Material Price 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 Price Variance ~ MPV
It is the variance between the standard cost of actual quantity and the actual cost of materials.
⇒ Material Price Variance (MPV)
=  SC(AQ) − AC Standard Cost of Actual Quantity − Actual Cost 
Standard Cost of Actual Quantity
SC(AQ)  =  AQ × SP 
Actual Cost
Based on inputs  
AC  =  AQ × AP 
Based on output  
=  AO × AC/UO 
Formula in useful forms
MPV  =  SC(AQ) − AC Standard Cost of Actual Quantity − Actual Cost 
Or  =  AQ × (SP − AP) Actual Quantity × Difference between standard and actual prices 
For each Material separately
Material Price variance for a MaterialMPV_{Mat}  =  SC(AQ)_{Mat} − AC_{Mat} 
Or  =  AQ_{Mat} × (SP_{Mat} − AP_{Mat}) 
For all Materials together
Total Material Price variance
TMPV  =  ΣMPV_{Mat} Sum of the variances measured for each material separately 
Material Price Variance for the mix
MPV_{Mix}  =  SC(AQ)_{Mix} − AC_{Mix} 
=  AQ_{Mat} × (SP_{Mat} − AP_{Mat}) [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. 
TMPV = MPV_{Mix}, when MPV_{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 Q is constant,
V = QP
⇒ V_{1} = Q × P_{1} → (1)
⇒ V_{2} = Q × P_{2} → (2)
(1) − (2) gives
V_{1} − V_{2} = Q × P_{1} − Q × P_{2}
⇒ V_{1} − V_{2} = Q × (P_{1} − P_{2})
⇒ ΔV = Q × ΔP, where Q is a constant
⇒ ΔV ∞ ΔP
⇒ Change in value varies as change in price
By taking both quantities at actual we are eliminating the effect of difference between the standard quantity and actual quantity, thereby leaving only the difference between prices.
Recalculating Standards does not effect MPV Calculations
The data used for calculating Material Price Variance, SP, AP, AQ does not change on standards being recalculated either based on the output or input.
Standard  Actual  

for SO  for AO  for AI  
SQ  SP  SQ(AO)  SC(AO)  SQ(AI)  SC(AI)  AQ  AP  AC  SC(AQ)  
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  36,000 81,900 41,800  33,750 87,750 46,750 
Total/Mix  1,900  35  4,560  1,59,600  4,750  1,66,250  4,750  1,67,400  1,68,250  
Input Loss  100  35  240  8,400  250  8,500  430  15,050  
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 
⋇ AC = AQ × AP
⋇ SC(AQ) = AQ × SP
⋇ SC(AQIL) = AQIL × SP
Illustration  Solution
MPV = SC(AQ) − AC
Material Price Variance due to
Material A,  
MPV_{A}  =  SC(AQ)_{A} − AC_{A}  
=  33,750 − 36,000  =  − 2,250 [Adv]  
Material B,  
MPV_{B}  =  SC(AQ)_{B} − AC_{B}  
=  87,750 − 81,900  =  + 5,850 [Fav]  
Material C,  
MPV_{C}  =  SC(AQ)_{C} − AC_{C}  
=  41,800 − 46,750  =  − 2,750 [Adv]  
TMPV  =  + 850 [Fav]  
Material Mix,  
MPV_{Mix}  =  SC(AQ)_{Mix} − AC_{Mix}  
=  1,68,250 − 1,67,400  =  + 850 [Fav] 
Illustration  Solution [alternative]
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 kgs SO  4,320 kgs AO 
MPV = AQ (SP − AP)
Material Price Variance due to
Material A,  
MPV_{A}  =  AQ_{A}(SP_{A} − AP_{A})  
=  2,250 kgs (15/kg − 16/kg)  
=  2,250 kgs (− 1/kg)  =  − 2,250 [Adv]  
Material B,  
MPV_{B}  =  AQ_{B}(SP_{B} − AP_{B})  
=  1,950 kgs (45/kg − 42/kg)  
=  1,950 kgs (3/kg)  =  + 5,850 [Fav]  
Material C,  
MPV_{C}  =  AQ_{C}(SP_{C} − AP_{C})  
=  550 kgs (85/kg − 90/kg)  
=  550 kgs (− 5/kg)  =  − 2,750 [Adv]  
TMPV  =  + 850 [Fav] 
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.
MPV  Miscellaneous Aspects
Nature of Variance
Based on the relations derived from the formulae for calculating MPV, we can identify the nature of Variance
 SC(AQ) ___ AC
 SP ___ AP
MPV_{Mat}
 SC(AQ)_{Mat} ___ AC_{Mat}
 SP_{Mat} ___ AP_{Mat}
MPV_{Mix}
 SC(AQ)_{Mix} ___ AC_{Mix}
 SP_{Mix} ___ AP_{Mix} (conditional)
only when SQMR = AQMR.
The variance would be
 zero when =
 Positive when >
 Negative when <
TMPV
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 total actual quantity
Variance Price paid/payable 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 actual acquisition/purchase price being more or less than the standard, the people or department responsible for deciding on the prices of purchased materials can be held responsible for this variance.
Formulae using Interrelationships among Variances
 MPV = MCV − MQV
 MPV = MCV − 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  — —  — —  — —  — — 
MPV + MPV  — − 2,250  — + 5,850  — − 2,750  — + 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