Material Variances - Single Material - Loss

S2 ↞ P1

Problem 2

A Ltd. has introduced Standard Costing System and has furnished the following information:

Standard:

Materials for 70 kg. of Finished Goods 100kg.
Price of materials 1 per kg.

Actual:

Output 2,10,000 kg.
Material used 2,80,000 kgs
Cost of materials 2,52,000

Calculate the various variances in respect of Material Cost.

Ans:
1
MYV/MSUV
MMV 		+ 20,000
0
MQV/MUV
MPV 		+ 20,000
+ 28,000
MCV + 48,000

Working Notes

The following data could be picked up from the problem

Standard Actual
SQ SP AQ AP AC
Material
(−) Loss 		100
 1 2,80,000 0.90 2,52,000
Net 70 2,10,000
Output 1 2,10,000

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

The underlined figures are obtained through the below calculations

AP =
AC
AQ
=
2,52,000
2,80,000
= 0.90

Assumptions

  • In the absence of information to the contrary, since output and input are in the same units, the difference between input and output is loss of materials.

We will be able to calculate all the variances without the information relating to losses.

The data relating to losses will enable us to calculate the Yield variance using an alternate formula based on losses.

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 3,000 2,800
Material 1 100 1 3,00,000 3,00,000 2,80,000 2,80,000 2,80,000 0.9 2,52,000 2,80,000
Total 100 1 3,00,000 3,00,000 2,80,000 2,80,000 2,80,000 2,52,000 2,80,000
(−) Loss
Standard
Actual

30
1 		[SQIL(AO)]
90,000 		[SCIL(AO)]
90,000
[AQIL]
70,000
[SC(AQIL)]
70,000
Net 70 2,10,000
Output 70
SO 		2,10,000
SO(AO) 		1,96,000
SO(AI) 		2,10,000
AO

Output (_O) is in kgs, 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

SQIL = Standard Input − Standard Output
= SQMix − SO
= 100 − 70
= 30 kg

Standard Output

SO = 70 kg (given)

Actual Loss

AQIL = Actual Input − Actual Output
= AQMix − AO
= 2,80,000 − 2,10,000
= 70,000 kg

Actual Output

AO = 2,10,000 kg (given)
(AO) =
AO
SO
=
2,10,000
70
= 3,000
(AI) =
AI
SI
=
AQMix
SQMix
=
2,80,000
100
= 2,800
1. SQ(AO) = SQ ×
AO
SO
= SQ × 3,000

2. SC(AO) = SQ(AO) × SP

3. SO(AO) = AO

4. SQ(AI) = SQ ×
AI
SI
= SQ × 2,800

5. SC(AI) = SQ(AI) × SP

6. SO(AI) = SO ×
AI
SI

7. SC(AQ) = AQ × SP

Calculations (for formulae based on Losses)

All these calculations can be completely ignored unless when we are required to find out the output based on losses for which the calculations at the beginning would suffice. All these calculations are required only if we intend to use the formula based on losses to calculate Material Yield Variance and that too for the mix.

8. NSQ = SQ − SQIL

9. NAQ = AQ − AQIL

10. SQIL(AO) = SQIL ×
AI
SI
= SQIL × 3,000
11. SPMix =
SC(AO)Mix
SQ(AO)Mix

11. SCIL(AO) = SQIL(AO) × SPMix

12. SC(AQIL) = AQIL × SPMix

The working table can be made simpler if the Loss and Net rows containing this data are eliminated from being presented.

Solution

Material Cost Variance

MCV = SC(AO) − AC

= 3,00,000 − 2,52,000 = + 48,000 [Fav]

Material Price Variance

MPV = SC(AQ) − AC

= 2,80,000 − 2,52,000 = + 28,000 [Fav]

Material Quantity/Usage Variance

MQV/MUV = SC(AO) − SC(AQ)

= 3,00,000 − 2,80,000 = + 20,000 [Fav]

Material Mix Variance

MMV = SC(AI) − SC(AQ)

= 2,80,000 − 2,80,000 = 0

Material Yield/Sub-Usage Variance

MYV/MSUV = SC(AO) − SC(AI)

= 3,00,000 − 2,80,000 = + 20,000 [Fav]

Material Yield/Sub-Usage Variance (alternative based on losses)

When there are losses and the relevant data is available, the following formula based on losses can also be used for calculating the yield variance for the mix

MYV/MSUV = SCSQIL(AO) − SC(AQIL)

= 90,000 − 70,000 = + 20,000 [Fav]

Solution (alternative presentation)

Material 1
MYV/MSUV

SC(AO)
3,00,000
−
−
SC(AI)
2,80,000
+ MMV

SC(AI)
2,80,000
−
−
SC(AQ)
2,80,000


+ 20,000


0
MQV/MUV

SC(AO)
3,00,000
−
−
SC(AQ)
2,80,000
+ MPV

SC(AQ)
2,80,000
−
−
AC
2,52,000


+ 20,000


+ 28,000
MCV

SC(AO)
3,00,000
−
−
AC
2,52,000


+ 48,000

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 1
MYV/MSUV
+ MMV 		SC(AO) − SC(AI)
SC(AI) − SC(AQ) 		+ 20,000
0
MQV/MUV
+ MPV 		SC(AO) − SC(AQ)
SC(AQ) − AC 		+ 20,000
+ 28,000
MCV SC(AO) − AC + 48,000

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
S2 ↠ P3