900 kgs of Material A @ Rs. 15 per kg, 800 kgs of Material B @ Rs. 45/kg and 200 kgs of Material C @ Rs. 85 per kg were planned to be purchased/used for manufacturing 9,500 units. 2,250 kgs of Material A @ Rs. 16 per kg, 1,950 kgs of Material B @ Rs. 42/kg and 550 kgs of Material C @ Rs. 90 per kg were purchased/used actually for manufacturing 22,800 units.
What is the variation in total cost on account of variation in purchase price?
This information is provided by the material price variance.
The problem data arranged in a working table:

Standard [Production: 9500 units] 
Actual [Production: 22,800 units] 

Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Material A 
900 
15 
13,500 
2,250 
16 
36,000 
Material B 
800 
45 
36,000 
1,950 
42 
81,900 
Material C 
200 
85 
17,000 
550 
90 
49,500 
Total
 1,900 
35 
66,500 
4,750 

1,67,400 
You need not calculate the data for SP_{Mix} and AP_{Mix} for the purpose of calculating Material Price Variances.

The Formulae » Material Price Variance (MPV)



The variance in the total cost of materials on account of a variation between the standard price (price at which the materials should have been purchased) and the actual price (price at which they have been purchased).
It is calculated as the difference between the standard cost of actual materials and the actual cost of materials.
⇒ Material Price Variance

= 
Standard Cost of Actual Quantity of Materials − Actual Cost of Materials


= 
(Actual Quantity × Standard Price) − (Actual Quantity × Actual Price)

Memorise this general formula for easier recollection (ignoring the specific formulae below)
For each Material Separately

For all Materials together [Total Material Price Variance :: TMPV]
When two or more types of materials are used for the manufacture of a product, the total Material Price variance is the sum of the variances measured for each material separately.
No Direct Formula
There is no direct formula for calculating the total material price variance.
TMPV ≠ AQ_{Mix} (SP_{Mix} − AP_{Mix})

MPV Formula interpretation



The above formulae for Material Price Variance can be used in all cases i.e. when AO = SO, AO ≠ SO, SQ _{Mix} = AQ _{Mix} and SQ _{Mix} ≠ AQ _{Mix}. Standard Price present in the formula is unaffected by standard recalculation. Standard Quantity which changes on recalculating standards is not found in the formula.
MPV = 0
Material Price Variance for each material would be zero if the price at which a material is purchased (AP) is the same as its standard price (SP).
TMPV = 0
When more than one type of material is used, the Total Material Price Variance may become zero
 When the MPV on account of each material is zero, or
 When the unfavourable variance due to one or more materials is set off by the favourable variance due to one or more other materials.
Therefore, it would not be appropriate to conclude that all the materials are bought at the standard rates just because the total MPV is zero.
Where the total MPV is zero, you have to verify individual variances before concluding that all the individual variances (MPV's) are zero.

Recalculating Standards does not effect MPV Calculations



Recalculating Standards does not affect the data used for calculating Material Price Variance. The formula for calculating Material Price Variance involves AQ, SP and AP. It does not involve and thus is not influenced by SQ. These data would not change on standards being recalculated either based on the output or input.
SO ≠ AO and SQ_{Mix} ≠ AQ_{Mix}

Standard [Production: 9500 units] 
Actual [Production: 22,800 units] 

Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Material A 
900 
15 
13,500 
2,250 
16 
36,000 
Material B 
800 
45 
36,000 
1,950 
42 
81,900 
Material C 
200 
85 
17,000 
550 
90 
49,500 
Total
 1,900 

66,500 
4,750 

1,67,400 
Standards Recalculated for the Actual Output

Standard [Production: 22,800 units] 
Actual [Production: 22,800 units] 

Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Material A 
2,160 
15 
32,400 
2,250 
16 
36,000 
Material B 
1,920 
45 
86,400 
1,950 
42 
81,900 
Material C 
480 
85 
40,800 
550 
90 
49,500 
Total
 4,560 

1,59,600 
4,750 

1,67,400 
Standards Recalculated for Actual Input

Standard [Production: 23,750 units] 
Actual [Production: 22,800 units] 

Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Material A 
2,250 
15 
33,750 
2,250 
16 
36,000 
Material B 
2,000 
45 
90,000 
1,950 
42 
81,900 
Material C 
500 
85 
42,500 
550 
90 
49,500 
Total
 4,750 

1,66,250 
4,750 

1,67,400 

The data that is used for calculating Material Price Variances can be picked up from the working table built with the data given (as it is) or with the data involving recalculated standards based on either the Actual Output or the Actual Input.
MPV = (AQ × SP) − (AQ × AP) ⇒ MPV = AQ (SP − AP)
Using MPV_{Mat} = AQ_{Mat} (SP_{Mat} − AP_{Mat})
Material Price Variance due to
• Material A 
= 
2,250 kgs (Rs. 15/kg − Rs. 16/kg) 

= 
2,250 kgs (− Rs. 1/kg) 

= 
− Rs. 2,250 
⇒ MPV_{A} 
= 
− Rs. 2,250 [Adv] 
• Material B 
= 
1,950 kgs (Rs. 45/kg − Rs. 42/kg) 

= 
1,950 kgs (Rs. 3/kg) 

= 
+ Rs. 5,850 
⇒ MPV_{B} 
= 
+ Rs. 5,850 [Fav] 
• Material C 
= 
550 kgs (Rs. 85/kg − Rs. 90/kg) 

= 
550 kgs (− Rs. 5/kg) 

= 
− Rs. 2,750 
⇒ MPV_{C} 
= 
− Rs. 2,750 [Adv] 


Total Material Price Variance 
= 
+ Rs. 850 [Pos or Fav] 

Formulae using Interrelationships among Variances



MCV = MPV + MUV/MQV → (1)
For each Material Separately
For All Materials Together
MUV/MQV = MMV + MYV → (2)
MCV = MPV + MMV + MYV → (3) [From (1) and (2)]
For each Material Separately
For All Materials Together

Who is held responsible for the Variance?



Since this variance is on account of the price being more or less than the standard, the people or department responsible for purchasing materials can be held responsible for this variance.


