# 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 - Labour/Labor Efficiency Variance ~ LEV

What is the variation in the total cost on account of the productive time worked being different from the standard time for the actual output achieved?

It is the difference between the standard cost for actual output and the standard cost of productive labour/labor time.

⇒ Labour/Labor Efficiency Variance (LEV)

 = SC(AO) − SC(PT) Standard Cost for Actual Output − Standard Cost of Productive Time

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

Based on output

Or = AO × SC/UO

## Standard Cost of Productive Time

 SC(PT) = PT × SR

## Formula in useful forms

 LEV = SC(AO) − SC(PT) Standard cost for actual output − Standard cost of productive time Or = [ST(AO) − PT] × SR Difference between Standard time for actual output and Productive time × Standard rate

## Note

• ×  AO SO
replaces the suffix (AO) in calculations

## For each Labour/Labor Type Separately

Labour/Labor Efficiency variance for a labour/labor type

 LEVLab = SC(AO)Lab − SC(PT)Lab Or = (ST(AO)Lab − PTLab) × SRLab

## For all Labour/Labor Types together

Total Labour/Labor Efficiency Variance

 ⇒ TLEV = ΣLEVLab Sum of the variances measured for each labour/labor type separately

Labour/Labor Efficiency variance for the Mix

 LEVMix = SC(AO)Mix − SC(PT)Mix Or = [ST(AO)Mix − PTMix] × SRMix (conditional) This formula can be used for the mix, only when the productive times mix ratio is the same as the standard time mix ratio.

TLEV = LEVMix, when LEVMix can be calculated.

# Illustration - Solution (by recalculating standards)

We need to recalculate standards based on AO for finding LEV.
Working Table with recalculated standards
Standard Actual
for SO for AO Total Idle Productive
ST SR ST(AO) SC(AO) AT AR IT PT SC(PT)
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
220
464
186
4,400
6,960
1,860
Total 750 720 11,040 960 90 870 13,220
Output 7,500
SO
7,200
SO(AO)
7,200
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. PT = AT − IT

5. SC(PT) = PT × SR

6. SO(AO) = AO

LEV = SC(AO) − SC(PT)

Labour/Labor Efficiency Variance due to

 Skilled Labour/Labor, LEVsk = SC(AO)sk − SC(PT)sk = 3,840 − 4,400 = − 560 [Adv] Semi Skilled Labour/Labor, LEVss = SC(AO)ss − SC(PT)ss = 5,760 − 6,960 = − 1,200 [Adv] Un Skilled Labour/Labor, LEVus = SC(AO)us − SC(PT)us = 1,440 − 1,860 = − 420 [Adv] TLEV = − 2,180 [Adv] Labour/Labor Mix, LEVMix = SC(AO)Mix − SC(PT)Mix = 11,040 − 13,220 = − 2,180 [Adv]

## Alternative

Where LEV is the only variance to be found we may avoid calculating cost/value data in the working table by using the formula with times and rates.

LEV = [ST(AO) − PT] × SR

Labour/Labor Efficiency Variance due to

 Skilled Labour/Labor, LEVsk = [ST(AO)sk − PTsk] × SRsk = (192 hrs − 220 hrs) × 20/hr = − 28 hrs × 20/hr = − 560 [Adv] Semi Skilled Labour/Labor, LEVss = [ST(AO)ss − PTss] × SRss = (384 hrs − 464 hrs) × 15/hr = − 80 hrs × 15/hr = − 1,200 [Adv] Un Skilled Labour/Labor, LEVus = [ST(AO)us − PTus] × SRus = (144 hrs − 186 hrs) × 10/hr = − 42 hrs × 10/hr = − 420 [Adv] TLEV = − 2,180 [Adv]

Standard Time Mix Ratio

 STMR = STsk : STss : STus = 200 hrs : 400 hrs : 150 hrs = 4 : 8 : 3

Productive Time Mix Ratio

 PTMR = PTsk : PTss : PTus = 220 hrs : 464 hrs : 186 hrs = 110 : 232 : 93

Since this formula involves the term PT × SR and STMR ≠ PTMR, it cannot be used for calculating the variance for the mix.

# Solution (Without recalculating standards)

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

Calculate SC and SC(PT) based on the given data in a working table and then use formulae based on costs.
Standard Actual
for SO Total Idle Productive
ST SR SC AT AR 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
20
36
34
220
464
186
4,400
6,960
1,860
Total 750 11,500 960 90 870 13,220
Output 7,500
SO
7,200
AO

1. SC = ST × SR

2. SC(PT) = PT × SR

LEV = SC × AO SO
− SC(PT)
• ## Using Formula with Time and Rate

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.
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
LEV = (ST × AO SO
− PT) × SR
LEV = [ST × AO SO
− PT] × SR
= [ST ×  AO SO
− (AT − IT)] × SR

Since this formula involves the term PT × SR and PTMR ≠ STMR, it cannot be used for calculating the variance for the Mix

# LEV - Miscellaneous Aspects

• ## Why Productive Time?

LUV/LGEV measures efficiency taking the total labour/labor time into consideration.

Abnormal loss of time may be on account of many reasons like, machinery breakdown, power breakdown, lack of material availability, natural calamities, improper scheduling, strike, lockout, etc..

Whether the labourers/laborers have worked efficiently or not is revealed by measuring the output achieved by them during the time they work. The labourers/laborers cannot be held responsible for the loss of production on account of abnormal idle time.

Thus the loss due to time lost on account of abnormal reasons would be dealt with separately and LEV wishes to measure only the level to which the worker performs his work during the time he/she works.

LEV thus is a labour/labor productivity indicator. The efficiency in utilising labour/labor time is revealed through this variance.

Where there is no idle time loss, actual time and productive time would be the same.

• ## Why use Total Time in Cost and Rate of Pay Variances??

The labour/labor cost variance reflects the total variance on account of all reasons and thus we take the total time into consideration in measuring the Labour/Labor Cost Variance.

Wages are to be paid to the workers for all the hours they work (both normal hours and abnormal idle hours). A variation in rate of pay would result in a gain or loss on account of all hours being paid for. Thus in measuring rate of pay variance total time is considered.

• ## Nature of Variance

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

• SC(AO) ___ SC(PT)
• ST(AO) ___ PT

## LEVLab

• SC(AO)Lab ___ SC(PT)Lab
• ST(AO)Lab ___ PTLab

## LEVMix

• SC(AO)Mix ___ SC(PT)Mix
• ST(AO)Mix ___ PTMix (conditional)

only when STMR = PTMR.

The variance would be

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

### TLUV/TLGEV

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.

• ## Interpretation of the Variance

For each labour/labor type, for the output achieved

Variance Productive 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 mix based on the mix variance. However, it should be noted that the mix variance is an aggregate of individual variances and as such reflects their net effect.

Mix variance data would be helpful to get an overall idea only. It would not be as useful as individual variances data in taking corrective actions.

Eg: When the Total Variance is zero, we cannot conclude that the cost incurred on all labour/labor types is as per standard, as it might have been zero on account of

1. each labour/labor type variance being zero, or
2. the unfavourable variance due to one or more labour/labor types is set off by the favourable variance due to one or more other labour/labor types.
• ## Who is answerable for the Variance?

Since this variance is on account of the productive labour/labor time used being more or less than the standard, the people or department responsible for production can be identified as the ones answerable for this variance.

# Formulae using Inter-relationships among Variances

• LEV = LUV/LGEV − LITV
• LEV = LMV/GCV + LYV/LSEV

## Verification

In problem solving, these inter relationships would also help us to verify whether our calculations are correct or not.

Building a table as below would help

Skilled Semi Skilled Unskilled Total/Mix
LYV/LSEV
+ LMV/GCV

LEV
+ LITV
− 560
− 400
− 1,200
− 540
− 420
− 340
− 2,180
− 1,280
LGEV/LUV
+ LRPV
− 960
− 480
− 1,740
+ 500
− 760
− 440
− 3,460
− 420
LCV − 1,440 − 1,240 − 1,200 − 3,880

By including a column for formula, this format would also work as the simplest format for calculating and presenting variances after building the working table