# Standards for Actual Input

The standard quantity and cost for actual input are useful in identifying the variance in the actual mix of and yield from the materials compared to the standard.

The following standard and actual data relating to an input of 1,200 kgs would help us in identifying the variance.

Standard Actual
for SO
SQ SP SC AQ AP AC
Material A
Material B
Material C
500
400
300
12
15
8
6,000
6,000
2,400
520
430
250
11
16
10
6,720
6,880
2,500
Total/Mix 1,200 14,400 1,200 17,100
Output 2,500
SO
2,400
AO

Output (_O) is in units, Quantities (_Q) are in kgs, Prices (_P) are in monetary value per unit quantity and Costs (_C) are in monetary values.

• Mix of materials.

Materials have been mixed in a proportion different from the standard.

Material A 520 kgs instead of 500kgs, Material B 430 kgs instead of 400 kgs and Material C 250 kgs instead of 300 kgs.

## Mix Ratios

There being a difference in mix can also be identified by using the mix ratios. However, this needs us to calculate the ratios and does not allow conclusion by a straight away comparison of material quantities.

Standard Quantity Mix Ratio

 SQMR = SQA : SQB : SQC = 500 kgs : 400 kgs : 300 kgs = 5 : 4 : 3

Actual Quantity Mix Ratio

 AQMR = AQA : AQB : AQC = 520 kgs : 430 kgs : 250 kgs = 52 : 43 : 25

AQMR is different from the SQMR

• Yield from materials.

A total input of 1,200 kgs has yielded an output of 2,400 units as against a standard of 2,500 units.

## Why Recalculate Standards?

Standards may be expressed for any level of activity. Where standards are available for an input other than that has been actually used i.e. when Standard Input and Actual Input are not equal (SI ≠ AI), we cannot get an idea of the variance by comparing the available data.

From the following data, we cannot straightaway say whether there is any variance on account of the mix as well as if the yield is as per the standard.

Standard Actual
for SO
SQ SP SC AQ AP AC
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
36,000
81,900
41,800
Total/Mix 1,900 66,500 4,750 1,67,400
Output 1,800
SO
4,320
AO

This is because the actual data pertains to an input of 4,750 kgs as against the standard known for an input of 1,900 kgs.

Comparing the quantities and yield for the actual input of 4,750 kgs with those of the standard input of 1,900 kgs is inappropriate. We cannot say that 2,250 kgs of A were actually used as against a standard of 900 kgs or the actual output/yield is 4,320 kgs as against a standard output of 1,800 kgs.

To be able to make a meaningful comparison straight away, we have to recalculate the standards such that the inputs are the same both in the actual data and the standard data, thereby enabling us to derive variances by comparison.

The comparison becomes meaningful once we obtain the standards for the actual input.

Standard Actual
for SO for AI
SQ SP SC SQ(AI) SC(AI) AQ AP AC
Material A
Material B
Material C
900
800
200
15
45
85
13,500
36,000
17,000
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
Total/Mix 1,900 66,500 4,750 1,66,250 4,750 1,67,400
Input Loss 100 3,500 250 8,750 430
Output 1,800
SO
4,500
SO(AI)
4,320
AO
• Mix of materials.

Materials B and C have been mixed in a proportion different from the standard.

Material A 2,250 kgs as per standard, Material B 1,950 kgs instead of 2,000 kgs and Material C 550 kgs instead of 500 kgs.

• Yield from materials.

The input has yielded an output of 4,320 kgs as against a standard of 4,500 kgs.

To find the variance in mix of and yield from material used we need the standard quantity for actual input [SQ(AI)] and the value of the variance we need the standard cost for actual input [SC(AI)] as well as the standard cost of actual quantity [SC(AQ)].

Since standards can be built for any production level we were able to recalculate the standards for the actual input.

# Illustration - Problem (for explanation)

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.

# Working Table

The data from the problem obtained as it is, arranged in a working table.

working table
Standard Actual
for SO
SQ SP SC 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 66,500 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 Standard cost data worked out and arranged in the working table.

SC = SQ × SP

working table
Standard Actual
for SO
SQ SP SC AQ AP
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
Total/Mix 1,900 35 66,500 4,750
Output 1,800
SO
4,320
AO

Notice that SI ≠ AI i.e. SQMix ≠ AQMix

We ignored other possible calculations like AC = AQ × AP, since we are only trying to recalculate standards primarily quantities and costs.

# Factor - (AI)

The factor with which the standard data has to be multiplied to obtain the required recalculated standard for actual input. It is represented by the symbol (AI).

By Input here we mean the quantity of Mix.

Logic (based on Cost of MaterialMix)

 If SI is SC is 1,900 kgs ⇒ 66,500 4,750 kgs ⇒ ?

Standard Cost for an Input of 4,750 kgs

= 66,500 ×
 4,750 kgs 1,900 kgs
= Standard Cost ×
 Actual Input Standard Input
⇒ SC(AI) = SC ×
 AI SI
Thus,
 AI SI
would be the factor with which the standard data has to be multiplied to obtain the recalculated standard for the actual input.
The same logic applies to recalculating both the quantities as well as costs for individual materials as well as the mix.

Using the data in the illustration above,

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

# Standard Quantity for Actual Input/Mix

Standard Quantity for Actual Input/Mix has relevance only when two or more types of materials are being used in the production process i.e. when there is a mix.

It represents the quantity of each material that should have been present in the actual mix had the materials been taken in ratio of standard mix.

SQ(AI)= SQ ×
 AI SI
• ## For Each Material Separately

Standard Quantity of a Material for the Actual Input

SQ(AI)Mat = SQMat ×  AI SI
• ## For all Materials together

SQ(AI)Mix = SQMix ×  AI SI
Or = ΣSQ(AI)Mat

Sum of the Standard Quantity for Actual Input of Individual Materials

Or = AQMix
= ΣAQMat

Since SQ(AI)Mix = AQMix, we don't need to calculate this.

Using the data in the illustration above,

SQ(AI)A = SQA ×
 AI SI
= 900 kgs × 2.5 = 2,250 kgs
SQ(AI)B = SQB ×
 AI SI
= 800 kgs × 2.5 = 2,000 kgs
SQ(AI)C = SQC ×
 AI SI
= 200 kgs × 2.5 = 500 kgs
SQ(AI)Mix = 4,750 kgs
SQ(AI)Mix = SQMix ×
 AI SI
= 1,900 kgs × 2.5 = 4,750 kgs
= AQMix

# Standard Cost for Actual Input

Standard Cost for Actual Input is the Standard Cost of Standard Quantity for Actual Input. It represents the cost that should have been incurred for each type of material had the actual materials been present in the ratio of standard mix and acquired at the standard price/rates.
SC(AI) = SC ×
 AI SI
Or = SQ × SP ×
 AI SI
= SQ ×
 AI SI
× SP
= SQ(AI) × SP

Standard Quantity for Actual Input × Standard Price

• ### For each Material separately

Standard Cost of a Material for the Actual Input

SC(AI)Mat = SCMat ×  AI SI
Or = SQ(AI)Mat × SPMat
• ## For all Materials together

Standard Cost of Mix for Actual Input

SC(AI)Mix = SCMix ×  AI SI
Or = SQ(AI)Mix × SPMix

## Standard Price of Mix

SPMix =  SCMix SQMix
=  ΣSCMat ΣSQMat

Using the data in the illustration above,

SC(AI)A = SCA ×
 AI SI
= 13,500 × 2.5 = 33,750
SC(AI)B = SCB ×
 AI SI
= 36,000 × 2.5 = 90,000
SC(AI)C = SCC ×
 AI SI
= 17,000 × 2.5 = 42,500
SC(AI)Mix = 1,66,250
SC(AI)Mix = SCMix ×
 AI SI
= 66,500 × 2.5 = 1,66,250

## Alternative

If SQ(AI) and SP are readily available

 SC(AI)A = SQ(AI)A × SPA = 2,250 kgs × 15/kg = 33,750 SC(AI)B = SQ(AI)B × SPB = 2,000 kgs × 45/kg = 90,000 SC(AI)C = SQ(AI)C × SPC = 500 kgs × 85/kg = 42,500 SC(AI)Mix = 1,66,250 SC(AI)Mix = SQ(AI)Mix × SPMix = 4,750 kgs × 35/kg = 1,66,250
SPMix =
 SCMix SQMix
=
 66,500 1,900 kgs
= 35/kg

# Standard Output/Yield for Actual Input

Standard Output/Yield indicates the output that should have been achieved for the material input, had the production been normal. The terms Yield and Output are synonymously used.
SO(AI) = SO ×
 AI SI

Consider the data from the illustration above.

• ## For each Material separately

AQMat may or may not be equal to AIMat for individual materials. But AQMix = AIMix.

For the purpose of this calculation, the input we intend to consider is the actual quantity of input and not the Actual input arrived at by recalculating the total actual input in the standard quantity mix ratio.

SO(AI)Mat = SO(AQ)Mat
= SO ×  AQMat SQMat

## Note

Measuring the output for each input material is improbable since the output/yield is relevant to all the inputs together.

This calculation is intended to give an idea of the possibility. It is not used anywhere in analysing variances.

• ## For all Materials together

Since AQMix = AIMix, taking either AI or AQ would give the same result for the mix.
SO(AI)Mix = SO ×  AQMix SQMix
= SO ×  AI SI

Using the data in the illustration above,

SO(AI)A = SO(AQ)A
= SO ×
 AQA SQA
= 1,800 kgs ×
 2,250 kgs 900 kgs
= 1,800 kgs × 2.5 = 4,500 kgs
SO(AI)B = SO(AQ)B
= SO ×
 AQB SQB
= 1,800 kgs ×
 1,950 kgs 800 kgs
= 1,800 kgs × 2.4375 = 4,387.50 kgs
SO(AI)C = SO(AQ)C
= SO ×
 AQC SQC
= 1,800 kgs ×
 550 kgs 200 kgs
= 1,800 kgs × 2.75 = 4,950 kgs
SO(AI)Mix ΣSO(AI)Mat
SO(AI)Mix = SO ×
 AI SI
= 1,800 kgs ×
 4,750 kgs 1,900 kgs
= 1,800 kgs × 2.5 = 4,500 kgs

## Note

• SO(AQ)Mix ≠ ΣSO(AQ)Mat

The standard output for the actual mix is not equal to the sum of the Standard Outputs for each material separately.

Each of the SO(AI) represents the total output that could have been achieved, whether we calculate it based on individual materials or the total input.

Thus the idea that Σ__Mat = __Mix should not be applied here. The values relating to individual materials do not add up to form the value relating to the mix.

• SO(AQ)Mix = SO(AQ)Mat under specific conditions

The standard output for the actual mix may be equal to the Standard Outputs for a material if the actual material is in the same proportion to the standard material as the actual mix to standard mix.

 AQMix SQMix
=  AQMat SQMat
⇒ SO ×  AQMix SQMix
= SO ×  AQMat SQMat

SO(AQ)Mix = SO(AQ)Mat

From the data in the above illustration

 AQMix SQMix
=  4,750 kgs 1,900 kgs
= 2.5

For Material A

 AQA SQA
=  2,250 kgs 900 kgs
= 2.5

SO(AQ)Mix = SO(AQ)A = 4,500 kgs

For Material B

 AQB SQB
=  1,950 kgs 800 kgs
= 2.4375

SO(AQ)Mix ≠ SO(AQ)B
[4,500 kgs ≠ 4,387.50]

•  AQMix SQMix
=  AQMat SQMat
can also be interpreted as  SQMat SQMix
=  AQMat AQMix

The proportion of a material to the mix is the same both in the actuals and standards.

• If the standard quantity mix ratio and the actual quantity mix ratio are the same, then all the materials would satisfy the relation  AQMat AQMix
=  SQMat SQMix
.

In such a case, SO(AQ)Mix = each of SO(AQ)Mat

# Standard Cost of Actual Quantity

The cost of actual quantity of material valued at the standard prices.
SC(AQ) = SC ×
 AQ SQ
= SQ × SP ×
 AQ SQ
= AQ × SP

Actual Quantity × Standard Price

• ### for each material separately

The cost of a material type valued at its standard price

SC(AQ)Mat = AQMat × SPMat

• ### for all materials together

The total cost of all material types valued at their standard prices together.

Standard Cost of Actual Quantity of Mix

 SC(AQ)Mix = ΣSC(AQ)Mat Sum of the Standard Costs of Actual (total) Time of Individual Materials Or = AQMix × SPMix (conditional) Actual Quantity of Mix × Standard Price of Mix This will be true only if the standard quantity mix ratio (SQMR) and the actual quantity mix ratio (AQMR) are the same.
If SC(AQ)Mix = AQMix × SPMix,

AQMix × SPMix = ΣSC(AQ)Mat

SPMix is the weighted average of Standard Prices taking standard times (ST) as weights and ΣSC(AQ)Mat consider actual quantities (AQ). Thus, if SQMR ≠ AQMR, then SC(AQ)Mix ≠ AQMix × SPMix

From the data in the illustration

 SC(AQ)A = AQA × SPA = 2,250 kgs × 15/kg = 33,750 SC(AQ)B = AQB × SPB = 1,950 kgs × 45/kg = 87,750 SC(AQ)C = AQC × SPC = 550 kgs × 85/kg = 46,750 SC(AQ)Mix = 1,68,250

Verification :

SC(AQ)Mix ≠ AQMix × SPMix

 AQMix × SPMix = 4,750 kgs × 35/kg = 1,66,250 ≠ SC(AQ)Mix = SC(AI)Mix

## SC(AI) and SC(AQ) are different

SC(AI) represents the standard cost of actual quantities of materials arrived at by taking the total actual quantity of material in the standard quantity mix ratio and valuing them at standard prices.

SC(AQ) represents that standard cost of actual quantities of materials taking the actual quantities and valuing them at standard prices.

SC(AI) = SC(AQ) if the standard quantity mix ratio and the actual quantity mix ratio are the same.

# Data table with recalculated Standard

The given data with the recalculated standards would be.
Standard Actual
for SO for AI
SQ SP SQ(AI) SC(AI) AQ AP AC SC(AQ)
Factor 2.5
Material A
Material B
Material C
900
800
200
15
45
85
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 4,750 1,66,250 4,750 1,67,400 1,68,250
Input Loss 100 35 250 8,750 430 15,050
Output 1,800
SO
4,500
SO(AI)
4,320
AO
 AI SI
=
 1,900 4,750
= 2.5

Using this factor, (AI), the SQ(AI) and from that the SC(AI) can be calculated straight away in the working table. To make these calculations convenient and avoid errors, present this factor also in the working table.

SQ(AI) = SQ ×
 AI SI
= SQ × 2.5

⋇ SC(AI) = SQ(AI) × SP

SO(AI) = SO ×
 AI SI
= SO × 2.5

⋇ SC(AQ) = AQ × SP

Where we need to recalculate the standards we may avoid ascertaining the values for the given standards as the recalculated values are the ones that would be useful.

After recalculating the standards we have Actuals and S_(AI) whose input (QMix) values are the same.

# Standards for Actual Output vs Standards for Actual Input

Standard for
Actual Output Actual Input
Basis for recalculation Actual Output Actual Input
Equates Standard Output
with Actual output
Standard Input
with Actual Input
After recalculation SO = AO SI = AI or SQMix = AQMix