Material Quantity/Usage 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 Quantity/Usage Variance (MQV/MUV)
It is the difference between the standard cost for actual output and the standard cost of actual quantity of materials used.
⇒ Material Quantity/Usage Variance (MQV/MUV)
=  SC(AO) − SC(AQ) Standard Cost for Actual Output − Standard Cost of Actual Quantity 
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 Quantity
SC(AQ)  =  AQ × SP 
Formula in useful forms
MQV/MUV  =  SC(AO) − SC(AQ) Standard Cost for Actual Output − Standard Cost of Actual Quantity 
=  [SQ(AO) − AQ] × SP Difference between Standard Quantity for Actual Output and Actual Quantity × Standard Price 
Note
 ×
replaces the suffix (AO) in calculationsAO SO  Finding the costs by building up the working table and using the formula involving costs is the simplest way to find variances.
 The formula involving costs can be used to find the Material Quantity/Usage Variance for individual materials as well as the mix of materials. Appropriate suffix _{Mat} or _{Mix} is used in the formula as an indicator.
For each Material separately
Material Quantity/Usage variance for a material
MQV/MUV_{Mat}  =  SC(AO)_{Mat} − SC(AQ)_{Mat} 
Or  =  [SQ(AO)_{Mat} − AQ_{Mat}] × SP_{Mat} 
For all Materials together
When two or more types of materials are used for the manufacture of a product, the total Material Quantity/Usage variance is the sum of the variances measured for each material separately.Total Material Quantity/Usage Variance
TMQV/TMUV  =  ΣMQV/MUV_{Mat} Sum of the variances measured for each material separately 
Material Quantity/Usage variance for the Mix
MQV/MUV_{Mix}  =  SC(AO)_{Mix} − SC(AQ)_{Mix} 
=  [SQ(AO)_{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. 
TMQV/TMUV = MQV/MUV_{Mix}, when MQV/MUV_{Mix} exists.
The Math
The variance in total cost is on account of two factors price and quantity.Consider the relation, Value (V) = Quantity (Q) × Price (P).
If P is constant,
V = QP
⇒ V_{1} = Q_{1} × P → (1)
⇒ V_{2} = Q_{2} × P → (2)
(1) − (2) gives
⇒ V_{1} − V_{2} = Q_{1} × P − Q_{2} × P
⇒ V_{1} − V_{2} = (Q_{1} − Q_{2}) × P
⇒ ΔV = ΔQ × P, where P is a constant
⇒ ΔV ∞ ΔQ
Change in value varies as change in quantity
By taking both prices at standard we are eliminating the effect of difference between the standard price and actual price, thereby leaving only the difference between usage quantities.
Illustration  Solution
Standard  Actual  

for SO  for AO  
SQ  SP  SQ(AO)  SC(AO)  AQ  AP  SC(AQ)  
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  33,750 87,750 46,750 
Total/Mix  1,900  4,560  1,59,600  4,750  1,68,250  
Input Loss  100  35  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
⋇ SC(AQ) = AQ × SP
MQV/MUV = SC(AO) − SC(AQ)
Material Quantity/Usage Variance due to
Material A,  
MQV/MUV_{A}  =  SC(AO)_{A} − SC(AQ)_{A}  
=  32,400 − 33,750  =  − 1,350 [Adv]  
Material B,  
MQV/MUV_{B}  =  SC(AO)_{B} − SC(AQ)_{B}  
=  86,400 − 87,750  =  − 1,350 [Adv]  
Material C,  
MQV/MUV_{C}  =  SC(AO)_{C} − SC(AQ)_{C}  
=  40,800 − 46,750  =  − 5,950 [Adv]  
TMQV/TMUV  =  − 8,650 [Adv]  
Material Mix,  
MQV/MUV_{Mix}  =  SC(AO)_{Mix} − SC(AQ)_{Mix}  
=  1,59,600 − 1,68,250  =  − 8,650 [Adv] 
Alternative
MQV/MUV = [SQ(AO) − AQ] × SP
Material Quantity/Usage Variance due to
Material A,  
MQV/MUV_{A}  =  [SQ(AO)_{A} − AQ_{A}] × SP_{A}  
=  (2,160 kgs − 2,250 kgs) × 15/kg  
=  − 90 kgs × 15/kg  =  − 1,350 [Adv]  
Material B,  
MQV/MUV_{B}  =  [SQ(AO)_{B} − AQ_{B}] × SP_{B}  
=  (1,920 kgs − 1,950 kgs) × 45/kg  
=  − 30 kgs × 45/kg  =  − 1,350 [Adv]  
Material C,  
MQV/MUV_{C}  =  [SQ(AO)_{C} − AQ_{C}] × SP_{C}  
=  (480 kgs − 550 kgs) × 85/kg  
=  − 70 kgs × 85/kg  =  − 5,950 [Adv]  
TMQV/TMUV  =  − 8,650 [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)
AO 
SO 
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.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
AOSC = SQ × SP
SC(AQ) = AQ × SP
MQV/MUV = SC ×
− SC(AQ)AO 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
AOMUV/MVQ = (SQ ×
− AQ) × SPAO SO Since this formula involves the term AQ × SP and SQMR ≠ AQMR, it cannot be used for calculating the variance for the mix.
Constituents of Material Quantity/Usage Variance
MQV/MUV  =  SC(AO) − SC(AQ) 
[Adding and deducting SC(AI)]  
=  SC(AO) − SC(AQ) + SC(AI) − SC(AI)  
=  [SC(AO) − SC(AI)] + [SC(AI) − SC(AQ)]  
=  Yield/SubUsage Variance + Mix Variance  
=  MYV/MSUV + MMV 
MQV/MUV  Miscellaneous Aspects
Nature of Variance
Based on the relations derived from the formulae for calculating MQV/MUV, we can identify the nature of Variance
 SC(AO) ___ SC(AQ)
 SQ(AO) ___ AQ
MQV/MUV_{Mat}
 SC(AO)_{Mat} ___ SC(AQ)_{Mat}
 SQ(AO)_{Mat} ___ AQ_{Mat}
MQV/MUV_{Mix}
 SC(AO)_{Mix} ___ SC(AQ)_{Mix}
 SQ(AO)_{Mix} ___ AQ_{Mix} (conditional)
Only when SQMR = AQMR
The variance would be
 zero when =
 Positive when >
 Negative when <
TMQV/TMUV
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 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 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 this variance is on account of the quantity of material used being more or less than the standard, the people or department responsible for production can be identified as the ones answerable for this variance.This conclusion would be appropriate when there is only type of material in use.
When there are two or more types of material
When two or more types of materials are being used for the manufacture of a product, making only the people responsible for production answerable for the variance may not be appropriate as there would be two factors influencing the usage of materials. the ratio in which the quantities of constituent materials are mixed and
 the actual yield from the mix.
That is the reason, when there are two or more types of material being used, the Quantity/Usage variance is further broken down into two parts called Mix Variance and Yield Variance.
Formulae using Interrelationships among Variances
 MQV/MUV = MCV − MPV
 MQV/MUV = MMV + 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  — —  — —  — —  — — 
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