# Illustration - Problem

1,800 kgs of a product are planned to be produced using 900 kgs of Material A @ 15 per kg, 800 kgs of Material B @ 45/kg and 200 kgs of Material C @ 85 per kg at a total cost of 66,500. 4,320 kgs of the product were manufactured using 2,250 kgs of Material A @ 16 per kg, 1,950 kgs of Material B @ 42/kg and 550 kgs of Material C @ 90 per kg.

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

Working Table
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

What is the variation in total cost on account of materials being acquired at a price other than the standard?

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 Material
 MPVMat = SC(AQ)Mat − ACMat Or = AQMat × (SPMat − APMat)

## For all Materials together

Total Material Price variance

 TMPV = ΣMPVMat Sum of the variances measured for each material separately

Material Price Variance for the mix

 MPVMix = SC(AQ)Mix − ACMix = AQMat × (SPMat − APMat) [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 = MPVMix, when MPVMix 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

⇒ V1 = Q × P1 → (1)

⇒ V2 = Q × P2 → (2)

(1) − (2) gives

V1 − V2 = Q × P1 − Q × P2

⇒ V1 − V2 = Q × (P1 − P2)

⇒ 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 formulae for calculating Material Price Variances involve AQ, SP and AP. They do not contain any terms involving standard quantity (SQ). Since recalculation of standard affects standard quantity (SQ) and thereby standard cost (SC) only, we do not need the recalculated standards for finding out material price variance.

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.

Working Table with recalculated standards
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) =
 AO SO
=
 4,320 1,800
= 2.4
SQ(AO) = SQ ×
 AO SO
= SQ × 2.4

⋇ SC(AO) = SQ(AO) × SP

SPMix =
 SC(AO) SQ(AO)

⋇ SO(AO) = AO

SQIL(AO) = SQIL ×
 AO SO
= SQIL × 2.4

⋇ SCIL(AO) = SQIL(AO) × SP

(AI) =
 AI SI
=
 AQMix SQMix
=
 4,750 kgs 1,900 kgs
= 2.5
SQ(AI) = SQ ×
 AI SI
= SQ × 2.5

⋇ SC(AI) = SQ(AI) × SP

SQIL(AI) = SQIL ×
 AI SI
= SQIL × 2.5

⋇ SCIL(AI) = SQIL(AI) × SP

SO(AI) = SO ×
 AI SI
= SO × 2.5

⋇ AC = AQ × AP

⋇ SC(AQ) = AQ × SP

⋇ SC(AQIL) = AQIL × SP

# Illustration - Solution

Standards need not be recalculated. But we need SC(AQ) and AC for calculating this variance.

MPV = SC(AQ) − AC

Material Price Variance due to

 Material A, MPVA = SC(AQ)A − ACA = 33,750 − 36,000 = − 2,250 [Adv] Material B, MPVB = SC(AQ)B − ACB = 87,750 − 81,900 = + 5,850 [Fav] Material C, MPVC = SC(AQ)C − ACC = 41,800 − 46,750 = − 2,750 [Adv] TMPV = + 850 [Fav] Material Mix, MPVMix = SC(AQ)Mix − ACMix = 1,68,250 − 1,67,400 = + 850 [Fav]

# Illustration - Solution [alternative]

If calculating the price variance is the only requirement, we may avoid calculating the cost/value data in the working table and use the formula involving quantities and prices. We need only the data relating to AQ, SP and AP for this calculation.
Working Table with given 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 kgs
SO
4,320 kgs
AO

MPV = AQ (SP − AP)

Material Price Variance due to

 Material A, MPVA = AQA(SPA − APA) = 2,250 kgs (15/kg − 16/kg) = 2,250 kgs (− 1/kg) = − 2,250 [Adv] Material B, MPVB = AQB(SPB − APB) = 1,950 kgs (45/kg − 42/kg) = 1,950 kgs (3/kg) = + 5,850 [Fav] Material C, MPVC = AQC(SPC − APC) = 550 kgs (85/kg − 90/kg) = 550 kgs (− 5/kg) = − 2,750 [Adv] TMPV = + 850 [Fav]

Standard Quantity Mix Ratio

 SQMR = SQA : SQB : SQC = 900 kgs : 800 kgs : 200 kgs = 9 : 8 : 2

Actual Quantity Mix Ratio

 AQMR = AQA : AQB : AQC = 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

## MPVMat

• SC(AQ)Mat ___ ACMat
• SPMat ___ APMat

## MPVMix

• SC(AQ)Mix ___ ACMix
• SPMix ___ APMix (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.

VarianceMix 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

1. each material variance being zero, or
2. 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 Inter-relationships 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