# 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/Sub-Usage Variance (MYV/MSUV)

What is the variation in total cost on account of the actual output/yield being different from the standard output for the actual input (AQMix).

Material Yield/Sub-Usage Variance is the difference between the Standard Cost of Actual Output and the Standard Cost of Actual Input.

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

 = SC(AO) − SC(AI) Standard Cost for Actual Output − Standard Cost of Actual Input

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

Based on output

Or = AO × SC/UO

SC(AI) = SC ×
 AI SI
Or = SQ(AI) × SP

## Formula in useful forms

MYV/MSUV = SC(AO) − SC(AI)

Standard Cost for Actual Output − Standard Cost of Actual Input

Or = SC × (
 AO SO
 AI SI
)

Standard Cost × difference of ratios of actual output to standard output and actual input to standard input.

Or =
[SQ(AO) − SQ(AI)] × SP

Difference in Standard Quantities for Actual Output and Actual Input × Standard Price

Or = [AO − SO(AI)] × SC/UO

Difference between actual output and standard output for actual input × Standard Cost for output per unit.

## Note

• ×  AO SO
replace the suffix (AO) and ×  AI SI
replace the suffix (AI) in calculations.
• AI = AQMix and SI = SQMix.

### For each Material Separately

Material Yield or Sub Usage Variance

MYV/MSUVMat = SC(AO)Mat − SC(AI)Mat
Or = SCMat × (
 AO SO
 AI SI
)
Or = [SQ(AO)Mat − SQ(AI)Mat] × SPMat
Or = [AOMat − SO(AI)Mat] × SC/UOMat

### For all Materials together

When two or more types of materials are used for the manufacture of a product, the total Material Yield/Sub-Usage variance is the sum of the variances measured for each material separately.

Total Material Yield/Sub-Usage variance

 TMYV/TMSUV = ΣMYV/MSUVMat Sum of the variances measured for each material separately

Material Yield/Sub-Usage variance for the Mix

MYV/MSUVMix = SC(AO)Mix − SC(AI)Mix
Or = SCMix × (
 AO SO
 AI SI
)
Or = [SQ(AO)Mix − SQ(AI)Mix] × SPMix
Or = [AOMix − SO(AI)Mix] × SC/UOMix

# Illustration - Solution

We need to recalculate standards based on both AO and AI for finding MYV/MSUV.
Working Table with recalculated standards
Standard Actual
for SO for AO for AI
SQ SP SQ(AO) SC(AO) SQ(AI) SC(AI) AQ AP
Factor 2.4 2.5
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
2,000
500
33,750
90,000
42,500
2,250
1,950
550
16
42
90
Total/Mix 1,900 35 4,560 1,59,600 4,750 1,66,250 4,750
Output 1,800
SO
4,320
SO(AO)
4,500
SO(AI)
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) SQ(AO)

⋇ SO(AO) = AO

SQIL(AO) = SQIL ×
 AO SO
= SQIL × 2.4

⋇ SCIL(AO) = SQIL(AO) × SP

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

⋇ SC(AI) = SQ(AI) × SP

SQIL(AI) = SQIL ×
 AI SI
= SQIL × 2.5

⋇ SCIL(AI) = SQIL(AI) × SP

SO(AI) = SO ×
 AI SI
= SO × 2.5

MYV/MSUV = SC(AO) − SC(AI)

Material Yield/Sub-Usage Variance due to

 Material A, MYV/MSUVA = SC(AO)A − SC(AI)A = 32,400 − 33,750 = − 1,350 [Adv] Material B, MYV/MSUVB = SC(AO)B − SC(AI)B = 86,400 − 90,000 = − 3,600 [Adv] Material C, MYV/MSUVC = SC(AO)C − SC(AI)C = 40,800 − 42,500 = − 1,700 [Adv] TMYV/TMSUV = − 6,650 [Adv] Material Mix, MYV/MSUVMix = SC(AO)Mix − SC(AI)Mix = 1,59,600 − 1,66,250 = − 6,650 [Adv]

## Alternative

Where MYV is the only variance to be calculated we may use the formula involving quantities and prices and avoid calculating costs/values in the working table.

MYV/MSUV = [SQ(AO) − SQ(AI)] × SP

Material Yield/Sub-Usage Variance due to

 Material A, MYV/MSUVA = [SQ(AO)A − SQ(AI)A] × SPA = (2,160 − 2,250) × 15 = − 90 × 15 = − 1,350 [Adv] Material B, MYV/MSUVB = [SQ(AO)B − SQ(AI)B] × SPB = (1,920 − 2,000) × 45 = − 80 × 45 = − 3,600 [Adv] Material C, MYV/MSUVC = [SQ(AO)C − SQ(AI)C] × SPC = (480 − 500) × 85 = − 50 × 85 = − 1,700 [Adv] TMYV/TMSUV = − 6,650 [Adv] Material Mix, MYV/MSUVMix = [SQ(AO)Mix − SQ(AI)Mix] × SPMix = (4,560 − 4,750) × 35 = − 190 × 35 = − 6,650 [Adv]

Even in this case, if we intend to use the formula for the mix, we need either the SCMix or SC(AO)Mix or SC(AI)Mix to be able to find the SPMix

SPMix =
 SC(AO)Mix SQ(AO)Mix
=
 1,59,600 4,560
= 35

# Illustration - Solution (without recalculating standards)

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

Calculate SC 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
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
Total/Mix 1,900 66,500 4,750
Output 1,800
SO
4,320
AO

⋇ SC = SQ × SP

MYV/MSUV = SC × ( AO SO
−  AI SI
)
• ## 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
MYV/MSUV = SQ × SP × ( AO SO
−  AI SI
)

Even in this case, if we intend to use the formula for the mix, we need the SCMix

• ## Using Formula Based on Outputs

Working Table
Standard Actual
for SO
SQ SP SC SC/UO AQ AP
Material A 900 15 13,500  27 19
2,250 16
Material B 800 45 36,000  72 19
1,950 42
Material C 200 85 17,000  34 19
550 90
Total/Mix 1,900 35 66,500 7 4,750
Output 1,800
SO
4,320
AO
SC/UO =  SC SO
MYV/MSUV = [AO − SO × AI SI
] × SC/UO

# MYV/MSUV - Miscellaneous Aspects

• ## Nature of Variance

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

• SC(AO) ___ SC(AI)
•  AO SO
___  AI SI
• SQ(AO) ___ SQ(AI)
• AO ___ SO(AI)

## MYV/MSUVMat

• SC(AO)Mat ___ SC(AI)Mat
•  AO SO
___  AI SI
• SQ(AO)Mat ___ SQ(AI)Mat
• AOMat ___ SO(AI)Mat

## MYV/MSUVMix

• SC(AO)Mix ___ SC(AI)Mix
•  AO SO
___  AI SI
• SQ(AO)Mix ___ SQ(AI)Mix
• AOMix ___ SO(AI)Mix

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.

• ## Individual Variances in Standard Cost Mix Ratio

This variance measures the efficiency in deriving output out of the total quantity of materials used as a whole and not of individual materials.

Any variation on account of varying the individual materials is revealed by the Material Mix Variance.

This can be identified from the fact that the calculation of the variance for individual materials is the equivalent of dividing the variance for the mix among the materials in the standard cost mix ratio (SCMR).

MYV/MSUMat

= MYV/MSUMix × standard cost mix proportion

From the data in the illustration,

Standard Cost Mix Ratio ~ SCMR

A : B : C = SCA : SCB : SCC
= 13,500 : 36,000 : 17,000
= 27 : 72 : 34
=  27 133
:  72 133
:  34 133

MYV/MSUMix = − 6,650

MYV/MSUVA = − 6,650 ×  27 133
= − 50 × 27
= − 1,350
MYV/MSUVB = − 6,650 ×  72 133
= − 50 × 72
= − 3,600
MYV/MSUVC = − 6,650 ×  34 133
= − 50 × 34
= − 1,700
• ## Interpretation of the Variance

For the material mix, 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 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.

• ## Who is answerable for the Variance?

Since this variance is on account of more or less yield for the input used, the people or department responsible for managing the production operations (say manufacturing department) is answerable for this variance.

# Formulae using Inter-relationships among Variances

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

## 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
− 1,350
0
− 3,600
+ 2,250
− 1,700
− 4,250
− 6,650
− 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