# Illustration - Problem

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.

Calculate Labor/Labour Variances.

# Working Table

Working table populated with the information that can be obtained as it is from the problem data

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 rest of the information that we make use of in problem solving is filled through calculations.

# Formulae - Labor/Labour Yield/Sub-Efficiency Variance ~ LYV/LSEV

What is the variation in total cost on account of the actual output/yield being different from the standard output for the actual input (PTMix).

Labor/Labour Yield/Sub-Efficiency Variance is the difference between the Standard Cost of Actual Output and the Standard Cost of Actual Input

⇒ Labour/Labor Yield/Sub-Efficiency Variance (LYV/LSEV)

 = SC(AO) − SC(AI) Standard Cost for Actual Output − Standard Cost of Actual Input

Based on inputs
SC(AO) = SC ×
 AO SO
Or = ST(AO) × SR

Based on output

Or = AO × SC/UO

SC(AI) = SC ×
 AI SI
Or = ST(AI) × SR

## Formula in useful forms

LYV/LSEV = SC(AO) − SC(AI)

Standard Cost for Actual Output − Standard Cost of Actual Input

Or = SC × (
 AO SO
 AI SI
)

Standard Cost × difference of ratios of actual output to standard output and actual input to standard input.

Or = [ST(AO) − ST(AI)] × SR

Difference in Standard Times for Actual Output and Actual Input × Standard Rate

Or = [AO − SO(AI)] × SC/UO

Difference between actual output and standard output for actual input × Standard Cost per unit output.

## Note

• ×  AO SO
replaces the suffix (AO) and ×  AI SI
replaces the suffix (AI) in calculations
• AI = PTMix and SI = STMix.

## For each Labour/Labor Type Separately

LYV/LSEVLab = SC(AO)Lab − SC(AI)Lab
Or = SCLab × (
 AO SO
 AI SI
)
Or = [ST(AO)Lab − ST(AI)Lab] × SPLab
Or = [AOLab − SO(AI)Lab] × SC/UOLab

## For all Labour/Labor Types together

Total Labour/Labor Yield/Sub-Efficiency variance

 TLYV/TLSEV = ΣLYV/LSEVLab Sum of the variances measured for each labour/labor type separately

Labour/Labor Yield/Sub-Efficiency variance for the Mix

LYV/LSEVMix = SC(AO)Mix − SC(AI)Mix
Or = SCMix × (
 AO SO
 AI SI
)
Or = [ST(AO)Mix − ST(AI)Mix] × SPMix
Or = [AOMix − SO(AI)Mix] × SC/UOMix

# Illustration - Solution

We need to recalculate standards based on both AO and AI for finding LYV/LSEV.
Working Table with recalculated standards
Standard Actual
for SO for AO for AI Total Idle
(Abnormal)
Productive
ST SR ST(AO) SC(AO) ST(AI) SC(AI) AT AR IT PT
Factor 2.4 2.5
Skilled
Semi-Skilled
Unskilled
200
400
150
20
15
10
192
384
144
3,840
5,760
1,440
232
464
174
4,640
6,960
1,740
240
500
220
22
14
12
20
36
34
220
464
186
Total 750 720 11,040 870 13,340 960 90 870
Output 7,500 units
SO
7,200 units
SO(AO)
8,700 units
SO(AI)
7,200 units
AO
1. (AO) =
 AO SO
=
 7,200 7,500
= 0.96
2. ST(AO) = ST ×
 AO SO
= ST × 0.96

3. SC(AO) = ST(AO) × SR

4. SO(AO) = AO

5. (AI) =
 AI SI
 AI SI
=
 PTMix STMix
=
 870 750
= 1.16
6. ST(AI) = ST ×
 AI SI
= ST × 1.16

7. SC(AI) = ST(AI) × SR

8. SO(AI) = SO ×
 AI SI
= SO × 1.16

LYV/LSEV = SC(AO) − SC(AI)

Labour/Labor Yield/Sub-Efficiency Variance due to

 Skilled Labour/Labor, LYV/LSEVsk = SC(AO)sk − SC(AI)sk = 3,840 − 4,640 = − 800 [Adv] Semi Skilled Labour/Labor, LYV/LSEVss = SC(AO)ss − SC(AI)ss = 5,760 − 6,960 = − 1,200 [Adv] Unskilled Labour/Labor, LYV/LSEVus = SC(AO)us − SC(AI)us = 1,440 − 1,740 = − 300 [Adv] TLYV/TLSEV = − 2,300 [Adv] Labour/Labor Type Mix, LYV/LSEVMix = SC(AO)Mix − SC(AI)Mix = 11,040 − 13,340 = − 2,300 [Adv]

## Alternative

Where LYV/LSEV is the only variance to be calculated we may use the formula involving times and rates and avoid calculating costs/values in the working table.

LYV/LSEV = [ST(AO) − ST(AI)] × SP

Labour/Labor Yield/Sub-Efficiency Variance due to

Skilled Labour/Labor,
LYV/LSEVsk = [ST(AO)sk − ST(AI)sk] × SPsk
= (192 − 232) × 20
= − 40 × 20 = − 800 [Adv]
Semi Skilled Labour/Labor,
LYV/LSEVss = [ST(AO)ss − ST(AI)ss] × SPss
= (384 − 464) × 15
= − 80 × 15 = − 1,200 [Adv]
Unskilled Labour/Labor,
LYV/LSEVus = [ST(AO)us − ST(AI)us] × SPus
= (144 − 174) × 10
= − 30 × 10 = − 300 [Adv]
Labour/Labor Type Mix,
LYV/LSEVMix = [ST(AO)Mix − ST(AI)Mix] × SPMix
= (720 − 870) ×
 46 3
= − 150 ×
 46 3

Even in this case, if we intend to use the formula for the mix, we need either the SCMix or SC(AO)Mix or SC(AI)Mix to be able to find the SPMix

SPMix =
 SC(AO)Mix ST(AO)Mix
=
 11,040 720
=
 46 3

# Illustration - Solution (without recalculating standards)

Where SI ≠ AI and SO ≠ AO, we can use the adjustment factors
 AI SI
and
 AO SO
respectively in the formula itself for finding the variance.
• ## Calculating Costs in a working table

Calculate SC based on the given data in a working table and then use formulae based on costs.
Working Table
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

SC = ST × SR

LYV/LSEV = SC × ( AO SO
−  AI SI
)
• ## Using Formula with Times and Rates

Using the time and rate 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 = time × rate.
Working Table
Standard Actual
for SO Total Idle Productive
ST SR SC AT AR IT PT
Skilled
Semi-Skilled
Unskilled
200
400
150
20
15
10
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

PT = AT − IT

LYV/LSEV = ST × SR × ( AO SO
−  AI SI
)

Even in this case, if we intend to use the formula for the mix, we need the SCMix for which we would need the SC values.

• ## Using Formula Based on Outputs

Working Table
Standard Actual
for SO Total Idle Productive
ST SR SC SC/UO AT AR iT PT
Skilled 200 20 4,000  8 15
240 22 20 220
Semi Skilled 400 15 6,000 0.8 500 22 36 464
Unskilled 150 10 1,500 0.2 220 12 34 186
Total 750  230 15
11,500  23 15
960 90 870
Output 7,500
SO
7,200
AO
SC/UO =  SC SO
LYV/LSEV = [AO − SO × AI SI
] × SC/UO

# LYV/LSEV - Miscellaneous Aspects

• ## Productive Time

Since labour/labor yiels/sub-efficiency variance is a part of labour/labor efficiency variance measured using productive time, the actual time considered in this variance is also Productive time.

Thus, AI = ΣPT

Where there is no idle time loss, the actual (total) time is productive time.

• ## Nature of Variance

Based on the relations derived from the formulae for calculating LYV/LSEV, we can identify the nature of Variance

• SC(AO) ___ SC(AI)
•  AO SO
___  AI SI
• ST(AO) ___ ST(AI)
• AO ___ SO(AI)

## LYV/LSEVLab

• SC(AO)Lab ___ SC(AI)Lab
•  AO SO
___  AI SI
• ST(AO)Lab ___ ST(AI)Lab
• AOLab ___ SO(AI)Lab

## LYV/LSEVMix

• SC(AO)Mix ___ SC(AI)Mix
•  AO SO
___  AI SI
• ST(AO)Mix ___ ST(AI)Mix
• AOMix ___ SO(AI)Mix

The variance would be

• zero when =
• Positive when >
• Negative when <

### TLYV/LSEV

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.

• ## Individual Variances in Standard Cost Mix Ratio

This variance measures the efficiency in deriving output out of the total labour/labor time used as a whole and not of individual labour/labor types.

Any variation on account of varying the times of individual labour/labor types is revealed by the Labour/Labor Mix/Gang-Composition Variance.

This can be identified from the fact that the calculation of the variance for individual labour/labor types is the equivalent of dividing the variance for the mix among the labour/labor types in the standard cost mix ratio (SCMR).

LYV/LSEVLab = LYV/LSEVMix × standard cost mix proportion

From the data in the illustration,

Standard Cost Mix Ratio ~ SCMR

sk : ss : us = SCsk : SCss : SCus
= 4,000 : 6,000 : 1,500
= 8 : 12 : 3
=  8 23
:  12 23
:  3 23

LYV/LSEVMix = − 11,500

LYV/LSEVsk = − 2,300 ×  8 23
= − 100 × 8
= − 800
LYV/LSEVss = − 2,300 ×  12 23
= − 100 × 12
= − 1,200
LYV/LSEVus = − 2,300 ×  3 23
= − 100 × 3
= − 300
• ## Interpretation of the Variance

For the labour/labor mix, for the output achieved

Variance Time 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 individual labour/labor types based on individual times input. However, it should be noted that the output is a result of the mix and measuring the influence of individual labour/labor times is inappropriate.

The individual variances data would be of little help in taking corrective actions.

• ## Who is answerable for the Variance?

Since this variance is on account of more or less yield for the input used, the people or department responsible for managing the production operations (say manufacturing department) is answerable for this variance.

# Formulae using Inter-relationships among Variances

• LYV/LSEV = LEV − LMV/GCV
• LYV/LSEV = LCV − LRPV − LMV/GCV − LITV

## Verification

Skilled Semi Skilled Unskilled Total
LYV/LSEV
+ LMV/GCV
− 800
+ 240
− 1,200
0
− 300
− 120
− 2,300
+ 120
LEV
+ LITV
− 560
− 400
− 1,200
− 540
− 420
− 340
− 2,180
− 1,280
LUV/LGEV
+ LRPV
− 960
− 480
− 1,740
+ 500
− 420
− 760
− 3,460
− 420
LCV − 1,440 − 1,240 − 1,200 − 3,880