# 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 Quantity/Usage Variance (MQV/MUV)

What is the variation in the total cost on account of the actual quantity being different from the standard quantity for the actual output achieved?

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

Based on inputs
SC(AO) = SC ×
 AO SO
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

• ×  AO SO
replaces the suffix (AO) in calculations
• 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/MUVMat = SC(AO)Mat − SC(AQ)Mat Or = [SQ(AO)Mat − AQMat] × SPMat

## 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/MUVMat Sum of the variances measured for each material separately

Material Quantity/Usage variance for the Mix

 MQV/MUVMix = SC(AO)Mix − SC(AQ)Mix = [SQ(AO)Mix − AQMix] × SPMix (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/MUVMix, when MQV/MUVMix 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

⇒ V1 = Q1 × P → (1)

⇒ V2 = Q2 × P → (2)

(1) − (2) gives

⇒ V1 − V2 = Q1 × P − Q2 × P

⇒ V1 − V2 = (Q1 − Q2) × 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

We need to recalculate standards based on AO for finding MQV/MUV.
Working Table with recalculated standards
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) =
 AO SO
=
 4,320 1,800
= 2.4
SQ(AO) = SQ ×
 AO SO
= SQ × 2.4

⋇ SC(AO) = SQ(AO) × SP

SPMix =
 SC(AO)Mix SQ(AO)Mix

⋇ SO(AO) = AO

SQIL(AO) = SQIL ×
 AO SO
= 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/MUVA = SC(AO)A − SC(AQ)A = 32,400 − 33,750 = − 1,350 [Adv] Material B, MQV/MUVB = SC(AO)B − SC(AQ)B = 86,400 − 87,750 = − 1,350 [Adv] Material C, MQV/MUVC = SC(AO)C − SC(AQ)C = 40,800 − 46,750 = − 5,950 [Adv] TMQV/TMUV = − 8,650 [Adv] Material Mix, MQV/MUVMix = SC(AO)Mix − SC(AQ)Mix = 1,59,600 − 1,68,250 = − 8,650 [Adv]

## Alternative

Where MQV/MUV is the only variance to be found we may avoid calculating cost/value data in the working table by using the formula with quantities and prices.

MQV/MUV = [SQ(AO) − AQ] × SP

Material Quantity/Usage Variance due to

 Material A, MQV/MUVA = [SQ(AO)A − AQA] × SPA = (2,160 kgs − 2,250 kgs) × 15/kg = − 90 kgs × 15/kg = − 1,350 [Adv] Material B, MQV/MUVB = [SQ(AO)B − AQB] × SPB = (1,920 kgs − 1,950 kgs) × 45/kg = − 30 kgs × 45/kg = − 1,350 [Adv] Material C, MQV/MUVC = [SQ(AO)C − AQC] × SPC = (480 kgs − 550 kgs) × 85/kg = − 70 kgs × 85/kg = − 5,950 [Adv] TMQV/TMUV = − 8,650 [Adv]

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.

# Illustration - Solution (without recalculating standards)

Where SO ≠ AO, we can use the adjustment factor
 AO SO
in the formula itself for finding the variance.
• ## 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 C
900
800
200
15
45
85
13,500
36,000
17,000
2,250
1,950
550
16
42
90
33,750
87,750
46,750
Total/Mix 1,900 66,500 4,750 1,68,250
Output 1,800
SO
4,320
AO

SC = SQ × SP

SC(AQ) = AQ × SP

MQV/MUV = SC × AO SO
− SC(AQ)
• ## 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 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
MUV/MVQ = (SQ × AO SO
− AQ) × SP

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

Material quantity/usage variance is a synthesis of two variances, Material Mix Variance and Material Yield 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/Sub-Usage 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/MUVMat

• SC(AO)Mat ___ SC(AQ)Mat
• SQ(AO)Mat ___ AQMat

## MQV/MUVMix

• SC(AO)Mix ___ SC(AQ)Mix
• SQ(AO)Mix ___ AQMix (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.

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 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

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 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.
1. the ratio in which the quantities of constituent materials are mixed and
2. 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 Inter-relationships 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