Material Variances - Formula Review - Illustration

Working Table

Making a working table would form the first step in our problem solving effort. Once the working table is built, the rest of the approach is stereotypical.

Factually, our problem solving capability is limited by our ability to interpret the problem. Whatever may be the way the problem is presented (what we call problem models), if we can arrange the information into the working table, the rest of the task becomes easy.

Understanding the meaning of the variance helps derive the formula for calculating the variance even if we fail recollecting.

Recalculating Standards

Building the following working table amounts to recalculating standards for both actual inputs and actual outputs. It enables us to use the simplest formulae involving costs for deriving the variances. It helps us solve almost all problems in a similar manner.
Working Table
Standard Actual
for SO for AO for AI
SQ SP SQ(AO) SC(AO) SQ(AI) SC(AI) AQ AP AC SC(AQ)
Factor (AO) (AI)
Material A
Material B
Material C
SQA
SQB
SQC
SPA
SPB
SPC
SQ(AO)A
SQ(AO)B
SQ(AO)C
SC(AO)A
SC(AO)B
SC(AO)C
SQ(AI)A
SQ(AI)B
SQ(AI)C
SC(AI)A
SC(AI)B
SC(AI)C
AQA
AQB
AQC
APA
APB
APC
ACA
ACB
ACC
SC(AQ)A
SC(AQ)B
SC(AQ)C
Total SQMix SPMix SQ(AO)Mix SC(AO)Mix SQ(AI)Mix SC(AI)Mix AQMix APMix ACMix SC(AQ)Mix
Output SO SO(AO) SO(AI) AO

Output (_O) is in units, Quantities (_Q) and Losses (_L) are in kgs, Prices (_P) are in monetary value per kg and Costs (_C) are in monetary values.

1. SQ(AO) = SQ ×
AO
SO

2. SC(AO) = SQ(AO) × SP

3. SO(AO) = AO

4. SQ(AI) = SQ ×
AI
SI

5. SC(AI) = SQ(AI) × SP

6. SO(AI) = SO ×
AI
SI

7. SC(AQ) = AQ × SP

Wish not to recalculate standards

In the formulae, use the adjustment factors
AO
SO
for (AO) and
AI
SI
for (AI).

Additionally using Q × P for C in the formulae may eliminate the need to build the cost column in the working table.

Formulae

Material
MCV
MPV
MQV/MUV
MMV
MYV/MSUV
=
=
=
=
=
SC(AO)
SC(AQ)
SC(AO)
SC(AI)
SC(AO)




AC
AC
SC(AQ)
SC(AQ)
SC(AI)
Cost Variance
Price Variance
Quantity/Usage Variance
Mix Variance
Yield/Sub-Usage Variance

We can derive all other forms of the formulae from these.

  • Keeping the suffix attached to quantity, replace
    • SC with SQ × SP
    • AC with AQ × AP

    Eg : SC(AO) − AC, gives SQ(AO) × SP − AQ × AP

  • To use formulae without having to recalculate standards, additionally replace
    • (AO) with ×
      AO
      SO
    • (AI) with ×
      AI
      SI
    • (AQ) with ×
      AQ
      SQ
      (whereby SC(AQ) gives AQ × SP)
    SQ(AO) × SP, gives SQ ×
    AO
    SO
    × SP

Where there are two or more materials being used, formulae containing the expression AQ × SP should not be used for calculating the variance for the mix.

Problem

Three materials X, Y and Z are utilized in the manufacture of a product. The standard usage being 1,500 kgs of X @ 10/kg, 1,000 kgs of Y @ 12/kg and 500 kgs of Y @ 15/kg. The processing would result in a normal loss of materials @8% of total input quantity.

During a particular production period, the organisation has utilised 2,800 kgs of X purchased @ 11/kg, 2,100 kgs of Y purchased @ 11/kg and 600 kgs of Z purchased @ 16/kg for manufacture. The loss incurred was 594 kgs of total input.

Calculate all possible variances relating to materials.

Working Table

Working table incorporating the data in the problem and the calculated values including recalculated standards
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 AC SC(AQ)
Material X
Material Y
Material Z
1,500
1,000
500
10
12
15
2,775
1,850
925
27,750
22,200
13,875
2,850
1,900
950
28,500
4,320
14,250
2,800
2,100
800
12
11
16
33,600
23,100
12,800
28,000
25,200
12,000
Total 3,000 5,550 63,825 5,700 65,550 5,700 61,800 65,200
(−) Loss
Standard
Actual

240


594
Net 2,760 5,106
Output 2,760
SO
5,106
SO(AO)
5,244
SO(AI)
5,106
AO

Output (_O) is in units, Quantities (_Q) and Losses (_L) are in kgs, Prices (_P) are in monetary value per kg and Costs (_C) are in monetary values.

Standard Loss

SQL = 8% of total standard input
= SQMix × 10%
= 3,000 × 8%
= 240

Standard Output

SO = SQMix − SQL
= 3,000 − 240
= 2,760

Actual Loss

AQL = 594 (given)

Actual Output

AO = AQMix − AQL
= 5,700 − 594
= 5,106
AO
SO
=
5,106
2,760
= 1.85
AI
SI
=
5,700
3,000
= 1.9
1. SQ(AO) = SQ ×
AO
SO
= SQ × 1.85

2. SC(AO) = SQ(AO) × SP

3. SO(AO) = AO

4. SQ(AI) = SQ ×
AI
SI
= SQ × 1.9

5. SC(AI) = SQ(AI) × SP

6. SO(AI) = SO ×
AI
SI

7. SC(AQ) = AQ × SP

8. NSQ = SQ − SQL

9. NAQ = AQ − AQL

Solution

Material Cost Variance

MCV = SC(AO) − AC

Material Cost Variance due to

Material X,
MCVX = SC(AO)X − ACX
= 27,750 − 33,600 = − 6,350 [Adv]
Material Y,
MCVY = SC(AO)Y − ACY
= 22,200 − 23,100 = − 900 [Adv]
Material Z,
MCVZ = SC(AO)Z − ACZ
= 13,875 − 12,800 = + 1,075 [Fav]
TMCV or MCVMix = − 6,175 [Adv]
Material Mix,
MCVMix = SC(AO)Mix − ACMix
= 63,825 − 61,800 = − 6,175 [Adv]

Material Price Variance

MPV = SC(AQ) − AC

Material Price Variance due to

Material X,
MPVX = SC(AQ)X − ACX
= 28,000 − 33,600 = − 5,600 [Adv]
Material Y,
MPVY = SC(AQ)Y − ACY
= 25,200 − 23,100 = + 2,100 [Fav]
Material Z,
MPVZ = SC(AQ)Z − ACZ
= 12,000 − 12,800 = − 800 [Adv]
TMPV = − 4,300 [Adv]
Material Mix,
MPVMix = SC(AQ)Mix − ACMix
= 65,200 − 61,800 = − 4,300 [Adv]

Material Quantity/Usage Variance

MQV/MUV = SC(AO) − SC(AQ)

Material Quantity/Usage Variance due to

Material X,
MQV/MUVX = SC(AO)X − SC(AQ)X
= 27,750 − 28,000 = − 250 [Adv]
Material Y,
MQV/MUVY = SC(AO)Y − SC(AQ)Y
= 22,200 − 25,200 = − 3,000 [Adv]
Material Z,
MQV/MUVZ = SC(AO)Y − SC(AQ)Y
= 13,875 − 12,000 = + 1,875 [Fav]
TMQV/TMUV = − 1,375 [Adv]
Material Mix,
MQV/MUVMix = SC(AO)Mix − SC(AQ)Mix
= 63,825 − 65,200 = − 1,375 [Adv]

Material Mix Variance

MMV = SC(AI) − SC(AQ)

Material Mix Variance due to

Material X,
MMVX = SC(AI)X − SC(AQ)X
= 28,500 − 28,000 = + 500 [Fav]
Material Y,
MMVY = SC(AI)Y − SC(AQ)Y
= 4,320 − 25,200 = − 2,400 [Adv]
Material Z,
MMVZ = SC(AI)Z − SC(AQ)Z
= 14,250 − 12,000 = + 2,250 [Fav]
TMMV = + 350 [Fav]
MMVMix = SC(AI)Mix − SC(AQ)Mix
= 65,550 − 65,200 = + 350 [Fav]

Material Yield Variance

MYV/MSUV = SC(AO) − SC(AI)

Material Yield/Sub-Usage Variance due to

Material X,
MYV/MSUVX = SC(AO)X − SC(AI)X
= 27,750 − 28,500 = − 750 [Adv]
Material Y,
MYV/MSUVY = SC(AO)Y − SC(AI)Y
= 22,200 − 4,320 = − 600 [Adv]
Material Z,
MYV/MSUVZ = SC(AO)Z − SC(AI)Z
= 13,875 − 14,250 = − 375 [Adv]
TMYV/TMSUV = − 1,725 [Adv]
Material Mix,
MYV/MSUVMix = SC(AO)Mix − SC(AI)Mix
= 63,825 − 65,550 = − 1,725 [Adv]

Solution (minimal detail)

Material Cost Variance

MCV = SC(AO) − AC

Material X,
Material Y,
Material Z,
27,750 − 33,600
22,200 − 23,100
13,875 − 12,800
=
=
=
− 6,350 [Adv]
− 900 [Adv]
+ 1,075 [Fav]
Mix/Total, 63,825 − 61,800 = − 6,175 [Adv]

Material Price Variance

MPV = SC(AQ) − AC

Material X,
Material Y,
Material Z,
28,000 − 33,600
25,200 − 23,100
12,000 − 12,800
=
=
=
− 5,600 [Adv]
+ 2,100 [Fav]
− 800 [Adv]
Mix/Total, 65,200 − 61,800 = − 4,300 [Adv]

Material Quantity/Usage Variance

MQV/MUV = SC(AO) − SC(AQ)

Material X,
Material Y,
Material Z,
27,750 − 28,000
22,200 − 25,200
13,875 − 12,000
=
=
=
− 250 [Adv]
− 3,000 [Adv]
+ 1,875 [Fav]
Mix/Total, 63,825 − 65,200 = − 1,375 [Adv]

Material Mix Variance

MMV = SC(AI) − SC(AQ)

Material X,
Material Y,
Material Z,
28,500 − 28,000
4,320 − 25,200
14,250 − 12,000
=
=
=
+ 500 [Fav]
− 2,400 [Adv]
+ 2,250 [Fav]
Mix/Total, 65,550 − 65,200 = + 350 [Fav]

Material Yield/Sub-Usage Variance

MYV/MSUV = SC(AO) − SC(AI)

Material X,
Material Y,
Material Z,
27,750 − 28,500
22,200 − 4,320
13,875 − 14,250
=
=
=
− 750 [Adv]
− 600 [Adv]
− 375 [Adv]
Mix/Total, 63,825 − 65,550 = − 1,725 [Adv]

Solution (alternative presentation)

Material X Material Y Material Z Mix/Total
MYV/MSUV

Material X
Material Y
Material Z
Mix
SC(AO)
27,750
22,200
13,875
63,825




SC(AI)
28,500
4,320
14,250
65,550
+ MMV

Material X
Material Y
Material Z
Mix
SC(AI)
28,500
4,320
14,250
65,550




SC(AQ)
28,000
25,200
12,000
65,200


− 750





+ 500




− 600





− 2,400





− 375





+ 2,250





− 1,725





+ 350
MQV/MUV

Material X
Material Y
Material Z
Mix
SC(AO)
27,750
22,200
13,875
63,825




SC(AQ)
28,000
25,200
12,000
65,200
+ MPV

Material X
Material Y
Material Z
Mix
SC(AQ)
28,000
25,200
12,000
65,200




AC
33,600
23,100
12,800
61,800


− 250





− 5,600



− 3,000





+ 2,100




+ 1,875





− 800





− 1,375





− 4,300
MCV

Material X
Material Y
Material Z
Mix
SC(AO)
27,750
22,200
13,875
63,825




AC
33,600
23,100
12,800
61,800


− 6,350



− 900




+ 1,075





− 6,175

Verification

If adopting the first and second presentation methods, it would help building the following table to enable us to verify whether our workings are correct or not.

Verification

Formula Material X Material Y Material Z Mix/Total
MYV/MSUV
+ MMV
SC(AO) − SC(AI)
SC(AI) − SC(AQ)
− 750
+ 500
− 600
− 2,400
− 375
+ 2,250
− 1,725
+ 350
MQV/MUV
+ MPV
SC(AO) − SC(AQ)
SC(AQ) − AC
− 250
− 5,600
− 3,000
+ 2,100
+ 1,875
− 800
− 1,375
− 4,300
MCV SC(AO) − AC − 6,350 − 900 + 1,075 − 6,175

Simplest

One may use this as the simplest presentation of calculations, since all the amounts used in the formula are present in the working table.

If it is for verification purposes, we may avoid the formula column.

Please adopt a presentation based on the examination you are attending, the proportion of marks allotted and time available to/for the problem.