Simple Problem on Material Variances involving three materials

S3 ↞ P1

Problem 2

From the following information compute material variances

Materials Standard Actual
Quantity
(Kilos) 		Unit
Price
 Total

 Quantity
(Kilos) 		Unit
Price
 Total

Material X
Material Y
Material Z 		15
20
15 		2
3
6 		30
60
90 		10
16
14 		3
2.5
5 		30
40
70
Total 50 3.6 180 40 3.5 140
Ans:
X Y Z Total
MYV/MSUV
MMV 		+ 6
+ 4 		+ 12
0 		+ 18
− 12 		+ 36
− 8
MQV/MUV
MPV 		+ 10
− 10		 + 12
+ 8		 + 6
+ 14		 + 28
+ 12
MCV 0 + 20 + 20 + 40

Working Notes

The following data could be picked up from the problem

Standard Actual
SQ SP AQ AP
Material X
Material Y
Material Z 		15
20
15 		2
3
6 		10
16
14 		3
2.5
5
Output 1 1

units : _Q in kgs, _P in value/kg and _O in units

Assumptions:

  • In the absence of information relating to output, the standard and actual data pertain to the same output which is taken to be 1 unit.

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)
Factor 1 0.8
Material X
Material Y
Material Z 		15
20
15 		2
3
6 		15
20
15 		30
60
90 		12
16
12 		24
48
72 		10
16
14 		3
2.5
5 		30
40
70 		20
48
84
Total/Mix 50 50 180 40 144 40 140 152
Output 1
SO 		1
SO(AO) 		0.8
SO(AI) 		1
AO

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

Standard Output

SO = 1 kilo (given)

Actual Output

AO = 1 kilo (given)
(AO) =
AO
SO
=
1
1
= 1
(AI) =
AI
SI
=
AQMix
SQMix
=
40
50
= 0.8
1. SQ(AO) = SQ ×
AO
SO
= SQ × 1

2. SC(AO) = SQ(AO) × SP

3. SO(AO) = AO

4. SQ(AI) = SQ ×
AI
SI
= SQ × 0.8

5. SC(AI) = SQ(AI) × SP

6. SO(AI) = SO ×
AI
SI

7. SC(AQ) = AQ × SP

Solution

Material Cost Variance

MCV = SC(AO) − AC

Material Cost Variance due to

Material X,
MCVX = SC(AO)X − ACX
= 30 − 30 = 0
Material Y,
MCVY = SC(AO)Y − ACY
= 60 − 40 = + 20 [Fav]
Material Z,
MCVZ = SC(AO)Z − ACZ
= 90 − 70 = + 20 [Fav]
TMCV or MCVMix = + 40 [Fav]
Material Mix,
MCVMix = SC(AO)Mix − ACMix
= 180 − 140 = + 40 [Fav]

Material Price Variance

MPV = SC(AQ) − AC

Material Price Variance due to

Material X,
MPVX = SC(AQ)X − ACX
= 20 − 30 = − 10 [Adv]
Material Y,
MPVY = SC(AQ)Y − ACY
= 48 − 40 = + 8 [Fav]
Material Z,
MPVZ = SC(AQ)Z − ACZ
= 84 − 70 = + 14 [Fav]
TMPV or MPVMix = + 12 [Fav]
Material Mix,
MPVMix = SC(AQ)Mix − ACMix
= 152 − 140 = + 12 [Fav]

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
= 30 − 20 = + 10 [Fav]
Material Y,
MQV/MUVY = SC(AO)Y − SC(AQ)Y
= 60 − 48 = + 12 [Fav]
Material Z,
MQV/MUVZ = SC(AO)Z − SC(AQ)Z
= 90 − 84 = + 6 [Fav]
TMQV/MUV or MQV/MUVMix = + 28 [Fav]
Material Mix,
MQV/MUVMix = SC(AO)Mix − SC(AQ)Mix
= 180 − 152 = + 28 [Fav]

Material Mix Variance

MMV = SC(AI) − SC(AQ)

Material Mix Variance due to

Material X,
MMVX = SC(AI)X − SC(AQ)X
= 24 − 20 = + 4 [Fav]
Material Y,
MMVY = SC(AI)Y − SC(AQ)Y
= 48 − 48 = 0
Material Z,
MMVZ = SC(AI)Z − SC(AQ)Z
= 72 − 84 = − 12 [Adv]
TMMV or MMVMix = − 8 [Adv]
Material Mix,
MMVMix = SC(AI)Mix − SC(AQ)Mix
= 144 − 152 = − 8 [Adv]

Material Yield/Sub-Usage Variance

MYV/MSUV = SC(AO) − SC(AI)

Material Yield/Sub-Usage Variance due to

Material X,
MYV/MSUVX = SC(AO)X − SC(AI)X
= 30 − 24 = + 6 [Fav]
Material Y,
MYV/MSUVY = SC(AO)Y − SC(AI)Y
= 60 − 48 = + 12 [Fav]
Material Z,
MYV/MSUVZ = SC(AO)Z − SC(AI)Z
= 90 − 72 = + 18 [Fav]
TMYV/MSUV or MYV/MSUVMix = + 36 [Fav]
Material Mix,
MYV/MSUVMix = SC(AO)Mix − SC(AI)Mix
= 180 − 144 = + 36 [Fav]

Solution (minimal detail)

Material Cost Variance

MCV = SC(AO) − AC

Material X,
Material Y,
Material Z, 		30 − 30
60 − 40
90 − 70 		=
=
= 		0
+ 20 [Fav]
+ 20 [Fav]
Mix/Total, 180 − 140 = + 40 [Fav]

Material Price Variance

MPV = SC(AQ) − AC

Material X,
Material Y,
Material Z, 		20 − 30
48 − 40
84 − 70 		=
=
= 		− 10 [Adv]
+ 8 [Fav]
+ 14 [Fav]
Mix/Total, 152 − 140 = + 12 [Fav]

Material Quantity/Usage Variance

MQV/MUV = SC(AO) − SC(AQ)

Material X,
Material Y,
Material Z, 		30 − 20
60 − 48
90 − 84 		=
=
= 		+ 10 [Fav]
+ 12 [Fav]
+ 6 [Fav]
Mix/Total, 180 − 152 = + 28 [Fav]

Material Mix Variance

MMV = SC(AI) − SC(AQ)

Material X,
Material Y,
Material Z, 		24 − 20
48 − 48
72 − 84 		=
=
= 		+ 4 [Fav]
0
− 12 [Adv]
Mix/Total, 144 − 152 = − 8 [Adv]

Material Yield/Sub-Usage Variance

MYV/MSUV = SC(AO) − SC(AI)

Material X,
Material Y,
Material Z, 		30 − 24
60 − 48
90 − 72 		=
=
= 		+ 6 [Fav]
+ 12 [Fav]
+ 18 [Fav]
Mix/Total, 180 − 144 = + 36 [Fav]

Solution (alternative presentation)

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

Material X
Material Y
Material Z
Mix
SC(AO)
30
60
90
180
−
−
−
−
−
SC(AI)
24
48
72
144
+ MMV

Material X
Material Y
Material Z
Mix
SC(AI)
24
48
72
144
−
−
−
−
−
SC(AQ)
20
48
84
152


+ 6





+ 4


+ 12





0



+ 18





− 12




+ 36





− 8
MQV/MUV

Material X
Material Y
Material Z
Mix
SC(AO)
30
60
90
180
−
−
−
−
−
SC(AQ)
20
48
84
152
+ MPV

Material X
Material Y
Material Z
Mix
SC(AQ)
20
48
84
152
−
−
−
−
−
AC
30
40
70
140


+ 10





− 10


+ 12





+ 8



+ 6





+ 14




+ 28





+ 12
MCV

Material X
Material Y
Material Z
Mix
SC(AO)
30
60
90
180
−
−
−
−
−
AC
30
40
70
140


0


+ 20



+ 20




+ 40

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) 		+ 6
+ 4 		+ 12
0 		+ 18
− 12 		+ 36
− 8
MQV/MUV
+ MPV 		SC(AO) − SC(AQ)
SC(AQ) − AC 		+ 10
− 10 		+ 12
+ 8 		+ 6
+ 14 		+ 28
+ 12
MCV SC(AO) − AC 0 + 20 + 20 + 40

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.

Author : The Edifier
S3 ↠ P3