# Standards for Actual Input

The standard time and cost for actual input are useful in identifying the variance in the actual mix of and yield from the labour/labor types compared to the standard.

The following standard and actual data relating to an input of 950 hrs would help us in identifying the variance.

Standard Actual
for SO Total
ST SR SC AT AR AC
Men
Women
Boys
1,400
1,200
800
12
20
10
16,800
24,000
8,000
1,800
1,000
600
11
22
10
19,800
22,000
6,000
Total 3,400 38,800 3,400 47,800
Output 8,500
SO
7,400
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.

• Mix of labour/labor types.

Labour/Labor types have been mixed in a proportion different from the standard.

Men 1,800 hrs instead of 1,400 hrs, Women 1,000 hrs instead of 1,200 hrs and Boys 600 hrs instead of 800 hrs.

## 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 labour/labor time.

Standard Time Mix Ratio

 STMR = STm : STw : STb = 1,400 hrs : 1,200 hrs : 800 hrs = 7 : 6 : 4

Actual Time Mix Ratio

 ATMR = ATm : ATw : ATb = 1,800 hrs : 1,000 hrs : 600 hrs = 9 : 5 : 3

ATMR is different from the STMR

• Yield from labour/labor types.

A total input of 3,400 hrs has yielded an output of 7,400 units as against a standard of 8,500 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 Total
ST SR SC AT AR AC
Machinist
Helpers
Supervisors
2,000
800
200
30
20
50
60,000
16,000
10,000
3,600
1,300
350
32
20
45
1,15,200
26,000
15,750
Total 3,000 86,000 5,250 1,56,950
Output 6,000
SO
11,000
AO

This is because the actual data pertains to an input of 5,200 hrs as against the standard known for an input of 3,000 hrs.

Comparing the times and yield for the actual input of 5,200 hrs with those of the standard input of 3,000 hrs is inappropriate. We cannot say that Machinists worked for 3,600 hrs as against a standard of 2,000 hrs or the actual output/yield is 11,000 units as against a standard output of 6,000 units.

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 Total
ST SR SC ST(AI) SC(AI) AT AR AC
Machinist
Helpers
Supervisors
2,000
800
200
30
20
50
60,000
16,000
10,000
3,500
1,400
350
1,05,000
28,000
17,500
3,600
1,300
350
32
20
45
1,15,200
26,000
15,750
Total 3,000 86,000 5,250 1,50,500 5,250 1,56,950
Output 6,000
SO
10,500
SO(AI)
11,000
AO
• Mix of labour/labor types.

Labour/Labor types, Machinists and Helpers have been employed in a proportion different from the standard.

Machinists 3,600 hrs instead of 3,500 hrs, Helpers 1,300 hrs instead of 1,400 hrs.

Supervisors have been employed for 350 hrs as per standard.

• Yield from labour/labor types.

A total input of 5,200 hrs has yielded an output of 11,000 units as against a standard of 10,500 units.

To find the variance in mix of and yield from labour/labor types used we need the standard time for actual input [ST(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 time[SC(AT)].

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

# Actual Time ⇒ Productive Time

While measuring variation in mix and yield, by actual time we mean productive time for which the labour/labor have been employed.

This idea is relevant when there is idle time, in which case

• Actual Time = Total time paid for
• Productive Time = Total time − Idle Time
Standard Actual
for SO Total Idle Productive
ST SR SC AT AR IT PT
Machinist
Foremen
Supervisor
700
200
60
50
80
100
35,000
16,000
6,000
800
158
76
52
80
98
50
18
6
750
140
70
Total 960 56,000 1,034 90 960
Output 80,000
SO
84,220
AO

If we consider

• ### AI = ΣAT

AI = 1,034 hrs ⇒ AI ≠ SI.

We have to recalcualte the standard for AI to enable comparison.

• ### AI = ΣPT

AI = 960 hrs ⇒ AI = SI.

We can straight away compare the times and yield.

When there is idle time loss, AI = ΣPT

# 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.

Standard Actual
for SO Total Idle
ST SR AT AR IT
Skilled
Semi-Skilled
Unskilled
200
400
150
20
15
10
240
500
220
22
14
12
20
36
34
Total 750 960 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 Productive Time data, Standard cost data worked out and arranged in the working table.

PT = AT × IT

SC = SQ × SR

Standard Actual
for SO Total Idle Productive
ST SR SC AT AR IT PT
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
220
464
186
Total 750 11,500 960 90 870
Output 7,500
SO
7,200
AO

Notice that SI ≠ AI i.e. STMix ≠ PTMix

We ignored other possible calculations like AC = AT × AR, since we are only trying to recalculate standards primarily time 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 time of Mix.

Logic (based on Cost of Labour/LaborMix)

 If SI is SC is 750 hrs ⇒ 11,500 870 hrs ⇒ ?

Standard Cost for an Input of 870 hrs

= 11,500 ×
 870 hrs 750 hrs
= 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 times as well as costs for individual labour/labor types as well as the mix.

Using the data in the illustration above,

(AI) =
 AI SI
=
 ATMix STMix
=
 870 hrs 750 hrs
= 1.16

# Standard Time for Actual Input/Mix

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

It represents the time of each labour/labor that should have been present in the actual mix had the labour/labor types been taken in ratio of standard mix.

ST(AI)= ST ×
 AI SI
• ## For each Labour/Labor type separately

Standard Time of a Labour/Labor type for the Actual Input

ST(AI)Lab = STLab ×  AI SI
• ## For all Labour/Labor Types together

ST(AI)Mix = STMix ×  AI SI
Or = ΣST(AI)Lab

Sum of the Standard Time for Actual Input of Individual Labour/Labor Types

Or = PTMix
= ΣPTLab

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

Using the data in the illustration above,

ST(AI)sk = STsk ×
 AI SI
= 200 hrs × 1.16 = 232 hrs
ST(AI)ss = STss ×
 AI SI
= 400 hrs × 1.16 = 464 hrs
ST(AI)us = STus ×
 AI SI
= 150 hrs × 1.16 = 174 hrs
ST(AI)Mix = 870 hrs
ST(AI)us = STMix ×
 AI SI
= 750 hrs × 1.16 = 870 hrs
= PTMix

When there is no idle time loss, ATLab = PTLab and ATMix = PTMix

# Standard Cost for Actual Input

Standard Cost for Actual Input is the Standard Cost of Standard Time for Actual Input. It represents the cost that should have been incurred for each labour/labor type had the actual labour/labor types been present in the ratio of standard mix and paid at the standard rates.
SC(AI) = SC ×
 AI SI
Or = ST × SR ×
 AI SI
= ST ×
 AI SI
× SR
= ST(AI) × SR

Standard Time for Actual Input × Standard Rate

• ### For each Labour/Labor type separately

Standard Cost of a Labour/Labor Type for the Actual Input

SC(AI)Mix = SCLab ×  AI SI
Or = ST(AI)Lab × SRLab
• ## For all Labour/Labor types together

Standard Cost of Mix for Actual Input

SC(AI)Mix = SCMix ×  AI SI
Or = ST(AI)Mix × SRMix

## Standard Rate of Mix

SRMix =  SCMix STMix
=  ΣSCLab ΣSTLab

Using the data in the illustration above,

SC(AI)sk = SCsk ×
 AI SI
= 4,000 × 1.16 = 4,640
SC(AI)ss = SCss ×
 AI SI
= 6,000 × 1.16 = 6,960
SC(AI)us = SCus ×
 AI SI
= 1,500 × 1.16 = 1,740
SC(AI)Mix = 13,340
SC(AI)Mix = SCMix ×
 AI SI
= 11,500 × 1.16 = 13,340

## Alternative

If ST(AI) and SR are readily available

SC(AI)sk = ST(AI)sk × SRsk
= 232 hrs × 20/hr = 4,640
= 464 hrs × 15/hr = 6,960
SC(AI)us = ST(AI)us × SRus
= 174 hrs × 10/hr = 1,740
SC(AI)Mix = 13,340
SC(AI)Mix = ST(AI)Mix × SRMix
= 870 hrs ×
 46 3
/hr
= 13,340
SRMix =
 SCMix STMix
=
 11,500 750 hrs
=
 46 3
/hr

# Standard Output/Yield for Actual Input ~ SO(AI)/SY(AI)

Standard Output/Yield indicates the output that should have been achieved for the labour/labor time 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 Labour/Labor type separately

PTLab may or may not be equal to AILab for individual labour/labor types. But PTMix = AIMix.

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

SO(AI)Lab = SO(PT)Lab
= SO ×  PTLab STLab

## Note

Measuring the output for each labour/labor type is improbable since the output/yield is relevant to all the labour/labor types together.

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

• ## For all Labour/Labor types together

Since PTMix = AIMix, taking either AI or PT would give the same result for the mix.
SO(AI)Mix = SO ×  PTMix STMix
= SO ×  AI SI

Using the data in the illustration above,

SO(AI)sk = SO(PT)sk
= SO ×
 PTsk STsk
= 7,500 units ×
 220 hrs 200 hrs
= 7,500 units × 1.1 = 8,250 units
SO(AI)ss = SO(PT)ss
= SO ×
 PTss STss
= 7,500 units ×
 464 hrs 400 hrs
= 7,500 units × 1.16 = 8,700 units
SO(PT)us = SO ×
 PTus STus
= 7,500 units ×
 186 hrs 150 hrs
= 7,500 units × 1.24 = 9,300 units
SO(AI)Mix ΣSO(AI)Lab
SO(AI)Mix = SO ×
 AI SI
= 7,500 units ×
 870 hrs 750 hrs
= 7,500 units × 1.16 = 8,700 units

## Note

• SO(PT)Mix ≠ ΣSO(PT)Lab

The standard output for the actual mix is not equal to the sum of the Standard Outputs for each labour/labor type separately.

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

Thus the idea that Σ__Lab = __Mix should not be applied here. The values relating to individual labour/labor types do not add up to form the value relating to the mix.

• SO(PT)Mix = SO(PT)Lab under specific conditions

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

 PTMix STMix
=  PTLab STLab
⇒ SO ×  PTMix STMix
= SO ×  PTLab STLab

SO(PT)Mix = SO(PT)Lab

From the data in the above illustration

 PTMix STMix
=  870 hrs 750 hrs
= 1.16

For Skilled Labour/Labor Type

 PTsk STsk
=  220 hrs 200 hrs
= 1.1

SO(PT)Mix ≠ SO(PT)sk
[8,700 units ≠ 8,250 units]

For Semi Skilled Labour/Labor Type

 PTss STss
=  464 hrs 400 hrs
= 1.16

SO(AT)Mix = SO(AT)ss = 8,700 units

•  PTMix STMix
=  PTLab STLab
can also be interpreted as  STLab STMix
=  PTLab PTMix

The proportion of a labour/labor type to the mix is the same both in the actuals and standards.

• If the standard time mix ratio and the actual time mix ratio are the same, then all the labour/labor types would satisfy the relation  PTLab PTMix
=  STLab STMix
.

In such a case, SO(PT)Mix = each of SO(PT)Lab

# Standard Cost for Actual Time

The standard cost of actual labor/labour time employed arrived at by valuing the time at the standard rate.
SC(AT) = SC ×
 AT ST
= ST × SR ×
 AT ST
= AT × SR

Actual Time × Standard Rate of Pay

• ### for each labour/labor type separately

The cost of actual (total) time of each labor/labour type valued at its standard rate of pay

SC(AT)Lab = ATLab × SRLab

• ### for all labour/labor types together ~ SC(AT)Mix

The total cost of actual (total) time of all labor/labour types valued at their standard rates together

Standard Cost of Actual Time of Mix

 SC(AT)Mix = ΣSC(AT)Lab Sum of the Standard Costs of Actual (total) Time of Individual Labour/Labor types Or = ATMix × SRMix (conditional) Actual (total) time of Mix × Standard Rate of Mix This will be true only if the standard time mix ratio (STMR) and the actual time mix ratio (ATMR) are the same.
If SC(AT)Mix = ATMix × SRMix,

ATMix × SRMix = ΣSC(AT)Lab

SRMix is the weighted average of Standard Rates taking standard times (ST) as weights and ΣSC(AT)Lab consider actual (total) times (AT). Thus, if STMR ≠ ATMR, then SC(AT)Mix ≠ ATMix × SRMix

From the data in the illustration

 SC(AT)sk = ATsk × SRsk = 240 hrs × 20/hr = 4,800 SC(AT)ss = ATss × SRss = 500 hrs × 15/hr = 7,500 SC(AT)us = ATus × SRus = 220 hrs × 10/hr = 2,200 SC(AT)Mix = 14,500

Verification : SC(AT)Mix ≠ ATMix × SRMix

ATMix × SRMix = 960 hrs ×
 46 3
/hr
= 14,720
SC(AT)Mix

# Standard Cost for Idle Time

The standard cost of actual labor/labour idle time arrived at by valuing the time at the standard rate.
SC(IT) = SC ×
 IT ST
= ST × SR ×
 IT ST
= IT × SR

Actual Idle Time × Standard Rate of Pay

• ### for each labour/labor type separately

The cost of idle time of each labor/labour type valued at its standard rate of pay

SC(IT)Lab = ITLab × SRLab

• ### for all labour/labor types together ~ SC(IT)Mix

The total cost of idle time of all labor/labour types valued at their standard rates together

Standard Cost of Actual Idle Time of Mix

 SC(IT)Mix = ΣSC(IPT)Lab Sum of the Standard Costs of Idle Time of Individual Labour/Labor types Or = ITMix × SRMix (conditional) Idle time of Mix × Standard Rate of Mix This will be true only if the standard time mix ratio (STMR) and the idle time mix ratio (ITMR) are the same.
If SC(IT)Mix = ITMix × SRMix,

ITMix × SRMix = ΣSC(IT)Lab

SRMix is the weighted average of Standard Rates taking standard times (ST) as weights and ΣSC(IT)Lab consider idle times (IT). Thus, if STMR ≠ ITMR, then SC(IT)Mix ≠ ITMix × SRMix

From the data in the illustration

 SC(IT)sk = ITsk × SRsk = 20 hrs × 20/hr = 400 SC(IT)ss = ITss × SRss = 36 hrs × 15/hr = 540 SC(AT)us = ATus × SRus = 34 hrs × 10/hr = 340 SC(IT)Mix = 1,280

Verification : SC(IT)Mix ≠ ITMix × SRMix

ITMix × SRMix = 90 hrs ×
 46 3
/hr
= 1,380
SC(IT)Mix

# Standard Cost for Productive Time

The standard cost of actual productive labor/labour time employed arrived at by valuing the time at the standard rate.
SC(PT) = SC ×
 PT ST
= ST × SR ×
 PT ST
= PT × SR

Productive Time × Standard Rate of Pay

• ### for each labour/labor type separately

The cost of each labor/labour type valued at its standard rate of pay

SC(PT)Lab = PTLab × SRLab

• ### for all labour/labor types together ~ SC(PT)Mix

The total cost of all labor/labour types valued at their standard rates together

Standard Cost of Productive Time of Mix

 SC(PT)Mix = ΣSC(PT)Lab Sum of the Standard Costs of Productive Time of Individual Labour/Labor types Or = PTMix × SRMix (conditional) Productive time of Mix × Standard Rate of Mix This will be true only if the standard time mix ratio (STMR) and the productive time mix ratio (PTMR) are the same.
If SC(PT)Mix = PTMix × SRMix,

PTMix × SRMix = ΣSC(PT)Lab

SRMix is the weighted average of Standard Rates taking standard times (ST) as weights and ΣSC(PT)Lab consider productive times (PT). Thus, if STMR ≠ PTMR, then SC(PT)Mix ≠ PTMix × SRMix

From the data in the illustration

 SC(PT)sk = PTsk × SRsk = 220 hrs × 20/hr = 4,400 SC(PT)ss = PTss × SRss = 464 hrs × 15/hr = 6,960 SC(PT)us = PTus × SRus = 186 hrs × 10/hr = 1,860 SC(PT)Mix = 13,220

Verification : SC(PT)Mix ≠ PTMix × SRMix

PTMix × SRMix = 870 hrs ×
 46 3
/hr
= 13,340
SC(PT)Mix

# Data table with recalculated Standard

The given data with the recalculated standards would be.

Standard Actual
for SO for AI Total Idle Productive
ST SR ST(AI) SC(AI) AT AR AC SC(AT) IT SC(IT) PT SC(PT)
Factor 1.16
Skilled
Semi-Skilled
Unskilled
200
400
150
20
15
10
232
464
174
4,640
6,960
1,740
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 750 870 13,340 960 14,920 14,500 90 1,280 870 13,220
Output 7,500
SO
8,700
SO(AI)
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.
 AI SI
=
 PT ST
=
 870 750
= 1.16

Using this factor, (AI), the ST(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.

2. ST(AI) = ST ×
 AI SI
= ST × 1.16

3. SC(AI) = ST(AI) × SR

4. SC(AT) = IT × SR

5. SC(IT) = AT × SR

6. SC(PT) = PT × SR

7. SO(AI) = SO ×
 AI SI
= SO × 1.16

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 (TMix) values are the same.

## Identities

The data in the above table while being interpreted will be addressed as below.
Standard Actual
for SO for AI Total Idle Productive
ST SR ST(AI) SC(AI) AT AR AC SC(AT) IT SC(IT) PT SC(PT)
Factor (AI)
Skilled
Semi-Skilled
Unskilled
STsk
STss
STun
SRsk
SRun
ST(AI)sk
ST(AI)ss
ST(AI)un
SC(AI)sk
SC(AI)ss
SC(AI)un
ATsk
ATss
ATun
ARsk
ARun
ACsk
ACss
ACun
SC(AT)sk
SC(AT)ss
SC(AT)un
ITsk
ITss
ITun
SC(IT)sk
SC(IT)ss
SC(IT)un
PTsk
PTss
PTun
SC(PT)sk
SC(PT)ss
SC(PT)un
Total STMix SRMix SR(AO)Mix SC(AO)Mix ATMix ARMix ACMix SC(AT)Mix ITMix SC(IT)Mix PTMix SC(PT)Mix
Output SO SO(AI) AO

# 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 STMix = PTMix