Material Yield 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 Yield/SubUsage Variance (MYV/MSUV)
Material Yield/SubUsage Variance is the difference between the Standard Cost of Actual Output and the Standard Cost of Actual Input.
⇒ Material Yield/SubUsage Variance (MYV/MSUV)
=  SC(AO) − SC(AI) Standard Cost for Actual Output − Standard Cost of Actual Input 
Standard Cost for Actual Output
Based on inputs  
SC(AO)  =  SC ×
 
Or  =  SQ(AO) × SP  
Based on output  
Or  =  AO × SC/UO 
Standard Cost of Actual Input
SC(AI)  =  SC ×
 
Or  =  SQ(AI) × SP 
Formula in useful forms
MYV/MSUV  =  SC(AO) − SC(AI) Standard Cost for Actual Output − Standard Cost of Actual Input  
Or  =  SC × (
 
Standard Cost × difference of ratios of actual output to standard output and actual input to standard input.  
Or  =  [SQ(AO) − SQ(AI)] × SP Difference in Standard Quantities for Actual Output and Actual Input × Standard Price  
Or  =  [AO − SO(AI)] × SC/UO Difference between actual output and standard output for actual input × Standard Cost for output per unit. 
Note
 ×
replace the suffix (AO) and ×AO SO
replace the suffix (AI) in calculations.AI SI  AI = AQ_{Mix} and SI = SQ_{Mix}.
For each Material Separately
Material Yield or Sub Usage Variance
MYV/MSUV_{Mat}  =  SC(AO)_{Mat} − SC(AI)_{Mat}  
Or  =  SC_{Mat} × (
 
Or  =  [SQ(AO)_{Mat} − SQ(AI)_{Mat}] × SP_{Mat}  
Or  =  [AO_{Mat} − SO(AI)_{Mat}] × SC/UO_{Mat} 
For all Materials together
When two or more types of materials are used for the manufacture of a product, the total Material Yield/SubUsage variance is the sum of the variances measured for each material separately.Total Material Yield/SubUsage variance
TMYV/TMSUV  =  ΣMYV/MSUV_{Mat} Sum of the variances measured for each material separately 
Material Yield/SubUsage variance for the Mix
MYV/MSUV_{Mix}  =  SC(AO)_{Mix} − SC(AI)_{Mix}  
Or  =  SC_{Mix} × (
 
Or  =  [SQ(AO)_{Mix} − SQ(AI)_{Mix}] × SP_{Mix}  
Or  =  [AO_{Mix} − SO(AI)_{Mix}] × SC/UO_{Mix} 
Illustration  Solution
Standard  Actual  

for SO  for AO  for AI  
SQ  SP  SQ(AO)  SC(AO)  SQ(AI)  SC(AI)  AQ  AP  
Factor  2.4  2.5  
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 2,000 500  33,750 90,000 42,500  2,250 1,950 550  16 42 90 
Total/Mix  1,900  35  4,560  1,59,600  4,750  1,66,250  4,750  
Output  1,800 SO  4,320 SO(AO)  4,500 SO(AI)  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
⋇  (AI)  = 
 
= 
 
=  2.5 
⋇  SQ(AI)  =  SQ ×
 
=  SQ × 2.5 
⋇ SC(AI) = SQ(AI) × SP
⋇  SQIL(AI)  =  SQIL ×
 
=  SQIL × 2.5 
⋇ SCIL(AI) = SQIL(AI) × SP
⋇  SO(AI)  =  SO ×
 
=  SO × 2.5 
MYV/MSUV = SC(AO) − SC(AI)
Material Yield/SubUsage Variance due to
Material A,  
MYV/MSUV_{A}  =  SC(AO)_{A} − SC(AI)_{A}  
=  32,400 − 33,750  =  − 1,350 [Adv]  
Material B,  
MYV/MSUV_{B}  =  SC(AO)_{B} − SC(AI)_{B}  
=  86,400 − 90,000  =  − 3,600 [Adv]  
Material C,  
MYV/MSUV_{C}  =  SC(AO)_{C} − SC(AI)_{C}  
=  40,800 − 42,500  =  − 1,700 [Adv]  
TMYV/TMSUV  =  − 6,650 [Adv]  
Material Mix,  
MYV/MSUV_{Mix}  =  SC(AO)_{Mix} − SC(AI)_{Mix}  
=  1,59,600 − 1,66,250  =  − 6,650 [Adv] 
Alternative
MYV/MSUV = [SQ(AO) − SQ(AI)] × SP
Material Yield/SubUsage Variance due to
Material A,  
MYV/MSUV_{A}  =  [SQ(AO)_{A} − SQ(AI)_{A}] × SP_{A}  
=  (2,160 − 2,250) × 15  
=  − 90 × 15  =  − 1,350 [Adv]  
Material B,  
MYV/MSUV_{B}  =  [SQ(AO)_{B} − SQ(AI)_{B}] × SP_{B}  
=  (1,920 − 2,000) × 45  
=  − 80 × 45  =  − 3,600 [Adv]  
Material C,  
MYV/MSUV_{C}  =  [SQ(AO)_{C} − SQ(AI)_{C}] × SP_{C}  
=  (480 − 500) × 85  
=  − 50 × 85  =  − 1,700 [Adv]  
TMYV/TMSUV  =  − 6,650 [Adv]  
Material Mix,  
MYV/MSUV_{Mix}  =  [SQ(AO)_{Mix} − SQ(AI)_{Mix}] × SP_{Mix}  
=  (4,560 − 4,750) × 35  
=  − 190 × 35  =  − 6,650 [Adv] 
Even in this case, if we intend to use the formula for the mix, we need either the SC_{Mix} or SC(AO)_{Mix} or SC(AI)_{Mix} to be able to find the SP_{Mix}
SP_{Mix}  = 
 
= 
 
=  35 
Illustration  Solution (without recalculating standards)
AI 
SI 
AO 
SO 
Calculating Costs in a working table
Calculate SC 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 Material A
Material B
Material C900
800
20015
45
8513,500
36,000
17,0002,250
1,950
55016
42
90Total/Mix 1,900 66,500 4,750 Output 1,800
SO4,320
AO⋇ SC = SQ × SP
MYV/MSUV = SC × (
−AO SO
)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
AOMYV/MSUV = SQ × SP × (
−AO SO
)AI SI Even in this case, if we intend to use the formula for the mix, we need the SC_{Mix}
Using Formula Based on Outputs
Working Table Standard Actual for SO SQ SP SC SC/UO AQ AP Material A 900 15 13,500 27 19 2,250 16 Material B 800 45 36,000 72 19 1,950 42 Material C 200 85 17,000 34 19 550 90 Total/Mix 1,900 35 66,500 7 4,750 Output 1,800
SO4,320
AO⋇ SC/UO = SC SO MYV/MSUV = [AO − SO ×
] × SC/UOAI SI
MYV/MSUV  Miscellaneous Aspects
Nature of Variance
Based on the relations derived from the formulae for calculating MYV/MSUV, we can identify the nature of Variance
 SC(AO) ___ SC(AI)
___AO SO AI SI  SQ(AO) ___ SQ(AI)
 AO ___ SO(AI)
MYV/MSUV_{Mat}
 SC(AO)_{Mat} ___ SC(AI)_{Mat}
___AO SO AI SI  SQ(AO)_{Mat} ___ SQ(AI)_{Mat}
 AO_{Mat} ___ SO(AI)_{Mat}
MYV/MSUV_{Mix}
 SC(AO)_{Mix} ___ SC(AI)_{Mix}
___AO SO AI SI  SQ(AO)_{Mix} ___ SQ(AI)_{Mix}
 AO_{Mix} ___ SO(AI)_{Mix}
The variance would be
 zero when =
 Positive when >
 Negative when <
TMYV/MSUV
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.
Individual Variances in Standard Cost Mix Ratio
This variance measures the efficiency in deriving output out of the total quantity of materials used as a whole and not of individual materials.Any variation on account of varying the individual materials is revealed by the Material Mix Variance.
This can be identified from the fact that the calculation of the variance for individual materials is the equivalent of dividing the variance for the mix among the materials in the standard cost mix ratio (SCMR).
MYV/MSU_{Mat} = MYV/MSU_{Mix} × standard cost mix proportion
From the data in the illustration,
Standard Cost Mix Ratio ~ SCMR
A : B : C = SC_{A} : SC_{B} : SC_{C} = 13,500 : 36,000 : 17,000 = 27 : 72 : 34 =
:27 133
:72 133 34 133 MYV/MSU_{Mix} = − 6,650
MYV/MSUV_{A} = − 6,650 × 27 133 = − 50 × 27 = − 1,350 MYV/MSUV_{B} = − 6,650 × 72 133 = − 50 × 72 = − 3,600 MYV/MSUV_{C} = − 6,650 × 34 133 = − 50 × 34 = − 1,700 Interpretation of the Variance
For the material mix, for the output achieved
Variance Quantity input is indicating None as per standard efficiency Positive lesser than standard efficiency Negative greater than standard inefficiency Similar conclusions can be drawn for the individual materials based on individual quantities input. However, it should be noted that the output is a result of the mix and measuring the influence of individual materials in quantitative terms is inappropriate.
The individual variances data would be of little help in taking corrective actions.
Who is answerable for the Variance?
Since this variance is on account of more or less yield for the input used, the people or department responsible for managing the production operations (say manufacturing department) is answerable for this variance.
Formulae using Interrelationships among Variances
 MYV/MSUV = MUV/MQV − MMV
 MYV/MSUV = MCV − MPV − MMV
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  − 1,350 0  − 3,600 + 2,250  − 1,700 − 4,250  − 6,650 − 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