Labour/Labor Cost Variance

... From Page L:5
A Problem  
 
7,500 units of a product are planned to be produced using 200 hrs of Skilled Labour/Labor @ Rs. 20 per hr, 400 hrs of Semi-Skilled Labour/Labor @ Rs. 15/hr and 150 hrs of Unskilled Labour/Labor @ Rs. 10 per hr at a total cost of Rs. 11,500. 7,125 units of the product were manufactured using 240 hrs of skilled labour/labor @ Rs. 22 per hr, 500 hrs of Semi-skilled labour/labor @ Rs. 14/hr and 220 hrs of Unskilled labour/labor @ Rs. 12 per hr. 24 hrs of Skilled Labour/Labor time, 50 hrs of Semi-Skilled Labour/Labor time and 22 hrs of Unskilled Labour/Labor time were lost due to break down which is abnormal.

Is the cost incurred as planned or is there any variation?
This information is provided by the Labour/Labor cost variance.

The problem data arranged in a working table:

Standard
[Production: 7,500 units]
Actual
[Production: 7,125 units]
Time
(hrs)
Rate
(Rs/hr)
Cost
(Rs)
Rate
(Rs/hr)
Gross/Total Net Abnromal
Time
(hrs)
Cost
(Rs)
Time
(hrs)
Cost
(Rs)
Time
(hrs)
Cost
(Rs)
Skilled 200 20 4,000 22 240 5,280 216 4,752 24 528
Semi Skilled 400 15 6,000 14 500 7,000 450 6,300 50 700
Un Skilled 150 10 1,500 12 220 2,640 198 2,376 22 264
Total 750   11,500   960 14,920 864 13,428 96 1,492

SRMix =
SCMix
STMix
⇒ SRMix =
Rs. 11,500
750 hrs
⇒ SRMix =
Rs.
46
3
/hr

ARMix =
ACMix
ATMix
⇒ ARMix =
Rs. 14,920
960 hrs
⇒ ARMix =
Rs.
373
32
/hr
You may be required to calculate these only if you are using the direct formula for finding the Total Labour/Labor Cost Variance.

The Formulae » Labour/Labor Cost Variance (LCV)  
 
Labour/Labor Cost Variance implies the variance in the total cost of labour/labor i.e. the difference between the actual cost of labour/labor and the standard cost of labour/labor for actual output.
⇒ Labour/Labor Cost Variance = Standard Cost of Labour/Labor for Actual OutputActual Cost of Labour/Labor

LCV = SC for AO − AC(G)
=
(
AO
SO
× ST × SR)
− (AT(G) × AR)

Memorise this general formula for easier recollection (ignoring the specific formulae below)

  • For each Labour/Labor Type Separately

    LCVLab = SCLab for AO − AC(G)Lab
    =
    (
    AO
    SO
    × STLab × SRLab)
    − (AT(G)Lab × ARLab)
  • For all Labour/Labor Types together [Total Labour/Labor Cost Variance :: TLCV]

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

    ⇒ TLCV = LCVSk + LCVSe + ...

    Direct Formula

    The Total Labour/Labor Cost Variance is nothing but the LCV for the mix.
    TLCV i.e. LCVMix = SCMix for AO − AC(G)Mix
    =
    (
    AO
    SO
    × STMix × SRMix)
    − (AT(G)Mix × ARMix)

    This can be interpreted as
    Total Labour/Labor Cost Variance = Standard Cost of Standard Mix for Actual OutputActual Cost of Actual (Gross) Mix

LCV Formula interpretation  
 
The above formulae for Labour/Labor Cost Variance, can be used in all cases i.e. both when AO = SO as well as when AO ≠ SO. When AO ≠ SO, the ratio AO/SO works as a correction factor to readjust the SQ to SQ for AO and thereby the SC to SC for AO.
  • Actual Time ⇒ Gross Time

    Wherever you find the presence of time in the formula, you should interpret it as Actual (Gross) Time. Where there abnormal loss of time, the actual time is segregated into two as abnormal loss time and net time. Even in such cases, for the purpose of calculating the Cost Variance, the total (Gross) time should be considered for actual time.
  • Where AO = SO

    When AO = SO,
    AO
    SO
    becomes 1 thus nullifying its effect, in which case the formula would read as:

    For each labour/labor type separately
    LCV = (STLab × SRLab) − (AT(G)Lab × ARLab)

    For all the labour/labor types together
    TLCV = (STMix × SRMix) − (AT(G)Mix × ARMix)

  • LCV = 0

    Labour/Labor cost variance for each labour/labor type would be zero, when the actual labour/labor time used and the standard labour/labor time for actual output are the same as well as the actual rate at which labour/labor is paid is equal to the standard rate at which labour/labor is paid.
  • TLCV = 0

    When more than one type of labour/labor is used, the Total LCV may become zero
    1. When the LCV on account of each labour/labor is zero, or
    2. when 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.

    Therefore, it would not be appropriate to conclude that there is no variance on account of any labour/labor type just because the total LCV is zero.

    Where the total LCV is zero, you have to verify individual variances before concluding that all the variances (LCV's) are zero.

Solution [Using the data as it is]  
 
For working out problems with the data consider as it has been given without having to do any recalculations, use the above formulae (which are capable of being used in all cases)

Consider the working table above:

Standard
[Production: 7,500 units]
Actual
[Production: 7,125 units]
Time
(hrs)
Rate
(Rs/hr)
Cost
(Rs)
Rate
(Rs/hr)
Gross/Total Net Abnromal
Time
(hrs)
Cost
(Rs)
Time
(hrs)
Cost
(Rs)
Time
(hrs)
Cost
(Rs)
Skilled 200 20 4,000 22 240 5,280 216 4,752 24 528
Semi Skilled 400 15 6,000 14 500 7,000 450 6,300 50 700
Un Skilled 150 10 1,500 12 220 2,640 198 2,376 22 264
Total 750   11,500   960 14,920 864 13,428 96 1,492

LCV = ({
AO
SO
× ST } × SR ) − (AT(G) × AR)

Using, LCVLab = ({
AO
SO
× STLab } × SRLab ) − (AT(G)Lab × ARLab)
Labour/Labor Cost Variance due to workers who are
• Skilled =
({
7,125 units
7,500 units
× 200 hrs } × Rs. 20/hr ) − (240 hrs × Rs. 22/hr)
= (0.95 × 200 hrs × Rs. 20/hr) − (Rs. 5,280)
= Rs. 3,800 − Rs. 5,280
= − Rs. 1,480 ⇒ LCVSk = − Rs. 1,480 [Adv]
• Semi-Skilled =
({
7,125 units
7,500 units
× 400 hrs } × Rs. 15/hr ) − (500 hrs × Rs. 14/hr)
= (0.95 × 400 hrs × Rs. 15/hr) − (Rs. 7,000)
= Rs. 5,700 − Rs. 7,000
= − Rs. 1,300 ⇒ LCVSe = − Rs. 1,300 [Adv]
• Unskilled =
({
7,125 units
7,500 units
× 150 hrs } × Rs. 10/hr ) − (220 hrs × Rs. 12/hr)
= (0.95 × 150 hrs × Rs. 10/hr) − (Rs. 2,640)
= Rs. 1,425 − Rs. 2,640
= − Rs. 1,215 ⇒ LCVUn = − Rs. 1,215 [Adv]
Total Labour/Labor Cost Variance (TLCV) = − Rs. 3,995 [Adv]

Alternative for Total Variance

The total labour/labor cost variance can be calculated wihthout calculating the variances for individual labour/labor types using the direct formula.
Using TLCV i.e. LCVMix =
(
AO
SO
× STMix × SRMix)
− (ATMix × ARMix)
=
(
7,125 units
7,500 units
× 750 hrs × Rs.
46
3
/hr) − (960 hrs × Rs.
373
32
/hr)
= (0.95 × Rs. 11,500) − (40 × Rs. Rs. 373)
= Rs. 10,925 − Rs. 14,920
= − Rs. 3,995 [Adv]

Solution [Using recalculated data]  
 
Where you find that the SO ≠ AO, you may alternatively recalculate the standard to make the SO = AO and use the figures relating to the recalculated standard in the working table. In such a case, the formulae that you use would look simpler (without the adjustment factor AO/SO).

From the data relating to the problem, it is evident that AO ≠ SO. Thus we recalculate the standard data for Actual Output [Refer to the calculations].

Consider the recalculated standard data and the actual data arranged in a working table.

Standard
[Production: 7,125 units]
Actual
[Production: 7,125 units]
Time
(hrs)
Rate
(Rs/hr)
Cost
(Rs)
Rate
(Rs/hr)
Total Normal Abnromal
Time
(hrs)
Cost
(Rs)
Time
(hrs)
Cost
(Rs)
Time
(hrs)
Cost
(Rs)
Skilled 190 20 3,800 22 240 5,280 216 4,752 24 528
Semi Skilled 380 15 5,700 14 500 7,000 450 6,300 50 700
Un Skilled 142.5 10 1,425 12 220 2,640 198 2,376 22 264
Total 712.5   10,925   960 14,920 864 13,428 96 1,492

LCV = (ST × SR ) − (AT(G) × AR)

Using, LCVlab = (STLab × SRLab ) − (AT(G)Lab × ARLab) Labour/Labor Cost Variance due to Workers who are
• Skilled = (190 hrs × Rs. 20/hr) − (240 hrs × Rs. 22/hr)
= Rs. 3,800 − Rs. 5,280
= − Rs. 1,480 ⇒ LCVSk = − Rs. 1,480 [Adv]
• Sem-Skilled = (380 hrs × Rs. 15/hr) − (500 hrs × Rs. 14/hr)
= Rs. 5,700 − Rs. 7,000
= − Rs. 1,300 ⇒ LCVSe = − Rs. 1,300 [Adv]
• Unskilled = (142.5 hrs × Rs. 10/hr) − (220 kgs × Rs. 12/hr)
= Rs. 1,425 − Rs. 2,640
= − Rs. 1,215 ⇒ LCVUn = − Rs. 1,215 [Adv]
Total Labour/Labor Cost Variance (TLCV) = − Rs. 3,995 [Adv]

Note:

The above formula can be used only when the standard output and the actual output are the same.

Alternative for Total Variance

The total labour/labor cost variance can be calculated wihthout calculating the variances for individual labour/labor types using the direct formula.

Using TLCV i.e. LCVMix = (STMix × SRMix) − (AT(G)Mix × ARMix)

⇒ TLCV i.e. LCVMix =
(712.5 hrs × Rs.
46
3
/hr ) − (960 hrs × Rs.
373
24
/hr)
= Rs. 10,925 &minusl Rs. 14,920
= − Rs. 3,995 [Adv]

You dont need to recalculate the standard

The formula with the adjustment factor AO/SO can be used in all cases i.e. both when AO = SO and AO ≠ SO. Therefore, you don't need to rebuild the working table by recalculating the standards for the purpose of finding the variances.

Check:

The same problem was solved in both the cases above. The only difference being that in the second case, the data was considered by recalculating the Standard for Actual Output to make AO = SO.

Who is held responsible 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.

Constituents of Labour/Labor Cost Variance  
 
In the overview of labour/labor variances we have seen that the labour/labor cost variance is actually a synthesis of three variances, "Labour/Labor Rate of Pay Variance" and "Labour/Labor Usage/Efficiecy Variance" and "Labour/Labor Idle Time Variance".

We know,
LCV = ({
AO
SO
× ST } × SR ) − (AT(G) × AR)
= ({
AO
SO
× ST } × SR ) + [− (AT(G) × AR)]
[Adding and deducting (AT(G) × SR)]
= ({
AO
SO
× ST } × SR ) + [− (AT(G) × SR) + (AT(G) × SR)] − (AT(G) × AR)]
[Adding and deducting the same quantity does not alter The value of the expression]
= [({
AO
SO
× ST } × SR ) − (AT(G) × SR)] + [(AT(G) × SR) − (AT(G) × AR)]
= [Labour/Labor (Gross) Efficiency/Usage Variance] + [Labour/Labor Rate of Pay Variance]
LCV = L(G)EV/L(G)UV + LRPV

Author Credit : The Edifier ... Continued Page L:7

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