# 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 Usage/Gross-Efficiency Variance ~ LUV/LGEV

What is the variation in the total cost on account of the actual time 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 actual labour/labor time.

⇒ Labour/Labor Usage/Gross-Efficiency Variance (LUV/LGEV)

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

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

Based on output

Or = AO × SC/UO

## Standard Cost of Actual Time

 SC(AT) = AT × SR

## Formula in useful forms

 LUV/LGEV = SC(AO) − SC(AT) Standard Cost for Actual Output − Standard Cost of Actual Time Or = [ST(AO) − AT] × SR Difference between Standard time for actual output and actual tme × Standard Rate

## Note

• ×  AO SO
replaces the suffix (AO) in calculations
• Finding the costs by building up the working table and using the formula involving costs is the simplest way to find variances.
• The formula involving costs can be used to find the Labour/Labor Usage/Gross-Efficiency Variance for individual labour/labor types as well as the mix of labour/labor types. Appropriate suffix Lab or Mix is used in the formula as an indicator.

## For each Labour/Labor type separately

Labour/Labor Usage/Gross-Efficiency variance for a labour/labor type

 LUEV/LGEVLab = SC(AO)Lab − SC(AT)Lab Or = [ST(AO)Lab − ATLab) × SRLab

## For all Labour/Labor types together

When two or more types of labour/labor are used for the manufacture of a product, the total Labour/Labor Usage/Gross-Efficiency variance is the sum of the variances measured for each labour/labor type separately.

Total Labour/Labor Usage/Gross-Efficiency Variance

 ⇒ TLUV/TLGEV = ΣLUV/LGEVLab Sum of the variances measured for each labour/labor type separately

Labour/Labor Usage/Gross-Efficiency variance for the Mix

 LUV/LGEVMix = SC(AO)Mix − SC(AT)Mix = [ST(AO)Mix − ATMix] × SRMix This formula is valid for the mix, only when the actual times mix ratio is the same as the standard time mix ratio.

TLUV/TLGEV = LEV/LGUVMix

## The Math

The variance in total cost is on account of two factors rate of pay and labour/labor time.

Consider the relation, Value (V) = Time (T) × Price (R).

If R is constant, V = TR

⇒ V1 = T1 × R → (1)
⇒ V2 = T2 × R → (2)

(1) − (2)

⇒ V1 − V2 = T1 × R − T2 × R
⇒ V1 − V2 = (T1 − T2) × R
⇒ ΔV = ΔT × R, where R is a constant
⇒ ΔV ∞ ΔT

Change in value varies as change in time

By taking both rate of pays at standard we are eliminating the effect of difference between the standard rate of pay and actual rate of pay, thereby leaving only the difference between time usage.

# Illustration - Solution

We need to recalculate standards based on AO for finding LGEV/LUV.
Working Table with recalculated standards
Standard Actual
for SO for AO Total Idle
ST SR ST(AO) SC(AO) AT AR AC SC(AT) 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
5,280
7,000
2,640
4,800
7,500
2,200
20
36
34
Total 750 720 11,040 960 14,920 14,500 90
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. SC(AT) = AT × SR

5. SO(AO) = AO

LEV/LGUV = SC(AO) − SC(AT)

Labour/Labor Usage/Gross-Efficiency Variance due to

 Skilled Labour/Labor, LUV/LGEVsk = SC(AO)sk − SC(AT)sk = 3,840 − 4,800 = − 960 [Adv] Semi Skilled Labour/Labor, LUV/LGEVss = SC(AO)ss − SC(AT)ss = 5,760 − 7,500 = − 1,740 [Adv] Un Skilled Labour/Labor, LUV/LGEVus = SC(AO)us − SC(AT)us = 1,440 − 2,200 = − 760 [Adv] TLUV/TLGEV = − 3,460 [Adv] Labour/Labor Mix, LUV/LGEVMix = SC(AO)Mix − SC(AT)Mix = 11,040 − 14,500 = − 3,460 [Adv]

## Alternative

Where LUV/LGEV 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/LGUV = (ST(AO) − AT) × SR

Labour/Labor Usage/Gross-Efficiency Variance due to

 Skilled Labour/Labor, LEV/LGUVsk = (ST(AO)sk − ATsk) × SRsk = (192 hrs − 240 hrs) × 20/hr = − 48 hrs × 20/hr = − 960 [Adv] Semi Skilled Labour/Labor, LEV/LGUVss = (ST(AO)ss − ATss) × SRss = (384 hrs − 500 hrs) × 15/hr = − 116 hrs × 15/hr = − 1,740 [Adv] Un Skilled Labour/Labor, LEV/LGUVus = (ST(AO)us − ATus) × SRus = (144 hrs − 220 hrs) × 10/hr = − 76 hrs × 10/hr = − 760 [Adv] TLUV/TLGEV = − 3,460 [Adv]

Standard Time Mix Ratio

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

Actual Time Mix Ratio

 ATMR = ATsk : ATss : ATus = 240 hrs : 500 hrs : 200 hrs = 12 : 25 : 10

Since this formula involves the term AT × SR and STMR ≠ ATMR, 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(AT) based on the given data in a working table and then use formulae based on costs.
Standard Actual
for SO Total Idle
ST SR SC AT AR AC SC(AT) IT
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
Total 750 11,500 960 14,920 14,500 90
Output 7,500
SO
7,200
AO

1. SC = ST × SR

3. AC = AT × AR

3. SC(AT) = AT × SR

LUV/LGEV = SC × AO SO
− SC(AT)
• ## 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
LUV/LGEV = (ST × AO SO
− AT) × SR

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

# Constituents of Labour/Labor Usage/Gross-Efficiency Variance

Labour/Labor Usage/Gross-Efficiency variance is a synthesis of two variances, Labour/Labor Idle Time Variance and Labour/Labor Efficiency Variance.
 LUV/LGEV = SC(AO) − SC(AT) Dividing AT into IT and PT = SC(AO) − [SC(PT) + SC(IT)] = SC(AO) − SC(PT) − SC(IT) = [SC(AO) − SC(PT)] + [− SC(IT)] Efficiency Variance + Idle Time Variance = LEV + LITV

Labour/Labor Idle Time variance represents a loss and is always a the value of a term and not a difference of two terms.

# LUV/LGEV - Miscellaneous Aspects

• ## Actual Time

LUV/LGEV measures the variance in utilisation of total time paid for. Thus the time in this case means actual time.
• ## Nature of Variance

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

• SC(AO) ___ SC(AT)
• ST(AO) ___ AT

## LUV/LGEVLab

• SC(AO)Lab ___ SC(AT)Lab
• ST(AO)Lab ___ ATLab

## LUV/LGEVMix

• SC(AO)Mix ___ SC(AT)Mix
• ST(AO)Mix ___ ATMix (conditional)

only when STMR = ATMR.

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 Total 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 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.

This conclusion would be appropriate when there is only one labour/labor type in use.

## When there are two or more labour/labor types

When two or more labour/labor types are being used for the manufacture of a product, making only the people responsible for production answerable for the variance may not be appropriate as there would be three factors influencing the usage of labour/labor types.
1. the idle time lost,
2. the ratio in which the productive times of constituent labour/labor types are mixed and
3. the actual yield from the labour/labor mix.

That is the reason, when there are two or more types of labour/labor type being used, the Usage/Gross-Efficiency variance is further broken down into two parts as Efficiency Variance and Idle Time variance and the Efficiency Variance further broken down into Mix Variance and Yield Variance.

# Formulae using Inter-relationships among Variances

• LUV/LGEV = LCV − LRPV
• LUV/LGEV = LEV + LITV
• LUV/LGEV = LMV/GCV + LYV/LSUV + LITV

## 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

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