Material Cost Variance
Illustration  Problem
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
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 Cost Variance ~ MCV
Material Cost Variance is the variance between the standard cost of materials for actual output and the actual cost of materials.
⇒ Material Cost Variance (MCV)
=  SC(AO) − AC Standard Cost for Actual Output − Actual Cost 
Actual Cost
Based on inputs  
AC  =  AQ × AP 
Based on output  
=  AO × AC/UO 
Standard Cost for Actual Output
Based on inputs  
SC(AO)  =  SC ×
 
Based on output  
Or  =  SQ(AO) × SP 
Formula in useful forms
MCV  =  SC(AO) − AC Standard Cost for Actual Output − Actual Cost 
Or  =  AO × (SC/UO − AC/UO) Actual Output × Difference in Standard and Actual Costs per unit output 
Note
 ×
replaces the suffix (AO) in calculationsAO SO  Using the formula based on output is prudent when the only data that is available is the data in the formula i.e. SC/UO, AC/UO and the AO.
In other cases where we are required to calculated SC/UO and AC/UO we need the SC and AC data which can be straight away used for finding the MCV.
For each Material separately
Material Cost variance for a material
MCV_{Mat}  =  SC(AO)_{Mat} − AC_{Mat} 
Or  =  AO (SC/UO_{Mat} − AC/UO_{Mat}) 
For all Materials together
Total Material Cost variance
TMCV  =  ΣMCV_{Mat} Sum of the variances measured for each material separately 
Material Cost variance for the Mix
MCV_{Mix}  =  SC(AO)_{Mix} − AC_{Mix} 
Or  =  AO (SC/UO_{Mix} − AC/UO_{Mix}) 
TMCV = MCV_{Mix}
Illustration  Solution
Standard  Actual  

for SO  for AO  
SQ  SP  SQ(AO)  SC(AO)  AQ  AP  AC  
Factor  2.4  
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 1,950 550  16 42 90  36,000 81,900 41,800 
Total/Mix  1,900  4,560  1,59,600  4,750  1,67,400  
Input Loss  100  240  8,400  430  15,050  
Output  1,800 SO  4,320 SO(AO)  4,320 AO 
⋇ SQIL = SI − SO
⋇ AQIL = AI − AO
⋇  (AO)  = 
 
= 
 
=  2.4 
⋇  SQ(AO)  =  SQ ×
 
=  SQ × 2.4 
⋇ SC(AO) = SQ(AO) × SP
⋇  SP_{Mix}  = 

⋇ SO(AO) = AO
⋇  SQIL(AO)  =  SQIL ×
 
=  SQIL × 2.4 
⋇ SCIL(AO) = SQIL(AO) × SP
MCV = SC(AO) − AC
Material Cost Variance due to
Material A,  
MCV_{A}  =  SC(AO)_{A} − AC_{A}  
=  32,400 − 36,000  =  − 3,600 [Adv]  
Material B,  
MCV_{B}  =  SC(AO)_{B} − AC_{B}  
=  86,400 − 81,900  =  + 4,500 [Fav]  
Material C,  
MCV_{C}  =  SC(AO)_{C} − AC_{C}  
=  40,800 − 41,800  =  − 8,700 [Adv]  
TMCV or MCV_{Mix}  =  − 7,800 [Adv]  
Material Mix,  
MCV_{Mix}  =  SC(AO)_{Mix} − AC_{Mix}  
=  1,59,600 − 1,67,400  =  − 7,800 [Adv] 
Alternative  Formula Based on Output
Calculation of SC/UO requires the SC data and AC/UO requires the AC data. When these are available we can straight away use the earlier formula instead of calculating SC/UO and AC/UO.
Illustration  Solution (without recalculating standards)
AO 
SO 
Calculating Costs in a working table
Calculate SC and AC 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 AC Material A
Material B
Material C900
800
20015
45
8513,500
36,000
17,0002,250
1,950
55016
42
9036,000
81,900
41,800Total/Mix 1,900 66,500 4,750 1,67,400 Output 1,800
SO4,320
AO⋇ SC = SQ × SP
⋇ AC = AQ × AP
MCV = SC ×
− ACAO SO 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 C900
800
20015
45
852,250
1,950
55016
42
90Total/Mix 1,900 4,750 Output 1,800
SO4,320
AOMCV = SQ ×
× SP − AQ × APAO SO Formula based on outputs
MCV = AO × (SC/UO − AC/UO)
Calculation of SC/UO requires the SC data and AC/UO requires the AC data. When these are available we can straight away use the other formulae instead of calculating SC/UO and AC/UO.
This formula does not require the data from recalculated standards.
Constituents of Material Cost Variance
MCV  =  SC(AO) − AC 
Adding and deducting SC(AQ) on the RHS we get  
MCV  =  SC(AO) − AC + SC(AQ) − SC(AQ) 
=  [SC(AO) − SC(AQ)] + [SC(AQ) − AC]  
=  Usage Variance + Price Variance  
=  MUV + MPV 
MCV  Miscellaneous aspects
Nature of Variance
Based on the relations derived from the formulae for calculating MCV, we can identify the nature of Variance
 SC(AO) ___ AC
MCV_{Mat}
 SC(AO)_{Mat} ___ AC_{Mat}
MCV_{Mix}
 SC(AO)_{Mix} ___ AC_{Mix}
The variance would be
 zero when =
 Positive when >
 Negative when <
TMCV
Variance of Mix and Total Variance are the same.Variance_{Mix} provides a method to find the total variance through calculations instead of by just adding up individual variances.
Interpretation of the Variance
For each material, for the actual output achieved
Variance Cost incurred is indicating None as per standard efficiency Positive lesser than standard efficiency Negative greater than standard inefficiency Similar conclusions can be drawn for the mix based on the mix variance. However, it should be noted that the mix variance is an aggregate of individual variances and as such reflects their net effect.
Mix variance data would be helpful to get an overall idea only. It would not be as useful as individual variances data in taking corrective actions.
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
 each material variance being zero, or
 the unfavourable variance due to one or more materials is set off by the favourable variance due to one or more other materials.
Who is answerable for the Variance?
Since Material Cost Variance represents the total difference on account of a number of factors it would not be possible to directly fix the responsibility for the variance. This explains the reason for analysing the variance and segregating it into its constituent parts.
Formulae based on interrelationship among variances
 MCV = MPV + MQV
 MCV = MPV + MMV + MYV
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  — —  — —  — —  — — 
MQV/MUV + MPV  — —  — —  — —  — — 
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