# Standards for Actual Output

The standard quantity, price and cost are useful in identifying the variances in the actual quantity, price and cost of materials compared to the standard.

The following standard and actual data relating to an output of 150 units would help us in identifying the variances.

Standard Actual
for SO
SQ SP SC AQ AP AC
Material Used 450 4 1,800 440 5 2,200
Output 150
SO
150
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.

• Quantity of materials.

440 kgs actual as against a standard of 450 kgs indicating efficiency in using materials.

• Price of materials.

5 actual as against a standard price of 4 indicating inefficiency in purchasing materials.

• Cost of materials.

2,200 actual as against a standard cost of 1,800 indicating burden on account of cost of materials.

## Why Recalculate Standards?

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

From the following data, we cannot straightaway say whether the output was obtained at a lesser or greater cost as well as whether the materials have been used efficiently.

Standard Actual
for SO
SQ SP SC AQ AP AC
Material Used 2,250 2 4,500 480 2 960
Output 1,000
SO
210
AO

This is because the actual data pertains to an output of 210 units as against the standard known for an output of 1,000 units.

Comparing the quantities and costs for the actual output of 210 units with those of the standard output of 1,000 units is inappropriate. We cannot say that 480 kgs were actually used as against a standard of 2,250 kgs or the actual cost is 960 as against a standard cost of 4,500.

However we would be able to say that the materials were acquired at a price of 2 as indicated by the standard. This conclusion can be drawn in spite of the standard output and actual output being different.

To be able to make a meaningful comparison straight away, we have to recalculate the standards such that the outputs 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 output

Standard Actual
for SO for AO
SQ SP SC SQ(AO) SC(AO) AQ AP AC
Material Used 2,250 2 4,500 472.5 945 480 2 960
Output 1,000
SO
210
SO(AO)
210
AO
• Quantity of materials.

480 kgs actual as against a standard of 472.5 kgs indicating inefficiency in using materials.

• Price of materials.

2 actual as against a standard price of 2 indicating efficiency in purchasing materials.

Note that we can draw this conclusion even without recalculating the standards.

• Cost of materials.

960 actual as against a standard cost 945 indicating a slight burden on account of cost of materials.

To find the variance in quantity of material used we need the standard quantity for actual output [SQ(AO)] and the variance in the cost of materials we need the standard cost for actual output [SC(AO)].

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

# 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 and loss data worked out and arranged in the 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
13,500
36,000
17,000
2,250
1,950
550
16
42
90
Total/Mix 1,900 35 66,500 4,750
Input Loss 100 35 3,500 430
Output 1,800
SO
4,320
AO

SQIL = SI − SO

AQIL = AI − AO

SC = SQ × SP

Notice that SO ≠ AO.

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

# Factor - (AO)

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

Logic (based on Cost of MaterialA)

 If SO is SC is 1,800 kgs ⇒ 13,500 4,320 kgs ⇒ ?

Standard Cost for an Output of 4,320 kgs

= 13,500 ×
 4,320 kgs 1,800 kgs
= Standard Cost ×
 Actual Output Standard Output
⇒ SC(AO) = SC ×
 AO SO
Thus,
 AO SO
would be the factor with which the standard data has to be multiplied to obtain the recalculated standard for the actual output.
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,

(AO) =
 AO SO
=
 4,320 kgs 1,800 kgs
= 2.4

# Standard Quantity for Actual Output

Standard Quantity for Actual Output represents the quantity of material that should have been used for the actual output, had the usage of materials been as per standard.
SQ(AO) = SQ ×
 AO SO
• ### For each Material separately

Standard Quantity of a Material for the Actual Output

SQ(AO)Mat = SQMat ×  AO SO
• ## For all Materials together

Standard Quantity of Mix for Actual Output

SQ(AO)Mix = SQMix ×  AO SO
Or = ΣSQ(AO)Mat

Sum of the Standard Quantity for Actual Output of Individual Materials

Using the data in the illustration above,

SQ(AO)A = SQA ×
 AO SO
= 900 kgs × 2.4 = 2,160 kgs
SQ(AO)B = SQB ×
 AO SO
= 800 kgs × 2.4 = 1,920 kgs
SQ(AO)C = SQC ×
 AO SO
= 200 kgs × 2.4 = 480 kgs
SQ(AO)Mix = 4,560 kgs
SQ(AO)Mix = SQMix ×
 AO SO
= 1,900 kgs × 2.4 = 4,560 kgs

# Standard Cost for Actual Output

Standard Cost for Actual Output represents the material cost that would have been incurred for the actual output, had the materials been used (quantity) as per the standard and procured (price) at the prices/rates as per the standard.
SC(AO) = SC ×
 AO SO
Or = SQ × SP ×
 AO SO
= SQ ×
 AO SO
× SP
= SQ(AO) × SP

Standard Quantity for Actual Output × Standard Price

• ## For each Material separately

Standard Cost of a Material for Actual Output

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

Standard Cost of Mix for Actual Output

SC(AO)Mix = SCMix ×  AO SO
Or = SQ(AO)Mix × SPMix

## Standard Price of Mix

SPMix =  SCMix SQMix
=  ΣSCMat ΣSQMat

Using the data in the illustration above,

SC(AO)A = SCA ×
 AO SO
= 13,500 × 2.4 = 32,400
SC(AO)B = SCB ×
 AO SO
= 36,000 × 2.4 = 86,400
SC(AO)C = SCC ×
 AO SO
= 17,000 × 2.4 = 40,800
SC(AO)Mix = 1,59,600
SC(AO)Mix = SCMix ×
 AO SO
= 66,500 × 2.4 = 1,59,600

## Alternative

If SQ(AO) and SP are readily available,

 SC(AO)A = SQ(AO)A × SPA = 2,160 kgs × 15/kg = 32,400 SC(AO)B = SQ(AO)B × SPB = 1,920 kgs × 45/kg = 86,400 SC(AO)C = SQ(AO)C × SPC = 480 kgs × 85/kg = 40,800 SC(AO)Mix = 1,59,600 SC(AO)Mix = SQ(AO)Mix × SPMix = 4,560 kgs × 35/kg = 1,59,600
SPMix =
 SCMix SQMix
=
 66,500 1,900 kgs
= 35/kg

# Standard Quantity of Input Loss for Actual Output

These are relevant only in cases where there is loss of input material in obtaining the output.

Standard quantity of input loss for the actual output represents the input quantity that would have been lost for the actual output had the materials been used (quantity) as per the standard.

SQIL(AO) = SQIl ×
 AO SO
• ### For each Material separately

Standard Quantity of input loss for the Actual Output

SQIL(AO)Mat = SQILMat ×  AO SO

Theoretically this measure can be calculated for each material separately. This would be of relevance only in cases where the input loss is being measured for each material separately and not over the mix.

• ## For all Materials together

Standard Quantity of input loss of Mix for Actual Output

SQIL(AO)Mix = SQILMix ×  AO SO
Or = ΣSQIL(AO)Mat

Sum of the Standard Quantity of input loss for Actual Output of Individual Materials

This would be relevant only when the input loss is being measured for each material separately.

Using the data in the illustration above,

SQIL(AO)A = SQILA ×
 AO SO
= NA = NA
SQIL(AO)B = SQILB ×
 AO SO
= NA = NA
SQIL(AO)C = SQILC ×
 AO SO
= NA = NA
SQIL(AO)Mix = NA
SQIL(AO)Mix = SQILMix ×
 AO SO
= 100 kgs × 2.4 = 240 kgs

# Standard Cost of Input Loss for Actual Output

Standard Cost of Input Loss for Actual Output represents the cost of the standard quantity of input loss valued at standard price.
SCIL(AO) = SCIL ×
 AO SO
Or = SQIL × SP ×
 AO SO
= SQIL ×
 AO SO
× SP
= SQIL (AO) × SP

Standard Quantity of Input Loss × Standard Price

• ## For each Material separately

Standard Cost of Input Loss of a Material for Actual Output

SCIL(AO)Mat = SCMat ×  AO SO
Or = SQIL (AO)Mat × SPMat
• ## For all Materials together

Standard Cost of Input Loss of Mix for Actual Output

SCIL(AO)Mix = SCMix ×  AO SO
Or = SQIL (AO)Mix × SPMix

## Standard Price of Mix

SPMix =  SI SQ
=  ΣSCMat ΣSQMat

Using the data in the illustration above,

SCIL(AO)A = SCA ×
 AO SO
= NA = NA
SCIL(AO)B = SCB ×
 AO SO
= NA = NA
SCIL(AO)C = SCC ×
 AO SO
= NA = NA
SCIL(AO)Mix = NA
SCIL(AO)Mix = SCMix ×
 AO SO
= 3,500 × 2.4 = 8,400

## Alternative

If SQIL (AO) and SP are readily available,

 SCIL(AO)A = SQIL (AO)A × SPA = NA = NA SCIL(AO)B = SQIL (AO)B × SPB = NA = NA SCIL(AO)C = SQIL (AO)C × SPC = NA = NA SCIL(AO)Mix = NA SCIL(AO)Mix = SQIL (AO)Mix × SPMix = 240 kgs × 35/kg = 8,400
SPMix =
 SCMix SQIL Mix
=
 66,500 1,900 kgs
= 35/kg

# Data Table with the recalculated Standard

The data for the standards based on the actual output is as below.

Standard Actual
for SO for AO
SQ SP SQ(AO) SC(AO) AQ AP
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
Total/Mix 1,900 4,560 1,59,600 4,750
Input Loss 100 240 8,400 430
Output 1,800
SO
4,320
SO(AO)
4,320
AO
1. (AO) =
 AO SO
=
 4,320 1,800
= 2.4

Using this factor, (AO), the SQ(AO) and SQIL(AO), from that the SC(AO) and SCIL(AO) 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.

2. SQ(AO) = SQ ×
 AO SO
= SQ × 2.4

3. SC(AO) = SQ(AO) × SP

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

SPMix will be required to calculate SCMix and SCILMix directly using a formula, instead of as the sum of the values for the constitutent materials.

5. SO(AO) = AO

6. SQIL(AO) = SQIL ×
 AO SO
= SQIL × 2.4

7. SCIL(AO) = SQIL(AO) × SP

After recalculating the standards we have Actuals and S_(AO) whose output values are the same.