Labour/Labor Cost Variance

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

Standard Cost for Actual Output

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