# Standards for Actual Output

The standard time, rate and cost are useful in identifying the variances in the actual time, rate and cost of labour/labor compared to the standard.

The following standard and actual data relating to an output of 80 units would help us in identifying the variances.

Standard Actual
for SO
ST SR SC AT AR AC
Operators 160 12 1,920 168 12.50 2,100
Output 80
SO
80
AO

Output (_O) is in units, Times (_T) are in hrs, Rates (_R) are in monetary value per unit time and Costs (_C) are in monetary values.

• labour/labor time

168 hrs as against a standard of 160 hrs indicating inefficiency.

• labour/labor rate of pay

12.50 actual as against a standard of 12 indicating inefficiency in rates paid.

• cost incurred on labour/labor

2,100 actual as against a standard of 1,920 indicating burden on account of labour/labor cost.

## 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 labour/labor time has been used efficiently.

Standard Actual
for SO
ST SR SC AT AR AC
Operators 1,000 12 12,000 880 12.50 11,000
Output 500
SO
400
AO

Output (_O) is in units, Times (_T) are in hrs, Rates (_R) are in monetary value per unit time and Costs (_C) are in monetary values.

This is because the labour/labor time actually employed and the cost incurred is for manufacturing 400 units whereas the standard known is for manufacturing 500 units.

Comparing the actual labour/labor time utilised and actual costs for 400 units of output with those of the standard output of 500 units is inappropriate. We cannot say that 880 hrs were actually used as against a standard of 1,000 hrs or the actual cost is 11,000 as against a standard cost of 12,000.

However we would be able to say that the rate of wages paid is 0.50 higher than 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, we have to recalculate the standards such that the AO and SO are the same, 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
ST SR SC ST(AO) SC(AO) AT AR AC
Operators 1,000 12 12,000 800 9,600 880 12.50 11,000
Output 500
SO
400
SO(AO)
400
AO

Output (_O) is in units, Times (_T) are in hrs, Rates (_R) are in monetary value per unit time and Costs (_C) are in monetary values.

• labour/labor time

880 hrs as against a standard of 800 hrs indicating inefficiency.

• labour/labor rate of pay

12.50 actual as against a standard of 12 indicating inefficiency in rates paid.

• cost incurred on labour/labor

11,000 actual as against a standard of 9,600 indicating burden on account of labour/labor cost.

To find the variance in labour/labor time used we need the standard time for actual output [ST(AO)] and the variance in the labour/labor cost 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.

## Standards for Actual Output/Input

We will be able to recalculate the standards for a level of activity other than the one given. This recalculation may be based on
1. The actual output where we obtain the Standard Time and Cost for Actual Output
2. The actual input where we obtain the Standard Time, Cost and Output for Actual Input.

# Illustration - Problem (for explanation)

7,500 units of a product are planned to be produced using 200 hrs of Skilled Labour/Labor @ 20 per hr, 400 hrs of Semi-Skilled Labour/Labor @ 15/hr and 150 hrs of Unskilled Labour/Labor @ 10 per hr at a total cost of 11,500. 7,200 units of the product were manufactured using 240 hrs of skilled labour/labor @ 22 per hr, 500 hrs of Semi-skilled labour/labor @ 14/hr and 220 hrs of Unskilled labour/labor @ 12 per hr. 20 hrs of Skilled Labour/Labor time, 36 hrs of Semi-Skilled Labour/Labor time and 34 hrs of Unskilled Labour/Labor time were lost due to break down which is abnormal.

# Working Table

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

working table
Standard Actual
for SO Total Idle
ST SR SC AT AR IT
Skilled
Semi-Skilled
Unskilled
200
400
150
20
15
10
240
500
220
22
14
12
20
36
34
Total 750   11,500 960 90
Output 7,500
SO
7,200
AO

Output (_O) is in units, Times (_T) are in hrs, Rates (_R) are in monetary value per unit time and Costs (_C) are in monetary values.

The standard cost data worked out and arranged in the working table.

working table
Standard Actual
for SO Total Idle
ST SR SC AT AR IT
Skilled
Semi-Skilled
Unskilled
200
400
150
20
15
10
4,000
6,000
1,500
240
500
220
22
14
12
20
36
34
Total 750   11,500 960 90
Output 7,500
SO
7,200
AO

We ignored other possible calculations like AC = AT × AR, PT = AT × IT etc., since we are only trying to recalculate standards primarily times and costs.

Notice that SO ≠ AO.

working table
Standard Actual
for SO Total Idle
(Abnormal)
Productive
(Normal)
ST SR SC AT AR AC SC(AT) IT SC(IT) PT SC(PT)
Skilled
Semi-Skilled
Unskilled
200
400
150
20
15
10
4,000
6,000
1,500
240
500
220
22
14
12
5,280
7,000
2,640
4,800
7,500
2,200
20
36
34
400
540
340
220
464
186
4,400
6,960
1,860
Total 750   11,500 960 14,920 14,500 90 1,280 870 13,220
Output 7,500 units
SO
7,200 units
AO

# 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 Labour/Laborsk)

 If SO is SC is 7,500 units ⇒ 4,000 7,200 units ⇒ ?

Standard Cost for an Output of 7,200 units

= 4,000 ×
 7,200 units 7,500 units
= 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 times as well as costs for individual labour/labor types as well as the mix.

Using the data in the illustration above,

(AO) =
 AO SO
=
 7,200 units 7,500 units
= 0.96

# Standard Time for Actual Output

Standard Time for Actual Output represents the time for which the labour/labor should have been used for the actual output, had the labour/labor usage been as per standard.
ST(AO) = ST ×
 AO SO
• ### For each Labour/Labor type separately

Standard Time of a labour/labor for the Actual Output

ST(AO)Lab = STLab ×  AO SO
• ## For all Labour/Labor types together

Standard Time of Mix for Actual Output

ST(AO)Mix = STMix ×  AO SO
Or = ΣST(AO)Lab

Sum of the Standard Times for Actual Output of Individual Labour/Labor types

Using the data in the illustration above,

ST(AO)sk = STsk ×
 AO SO
= 200 hrs × 0.96 = 192 hrs
ST(AO)ss = STss ×
 AO SO
= 400 hrs × 0.96 = 384 hrs
ST(AO)us = STus ×
 AO SO
= 150 hrs × 0.96 = 144 hrs
ST(AO)Mix = 720 hrs
ST(AO)Mix = STMix ×
 AO SO
= 750 hrs × 0.96 = 720 hrs

# Formula - Standard Cost for Actual Output

Standard Cost for Actual Output represents the labour/labor cost that would have been incurred for the actual output, had the labour/labor time been used as per the standard and paid for at the rates as per the standard.
SC(AO) = SC ×
 AO SO
Or = ST × SR ×
 AO SO
= ST ×
 AO SO
× SR
= ST(AO) × SR

Standard Time for Actual Output × Standard Rate of Pay

• ## For each Labor/Labour type separately

Standard Cost of a Labor/Labour for Actual Output

SC(AO)Lab = SCLab ×  AO SO
Or = ST(AO)Lab × SRLab
• ## For all Labor/Labour types together

Standard Cost of Mix for Actual Output

SC(AO)Mix = SCMix ×  AO SO
Or = ST(AO)Mix × SRMix

## Standard Rate of Mix

SRMix =  SCMix STMix
=  ΣSCLab ΣSTLab

Using the data in the illustration above,

SC(AO)sk = SCsk ×
 AO SO
= 4,000 × 0.96 = 3,840
SC(AO)ss = SCss ×
 AO SO
= 6,000 × 0.96 = 5,760
SC(AO)us = SCus ×
 AO SO
= 1,500 × 0.96 = 1,440
SC(AO)Mix = 11,040
SC(AO)Mix = SCMix ×
 AO SO
= 11,500 × 0.96 = 11,040

## Alternative

If ST(AO) and SR are readily available,

SC(AO)sk = ST(AO)sk × SRsk
= 192 hrs × 20/hr = 3,840
= 384 hrs × 15/hr = 5,760
SC(AO)us = ST(AO)us × SRus
= 144 hrs × 10/hr = 1,440
SC(AO)Mix = 11,040
SC(AO)Mix = ST(AO)Mix × SRMix
= 720 hrs ×
 46 3
/hr
= 11,040
SRMix =
 SCMix STMix
=
 11,500 750 hrs
=
 46 3
/hr

# 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 Total Idle
ST SR ST(AO) SC(AO) AT AR IT
Factor 0.96
Skilled
Semi-Skilled
Unskilled
200
400
150
20
15
10
192
384
144
3,840
5,760
1,440
240
500
220
22
14
12
20
36
34
Total 750 720 11,040 960 90
Output 7,500
SO
7,200
SO(AO)
7,200
AO

Output (_O) is in units, Times (_T) are in hrs, Rates (_R) are in monetary value per unit time and Costs (_C) are in monetary values.

1. (AO) =
 AO SO
=
 7,200 7,500
= 0.96

Using this factor, (AO), the ST(AO) and from that the SC(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. ST(AO) = ST ×
 AO SO
= ST × 0.96

3. SC(AO) = ST(AO) × SR

4. SO(AO) = AO

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 Actual and S_(AO) whose output values are the same.

## Identities

The data in the above table while being interpreted will be addressed as below.
Standard Actual
for SO for AO Total Idle
ST SR ST(AO) SC(AO) AT AR IT
Factor (AO)
Skilled
Semi-Skilled
Unskilled
STsk
STss
STun
SRsk
SRun
ST(AO)sk
ST(AO)ss
ST(AO)un
SC(AO)sk
SC(AO)ss
SC(AO)un
ATsk
ATss
ATun
ARsk