Material Mix 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 Mix Variance ~ MMV
It is the difference between the Standard Cost of Standard Quantity for Actual Input and the Standard Cost of Actual Quantity.
⇒ Material Mix Variance (MMV)
=  SC(AI) − SC(AQ) Standard Cost for Actual Input − Standard Cost of Actual Quantity 
Standard Cost of Actual Input
SC(AI)  =  SC ×
 
Or  =  SQ(AI) × SP 
Standard Cost of Actual Quantity
SC(AQ)  =  AQ × SP 
Formula in useful forms
MMV  =  SC(AI) − SC(AQ) Standard Cost for Actual Input − Standard Cost of Actual Quantity 
Or  =  [SQ(AI) − AQ] × SP Difference between Standard Quantity for Actual Input and Actual Quantity × Standard Price 
Note
 Material Mix Variance is a part of Material Usage Variance whose calculations are based on the gross input before deducting any losses and as such the Material Mix Variance should also be based on gross input.
Thus, actual input (AI) in the formulae is gross input AQ_{Mix}.
 ×
replaces the suffix (AI) in calculations.AI SI
For each Material Separately
Material Mix Variance
MMV_{Mat}  =  SC(AI)_{Mat} − SC(AQ)_{Mat} 
Or  =  [SQ(AI)_{Mat} − AQ_{Mat}] × SP_{Mat} 
For all Materials together
Total Material Mix Variance
TMMV  =  ΣMMV_{Mat} Sum of the variances measured for each material separately 
Material Mix variance for the Mix
MMV_{Mix}  =  SC(AI)_{Mix} − SC(AQ)_{Mix} 
=  [SQ(AI)_{Mix} − AQ_{Mix}] × SP_{Mix} (conditional) This formula can be used for the mix only when the actual quantity mix ratio is the same as the standard quantity mix ratio. 
TMMV = MMV_{Mix}, when MMV_{Mix} exists.
Illustration  Solution
Standard  Actual  

for SO  for AI  
SQ  SP  SQ(AI)  SC(AI)  AQ  AP  SC(AQ)  
Factor  2.5  
Material A Material B Material C  900 800 200  15 45 85  2,250 2,000 500  33,750 90,000 42,500  2,250 1,950 550  16 42 90  33,750 87,750 46,750 
Total/Mix  1,900  4,750  1,66,250  4,750  1,68,250  
Input Loss  100  35  250  8,500  340  15,050  
Output  1,800 SO  4,500 SO(AI)  4,320 AO 
⋇ SQIL = SI − SO
⋇ AQIL = AI − AO
⋇  (AI)  = 
 
= 
 
= 
 
=  2.5 
⋇  SQ(AI)  =  SQ ×
 
=  SQ × 2.5 
⋇ SC(AI) = SQ(AI) × SP
⋇  SP_{Mix}  = 

⋇  SO(AI)  =  SO ×
 
=  SO × 2.5 
⋇  SQIL(AI)  =  SQIL ×
 
=  SQIL × 2.5 
⋇ SCIL(AO) = SQIL(AO) × SP
⋇ SC(AQ) = AQ × SP
MMV = SC(AI) − SC(AQ)
Material Mix Variance due to
Material A,  
MMV_{A}  =  SC(AI)_{A} − SC(AQ)_{A}  
=  33,750 − 33,750  =  0  
Material B,  
MMV_{B}  =  SC(AI)_{B} − SC(AQ)_{B}  
=  90,000 − 87,750  =  + 2,250 [Fav]  
Material C,  
MMV_{C}  =  SC(AI)_{C} − SC(AQ)_{C}  
=  42,500 − 46,750  =  − 4,250 [Adv]  
TMMV  =  − 2,000 [Adv]  
MMV_{Mix}  =  SC(AI)_{Mix} − SC(AQ)_{Mix}  
=  1,66,250 − 1,68,250  =  − 2,000 [Adv] 
Alternative
MMV = [SQ(AI) − AQ] × SP
Material Mix Variance due to
Material A,  
MMV_{A}  =  [SQ(AI)_{A} − AQ_{A}] × SP_{A}  
=  (2,250 kgs − 2,250 kgs) × 15/kg  
=  0 kgs × 15/kg  =  0  
Material B,  
MMV_{B}  =  [SQ(AI)_{B} − AQ_{B}] × SP_{B}  
=  (2,000 kgs − 1,950 kgs) × 45/kg  
=  50 kgs × 45/kg  =  + 2,250 [Fav]  
Material C,  
MMV_{C}  =  [SQ(AI)_{C} − AQ_{C}] × SP_{C}  
=  (500 kgs − 550 kgs) × 85/kg  
=  − 50 kgs × 85/kg  =  − 4,250 [Adv]  
TMMV  =  − 2,000 [Adv] 
Standard Quantity Mix Ratio
SQMR  =  SQ_{A} : SQ_{B} : SQ_{C} 
=  900 kgs : 800 kgs : 200 kgs  
=  9 : 8 : 2 
Actual Quantity Mix Ratio
AQMR  =  AQ_{A} : AQ_{B} : AQ_{C} 
=  2,250 kgs : 1,950 kgs : 550 kgs  
=  45 : 39 : 11 
Since this formula involves the term AQ × SP and SQMR ≠ AQMR, it cannot be used for calculating the variance for the mix.
Illustration  Solution (without recalculating standards)
AI 
SI 
Calculating Costs in a working table
Calculate SC and SC(AQ) 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 SC(AQ) Material A
Material B
Material C900
800
20015
45
8513,500
36,000
17,0002,250
1,950
55016
42
9033,750
87,750
46,750Total/Mix 1,900 66,500 4,750 1,68,250 Output 1,800
SO4,320
AO⋇ SC = SQ × SP
⋇ SC(AQ) = AQ × SP
MMV = SC ×
− SC(AQ)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 C900
800
20015
45
852,250
1,950
55016
42
90Total/Mix 1,900 4,750 Output 1,800
SO4,320
AOMMV = (SQ ×
− AQ) × SPAI SI Since this formula involves the term AQ × SP and SQMR ≠ AQMR, it cannot be used for calculating the variance for the mix.
MMV  Miscellaneous Aspects
MUV vs MMV
Variance Formula Measures Variation in MUV
MMVSC(AO) − SC(AQ)
SC(AI) − SC(AQ)Quantity of Material used
Material Quantity Mix RatiosNature of Variance
Based on the relations derived from the formulae for calculating MMV, we can identify the nature of Variance
 SC(AI) ___ SC(AQ)
 SQ(AI) ___ AQ
MMV_{Mat}
 SC(AI)_{Mat} ___ SC(AQ)_{Mat}
 SQ(AI)_{Mat} ___ AQ_{Mat}
MMV_{Mix}
 SC(AI)_{Mix} ___ SC(AQ)_{Mix}
The variance would be
 zero when =
 Positive when >
 Negative when <
We do not draw such a conclusion based on SQ(AI)_{Mix} ___ AQ_{Mix} as they both are the same.
TMMV
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.
Where there is only one material being used, there is no meaning in thinking of the Material Mix Variance. TMMV = 0 as well as MMV_{Mat} = 0 in such a case.
Interpretation of the Variance
For each material, for the input used
Variance Quantity input is indicating None as per standard efficiency Positive lesser than standard efficiency Negative greater than standard inefficiency Using a material lesser than the standard is considered efficiency only in terms of cost.
To conclude that using a lesser quantity is efficiency in general may not be appropriate as it results in other materials being used in higher quantities. Changing the mix ratio may affect the quality of the output also.
Similar conclusions can be drawn for the mix based on the mix variance. The value of mix variance should not be viewed in isolation as it is an aggregate of individual variances and as such reflects their net effect.
Mix variance data would be helpful to get an overall idea. In terms of cost, the mix variance data would give an immediate understanding of the gain/loss on account of variation in ratio of quantity mix. In taking corrective actions both the mix as well as individual variances should be considered.
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.
If the total variance is zero on account of this reason, it would be wrong to conclude that the SQMR and AQMR are the same.
Who is answerable for the Variance?
Since this variance is on account of the variation in the ratio in which the constituent materials are mixed, the actual ratio being different from the standard ratio, the people or department responsible for authorising the usage and mixing of component materials for production would be made answerable for this variance.Conclusions based on Mix Ratios
If the Standard Mix Ratio (SMR) and the Actual Mix Ratio (AMR) are the same, then there is no Mix variance either for individual materials or for the total mix.SQMR and AQMR being different is an indicator of existence of mix variance relating to individual materials.
Standard Quantity Mix Ratio ~ SQMR
A : B : C = 900 kgs : 800 kgs : 200 kgs = 9 : 8 : 2 =
:9 19
:8 19
[=2 19
:AQ_{A} AQ_{Mix}
:AQ_{B} AQ_{Mix}
]AQ_{C} AQ_{Mix} = 0.474 : 0.421 : 0.105 (approximately) Actual quantity Mix Ratio ~ AQMR
A : B : C = 2,250 kgs : 1,950 kgs : 550 kgs = 45 : 39 : 11 =
:45 95
:39 95
[=11 95
:SQ_{A} SQ_{Mix}
:SQ_{B} SQ_{Mix}
]SQ_{C} SQ_{Mix} = 0.474 : 0.411 : 0.116 (approximately) We will be able to tell which materials are causing the variance by comparing the terms of the ratio.
 AQMR value = SQMR value
No variance since Materials have been taken in the same proportion as the standard
 AQMR value < SQMR value
Materials have been taken in a lesser proportion compared to the standard resulting in a negative variance
 AQMR value > SQMR value
Materials have been taken in a greater proportion compared to the standard resulting in a negative variance
AQMR SQMR Variance Material A
Material B
Material C0.474
0.411
0.116=
<
>0.474
0.421
0.105None
Positive
NegativeAlternative 1
Standard Quantity Mix Ratio ~ SQMR
A : B : C = 900 kgs : 800 kgs : 200 kgs = 9 : 8 : 2 Multiplying all terms with
, i.e. 2.5.AI SI To make it a whole number, 5, multiply with 2 (2.5 × 2)
Use this number, 5, to derive the terms in the next step
= 45 : 40 : 10 We get values as whole numbers
Actual Quantity Mix Ratio ~ AQMR
A : B : C = 2,250 kgs : 1,950 kgs : 550 kgs = 45 : 39 : 11 AQMR SQMR Variance Material A
Material B
Material C45
39
11=
<
>45
40
10None
Positive
NegativeAlternative 2
Comparing the proportion of AQ to SQ with (AI) value.(AI) = 2.5
AQ_{A} SQ_{A} = 2,250 kgs 900 kgs = 2.5 = (AI) No Variance AQ_{A} SQ_{A} = 1,950 kgs 800 kgs = 2.4375 < (AI) Positive Variance AQ_{C} SQ_{C} = 550 kgs 200 kgs = 2.75 > (AI) Negative Variance  AQMR value = SQMR value
Formulae using Interrelationships among Variances
 MMV = MUV/MQV − MYV/MSUV
 MMV = MCV − MPV − MYV/MSUV
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  — 0  — + 2,250  — − 4,250  — − 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