# 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 Cost Variance ~ LCV

For the output obtained, does the actual cost incurred vary from the standard cost that should have been incurred?
Labour/Labor Cost Variance is the variance between the standard cost of labour/labor for actual output the actual cost of labour/labor.

⇒ Labour/Labor Cost Variance (LCV)

 = SC(AO) − AC Standard Cost for Actual Output − Actual Cost

## Actual Cost

 Based on inputs AC = AT × AR Based on output = AO × AC/UO

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

Based on output

Or = AO × SC/UO

## Formula in useful forms

 LCV = SC(AO) − AC Standard Cost for Actual Output − Actual Cost Or = AO × (SC/UO − AC/UO) Actual Output × Difference in Standard and Actual Costs per unit output

## Note

• ×  AO SO
replaces the suffix (AO) in calculations
• Using the formula based on output is prudent when the only data that is available is the data in the formula i.e. SC/UO, AC/UO and the AO.

In other cases where we are required to calculated SC/UO and AC/UO we need the SC and AC data which can be straight away used for finding the LCV.

## For each Labour/Labor type separately

Labour/Labor Cost variance for a labour/labor type

 LCVLab = SC(AO)Lab − ACLab Or = AO (SC/UOLab − AC/UOLab)

## For all Labour/Labor types together

Total Labour/Labor Cost variance

 TLCV = ΣLCVLab Sum of the variances measured for each labour/labor type separately

Labour/Labor Cost variance for the Mix

 LCVMix = SC(AO)Mix − ACMix Or = AO (SC/UOMix − AC/UOMix)

TLCV = LCVMix

# Illustration - Solution

We need to recalculate standards based on AO for finding LCV.
Working Table with recalculated standards
Standard Actual
for SO for AO Total Idle
ST SR ST(AO) SC(AO) AT AR AC 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
20
36
34
Total 750 720 10,925 960 14,920 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. SO(AO) = AO

5. AC = AT × AR

LCV = SC(AO) − AC

Labour/Labor Cost Variance due to

 Skilled Labour/Labor, LCVsk = SC(AO)sk − ACsk = 3,840 − 5,280 = − 1,440 [Adv] Semi-Skilled Labour/Labor, LCVss = SC(AO)ss − ACss = 5,760 − 7,000 = − 1,240 [Adv] Unskilled Labour/Labor, LCVus = SC(AO)us − ACus = 1,440 − 2,640 = − 1,200 [Adv] TLCV or LCVMix = − 3,880 [Adv] Labour/Labor Mix, LCVMix = SC(AO)Mix − ACMix = 11,040 − 14,920 = − 3,880 [Adv]

## Alternative - Formula Based on Output

LCV = AO × (SC/UO − AC/UO)

Calculation of SC/UO requires the SC data and AC/UO requires the AC data. When these are available we can straight away use the earlier formula instead of calculating SC/UO and AC/UO.

# Illustration - 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 AC based on the given data in a working table and then use formulae based on costs.
Working Table
Standard Actual
for SO Total Idle
ST SR SC AT AR AC 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
20
36
34
Total 750 11,500 960 14,920 90
Output 7,500
SO
7,200
AO

1. SC = ST × SR

2. AC = AT × AR

LCV = SC × AO SO
− AC
• ## Using Formula with Times and Rates

Using the time and rate of pay 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 of pay.
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
LCV = ST × AO SO
× SR − AT × AR
• ## Formula based on outputs

LCV = AO × (SC/UO − AC/UO)

Calculation of SC/UO requires the SC data and AC/UO requires the AC data. When these are available we can straight away use the other formulae instead of calculating SC/UO and AC/UO.

This formula does not require the data from recalculated standards.

# Constituents of Labour/Labor Cost Variance

Labour/labor cost variance is a
• ## synthesis of two variances

 LCV = SC(AO) − AC Adding and deducting SC(AT) on the RHS we get LCV = SC(AO) − AC + SC(AT) − SC(AT) = [SC(AO) − SC(AT)] + [SC(AT) − AC] = Usage/Gross-Efficiency Variance + Rate of Pay Variance = LUV/LGEV + LRPV
• ## synthesis of three variances

 LCV = SC(AO) − AC Adding and deducting SC(AT) on the RHS we get LCV = SC(AO) − AC + SC(AT) − SC(AT) = [SC(AO) − SC(AT)] + [SC(AT) − AC] Segregating Actual Time into Idle Time and Productive Time = [SC(AO) − {SC(PT) + SC(IT)}] + [SC(AT) − AC] = [SC(AO) − SC(PT) − SC(IT)] + [SC(AT) − AC] = [SC(AO) − SC(PT)] − SC(IT) + [SC(AT) − AC] = [SC(AO) − SC(PT)] + [SC(AT) − AC] + [− SC(IT)] = Usage/Efficiency Variance + Rate of Pay Variance + Idle Time Variance = LUV/LEV + LRPV + LITV

# LCV Miscellaneous Aspects

• ## Nature of Variance

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

• SC(AO) ___ AC

## LCVLab

• SC(AO)Lab ___ ACLab

## LCVMix

• SC(AO)Mix ___ ACMix

The variance would be

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

### TLCV

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,

Variance Cost incurred 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 and as such reflects the net effect of individual variances.

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 Labour/Labor Cost Variance represents the total difference on account of a number of factors it would not be possible to directly fix the responsibility for the variance. This explains the reason for analysing the variance and segregating it into its constituent parts.

# Formulae based on interrelationship among variances

Material Cost variance can also be obtained from the other variances using the interrelationship among variances.
• LCV = LRPV + LUV/LGEV
• LCV = LRPV + LEV + LITV
• LCV = LRPV + LMV/GCV + LYV + 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

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