard Actual
for SO for AI
SQ SP SQ(AI) SC(AI) AQ AP SC(AQ)
Factor 2.5
Material A
Material B
Material C
900
800
200
15
45
85
2,250
2,000
500
33,750
90,000
42,500
2,250
1,950
550
16
42
90
33,750
87,750
46,750
Total/Mix 1,900 4,750 1,66,250 4,750 1,68,250
Input Loss 100 35 250 8,500 340 15,050
Output 1,800
SO
4,500
SO(AI)
4,320
AO

⋇ SQIL = SI − SO

⋇ AQIL = AI − AO

(AI) =
 AI SI
=
 AQMix SQMix
=
 1,900 4,750
= 2.5
SQ(AI) = SQ ×
 AI SI
= SQ × 2.5

⋇ SC(AI) = SQ(AI) × SP

SPMix =
 SC(AI)Mix SQ(AI)Mix
SO(AI) = SO ×
 AI SI
= SO × 2.5
SQIL(AI) = SQIL ×
 AI SI
= SQIL × 2.5

⋇ SCIL(AO) = SQIL(AO) × SP

⋇ SC(AQ) = AQ × SP

MMV = SC(AI) − SC(AQ)

Material Mix Variance due to

 Material A, MMVA = SC(AI)A − SC(AQ)A = 33,750 − 33,750 = 0 Material B, MMVB = SC(AI)B − SC(AQ)B = 90,000 − 87,750 = + 2,250 [Fav] Material C, MMVC = SC(AI)C − SC(AQ)C = 42,500 − 46,750 = − 4,250 [Adv] TMMV = − 2,000 [Adv] MMVMix = SC(AI)Mix − SC(AQ)Mix = 1,66,250 − 1,68,250 = − 2,000 [Adv]

## Alternative

Where MMV 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.

MMV = [SQ(AI) − AQ] × SP

Material Mix Variance due to

 Material A, MMVA = [SQ(AI)A − AQA] × SPA = (2,250 kgs − 2,250 kgs) × 15/kg = 0 kgs × 15/kg = 0 Material B, MMVB = [SQ(AI)B − AQB] × SPB = (2,000 kgs − 1,950 kgs) × 45/kg = 50 kgs × 45/kg = + 2,250 [Fav] Material C, MMVC = [SQ(AI)C − AQC] × SPC = (500 kgs − 550 kgs) × 85/kg = − 50 kgs × 85/kg = − 4,250 [Adv] TMMV = − 2,000 [Adv]

Standard Quantity Mix Ratio

 SQMR = SQA : SQB : SQC = 900 kgs : 800 kgs : 200 kgs = 9 : 8 : 2

Actual Quantity Mix Ratio

 AQMR = AQA : AQB : AQC = 2,250 kgs : 1,950 kgs : 550 kgs = 45 : 39 : 11

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

# Illustration - Solution (without recalculating standards)

Where SI ≠ AI, we can use the adjustment factor
 AI SI
in the formula itself for finding the variance.
• ## 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.

# MMV - Miscellaneous Aspects

• ## 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

## MMVMat

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

## MMVMix

• 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 ___ AQMix as they both are the same.

### TMMV

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.

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

# Formulae using Inter-relationships among Variances

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

## 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

0

+ 2,250

− 4,250

− 2,000
MQV/MUV
+ MPV
− 1,350
− 2,250
− 1,350
+ 5,850
− 5,950
− 2,750
− 8,650
+ 850
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